III-V Semiconductor Structures for Biosensor and Molecular Electronics Applications

Lehrstuhl für experimentelle Halbleiterphysik I Walter Schottky Institut Technische Universität München

Sebastian M. Luber

Vollständiger Abdruck der von der Fakultät für Physik der Technischen Universität München zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigten Dissertation.

Vorsitzender: Univ.-Prof. Dr. Roland Netz Prüfer der Dissertation 1. Univ.-Prof. Dr. Gerhard Abstreiter 2. Univ.-Prof. Paolo Lugli, Ph. D.

Die Dissertation wurde am 13.07.2006 bei der Technischen Universität München eingereicht und durch die Fakultät für Physik am 18.10.2006 angenommen.

1. Auflage Januar 2007

Verein zur Förderung des Walter Schottky Instituts der Technischen Universität München e.V., Am Coulombwall, 85748 Garching. Alle Rechte vorbehalten. Dieses Werk ist urheberrechtlich geschützt. Die Vervielfältigung des Buches oder von Teilen daraus ist nur in den Grenzen der geltenden gesetzlichen Bestimmungen zulässig und grundsätzlich vergütungspflichtig.

Titelbild: The left panel of the cover picture demonstrates the operational principle of a gallium arsenide based biosensor. The analyte binds to a receptor molecule which is embedded in a biphenyl functional layer on the sensor surface. This binding event is detected by a shallow two dimensional electron gas which is sensitive to surface potential changes. The right panel illustrates a similar semiconductor structure which was used for molecular electronics experiments. Organic pi-conjugated molecules are attached to nanometer spaced electrodes which have been previously deposited on a cleaved heterostructure. Thereby, the current carrying properties of the molecules can be evaluated.

Druck: Printy Digitaldruck, München (http://www.printy.de)

ISBN: 978-3-932749-83-4 Für Nicola und Maja

Zusammenfassung

Die vorliegende Arbeit beschäftigt sich mit der Verwendung von elektronischen, auf III-V Halbleitern basierenden Bauelementen für die Biosensorik und die molekulare Elektronik. Da- zu wird im ersten Teil ein Sensor, der aus einem oberflächennahen, zweidimensionalen Elek- tronengas in einer Aluminiumgalliumarsenid-Galliumarsenid (AlGaAs-GaAs) Heterostruktur besteht, für eine Anwendung in biologischer Umgebung untersucht. Zur Stabilisierung in dabei vorkommenden wässrigen Lösungen wird der Sensor mit einer geordneten organischen Schicht aus substituierten Mercaptobiphenyl-Molekülen passiviert. Der Einfluss dieser Moleküle auf die elektronische Struktur der GaAs-Oberfläche wird daraufhin anhand von Kelvin-Probe Messun- gen in Luft diskutiert. Dabei wird eine Abhängigkeit der Elektronenaffinität vom intrinsischen molekularen Dipolmoment der Mercaptobiphenyle festgestellt. Des Weiteren werden zeitauf- gelöste Messungen präsentiert, die einen Einfluss der Mercaptobiphenyl-Beschichtung auf die Ladungsträgerrekombination zeigen. Bei einer Charakterisierung in physiologischen Pufferlö- sungen zeigt sich dann anhand von Leitfähigkeitsmessungen eine Abhängigkeit des Sensor- Oberflächenpotenzials von pH-Wert und Salzgehalt der Elektrolytlösung. Durch Simulations- rechnungen unter Verwendung der Poisson-Boltzmann Theorie ergeben sich als mögliche Ursa- chen sowohl eine Bindung von OH- Ionen an die Oberfläche, als auch die Dissoziation von OH Gruppen in Oberflächenoxiden. Ein Vergleich zwischen Simulationsparametern und physika- lischer Beschaffenheit des Sensors deutet dabei auf die OH- Absorption als wahrscheinlichere Ursache hin. Im zweiten Teil der Arbeit wird die Eignung von MBE gewachsenen III-V Halbleiterstruk- turen für die molekulare Elektronik untersucht. Dabei wird eine Methode für die Herstellung metallischer Elektroden im Abstand von wenigen Nanometern auf einer GaAs-AlGaAs Träger- struktur präsentiert und erfolgreich produzierte Strukturen topographisch und elektrisch untersucht. Die erfolgreiche Funktion des Bauelements wird dabei durch das Einfangen einzelner Gold-Nanopartikel demonstriert. Eine erste Anwendung für die molekulare Elektronik wird durch die elektrische Charakterisierung von molekularen Schichten aus Oligophenylenvinylen- Derivaten aufgezeigt. Simulationen an vereinfachten Molekülen mittels erweiterter Hückel Theo- rie und der Methode der Greens-Funktionen zeigen eine gute qualitative Übereinstimmung zwischen Theorie und Experiment. Außerdem werden viel versprechende Erweiterungen der Her- stellungsmethode präsentiert. Diese umfassen die Fabrikation von T-strukturierten Elektroden zur Untersuchung einzelner Moleküle, und den Übergang zu reinen Halbleiterelektroden beste- hend aus Indiumarsenid Schichten.

I Abstract

The present work reports on the employment of III-V semiconductor structures to biosensor and molecular electronics applications. In the first part a sensor based on a surface-near two dimensional electron gas for a use in biological environment is studied. Such a two dimensional electron gas inherently forms in a molecular beam epitaxy (MBE) grown, doped aluminum gallium arsenide - gallium arsenide (AlGaAs-GaAs) heterostructure. Due to the intrinsic instability of GaAs in aqueous solutions the device is passivated by deposition of a monolayer of 4’-substituted mercaptobiphenyl molecules. The influence of these molecules which bind to the GaAs via a sulfur group is investigated by Kelvin probe measurements in air. They reveal a dependence of GaAs electron affinity on the intrinsic molecular dipole moment of the mercaptobiphenyls. Furthermore, transient surface photovoltage measurements are presented which demonstrate an additional influence of mercaptobiphenyl chemisorption on surface carrier recombination rates. As a next step, the influence of pH-value and salt concentration upon the sensor device is discussed based on the results obtained from sensor conductance measurements in physiological solutions. A dependence of the device surface potential on both parameters due to surface charging is deduced. Model calculations applying Poisson-Boltzmann theory reveal as possible surface charging mechanisms either the adsorption of OH- ions on the surface, or the dissociation of OH groups in surface oxides. A comparison between simulation settings and physical device properties indicate the OH- adsorption as the most probable mechanism. In the second part of the present study the suitability of MBE grown III-V semiconductor structures for molecular electronics applications is examined. In doing so, a method to fabricate nanometer separated, coplanar, metallic electrodes based on the cleavage of a supporting AlGaAs-GaAs heterostructure is presented. This is followed by a thorough topographical and electrical characterization of fabricated devices which includes the electrostatic trapping of single gold nanoclusters between the electrodes. A first application to molecular electronics is presented by conductance measurements on a molecular layer of oligophenylenvinylene derivatives. Simulations on model molecules applying extended Hückel theory and the non- equilibrium Greens function formalism reveal a good qualitative agreement between theory and experiment. Furthermore, promising extensions to the present fabrication method are discussed. These include the processing and characterization of broken T-shaped electrodes suitable for measurements on single molecules, and the transition to pure semiconductor electrodes based on indium arsenide.

II Table of Contents

Motivation and Outline 1

I Gallium Arsenide Based Devices for Biosensing Applications 5

1 Introduction 7 1.1 The Sensor Element - A Two Dimensional Electron Gas ...... 9 1.2 Sensor Passivation and Functionalization ...... 10

2 Fundamentals of Semiconductors in Electrolytes 13 2.1 Semiconductor Surface Electronic Structure ...... 13 2.1.1 The GaAs Surface ...... 15 2.1.2 Inﬂuence of Chemisorbed Molecules ...... 15 2.2 Buffered Electrolyte Solutions ...... 17 2.2.1 Buffer Action ...... 18 2.2.2 Effect of Temperature and Ionic Strength ...... 19 2.2.3 Phosphate Buffers ...... 19 2.3 Semiconductor-Electrolyte Interface ...... 19 2.3.1 Poisson-Boltzmann Theory ...... 21 2.3.2 Site-Dissociation Theory ...... 25 2.3.3 Alternative Adsorption Models ...... 28 2.3.4 Capacitance and Mott-Schottky Analysis ...... 29 2.4 Numerical Calculations ...... 31 2.4.1 Simulation of the Semiconductor Electrolyte Interface ...... 31 2.4.2 Simulation of Molecular Properties ...... 35

III IV Contents

3 Experimental Techniques and Measurement Setup 39 3.1 Sample Design and Fabrication ...... 39 3.1.1 Molecular Beam Epitaxy Growth ...... 40 3.1.2 Device Layout and Patterning ...... 40 3.1.3 Deposition of Mercaptobiphenyl Monolayers ...... 41 3.2 Experimental Setup and Measurement Details ...... 42 3.2.1 Kelvin Probe Measurements ...... 42 3.2.2 Electrochemical Setup and Fluid Handling ...... 45 3.2.3 Transport Measurements ...... 46 3.2.4 Impedance Measurements ...... 48

4 Surface Electronic Structure Changes of GaAs by Molecular Adsorption 51 4.1 Inﬂuence of Mercaptobiphenyl Deposition on Work Function and Band Bending 51 4.2 Electron Afﬁnity Changes Upon Mercaptobiphenyl Adsorption ...... 53 4.3 Surface Characterization by Transient Surface Photovoltage ...... 56 4.4 Conclusion ...... 59

5 Influence of Aqueous Electrolytes on 2DEG Sensor Devices 61 5.1 Stability and Sensitivity ...... 61 5.2 Influence of pH Changes on the Surface Potential of 2DEG Sensors ...... 63 5.2.1 Measurement Procedure ...... 63 5.2.2 Relationship between Resistance and Surface Potential Changes .... 65 5.2.3 Control Experiments ...... 66 5.2.4 Behavior of MBP-OH Coated Samples on pH Variations ...... 70 5.2.5 Behavior of MBP-CH3 and MBP-H Coated Samples on pH Variations . 73 5.2.6 Behavior of Bare, non-Protected Samples ...... 77 5.2.7 Summary ...... 77 5.3 Capacitance-Voltage Measurements on pH Sensitivity ...... 78 5.3.1 Bare, non-Protected Samples ...... 78 5.3.2 MBP-CH3 and MBP-OH Coated Samples ...... 79 5.3.3 Summary ...... 80 5.4 Influence of Salt Concentration Changes ...... 80 5.4.1 Measurement Procedure ...... 81 5.4.2 Surface Potential Variation due to Salt Concentration Changes ..... 81 5.4.3 Summary ...... 84 Contents V

5.5 Conclusion ...... 84

6 Summary and Outlook 87

II III-V Semiconductor Devices for Molecular Electronics 91

7 Introduction 93

8 Fundamentals of Molecular Conduction 101 8.1 Molecular Conductance Theory ...... 101 8.1.1 Introduction ...... 102 8.1.2 Landauer Formula ...... 103 8.1.3 Electron Transfer and its Connection to Molecular Conductance .... 104 8.1.4 Classical and Quantum Mechanical Transmission ...... 106 8.1.5 Simple Model for Molecular Conduction Including Charging Effects .. 109 8.1.6 NEGF Formalism and Extended Hückel Theory ...... 116 8.2 Molecules of Interest and Deposition Technique ...... 117 8.2.1 Required Molecular Structure ...... 118 8.2.2 Molecular Wires: Oligophenylenevinylene ...... 118 8.2.3 Deposition of Oligophenylenevinylene Molecules ...... 119

9 Experimental Techniques and Measurement Setup 121 9.1 Surface Characterization Methods ...... 121 9.1.1 Atomic Force Microscope ...... 121 9.1.2 Scanning Electron Microscope ...... 124 9.2 Characterization of Molecules and Molecular Layers ...... 125 9.2.1 Ellipsometry ...... 126 9.2.2 UV-VIS Spectroscopy ...... 127 9.3 Electrical Setup ...... 128 9.3.1 Low-Temperature Conductance Measurements ...... 128 9.3.2 Electrostatic Trapping ...... 129

10 Fabrication and Characterization of a Co-Planar Nanogap Device 131 10.1 Nanogap Electrode Fabrication ...... 131 10.2 Optimization of Process Parameters ...... 134 10.2.1 Choice of Electrode Materials ...... 135 VI Contents

10.2.2 Etching Duration and Metal Layer Thicknesses ...... 137 10.2.3 Summary ...... 138 10.3 Electrode Separation ...... 138 10.3.1 Surface Characterization ...... 138 10.3.2 Estimation of the Minimum Possible Electrode Separation ...... 141 10.3.3 Etch Selectivity and Inverted Structure ...... 142 10.3.4 Summary ...... 144 10.4 Device Failure Mechanisms ...... 144 10.5 Electrical Characterization - Trapping of Gold Nanoparticles ...... 145 10.6 Omitting the Metal: Nanometer-Spaced Semiconductor Electrodes ...... 148 10.6.1 InAs-InAlAs-InAs System ...... 148 10.6.2 InAs-GaSb-InAs System ...... 150 10.6.3 Summary ...... 152 10.7 Conclusion ...... 152

11 Conductance of Oligophenylenevinylene Molecules 153 11.1 Electrical Measurements on Planar Nanogap Electrodes ...... 153 11.1.1 Deposition of Oligophenylenevinylene Molecules ...... 153 11.1.2 Current-Voltage Characteristics ...... 155 11.1.3 Summary ...... 157 11.2 Comparison to Model Calculations Employing EHT and NEGF ...... 158 11.2.1 Molecular Electronic Structure ...... 158 11.2.2 IV Curve Calculations on Simpliﬁed Molecules with Hückel-IV .... 161 11.2.3 Comparison between Theory and Experiment ...... 164 11.2.4 Summary ...... 166 11.3 Conclusion ...... 166

12 Fabrication and Characterization of a CEO Nanogap Device 167 12.1 Electrode Fabrication by Cleaved Edge Overgrowth ...... 167 12.1.1 CEO Nanogap Electrode Fabrication ...... 168 12.1.2 Integrating Multiple Devices on One Sample ...... 172 12.2 Electrode Characterization and Failure Mechanisms ...... 173 12.3 Conclusion ...... 177 Contents VII

13 Summary and Outlook 179 13.1 Implementation of a Gate Electrode ...... 180 13.2 InAs-InP-InAs System ...... 181

Bibliography 185

Appendix 201 A.1 List of Abbreviations ...... 201 A.2 List of Symbols ...... 202 A.3 Processing Details for Biosensor Fabrication ...... 205 A.3.1 Standard Photolithography and Mesa Etching Step ...... 205 A.3.2 Standard Lift-Off Step ...... 205 A.4 Evaluation of Gaussian 03W Electronic Structure Calculations ...... 206 A.5 Nanogap Device Processing Details ...... 206 A.5.1 Preparation of Citric Acid Based Solution (CAS) ...... 206 A.5.2 Mesa Etching ...... 206 A.5.3 Contact Pad Deposition ...... 207 A.5.4 Cleavage and Selective Etching ...... 208 A.5.5 Nanogap Electrode Deposition ...... 208 A.5.6 Bonding and Packaging ...... 208

List of Publications 209

Acknowledgement 211 VIII Contents Motivation and Outline

Compound, group III-V semiconductor devices attract considerable attention from various research fields due to their interesting electronic, optical, and structural properties. Especially gallium arsenide (GaAs) based systems offer a wide variety of applications as the combination with aluminum gallium arsenide (AlGaAs) having almost an identical lattice constant allows for a strain-free molecular beam epitaxy (MBE) growth of GaAs-AlGaAs heterostructures. This enables a highly flexible band gap engineering which can be applied to form two-dimensional electron systems (2DEGs) very close to the surface. The sensitivity of such shallow electron systems to surface potential changes due to the field effect can readily be used to build a sensor for molecular interactions taking place at the surface. Especially biosensors are interesting due to the increasing demand in biological and medical sciences for protein sensors [1, 2]. Existing techniques for protein detection usually involve the attachment of radio-, enzymatic- or fluo- rescent markers to report the binding event, however, this labeling step can interfere with the molecular interaction or protein function. Therefore, increasing effort is spent on the investigation of label-free techniques to overcome this limitation [3, 4]. Here, a GaAs based biosensor shows great potential as it combines label-free detection based on the field effect principle with very high sensitivity and compatibility to common semiconductor processing technology. How- ever, due to the intrinsic instability of GaAs based devices in biological environments a proper surface passivation is necessary [5]. An ideal structure which at the same time provides for stabilization and biocompatibility of the surface conserving the high sensitivity of the device is an ordered monolayer of organic molecules [6] (see also chapter 1 on page 7 for a more extensive introduction). Accordingly, the first part of the present thesis deals with the fabrication and characterization in air and in aqueous solutions of a GaAs based 2DEG sensor device passivated by organic molecules which is suitable to detect surface reaction events such as affinity binding reactions of biomolecules. Furthermore, model calculations are performed to elucidate the physics taking place at the sensor surface. A further peculiarity of certain III-V heterostructures is their facile cleavage along preferen- tial crystal planes which exposes an atomically flat surface. In combination with the monolayer precision of MBE growth this allows for the fabrication of smooth surfaces that are laterally structured into multiple, nanometer precise layers. This particular feature offers a great poten-

1 2 Motivation and Outline tial for a second, rapidly growing research field: molecular electronics, which deals with the use of single molecules or molecular layers as functional units in an electrical circuit [7]. Research in molecular electronics is driven by the ongoing miniaturization in semiconductor manufacturing technology which is highlighted by the empirical law of Gordon E. Moore, that every 18 months the complexity of integrated circuits doubles [8]. Naturally, the accompanying shrinkage of minimum feature sizes in existing semiconductor technology will encounter physical limitations sooner or later [9, 10, 11]. Instead of following this top-down approach, molecular electronics offers inherent advantages by constructing circuits from the bottom-up: e.g., easy and cost-effective mass production of identical molecules, i.e. electronic elements, or custom- designed molecules to meet the specific needs of circuit designers [12, 13, 14]. The reliable contacting of such molecules is still a demanding task as existing electrode fabrication methods imply certain drawbacks, e.g., regarding the predetermination of electrode separation, a possible implementation of more than two electrodes in one device structure, or an accessibility to surface manipulation tools (see chapter 7 on page 93 for a more detailed introduction into the field of molecular electronics). To solve some of these problems, GaAs-AlGaAs heterostructures can be used as a supporting template to define metallic, nanometer spaced electrodes of predetermined separation with a smooth, accessible surface. This is the topic of the second part of this thesis. A further extension of the MBE growth by using a second MBE growth step perpendicular to the first growth direction, the cleaved edge overgrowth method (CEO), enables an integration of multiple electrodes of varying size in one device. The expertise collected in both research fields can be merged by omitting the metal, and instead using the supporting semiconductor structure actively as electrodes to contact molecules: The insight into molecular chemisorption on semiconductors gained in the biosensor part of the thesis in combination with the experience from nanometer precise layered structures obtained from the molecular electronics part can be used to build a semiconductor-molecule- semiconductor structure with superior properties. A promising material for this purpose is indium arsenide (InAs) as it shows a surface electron accumulation layer [15, 16], thereby enabling a direct contacting of an attached molecule. This topic was in part addressed in the second part of the thesis.

Outline The thesis is divided into two parts according to the addressed research topics. It starts with the examination of a GaAs-AlGaAs based sensor suitable for biosensing applications by giving an introduction to the broad field of biosensors in chapter 1 with special emphasis on the needs of GaAs devices. This is followed by a brief introduction into the fundamental interactions be- Motivation and Outline 3 tween semiconductors and electrolytes in chapter 2, and a presentation of applied experimental methods in chapter 3. The discussion of experimental results commences in chapter 4 with the influence of mercaptobiphenyl adsorption on the electronic structure of GaAs surfaces. This is elucidated by Kelvin probe measurements on GaAs samples coated with various 4’-substituted mercaptobiphenyls. In chapter 5, the GaAs based sensors are characterized in aqueous electrolyte by conductance measurements whilst changing the pH and the salt concentration of the solution. The first part is subsequently concluded by a summary and an outlook in chapter 6. The second part deals with the application of III-V semiconductor structures to molecular electronics. An introduction to this topic with emphasis on nanogap electrode fabrication techniques is given in chapter 7. Then, the fundamentals of molecular charge transport and molecules of interest are presented in chapter 8. Subsequently, chapter 9 explains the experimental methods and the measurement setup used throughout the molecular electronics study. First experimental results are presented in chapter 10 addressing the fabrication of planar nanogap electrodes. This includes metal electrodes on GaAs-AlGaAs heterostructures and InAs based semiconductor electrodes. In chapter 11, a first application by a characterization of oligophenylenevinylene molecules is highlighted. Experimental results are furthermore compared to theoretical calculations on simplified model molecules. After that, the extension of the fabrication technique by applying the cleaved edge overgrowth method is demonstrated in chapter 12. This is concluded in chapter 13 by a general summary and an outlook on possible future projects. In general, technical details were omitted throughout the text, and are instead listed in the appendix. Furthermore, it includes a list of abbreviations and used symbols. 4 Motivation and Outline Part I

Gallium Arsenide Based Devices for Biosensing Applications

Chapter 1

Introduction

The first part of the present work deals with the use of Gallium Arsenide (GaAs) based semiconductor structures as biosensors. A biosensor, in general, is a device combining a bioreceptor, which specifically senses a substance of interest (analyte), and a transducer which transforms the sensing event into a measurable signal (cf. figure 1.1). For the bioreceptor part a variety of recognizing materials have already been used, such as enzymes, antibodies, DNA, or even whole cells. These materials need an appropriate “bio-friendly” environment which is often provided by a special intermediate layer on the signal transducer. The deposition of a self-assembled monolayer of molecules (SAM) is a commonly used technique for such an interfacial layer which also helps to passivate the transducer against unwanted influences from the biological environment. For the transducing mechanism, in principle, all physical effects can be exploited such as optical, thermal, magnetic, mass or electrical changes. The use of biosensors to specifically sense molecular interactions at surfaces has gained more and more interest in recent years. One reason is a shift of research interest after the successful Human Genome Project [17] from DNA sequencing toward protein sensing [1, 2]. For DNA sequencing standard experimental tools had been developed and widely used but for the sensing of proteins there is still a need of developing new methods. Especially label- free techniques are sought, which solve the problem of possible protein dysfunction due to the attachment of marker molecules [3, 4]. The existing methods include two-dimensional (2D) gel electrophoresis where proteins are moving in a gel driven by an electric field and separate according to their isoelectric point1 and mass. Protein spots are then cut from the gel, and identified using mass spectrometry. However, standardization and automation of 2D gel electrophoresis has proved very difficult

1isoelectric point = pH value at which the protein carries zero net charge

7 8 Introduction

! Electrical Enzyme Potentiometric Antibody Amperometric Micro- ! Optical Signal organism Analyte ! Thermal DNA SAM ! Magnetic Cell ! Masschange Recognizing Inter- Transducer Material face Figure 1.1: Schematic of a biosensor. The substance of interest, the analyte, is recognized by a certain functional unit, the bioreceptor. This unit is located on a transducing device which transforms the recognizing event into a measurable signal. Often it is necessary to provide a bio-friendly environment on the transducer using an interface layer such as a self-assembled monolayer (SAM).

[18]. Another prominent example to detect protein interactions at surfaces is surface plasmon resonance (SPR). Here changes in the refractive index at the surface of a conductor are directly reﬂected by a change in plasmon excitation efﬁciency. In this way the adsorption of molecules such as the binding of proteins to immobilized antibodies can be detected. SPR is very sensitive to mass changes at the interface and has been successfully used to detect proteins [19], but its applicability to screen many interactions in parallel is limited although recently progress has been made [20]. A promising and also extensively studied system for biosensing applications are Field Effect Transistors (FETs), where the metal gate is replaced by an analyte-sensitive region. The obvious advantages of using such a technique are the suitability to massive parallelization and cheap production due to existing semiconductor manufacturing methods. Furthermore, the obtained signal is electrical in nature, thus, a further signal processing is easily implemented. FETs based on standard silicon technology have been shown to be a versatile tool to detect chemical and enzymatic reactions as well as DNA hybridization [21, 22, 23]. Silicon nanowires have been demonstrated to detect the binding of streptavidin to immobilized biotin with very high sensitivity [24], and even a direct electrical detection of neuron activity was realized with silicon based chips [25, 26]. A similar experiment was performed with Gallium Nitride (GaN) based devices [27] and even diamond has been used as a biosensor [28]. However, the development of the respective surface chemistry for GaN and diamond based devices has hindered the application of these systems so far. The material of choice for the present work was GaAs as it has some electronic properties which are superior to silicon’s. GaAs based devices usually generate less noise than silicon devices and leakage currents are expected to be smaller as semi-insulating substrates can be used 1.1 The Sensor Element - A Two Dimensional Electron Gas 9

[29]. Furthermore, it provides together with Aluminum-Gallium-Arsenide (AlGaAs) a material system which can easily be band engineered using Molecular Beam Epitaxy (MBE). Thereby it is possible to fabricate custom-tailored sensors with transducing layers at deﬁned distances from the surface. A disadvantage of GaAs based sensors is their intrinsic instability in aqueous solutions which makes a biological application difﬁcult. Therefore an appropriate interfacial layer has to be found to provide both biocompatibility and stabilization of the sensor. However, for most other material systems such a layer is also indispensable to provide a platform for further functionalization. Due to its very good electrical properties GaAs based devices have already been used for various sensing applications including biological purposes [30, 31, 32]. A further advantage of GaAs based devices is the possibility to easily include optically active elements such as InAs quantum dots in the device [33]. Thereby both electrical and optical detection schemes can be used in parallel for analyte detection pushing the limits of available sensor techniques.

1.1 The Sensor Element - A Two Dimensional Electron Gas

As transducing unit of the GaAs based sensor device a quasi two dimensional electron gas (2DEG) is used which forms in a silicon (Si) doped GaAs-AlGaAs heterostructure. The 2DEG is a conductive layer with high electron density confined to a few nanometers (nm) of the heterostructure. The electron density in the 2DEG is very sensitive to changes in the band structure which can easily be provoked by surface potential changes. This makes a detection of analyte recognition events at the surface possible (provided they change the surface potential). The 2DEG is fabricated by bringing the two lattice matching materials GaAs and AlGaAs together, e.g., by MBE growth. Because of the different band gap energies, discontinuities in the valence and conduction band arise. With certain boundary conditions, such as Fermi level pinning at the surface, a triangular potential well is formed at the GaAs-AlGaAs interface which is filled by electrons provided by a doping material (see figure 1.2). To reach higher mobilities so-called modulation doped structures are used, where the doping layer is spatially separated from the 2DEG region to reduce impurity scattering. At higher temperatures electrons may also be thermally excited to the potential well formed by the dopant atoms. However, this does not hinder the sensing mechanism as still a change in surface potential leads to a change in electron density. 10 Introduction

1.0

0.5 Figure 1.2: Top: Calculated conduction band edge (solid) of a typical

0.0 GaAs-AlGaAs heterostructure forming V Energy [eV] Energy

a 2DEG at room temperature. The het-

GaAs Al Ga As

0.3 0.7

4x10 erostructure is sketched in the middle

Si -doping metal 2DEG of the graph. A change in surface po- ] tential is simulated by applying a gate

1/cm³ voltage V (dashed). Bottom: Respec- density density g [ .

El tive electron densities. In the case with 0 gate voltage a parallel channel opens in 100 80 60 40 20 0

Depth [nm] the doping region.

1.2 Sensor Passivation and Functionalization

To overcome the problem of the intrinsic instability of GaAs in biological environments a pro- tective coating has to be applied which does not impair the transducing properties of the 2DEG. At the same time the coating should provide a biocompatible surface suitable for further functionalization with analyte sensing units. Both requirements can be fulfilled by self-assembled monolayers which, in general, are ordered molecular assemblies formed by the adsorption of an active surfactant on a solid surface. The order in these two-dimensional systems is produced by a spontaneous chemical synthesis at the interface and by intermolecular interactions (cf. figure 1.3). In most cases an assembly from solution is possible which simplifies the fabrication process significantly. By immersing the substrate into a solution containing the molecules of interest, the SAM formation is initiated. With an adequate choice of parameters only one monolayer is formed. Most research on SAMs so far was done on long alkyl chain like molecules on gold [34, 35],

solutionof chemisorption substrate surface-active onsurface intermolecular molecules interactions functional Figure 1.3: Schematic of the self endgroup assembly process from solution. The substrate is immersed into a so- spacer lution containing the molecules of interest. The surface-active head- surface- 1. 2. active group binds to the substrate and headgroup molecular interactions cause the substrate molecules to stand up and build an self-assemblingprocess ordered monolayer. 1.2 Sensor Passivation and Functionalization 11 but in recent years the diversity of molecules and substrates has expanded significantly. Aro- matic thiolated molecules have received increasing attention due to their high electronic conductivity and optical properties. Other characteristics such as their rigid molecular backbone and their larger cross-section make them interesting candidates for the interfacial layer of the GaAs based sensor. In the group of Motomu Tanaka at the Lehrstuhl für Biophysik E22 of the Technische Universität München experiments on SAM formation on GaAs using 4’-substituted Mercapto-Bi-Phenyls (MBPs) with different functional endgroups (see figure 1.4) were performed by K. Adlkofer and D. Gassull. The binding to the surface in this case was obtained by the sulfur group at one end of the molecule which has a strong affinity to transition metals as well as to III-V semiconductors [34]. They applied High-Resolution X-ray Photoelectron Spec- troscopy (HRXPS) and Near-Edge X-ray Absorption Fine Structure Spectroscopy (NEXAFS) showing that MBPs with hydrogen, hydroxyl and methyl endgroups form ordered monolayers on GaAs [36, 37]. Furthermore, they demonstrated a remarkable increase in stability of the coated samples with respect to bare GaAs samples in electrolytes using Impedance Spec- troscopy (IS) [38, 39]. In transport measurements the same behavior was observed by the author and coworkers for devices coated by non-substituted MBPs [40]. Because of this success the MBP-SAMs were the material of choice for the present biosensor study. With the different endgroups a further experimental parameter was available. From ellipsometry measurements and NEXAFS data information on the detailed surface structure of the molecular film was deduced: The MBP-SAM showed a thickness of 10±2Å and an average molecular tilt angle of approx. 30-40° with respect to the surface normal [41, 37]. Further geometrical considerations lead to a simplified microscopic picture of the MBP-SAM on the surface [42] as schematically sketched in figure 1.4.

cross-sectional A =-H,-OH,-CH area ~21Å2 3 AB A A

A A A A A A A A ~10

S S S S S S S S S ~8Å S GaAs(100) [011] GaAs(100) [011] As As As Ga Ga Ga Ga

Figure 1.4: Schematic of the sensor passivation by a SAM. Without SAM protection the substrate surface is easily harmed by an aqueous environment (A) whereas an ordered SAM is able to resist environmental stress (B). The magniﬁcation illustrates the microscopic structure of the mercaptobiphenyl monolayer on the GaAs surface. 12 Introduction Chapter 2

Fundamentals of Semiconductors in Electrolytes

A main task of the present thesis was to understand the effect of a self-assembled monolayer on the semiconductor and to characterize the passivated sensor in electrolyte solutions. Therefore the properties of semiconductor surfaces are discussed in the beginning of this chapter (section 2.1) and all relevant parameters are introduced. Furthermore, the influence of molecular chemisorption on the electronic surface structure is described in a simplified manner. In section 2.2 the special characteristics of buffered electrolytes are explained with an emphasis on Phos- phate Buffered Saline (PBS). In the following part 2.3 a semiconductor surface in electrolyte solutions is theoretically described and models dealing with surface charging are introduced which are necessary to understand the experimental results. In the last section (2.4) the methods used to simulate semiconductor-electrolyte structures and molecular properties are briefly discussed.

2.1 Semiconductor Surface Electronic Structure

Molecular interactions at surfaces are frequently used in biosensor applications to detect an analyte. Here a surface, in general, is deﬁned as the boundary of a media. It is a complex structure showing a variety of properties not known from the bulk as the symmetry and periodicity from inside a solid is broken at the surface. This leads to phenomena such as surface-localized electronic states within the bandgap and/or a double layer of charge, known as a surface dipole. The appearance of surface-localized states also induces a charge transfer between bulk and surface in order to establish thermal equilibrium between the two. The charge transfer results in a

13 14 Fundamentals of Semiconductors in Electrolytes non-neutral region (with a non-zero electric field) in the semiconductor bulk, usually referred to as the surface space charge region (SCR). This region may extend quite deeply into the bulk. The difference between the conduction (or valence) band edge at the surface and in the bulk is defined as the band bending energy eVbb. As an example the electronic structure of an n-type semiconductor is illustrated in figure 2.1. A magnitude which is easily experimentally accessible, e.g., by Kelvin-probe measurements, is the energy difference between the Fermi level EF and the local vacuum level EVL, the so-called work-function φW . It represents the energy necessary to remove an electron from inside the bulk and transfer it through the surface to a region outside the semiconductor but still close to the surface. In this region the electron is at the local vacuum level, still affected by the potential of the solid. If it moves further away from the surface into free space it feels the

“normal” vacuum level EV . This concept of a local vacuum level was necessarily introduced to explain the experimental ﬁnding of different work functions for different crystal faces of the same material. From the work function and the band bending another parameter can be deduced, the electron afﬁnity χ. It is the energy needed to bring an electron from the conduction band bottom to the vacuum:

χ = φW −VBB − (ECB − EF ) (2.1)

The last term can often be neglected for high doping levels.

localvacuum

levelEVL electronaffinity c workfunction energye fW band + + + conductionband bendingeVBB surfaceFermi FermilevelE levelE - - F FS - - - surface bandgap energyE states g

valenceband space

energy charge region DOS distance (SCR)

Figure 2.1: Illustration of the surface electronic structure of an n-type semiconductor. The vertical solid line indicates the surface. 2.1 Semiconductor Surface Electronic Structure 15

A surface effect neglected throughout this thesis due to its complexity is surface reconstruction. Because of the absence of neighboring atoms, the equilibrium conditions for surface atoms are modiﬁed with respect to the bulk. Therefore altered atomic positions are expected leading to a changed surface atomic structure, the surface reconstruction.

2.1.1 The GaAs Surface

In GaAs the Fermi level is usually pinned in the middle of the band gap, which is a problem in the application of GaAs-based devices as surface sensitive sensors. The pinning is caused by either intrinsic surface states due to surface reconstruction or dangling bonds, or by oxidation or other types of chemical bonds to the surface. In literature, a certain agreement about the density of surface states exists, usually a value of ∼ 1013cm−2 is assumed [43]. Ludeke et. al. [44] investigated clean and oxygen exposed GaAs surfaces and found out that dangling Ga bonds are responsible for empty surface states 0.9±0.2 eV above the bulk valence band edge. However, nowadays it is believed that the Fermi-level pinning results mainly from oxide formation at the surface. Experiments on the change in Fermi-level pinning due to surface treatments substantiate this [45], but still the detailed description of the surface states is a matter of debate.

2.1.2 Inﬂuence of Chemisorbed Molecules

By adsorption onto a surface a molecule’s electronic structure is disturbed to some extent. Ac- cording to the extent of this perturbation an adsorption process can be classified in two types: 1. Physisorption is a process in which the electronic structure of the molecule is hardly perturbed upon adsorption. A main driving force for physisorption can be van-der-Waals bonding where the attractive force is caused by correlated charge fluctuations in the two bonding partners. 2. Chemisorption on the other hand is an adsorption process that resembles the formation of covalent or ionic bonds in molecular physics: the electronic structure of the binding partners is strongly perturbed, new hybrid orbitals are formed and charge transfer from one partner to the other occurs. The accompanying modification of the energy distribution and/or the surface density of states (SDOS) can shift the position of EFS and give rise to measurable changes in electrical and optical properties. To give an example, a schematic of an adsorption process for a donor adsorbate on an n-type semiconductor is shown in figure 2.2. A donor is able to bind to the semiconductor, if its Highest Occupied Molecular Orbital (HOMO) lies energetically close to a vacant semiconductor surface state. Then, interaction occurs enabling electron transfer to 16 Fundamentals of Semiconductors in Electrolytes the semiconductor. Similarly, acceptor binding is possible by shifting electrons from the semiconductor surface states to the molecules’s Lowest Unoccupied Molecular Orbital (LUMO). So by chemisorption the surface charge density in the semiconductor can be altered, allowing for a detection of molecules at the surface. A simplified picture of the influence of adsorption processes on the surface electronic structure is shown in figure 2.3. Usually, all prominent parameters of semiconductor surfaces, the work function φW , the electron affinity χ, and the band bending VBB are changed by an adsorbate. A change of the surface electron density by chemisorption moves the surface Fermi 0 0 level from EFS to EFS leading to a change in the band bending VBB to VBB. Furthermore, surface dipoles might be induced or changed by the adsorbed molecules through modifying the surrounding environment of the surface atoms. Moreover, the adsorbing species can carry a dipole moment itself which causes a potential drop through the adsorbed layer as is illustrated 0 in figure 2.3 B. This potential step gives rise to a change in the work function from φW to φW , and consequently the electron affinity is also changed to χ0. The effect of intrinsic molecular dipoles can be expressed in terms of the dipole potential

∆φDip. For an ordered monolayer of molecules at the surface carrying a dipole moment µ this potential drop can be easily estimated applying a parallel plate capacitor model [46]. Let N be the molecule density and θ be the angle of the molecule with respect to the surface normal, then

Nµ cos(θ) ∆φDip = (2.2) εε0

Equation 2.2 is only an estimate because the dielectric coefﬁcient ε of the dipole layer is an ill-deﬁned property since the dipole layer is not a bulk entity. Moreover, if the dipole layer is not perfectly ordered, the angle θ should be considered as an average angle.

EVL

efW eVBB

Figure 2.2: Simpliﬁed picture of + c + + cb chemisorption on a semiconductor. Semi- conductor surface states interact with - - - - EFS EF donor - molecular orbitals of the adsorbate. In - - E HOMO g - - the case of a donor-adsorbate on an n-type semiconductor the Highest Occu-

vb pied Molecular Orbital (HOMO) of the adsorbate interacts with an unoccupied surface space adsorbate charge surface state to build new orbitals in the complex region surface-adsorbate complex. 2.2 Buffered Electrolyte Solutions 17

AB E VL ´ EVL eDfDip c c´ ef W ´ efW eV + eV´BB + BB ++ Ecb EF Ecb EFS - - - - ´ - - - - - EFS EF - - -

Eg Eg

Evb Evb

vacuum space bulk adsorbed space bulk charge surface charge region region

Figure 2.3: Schematic of chemisorption effects on the electronic structure of an n-type semiconductor, A) before chemisorption, B) after chemisorption. The adsorption process can cause a shift in work function φW , band bending VBB and electron afﬁnity χ as well as in surface state density and energy. An intrinsic molecular dipole moment results in a shift of the local vacuum level EVL. A more detailed explanation is given in the text.

2.2 Buffered Electrolyte Solutions

The GaAs based devices examined in this thesis are designed for a use under physiological conditions. These conditions imply an operation at room or slightly higher temperatures in electrolyte solutions with a proper pH-value. Electrolytes can be found frequently in biology and are substances with ionic DC conductivity, i.e., electrolytic currents are ionic in contrast to the electronic current in metals or semiconductors. This implies a matter transport preventing an externally applied DC current to ﬂow forever without changing the conductor. Electrolyte solutions can be made simply by adding salts such as sodium chloride (NaCl) to water. The salt molecules react with the water molecules to form separate ions which give the solution the ionic conductivity. For an application to biological systems it is furthermore very important to control the pH value of the electrolyte, which is deﬁned by the concentration of hydrogen ions [H+]: pH = + −log10[H ]. Intracellular environment in most biological systems has a pH-value near to 7, i.e., neutrality, because both the hydrogen and hydroxide ions in aqueous solutions are very reactive and can damage biological structures. Thus, the electrolyte has to be buffered against abrupt changes in acidity or alkalinity. In the following a short introduction to buffer solutions will be 18 Fundamentals of Semiconductors in Electrolytes given. An excellent and more detailed discussion of buffered electrolytes can be found in [47].

2.2.1 Buffer Action

A buffer is a substance, usually a weak acid, which is added to an electrolyte to prevent pH changes of the solution. This can easily happen in non-buffered systems, e.g., by dissolution of

CO2 from air. When an acid [HA] is put into water, it dissociates forming its conjugate base [A−] and the equilibrium reaction can be written as:

Ka + conjugate acid + H2O conjugate base + H3O (2.3) Ka − + HA + H2O A + H3O (2.4)

Here the reaction constant Ka is deﬁned as:

[H O+ ][A−] K = K · [H O ] = 3 (2.5) a eq 2 [HA]

Ka takes into account, that the concentration of water can be considered as constant for small amounts of added acids. Often the logarithmic scale is used for the reaction constant, pKa =

−log10[Ka]. With the knowledge of the dissociation reaction it is now possible to understand that weak acids and bases are able to resist pH changes, i.e., they can buffer the pH - value. Adding an acid, which increases the H+-ion concentration, moves the reaction equilibrium of equation 2.4 to the left and most of the added H+-ions are mopped up by the conjugate base A−. Therefore the pH-value stays more or less constant. For an added base the equilibrium is shifted to the right with the same effect. For calculating the pH of a buffered electrolyte one can use the Henderson-Hasselbalch equation which can be derived from the equations above [47]:

[A−] [base] pH = pK + log = pK + log (2.6) a 10 [HA] a 10 [acid]

This equation was used throughout the thesis to calculate buffer concentrations at a certain pH.

Obviously a buffer species has its best buffering capacity at its pKa value, as both components are then equally available and can buffer against both acids (H+ donator) and bases (H+ acceptor). 2.3 Semiconductor-Electrolyte Interface 19

2.2.2 Effect of Temperature and Ionic Strength

One problem in designing a buffer is that both the ionic strength of a solution and the temperature change the dissociation constant Ka. Ions in solution shield the buffer components and thereby change their activity. This inﬂuences the reaction equilibrium and Ka. The effect of all ions on the reaction constant can be compressed into one single term also known as the Debye-Hückel relationship [47]. " √ # 0 A I pK = pKa + (2zacid − 1) · √ − 0.1 · I (2.7) a 1 + I

In this equation zacid is the charge on the conjugate acid, A is a temperature dependent constant, and I is the ionic strength deﬁned as:

1 2 I = ∑(ci · zi ) (2.8) 2 i

Here ci is the concentration and zi the charge valency of the ions. The temperature also has an effect on the reaction constant Ka which is usually expressed through the term dpKa/dT. It can be either negative or positive depending on the buffer.

2.2.3 Phosphate Buffers

Phosphate buffer saline1 (PBS) is a commonly used buffer system and suitable for neutral pH values and acidic or alkalic conditions. It is made of ortho-phosphoric acid and shows three dissociation reactions:

K K K PBS,1 − + PBS,2 2− + PBS,3 3− + H3PO4 H2PO4 + H HPO4 + 2H PO4 + 3H

PBS was used throughout this study for all measurements in wet environment. Its properties are summarized in table 2.1.

2.3 Semiconductor-Electrolyte Interface

In the previous sections both the semiconductor and the electrolyte were treated separately. Bringing them together leads to a new set of phenomena which will be discussed in this sec-

1saline = salt solution 20 Fundamentals of Semiconductors in Electrolytes

Dissociation reaction pKPBS dpKPBS/dT − + H3PO4 H2PO4 + H 2.15 +0.0044/°C − 2− + H2PO4 HPO4 + H 7.21 -0.0028/°C 2− 3− + HPO4 PO4 + H 12.33 -0.026/°C Table 2.1: Reaction constants and temperature dependence of a phosphate buffer [47].

tion. A rather detailed introduction will be given here because a thorough understanding of the underlying physics and theories is important for the interpretation of the experimental results. This introduction is mainly based on a variety of textbooks [48, 49, 50, 51, 52, 53], diploma theses [54, 55] and a few journal articles as cited at the adequate position. If one brings two different materials into contact then charged layers form almost inevitably at the interface due to the energy difference of charge carriers in the two materials. This is also the case for the solid-liquid interface. The charges have to be neutralized which leads to electrical double layers, consisting of layers of positive charge, layers of negative charge, and regions of high electric field between, or within, the charged layers. Such double layers are dominant in controlling the electrical and chemical properties of the interface. Usually three distinct double layers can be distinguished at the semiconductor-liquid interface as is indicated in figure 2.4. The space charge region in the semiconductor is neutralized by an equivalent amount of charge in the electrolyte. This charge is distributed among a thin Stern layer of adsorbed ions followed by a diffuse double layer, the Gouy-Chapman region. In the present section first a treatment of the diffuse layer with the Poisson-Boltzmann theory

Figure 2.4: Double layers at the semiconductor-liquid interface. The dashed line through the liquid indicates the variation in potential energy per unit negative charge, determined only by the double layer voltages, as it moves from the conduction band into solution. The bottom parts illustrates a possible ion distribution. The Stern layer of adsorbed ions can be divided into two planes, the inner (IHP) and the outer Helmholtz plane (OHP). 2.3 Semiconductor-Electrolyte Interface 21 will be given. Then, various charging models will be explained which show how an additional charge can be put on the solid-liquid interface by surface reactions. Furthermore, an adsorption into the Stern layer will be treated and in the end the presented theories will be applied to capacitance measurements.

2.3.1 Poisson-Boltzmann Theory

If a charged particle is brought into contact with an electrolyte it will be screened by a cloud of ions of opposite charge in the liquid. The charge on the particle can either be caused externally by an applied voltage if it is electrically contacted, or it forms inherently by the energy difference electrons feel at the interface. The screening ion distribution together with the potential in the electrolyte is governed by two equations. The ﬁrst is the Poisson equation known from electrostatics which relates the electric potential ψ to the charge density of a medium (in SI units): − ∇~r (ε0ε(~r) ∇~rψ(~r)) = ∑zieρi(~r) (2.9) i

Here ε(~r) denotes the dielectric constant and zieρi is the charge density caused by particles of type i carrying a charge of zie. From the equilibrium requirement that the chemical potential be uniform throughout the system one obtains the second equation, the Boltzmann distribution for ions of type i at position~r: µ ¶ z e(ψ(~r) − ψ ) ρ (~r) = ρ exp − i ∞ (2.10) i i,∞ kT where ψ∞ denotes the potential at inﬁnity which is usually set to zero. The combination of the Poisson equation 2.9 and the Boltzmann distribution 2.10 leads to the Poisson-Boltzmann (PB) equation in three dimensions. µ ¶ zie(ψ(~r) − ψ∞) εε0 ∆~rψ(~r) = ∑zieρi,∞ exp − (2.11) i kT

This equation very well describes the behavior of an electrolyte and is an example of a mean ﬁeld approximation since it is assumed that the distribution of ions in the solution is determined by the averaged potential ψ. Unfortunately, this nonlinear differential equation cannot be solved analytically in general. 22 Fundamentals of Semiconductors in Electrolytes

Debye-Hückel Approximation

In case of small potentials eψ(~r) ¿ kT an analytical solution is possible by linearization of equation 2.11. A ﬁrst order expansion of the exponential together with the electroneutrality requirement in the bulk gives the Debye-Hückel equation.

¡ 2¢ ∆~r − κ ψ(~r) = 0 (2.12)

Here a new parameter, the Debye screening length 1/κ was introduced. It is a descriptive parameter of the system of the order of a few nanometers and is deﬁned as: s εε kT κ−1 = 0 (2.13) ∑ 2 2 i zi e ρi,∞

The Debye-Hückel approximation yields a limiting result to which general solutions must con- verge for small potentials. Particularly in the limit of zero salt concentration the solution of equation 2.12 becomes exact.

Gouy-Chapman Solution and the Electrical Double Layer

In the case of a planar geometry the general three-dimensional problem can be reduced to one dimension. For an inﬁnitely extending surface in an electrolyte solution let x be the distance from the surface. Then, the general PB equation 2.11 reduces to:

2 µ ¶ d ψ(x) zie(ψ(x) − ψ∞) εε0 2 = ∑zieρi,∞ exp − (2.14) dx i kT

For a unique solution to this second order differential equation two boundary conditions have to be specified. They result on the one hand from the electroneutrality condition, i.e., the surface charge density σs needs to be fully compensated by the ion distribution in the solution which yields σs = εε0|~Es|. On the other hand the electric field in infinity is set to zero |~E∞| = 0. Omitting a few intermediate steps this leads to the relationship between the surface ionic concentration ρi,s and the bulk concentration ρi,∞.

2 ∑ρi,s = ∑ρi,∞ + σs /2εε0kT (2.15) i i 2.3 Semiconductor-Electrolyte Interface 23

Together with the Boltzmann distribution 2.10 one obtains the Grahame equation which relates the surface potential to the surface charge density. s · µ ¶ ¸ p −zie(ψs − ψ∞) σs = 2εε0kT ∑ρi,∞ exp − 1 (2.16) i kT

The Grahame equation naturally follows from the boundary conditions and the Boltzmann distribution. Giving an example, for the case of a monovalent salt NaCl and a divalent salt CaCl2 the Grahame equation can be written as:2 ³ ´q p eψs ¡ ¢ σ = 8εε kT sinh [NaCl ] + [CaCl ] 2 + e−eψs/kT (2.17) s 0 2kT 2

Please note that positive surface charges σs will result in other absolute potential values than negative surface charges because the divalent salt CaCl2 is not symmetrical. As is depicted in figure 2.5, even low amounts of divalent ions have a large impact on the surface potential. For a wide range of monovalent ion concentrations the potential is fixed at a certain value by the divalent ions. Only at comparably high concentrations a change is visible. This effect makes a treatment of the PBS for the theoretical interpretation of the experimental results so important as the PBS can contain double or even triple charged ions. The whole potential distribution in the electrolyte can also be obtained after certain mathematical operations as the Gouy-Chapman (GC) solution of the PB equation 2.14 in the case of symmetric salts3 (e.g., see [55, 54]): " ¡ ¢ # 2kT 1 + tanh eψs e−κx ψ(x) = ln ¡ 4kT ¢ (2.18) eψs −κx e 1 − tanh 4kT e where ψs denotes the potential at the surface, and κ is the Debye length defined in equation 2.13. The Poisson-Boltzmann model suffers of several limitations. Effects like ion-correlation, steric hindrance, and image forces are not included. Even more important is the disregard of the finite ion size and ion adsorption. An illustration of this inadequacy is shown in figure 2.6. At salt concentration above 100 mM most of the potential drop occurs in a region of 1-2 nm which is already in the order of the ion size. Furthermore, the surface ion concentrations can exceed 10 M reaching the solubility limit of salts in water. Therefore Otto Stern [56] modified

2sinh(x) = (ex − e−x)/2 3anions and cations have the same valency z. 24 Fundamentals of Semiconductors in Electrolytes

Figure 2.5: Surface potential for an electrolyte with monovalent (e.g., NaCl) and divalent (e.g., CaCl2) salts according to the Grahame equation 2.17. The surface charge density was -0.2 C/m2. the original GC solution to include the adsorption of ions at the surface.

The Helmholtz and Stern Layers - An Extension

In close proximity to the surface the ion distribution is discrete and adsorption of the ions to the surface is probable. Stern therefore modiﬁed the existing theory by insertion of a layer of ions adsorbed to surface sites between the diffuse double-layer and the surface, the Stern layer (cf. ﬁgure 2.7)[56]. He assumed that the fraction of surface sites occupied by adsorbed ions was determined by a Boltzmann distribution and then applied the Langmuir adsorption

-300

-250

-200

-150

-100

0.1mM Potential [mV] Potential

-50 1mM

10mM 1M

0.1M

0 2 4 6 8 10 12 14

x [nm]

Figure 2.6: Left: Potential distribution according to the Gouy-Chapman solution for a surface at x = 0 2 with surface charge σs = −0.2 C/m in a monovalent electrolyte with concentrations from 0.1 mM (solid) to 1 M (-··). The corresponding Debye lengths are marked by a star. Right: Potential and ion distribution for a 0.1 M NaCl electrolyte. The multiples of the Debye length are marked by a star. 2.3 Semiconductor-Electrolyte Interface 25

theory. If Ns denotes the number density of occupiable sites on the surface, then the maximum surface charge density is σads,max = zeNs and σads/(σads,max − σads) is the ratio of occupied to unoccupied sites. The corresponding parameter in the bulk solution is the ratio of the molecule numbers N: N N c ads,bulk ≈ ads,bulk = ads,bulk Nall,bulk − Nads,bulk Nall,bulk call,bulk

Here Nads,bulk denotes the number of active adsorbant molecules in solution, Nall,bulk the maximum number of molecules in solution, and ci are the respective molar concentrations. Stern considered the two ratios to be related as follows:

σads cads,bulk = e(zeψδ +Φ)/kT (2.19) σads,max − σads call,bulk where ψδ is the potential at the boundary between the compact and diffuse layers and Φ allows for any additional chemical adsorption potential. The adsorbed charge is then:

c ads,bulk ezeψδ +Φ/kT call,bulk σads = zeNs · cads,bulk (2.20) 1 + ezeψδ +Φ/kT call,bulk an expression often simpliﬁed by neglecting the second term in the denominator. Within the compact layer of thickness δ, the potential gradient −dψ/dx can be approximated by (ψs −

ψδ )/δ; hence ψ − ψ σ = ε0ε s δ (2.21) ads 0 δ where ε0 is a local dielectric constant that may differ from that of the bulk solvent. The compact layer must be further subdivided, especially when considering the dissociation or dissolution of charge groups determining the surface potential as discussed in the next section 2.3.2. The

Stern layer is rather immobile in the sense of resisting shear, thus, often ψδ is identiﬁed as the so-called zeta potential of the shear plane. However, there is no reason for the shear plane to coincide exactly with the Stern layer boundary.

2.3.2 Site-Dissociation Theory

In the previous section the original surface charge density σs was already modiﬁed by the adsorbed ions σads leading to a new overall charge density governing the GC double layer region. However, there are other effects which might alter this charge density such as chemical reactions taking place at the surface. Such a chemical reaction might be the association or dissociation 26 Fundamentals of Semiconductors in Electrolytes

Stern layer Figure 2.7: Schematic representation of the Stern layer. It can be structured into what is yd diffuse - layer called an inner Helmholtz plane (IHP), located at + the surface of Stern adsorbed ions, and an outer - Helmholtz plane (OHP), located on the centers + innerHelmholtzplane(IHP) - outerHelmholtzplane(OHP) of the next layer of ions marking the beginning x of the diffuse layer.

of H+ or OH−-ions, or of any other ions from solution to reactive surface sites. If these surface sites can be both negatively or positively charged by the same type of ions one speaks of an amphoteric surface which will be treated in this section. The presented theoretical description is mainly based on journal articles [57, 58, 59, 60], review articles [61] and diploma theses [55, 54]. In these sources also a treatment of other surfaces such as zwitterionic can be found.

The surface dissociation and association reaction taking place at a surface with reactive surface groups A sensitive to H+-ions can be written in the following way:

Ka Ka A− + H+ AH ⇐⇒ A − O− + H+ A − OH (2.22) + Kb + + Kb + AH + H AH2 ⇐⇒ A − OH + H A − OH2 (2.23)

Often the reactive sites are caused by surface oxides, therefore A is replaced by A-O, and the reactions constants are deﬁned as

[A − O−][H+] K = s (2.24) a [A − OH] + [A − OH][H ]s Kb = + (2.25) [A − OH2 ]

Obvious relationships come from the surface charge density σs and the total number of active surface sites Ns: ¡ + − ¢ σs = q [A − OH2 ] − [A − O ] (2.26) + − Ns = [A − OH] + [A − OH2 ] + [A − O ] (2.27) 2.3 Semiconductor-Electrolyte Interface 27

These equations can be combined to the following charge-potential relationship:

³ + ´ [H ]s Ka −qNs − + Kb [H ]s σs = + (2.28) Ka [H ]s 1 + + + [H ]s Kb

Here the surface potential is hidden in the surface proton concentration as the latter relates to the surface potential by the Boltzmann distribution: µ ¶ −qψ [H+] = [H+] exp s (2.29) s ∞ kT

Solution by Linearization of the Gouy-Chapman Model - Nernstian pH Sensitivity

For high salt concentrations this complicated relationship can be further simpliﬁed by a linearization of the Gouy-Chapman model. It can be seen as a full condensation of the Gouy- Chapman layer into the Stern layer. Therefore one can relate surface charge and potential with the basic capacitor equation:

σs = ψsCDL (2.30)

Here CDL denotes the capacity per unit area of the double layer region. Assumption 2.30 is only valid for either high salt concentrations or high surface charges. This is illustrated in ﬁgure 2.8 showing an accurate calculation of the surface charge - surface potential relationship using the Grahame equation 2.16 in contrast to the linearization of equation 2.30. With the assumption that saturation does not occur

− + 2 [A − O ] · [A − OH2 ] ¿ [A − OH] (2.31)

σs ¿ qNs (2.32)

1mM NaCl 250

200

150

100 Figure 2.8: Surface potential ψs(σs) according to the Grahame equation 2.16 for monovalent salt 50 1M NaCl concentrations from 1 mM to 1 M (logarithmic SurfacePotential [mV] 0 spacing). Only for high salt concentrations or

0.00 0.05 0.10 0.15 0.20 large surface charges the linearization of ψs(σs)

Surface Charge [C/m²] is valid. 28 Fundamentals of Semiconductors in Electrolytes

it is possible to simplify equation 2.28. Introducing furthermore the pH of zero charge, pHpzc = √ + −log10 KaKb, and substituting [H ]∞ leads to: µ ¶ ¡ ¢ qψ qψ 1 2.303 pH − pH = s + arcsinh s (2.33) pzc kT kT β where ³ ´ 1 2 Ka 2 2q Ns K β = b kTCDL For large β-values the arcsinh vanishes and one obtains the maximum (Nernstian) sensitivity for the surface potential ψs in terms of pH at room temperature:

ψs/pH = 2.303 kT/q ≈ 60mV/pH (2.34)

General Solution Using the Grahame Equation

In general, one has to replace equation 2.30 with the Grahame equation 2.16. Combining it with equation 2.28 and expanding the terms for the surface proton concentration using the Boltzmann distribution 2.29 gives:

µ ¶ + −qψs [H ]∞ exp( kT ) Ka −qNs − + −qψs Kb [H ]∞ exp( ) kT = σ = + −qψs Ka [H ]∞ exp( kT ) 1 + + −qψs + K [H ]∞ exp( kT ) b s · µ ¶ ¸ p −zieψs = 2εε0kT ∑ρi,∞ exp − 1 (2.35) i kT

This equation was used for the simulation of the 2DEG sensor in electrolytes applying a site-dissociation model with the self written PoBoSim software. Please refer to section 2.4.1 for further details.

2.3.3 Alternative Adsorption Models

Surfaces which do not have reactive surface sites also can experience charging in electrolyte solutions, e.g., K. Marinova and coworkers found in their experiments on the electrophoretic velocity of oil droplets in water a charging of the hydrophobic oil surface [62]. This cannot be 2.3 Semiconductor-Electrolyte Interface 29 explained by the above introduced site-dissociation theory because of the lack of active surface reaction sites. Instead they successfully described the charging by the adsorption of OH−-ions following the Stern isotherm 2.20 writing it in the following way: ³ ´ − Φ+zeψs −eΓ0 v0 [OH ]∞ exp − kT σads = −eΓ = ³ ´ (2.36) − Φ+zeψs 1 + v0 [OH ]∞ exp − kT

−28 3 Here Γ0 is the saturation adsorption, v0 = 1.1 · 10 m is the volume of a hydrated hydroxyl − ion in solution, Φ accounts for the energy a hydroxyl ion gets upon adsorption, and [OH ]∞ is the bulk concentration of the hydroxyl ions. By the following transformation it is obvious that, from a mathematical point of view, this Stern layer adsorption is a special case of equation 2.28 found for the site-dissociation theory. Using the relationship between hydronium and hydroxyl ions in water, [H+]·[OH−] = 10−14 M2 [47], and the Boltzmann distribution 2.29 one can rewrite equation 2.36 as:

−eΓ v N2 · 10−8 · e(Φ/kT) −eΓ K σ = 0 0 A = 0 a (2.37) s + (−zeψ/kT) 2 −8 (Φ/kT) + [H ]∞ e + v0NA · 10 · e [H ]s + Ka

2 −8 (Φ/kT) where Ka = v0NA · 10 · e . This is exactly equation 2.28 for Kb = ∞ and Ns = Γ0.

2.3.4 Capacitance and Mott-Schottky Analysis

An important, experimentally observable parameter in electrochemistry is the capacitance of a system. Capacitance-voltage or capacitance-frequency curves are often used to determine the effect of surface treatments on a studied system. A difficult task is to conclude from the measured capacitance on the real system as it usually consists of several layers, in parallel or series, each with its own capacity and leakage paths represented by various electrical circuit elements. However, in some special cases a gross simplification is valid for the semiconductor- electrolyte interface leading to Mott-Schottky capacitance plots. As already mentioned in section 2.3.2 on page 27 it is possible to neglect the diffuse double layer for salt concentrations above 100 mM. In this case one has to treat only the space charge (sc.) layer in the semiconductor and the Stern layer in the electrolyte as illustrated in figure 2.9.

To each layer a capacitance can be assigned, Csc to the space charge layer and CDL to the Stern layer. An applied voltage then drops over the whole system according to the equivalent circuit 30 Fundamentals of Semiconductors in Electrolytes

A space Sternor charge Helm- region holtz region ~100nm ~0.3nm Figure 2.9: Schematic representation of an ideally polarizable semiconductor electrode in electrolyte with high salt concentration. (A) The potential drop V V sc in the interface region can be divided into the space VDL charge region Vsc and the Stern layer VDL. (B) A simple equivalent circuit for the semiconductor-liquid in- semiconductor electrolyte terface is characterized by two capacitances in series, B the space charge capacitance Csc in the solid and the Stern layer capacitance CDL in the liquid. In this ide-

Csc CDL alized picture no Faradaic currents are present. shown in ﬁgure 2.9. The voltage drops relate inversely with the corresponding capacitances:

V C sc = DL (2.38) VDL Csc

If the applied potential is in a range that causes a semiconductor surface depletion, and not inversion or accumulation, then Csc is far smaller than CDL because the space charge region is far thicker then the Stern layer. So, in a first approximation, the applied potential fully drops over the space charge region and the measured capacitance is determined by the space charge capacitance Csc. Under these conditions the rather complex relationship between CDL and the potential dropping over the sc. region Vsc can be considerably simplified to the Mott-Schottky equation (pages 126-130 of [50], [53]): r r εε N e k T C = 0 D · V − B (2.39) sc 2 sc e where ND is the donor concentration in the case of an n-doped semiconductor. For p-type electrodes ND must be replaced by the acceptor concentration. Often the flat-band potential Vf b is introduced which indicates the potential at which no sc. layer exists. Including a potential drop φ at a reference electrode the applied electrode potential can be represented as V = Vsc +

VDL + φ. The ﬂat-band potential is then obtained from the deﬁning condition Vsc = 0 as Vf b = VDL + φ. Therefore the Mott-Schottky relationship after a rearrangement can be written as: µ ¶ 1 2 kBT 2 = · V −Vf b − (2.40) Csc εε0NDe e

2 Accordingly, a plot of 1/Csc versus V yields a straight line. 2.4 Numerical Calculations 31

2.4 Numerical Calculations

2.4.1 Simulation of the Semiconductor Electrolyte Interface nextnano3 and PoBoSim

A simulation of the semiconductor-electrolyte interface was performed using two software programs: nextnano3 and PoBoSim. nextnano3 is a fully quantum mechanical device simulator in 3D developed at the WSI [63, 64]. It is able to solve a combination of the Poisson equation, the Schrödinger equation and the drift-diffusion equations together with strain minimization. Recently also the treatment of semiconductor-electrolyte interfaces including the standard site- binding model was incorporated in the 2D/3D version of the program. The structure used for the simulation in nextnano3 in this thesis is shown in figure 2.10. The semiconductor-electrolyte structure is placed between two metal electrodes which are necessary to define the potentials of the system. The thicknesses of the bulk GaAs layer (500 nm) and the electrolyte layer (438 nm) were chosen large enough to give a realistic electronic picture of the far bigger real structure. The region of interest with the thin AlGaAs layer (50 nm) and the GaAs cap layer (10 nm) is identical to the real MBE grown samples. The semiconductor potential USa was usually chosen in such a way that the Fermi energy lies mid gap at the metal- semiconductor boundary. However, sometimes also a von Neumann boundary condition with zero electric field was used. This had no influence on the potentials in the interesting region of the 2DEG and the solid-liquid interface. Additional input parameters were a constant surface charge σadd for trapped charges at the solid-liquid interface, and the parameters necessary for the site binding model: The density NS of active surface sites and the reaction constants Ka and

Kb. Furthermore, the pH and the ion concentrations of the electrolyte were speciﬁed.

YS, sS

U GaAs AlGaAs GaAs Electrolyte Sa 500nm 50nm 10nm 438nm UEl 2DEG x 0 1 501 530-532 551 561 999 1000

Sid -doping sadd; 19 (210· /cm³) NS ;K a ;K b

Figure 2.10: GaAs/AlGaAs heterostructure - electrolyte system used for nextnano3 simulations. The input paramters included the electrolyte potential UEl and a trapped surface charge σadd. The output included surface potential ψS and surface charge σs beneath carrier densities, band structure and potential proﬁle. 32 Fundamentals of Semiconductors in Electrolytes

Unfortunately, some special properties of the semiconductor-electrolyte interface are not yet implemented in nextnano3. Especially for the present study important features like the pH dependent composition change of a phosphate buffer and counter-ion adsorption on the surface cannot be treated by nextnano3 so far. Therefore a new simulation tool named PoBoSim was developed in the framework of this thesis using the MATLAB® package. PoBoSim treats only the electrolyte part of the whole structure (in contrast to nextnano3) solving the Poisson-Boltzmann equation including advanced surface charging models and PBS composition changes. The program ﬂow is sketched in ﬁgure 2.11. With the same input parameters as for the nextnano3 simulation plus the PBS concentration [PBS] the exact electrolyte composition is calculated iteratively. The effect of the ionic strength I on the PBS dissociation constants KPBS,i is taken 0 into account as described in section 2.2.2. This results in new constants KPBS,i which then yield 0 a new ionic strength I . After the calculation converged the concentrations of all ions ρi in solution can be determined. These values are then used to calculate the surface potential ψs. With

ψs all other variables like the surface charge σs or the sensitivity can be determined. For most conditions the disregard of the semiconductor part to describe the whole system is justiﬁed because the semiconductor is in comparison to the electrolyte "electronically weak". The electrolyte can be seen as a metal gate with respect to the semiconductor and any applied

Inputparameter

pH,[NaCl],[PBS],NS ,K a ,K b

Calculationofelectrolytecomposition

CalculationofK'PBS,i (I')

CalculationofI'(K'PBS,i )

SolveGrahameequationwithsurface chargingmodel:

Findzerooffunction f f =sSSS ( Y ,NS ,K a ,K b , r i )- s usingMATLABfzero function Figure 2.11: PoBoSim ﬂow scheme. Starting from the input variables the exact electrolyte concentration is calculated self-consistently. Then, the Poisson- Output Boltzmann equation with an adequate surface charging Y(,,K,K,) s N r SS S a b i model is solved which gives the surface potential ψs. 2.4 Numerical Calculations 33

2.005

2.06

Potential 1M NaCl

2 U = 2.000V

2.000

2.04

1mM NaCl meV Energy [eV] Energy

U = 1.952V

CB El

2.02 1.995 0 48

561 562 563

2DEG Si -doping Electro- 2.00 cm³] /

lyte

17 4 Energy [eV] Energy

10 1.98 surface [ meV

2 . 48 semiconductor semiconductor

1.96 ens

0 d

400 450 500 550 600 560 580 600 620 E

x [nm] x [nm]

Figure 2.12: Left, top: nextnano3 simulations of the conduction band edge and potential profile of a GaAs-AlGaAs heterostructure in electrolyte (solid line). A change of the electrolyte potential by 0.5 V (dashed line) mainly influences the semiconductor and leaves the potential profile of the electrolyte unchanged. Left, bottom: Effect of the applied voltage to the electron density in the heterostructure. At certain conditions a parallel conduction channel forms in the doping region (at 530 nm). Right: Equivalence of potential changes (dashed lines) and electrolyte composition changes (solid lines). See text for details. voltage usually appears in the space charge region and does not change the potential profile in the electrolyte. The whole electrolyte profile is only shifted by the applied voltage ([50], sec. 3.2). This assumption was tested with nextnano3 simulation on the structure of figure 2.10. The upper left part of figure 2.12 shows the influence of an electrolyte potential change (∆Uel) on 3 the electronic structure as calculated with nextnano . As can be seen the change of ∆Uel shifts the electrolyte potential as a whole without changing its profile which looks as a horizontal line in the used scale. Instead all changes occur in the semiconductor leading to a change in electron densities as is depicted in the left bottom part. This is the main reason why it is possible to use the 2DEG sensor device as a biosensor. If a binding event of molecules to the surface, or pH changes, or any other effects inside the electrolyte induces a shift in surface potential then the resistance of the 2DEG device will change! This is equivalent to a shift in electrolyte potential as a whole and can also be seen as changing the voltage applied to a metal gate on top of the 2DEG device. An illustration of this behavior is depicted in the right panel of figure 2.12. An increase of salt concentration from 1 mM to 1 M

(solid lines) decreases the surface potential ψs by 48 mV. A change of the electrolyte potential Uel (dotted lines) by 48 mV has the same effect on ψs.

From the reasoning above a simulation with PoBoSim should yield the same results of ψs as 3 in nextnano . Indeed for typical conditions the ψs values obtained from both programs agree reasonably well as is shown in ﬁgure 2.13. 34 Fundamentals of Semiconductors in Electrolytes

0.20

0.15 2

= 0.3C/m [V] add s

0.10

0.05

0.00

= 0 -0.05

add

-0.10

-0.15 Surfacepotential

-0.20

3 4 5 6 7 8 9

Figure 2.13: Potential at the semiconductor electrolyte interface as a function of pH. The PoBoSim simulation which is restricted to the electrolyte region (dashed lines) matches the treatment of the full system with nextnano3 (solid lines) reasonably well.

Choice of Simulation Parameters

To right choice of parameters in order to simulate the real situation is rather difficult. In the 3 case of nextnano simulations it is important to choose the correct electrolyte potential UEl. Experiments showed that immersing a 2DEG sensor device in PBS of typical conditions with controlled electrolyte potential of approx. -400 mV did not change the device resistance by more than 15%. Therefore it was concluded that the band structure of the sensor in electrolyte solution resembles the band structure in vacuum. In nextnano3 simulations this could be reproduced using UEl = 1.7 V. Fortunately rather large ranges of electrolyte and sample potentials USa and UEl do not change the relative pH dependence of the surface potential significantly although they naturally influence the electron density of the device. This is illustrated in figure 2.14. In most cases the effect of surface charging, e.g. by site-dissociation, is dominant. Only in extreme cases where a strong accumulation or inversion occurs at the interface a significant change in

ψs(pH) curves can be seen (cf. also figure 2.15). The observed offsets between the various curves seen in figure 2.14 are not significant to the experiments as only potential changes and not absolute values are measureable. Another important parameter is the dielectric constant of the electrolyte solutions. Here the value for pure water ε = 80 was chosen. For high salt concentrations especially at the surface this could introduce a small error in the simulation.A detailed list of all relevant parameters for 2.4 Numerical Calculations 35

the simulations used to obtain ﬁgures 2.12 - 2.15 are given in table 2.2 .

2.4.2 Simulation of Molecular Properties

For the interpretation of the experiments in air it was necessary to obtain information on the molecular properties (e.g., molecular dipole moment) of the mercaptobiphenyls. Unfortunately, it was not successful to gather this information from common databases ([65, 66] so other methods had to be used. A powerful and widely applied tool to examine molecular properties is the

0.20

U = -0.8V V]

0.15 el [ s

0.10

0.05

0.00

-0.05

U = 4.2V

-0.10 Surfacepotential

3 4 5 6 7 8 9

Figure 2.14: Effect of electrolyte potential Uel on the surface potential ψs. Only at extreme potentials a signiﬁcant change of ψs(pH) can be observed. The energy bands of the points marked with a star are shown in ﬁgure 2.15.

2 Semiconductor Elec. 2 Semiconductor Elec. 2 Semiconductor Elec.

1 1 1 eV] eV] eV]

CB CB CB [ [ [

0 0 0

-1 -1 -1 nergy nergy nergy E E E

VB VB VB

-2 -2 -2

480 500 520 540 560 580 480 500 520 540 560 580 480 500 520 540 560 580

x [nm] x [nm] x [nm]

Figure 2.15: Energy band diagrams for the conﬁgurations marked in ﬁgure 2.13. Extreme electrolyte potentials (left: Uel = −0.8 V, pH=4; right: Uel = 4.2 V, pH=8) lead to an enormous band bending with high charge accumulation at the solid-electrolyte interface. Normal operation conditions (e.g., center: Uel = 1.7 V, pH=6), as used in this study, create only minor band changes. 36 Fundamentals of Semiconductors in Electrolytes

Figure on page σadd UEl [NaCl] [C/m2] [V] [mM] 2.12 left, solid 33 0 2.0 V 100 2.12 left, dashed 33 0 1.5 V 100 2.12 right 33 0 var. var. 2.13 34 var. 1.7 V 100 2.14 35 0.3 var. 100 2.15 35 0.3 var. 100

Table 2.2: Simulation parameters which have been used to obtain the denoted figures. For all figures the 14 following values were kept constant: NS = 4.5 · 10 , pKa = -6.5, pKb = 0.5, and USa was defined by a von Neumann condition.

Density-Functional-Theory (DFT). DFT belongs to the ab-initio methods, i.e., it does not need any empirical parameters obtained from experiments to simulate molecular properties. Only a short sketch of DFT will be given in the following as a complete description and discussion of DFT is beyond the scope of this thesis. For more information please refer to standard textbooks of quantum chemistry or to other sources like [42] or [67]. Usually, such as in Hartree-Fock methods, a quantum mechanical system is described by a multi-particle wave function which is obtained from the solution of the time-independent many- particle Schrödinger equation for all involved atoms and their electrons. In minimizing the energy of the system one obtains the ground state of the molecule. In contrast to this approach DFT uses the total electron density ρ(~r) as the fundamental variable. Electron density, which depends only on x, y and z, is more attractive than a many-particle wave function which depends on all coordinates of all particles. It can be shown that the knowledge of the total electron density is as good as the knowledge of the wave functions in ﬁnding the ground state. The latter is usually found by applying a variational principle on the energy functional of the molecule: Z E[ρ] = T0[ρ] + [Vion−el(~r) +Vcoul(~r)]ρ(~r) d~r + Exc[ρ] (2.41)

Here is T0 the energy of the electron system as if there were no electron-electron interactions, Vion−el is the ion-electron interaction and Vcoul the classical Coulomb interaction between electrons. Exc includes all parts of the kinetic energy which were not accounted for by previous terms. It is the only term which cannot be calculated exactly so a proper choice for this functional is crucial. First implementations of the DFT method used a Local Density Approximation 2.4 Numerical Calculations 37

(LDA) for Exc which was split into two parts for historical reasons: The exchange energy Ex[ρ] and the correlation energy Ec[ρ]. Several attempts to improve the functionals were made. Among them is the widely used B3LYP functional which was also chosen for all calculations in this thesis. It consists of the Becke three parameter hybrid exchange functional [68] together with the Lee-Yang-Parr correlation functional [69]. Besides the proper choice of the functional, DFT calculations vary in the applied basis set. For the calculation of the electron density atomic or molecular orbitals are used which have to be described in a mathematical basis set. A commonly, and also in this thesis, used basis set is the 6-31G+(p,d) basis which includes polarization and diffuse functions. Typically a simulation of molecular properties was performed with Gaussian 03W [70] and consisted of a two step procedure: First the geometry was optimized using the B3LYP functional and the 6-31G(p,d) basis set. Then, an energy optimization was performed and the molecular properties of interest were identiﬁed. Further information about the strategy how to calculate molecular properties is given at the appropriate positions in this thesis. 38 Fundamentals of Semiconductors in Electrolytes Chapter 3

Experimental Techniques and Measurement Setup

The present work deals with the use of GaAs based 2DEG devices in wet environment. This implies certain requirements on experimental setup and sample fabrication. An appropriate sample layout suitable for high sensitivity measurements had to be developed as will be described in the ﬁrst part of this chapter together with the sample fabrication. Furthermore, an experimental setup for measurements in solutions was necessary allowing for liquid exchange and electrolyte potential control. At the same time the sensor structure had to be contacted electrically. This was accomplished with the development of a ﬂow chamber as described in section 3.2. There also the Kelvin probe setup will be explained and further information on the measurement details will be given.

3.1 Sample Design and Fabrication

The fabrication of a fully functional sensor device can be subdivided into three steps. First, the appropriate GaAs/AlGaAs heterostructure is grown by Molecular Beam Epitaxy (MBE). Then, standard semiconductor processing tools are used to pattern a sample into individual device regions and to deposit contact pads for a connection to external electrical circuits. Last the protecting monolayer of mercaptobiphenyls is deposited from solution. In the following the fabrication and layout details are given. In general, technical details were omitted if known from standard semiconductor processing technology.

39 40 Experimental Techniques and Measurement Setup

3.1.1 Molecular Beam Epitaxy Growth

All wafers for the GaAs based biosensors were bought from either Wafer Technology Ltd., UK, or Freiberger Compounds Materials GmbH, Germany. Then, epitaxial layers were MBE grown by Dr. D. Schuh or M. Bichler with the in-house MBE equipment for high-mobility GaAs samples. A sketch of the grown layer structure is illustrated in ﬁgure 3.1. On the GaAs bulk a 50 nm thick Al0.3Ga0.7As layer was grown followed by a 10 nm thick GaAs cap layer to prevent surface oxidation. In the AlGaAs layer a Si-δ-doping was embedded at 30 nm from the surface as n-dopant. Most of the wafers were characterized prior to further processing in a Hall measurement setup at 4.2K and room temperature (r.t.). All examined wafers showed good Shubnikov de Haas oscillations proving the existence of a 2D system. Furthermore, electron densities and mobilities were measured. Typical values were 1-5·1011/cm2 and 3-5·1011/cm2 for the electron density at 4.2 K (after illumination, a.i.) and r.t. respectively. The according mobilities were 0.6-2·106 cm2/Vs at 4.2 K (a.i.) and 6000-8000 cm2/Vs at room temperature. At such elevated temperatures the positive effect of the modulation doping was hardly noticeable as phonon scattering is dominant over impurity scattering. On some samples the 2DEG layers were separated from the GaAs wafer by a GaAs-AlGaAs superlattice to prevent electrons escaping from the 2DEG to the bulk. However, at room temperature no difference in electrical properties could be observed between samples with and without superlattice.

3.1.2 Device Layout and Patterning

After MBE growth and electrical testing the Gallium, used during MBE growth, was removed from the backside of the wafer using concentrated HCl. The wafer front was protected with standard photoresist (Shipley S1818) during this step. Then, the wafer was cut into approx. 1cm x 1cm large pieces. After that each piece was patterned into device structures. A typical device layout used throughout this thesis is shown in ﬁgure 3.2. On each sample three independent sensor devices suitable for four-point measurements were fabricated where each n o i 0 GaAscap

ct 10

e 30

r Si-d -doping i

d 60 2DEG h t Al0.3G 0.7As

w a

o x-axis r

g [nm] Figure 3.1: Schematic of the MBE grown Ga As bulk GaAs-AlGaAs heterostructure. 3.1 Sample Design and Fabrication 41 device consisted of a Hall bar-like structure with two side contacts. The Hall bar width was 100 µm as was the separation of the leads for the four point measurement. The lead width was 10 µm ensuring a good electrical connection to the Hall bar with sufficiently small error in potential measurements. It was not possible to put more than three devices on one sample as the maximum number of contacts was limited by the setup for liquid handling. Before each patterning step, a device was cleaned by consecutive sonication in acetone and isopropanol (IPA) and then purged dry by a nitrogen (N2) flow. The first processing step consisted of a mesa etch (cf. figure 3.2A-C) using wet chemical etching (H3PO4 :H2O2 :H2O = 1:1:38) in a standard photolithography step (see appendix A.3 for details). The etch depth was controlled by a Dektak profilometer for each sample with typical etch depths being 100-150 nm. After that a standard lift-off process was used to deposit typical n-type contacts to GaAs (cf. figure 3.2D and see appendix A.3 for details). The contacts were formed by electron beam evaporation of 5 nm Nickel (Ni), 25 nm Germanium (Ge), 50 nm gold (Au), 20 nm Ni, and 200 nm Au. After the lift-off the samples were annealed at 430°C for 60 s under forming gas atmosphere to build the electrical contact between the metal layer and the 2DEG. Then, the samples were ready for an electrical characterization and the deposition of mercaptobiphenyls. All process steps were controlled by an optical microscope.

3.1.3 Deposition of Mercaptobiphenyl Monolayers

The protecting layer of 4’-substituted 4-mercaptobiphenyls was deposited on the GaAs based samples using the self-assembly technique as introduced in section 1.2. The grafting process of all samples was carried out by D. Gassull from Prof. Dr. M. Tanaka’s group at the Lehrstuhl für Biophysik E22 of the Technische Universität München1.

1Prof. Dr. M. Tanaka is presently working at the Universität Heidelberg, Germany.

ABCD

100µm 100µm 1 2 3

Figure 3.2: Mask layout for sensor fabrication. A) Mask for mesa etching a sample with three different sensor regions. Black: Etched region. Hatched: Sensing 2DEG channel used for 4-point measurements. White: Remaining source and drain 2DEG channels for 2-point measurements. B) Magnification of the center region. The three distinct sensor regions are indicated by numbers and the current flow is illustrated by gray arrows. C) Magnification of B. The area of each sensor was 100µm x 100µm. D) Mask for contact pad deposition via a standard lift-off process. 42 Experimental Techniques and Measurement Setup

A typical assembly procedure consisted of following steps: Prior to the surface modiﬁca- tion, the samples were brieﬂy sonicated in acetone (approx. 3min.) and rinsed with ethanol. The native oxide of GaAs was stripped by soaking the sample in concentrated HCl for 1min., resulting in a stoichiometric GaAs [100] surface. Self-assembled monolayers were deposited by immersing freshly prepared substrates into 0.1mM mercaptobiphenyl solution in dry ethanol at

50°C for 20h. The reactions were carried out under nitrogen (N2) atmosphere to avoid surface oxidation. After deposition, the sample was taken out from the reactor, sonicated brieﬂy (30 s) in ethanol, and dried by a N2 ﬂow. For more details of the deposition process please refer to [41].

3.2 Experimental Setup and Measurement Details

3.2.1 Kelvin Probe Measurements

Coated and uncoated homogeneous GaAs samples were characterized in air using a Kelvin probe. With a commercial setup from KP Technology, Ltd. (Wick, Scotland) the work function, the band bending and thereby the electron affinity of n- and p-GaAs samples in air were determined (compare also section 2.1 for a definition of the parameters). The setup is illustrated in figure 3.3. A Kelvin probe consists mainly of an oscillating metallic tip with known work function, often gold, in combination with a voltage source. If an additional light source is included in the setup then also measurements of the band bending are possible using the Surface Photo-Voltage (SPV) [46]. The working principle of a Kelvin probe is sketched in figure 3.4. If the work function of a certain material 1 has to be measured, another material 2 with known work function can be used. The difference in work functions results in an electron energy level diagram of figure 3.4A. If the two materials are electrically connected, the Fermi levels align causing a charging of the two materials with a corresponding potential drop, the contact potential VC (figure 3.4B). By including a voltage source with variable “backing voltage VB” it is possible to decharge the system again. At the point where VB = −VC the system has zero charge and φW,1 can be

Figure 3.3: Schematic of the Kelvin probe setup. 3.2 Experimental Setup and Measurement Details 43

calculated being φW,1 = φW,2 +VB (figure 3.4C). The backing voltage at which the system is uncharged is usually determined by forming a capacitor with a vibrating, circular tip of material 1 in close proximity to material 2. The alternating current through the system is proportional to the charge on the capacitor plates, which is influenced by the backing potential as described above. The contact potential is then identified by the point of zero output signal. Measurements were performed with an Au tip of approx. 1 mm2 cross section. The Kelvin probe system was operated near its eigenfrequency at approx. 60 Hz and maximum backing voltages of ±5V were applied to determine the contact potential in the off-null technique of the KP Technologies device. The tip-sample distance was small enough to get stable results, i.e., a further approach of the tip did not change the obtained contact potential. The samples used for KP measurements were approx. 5 x 5 mm pieces cut from commercially available wafers from Wafer Technology, UK. Both silicon n+-doped, and zinc p+-doped wafers were used during this study. The carrier concentrations according to the supplier were 1−5·1018/cm3 for the n-doped and 5−50·1018/cm3 for the p-doped samples. For the n-doped samples this was verified by Hall measurements. Ohmic contacts were deposited on the backside of the n-GaAs samples and annealed in order to get a defined electrical connection to the system. For p-GaAs it was found that a deposition of metal contacts was not necessary. Simply by physical contact to an electrode reproducible results were obtained.

Surface Photovoltage Measurements

The potential drop VBB over the space charge region in the semiconductor (compare section 2.1) can be reduced to nearly ﬂat band conditions by high intensity illumination. For this purpose an Argon laser was used at 515 nm wavelength. By measuring the work function difference

A B C

VC fW,2 fW,2 fW,1 fW,1 fW,1

E fW,2 E F,2 - + F,2 EF,1 EF,1 - + EF,2 EF,1 - + +

VBC =-V

Figure 3.4: Kelvin probe working principle. A) φW,i represent the work function of two different conducting but isolated samples. B) If an electrical contact is made their potential equalize and the resulting ﬂow of charge produces a potential gradient, termed the contact potential VC, between the plates. C) Inclusion of a variable “backing potential” VB in the external circuit permits biasing of one electrode with respect to the other until the electric ﬁeld vanishes. 44 Experimental Techniques and Measurement Setup

with and without illumination the band bending VBB can be determined (see figure 3.5). The change in work function with illumination is also called the Surface Photo-Voltage (SPV). With the band bending, the electron affinity χ can be calculated according to equation 2.1. The light intensity is an important parameter as bright illumination is necessary to obtain really flat-band conditions. However, a too intense illumination is able to damage the sample surface as was observed from Raman measurements on GaAs samples using an Argon laser at 800 mW power (data not shown). The optimum operation conditions can be determined in a contact potential - illumination power graph as shown in figure 3.6. The contact potential should saturate with illumination power. However, this could not be achieved with the present experimental setup. Nevertheless it was assumed that nearly flat band conditions were obtained and the measured values were taken as a good guess for the real values. Other groups obtained only slightly (25%) higher values on similar experiments on GaAs [71]. The light intensity on the samples was kept constant at 0.1W/cm2 throughout all measurements. Therefore at least a qualitative interpretation of obtained results is justified.

Laser On Laser On Laser On

-100 [mV] C

-200

SPV

tential V tential band Figure 3.5: Determination of the band o

-300 bending bending from the Surface Photovoltage (SPV) of an n-GaAs sample. The SPV is

ntact p ntact the difference in work function of a sam-

-400 Co ple with and without illumination. In the

30 35 40 45 50 case of sufﬁciently intense illumination it

Time [sec.] is equal to the band bending.

-480 (mV) C

-500

-520 Figure 3.6: Laser power calibration on a p-GaAs sample. In a logarithmic plot

Contact potential V potential Contact the contact potential should saturate with -540

10 100 500 laser illumination power. This could not

Laser power [mW] be achieved. 3.2 Experimental Setup and Measurement Details 45

3.2.2 Electrochemical Setup and Fluid Handling

Flowcell

For measurements in liquid environment a special “flowcell” was developed2 which restricted the liquid exposure to the center of the sample and allowed for an electrical connection to an external circuit. A photograph of the flowcell is shown in figure 3.7. The electrical connection was obtained using spring contacts embedded in the PMMA body of the flow cell. A Viton O-ring mechanically pressed to the sample by the flow chamber provided for a proper sealing. An Ag/AgCl reference electrode (MI-402 from Microelectrodes, Inc., Bedford, NH, USA) and a standard Au counter electrode were mounted in the flow chamber reaching a small pocket of approx. 0.1cm3 volume above the sample. Liquid inlet and outlet was provided by tubes connected to channels through the flow chamber. The whole setup was built into an Aluminum cage for electrical shielding and to provide for a dark environment. This was necessary because the GaAs devices were highly sensitive to light. Liquids were injected into the system using a standard peristaltic pump. For pH-sensitive measurements a standard pH-meter (CG843 from Schott Instruments GmbH, Mainz, Germany), was used to measure temperature and pH of all liquids injected to the flow cell. The backside of the sample was grounded via a copper block which was also used to control the temperature of the sample. For this purpose a circulator temperature controller from JULABO Labortechnik GmbH, Seelbach, Germany was used. For all experiments the temperature was set to 23°C.

2The ﬂowcell was designed in collaboration with Dr. M. Nikolaides, S. Rauschenbach, and Dr. K. Buchholz.

Figure 3.7: PMMA ﬂow chamber used for liquid handling (see text for details). 46 Experimental Techniques and Measurement Setup

Three Electrode Setup and Potentiostat

The potential of the electrolyte on top of the sample was controlled using an Autolab PGSTAT 30 potentiostat from Metrohm, Herisau, CH in a standard three electrode setup. In this setup the sample acted as the working electrode, a Ag/AgCl electrode measured the electrolyte potential and a Au counter electrode was used to control the potential. Such a three electrode setup is commonly used in electrochemistry and is necessary to minimize measurement errors in the system. Due to the ionic currents combined with electrode reactions in electrolytes it is not convenient to use the same electrode for potential measurements and for currents necessary to maintain the desired potential. As explained in section 2.3 every surface in an electrolyte causes a certain potential difference between surface and bulk electrolyte. This potential difference is altered by chemical reactions or adsorption processes at the surface. However, such processes are necessary to drive a current in an electrolyte which in turn is needed to change the electrolyte potential. Therefore an electrode which at the same time measures the potential and implies a current would result in wrong and unstable results. Thus, the potential measuring unit, the Ag/AgCl reference electrode, is separated from the current driving unit, the counter electrode. The potentiostat is a device which handles the three electrode setup and allows to set and control a certain potential difference between a working electrode and the reference electrode. The current of the counter electrode necessary to maintain the potential difference can be monitored at the same time. Please refer to [72] for a more detailed explanation of the potentiostat working principle. Throughout this thesis typically a potential of -400 mV was applied to the GaAs sample with respect to the Ag/AgCl reference electrode (if not stated otherwise). At this potential the observed leakage currents (= counter electrode currents) through the system were close to zero and the GaAs sensor experienced its highest stability.

3.2.3 Transport Measurements

Electrical Setup

Transport measurements on the GaAs based 2DEG biosensor device were carried out on a Hall bar like structure suitable for two-point and four-point measurements. See figure 3.8 for a schematic of the setup and compare also section 3.1.2 for the patterning. The dimensions were w × l = 100 µm × 100µm. Current-voltage characteristics were recorded by sweeping a voltage VSD to source and drain contacts and measuring the resulting current ISD together with the four point voltage V4P. The voltage control was preferred over a current control as the potential difference between the sample and the electrolyte should not change by large values 3.2 Experimental Setup and Measurement Details 47 over the whole sample in order to prevent electrochemical surface reactions. At the same time the current through the counter electrode ILeak was monitored which is the leakage current flowing vertically across the electrolyte - semiconductor interface into the 2DEG channel. This gives an information on the stability of the device. The experimental data was analyzed in terms of the sample resistance RSa and the sheet resistance RSh which were determined from linear fits to VSD(ISD) and V4P(ISD) plots. Only DC configuration was used for the electrical characterization with typical values being ±10 mV for the maximum applied potential VSD, 200-300 nA for ISD, and 1 mV for the maximum of V4P. Hence typical sample resistances RSa were in the order of 30kΩ and sheet resistances around 3kΩ in the dark. Typical leakage currents through the counter electrode were below 10 nA. As electrical equipment the following devices have been used: A Keithley K2400

Sourcemeter for VSD and ISD, a Keithley K2000 DMM for V4P, a Keithley K617 Electrometer for ILeak, a Knick S252 DC-Calibrator for VSa, and several standard lab voltage and current sources for peripheral devices.

Controlling Software

To control the different measuring instruments, a measurement program was written with Lab- view. Figure 3.9 shows a screen shot of the front panel. In this panel, all relevant parameters

Figure 3.8: Electrical setup for transport measurements in two-point and four-point geometry on a Hall bar like structure of width w and distance l between leads. The hatched areas are etched parts to separate the current carrying and sensing parts of the sample. CE, RE, and WE denote the counter, reference, and working electrode. 48 Experimental Techniques and Measurement Setup

such as VSD, VSa, delay times and datapoint numbers are controlled and the obtained characteristics are monitored online. Furthermore, parameters such as the pH or the leakage current ILeak are recorded and graphically shown. The sheet resistance RSh is calculated by the software, so that resistance changes can also be observed in real time. The software writes all relevant data into designated folders on the computer for later analysis with data processing software.

3.2.4 Impedance Measurements

For impedance measurements the same electrochemical setup as for transport measurements was used as described in section 3.2.2. However, the measurements were made on the same highly n-doped samples used for KP measurements, and not on 2DEG samples. Furthermore, the software “FRA” from Metrohm was used to control the experiments.

In impedance measurements a sinusoidal potential V(t) = VSa +V0 sin(ωt) with a bias potential VSa, frequency ω, and amplitude V0 is applied across the interface, and the current I(t) = I0 sin(ωt + φ) is monitored. Applying the complex version of Ohm’s law I · Z = V the impedance Z can be determined. Mainly two measurement modes are available: Either record the impedance Z of a sample at a constant frequency f but with varying potential VSa or measure

Figure 3.9: Data window of the Labview controlling program. 3.2 Experimental Setup and Measurement Details 49

Z at constant potential but different frequencies. The impedance spectra can then be fitted to equivalent circuit models [52]. These models consist of resistors and capacitors, which represent the individual electrochemical properties of the interface. From the fit the individual values of capacitances and resistances are obtained. In a gross simplification of the complex circuit for the GaAs-Electrolyte interface [41] the equivalent circuit of figure 2.9B was applied yielding Mott-Schottky plots. The impedance measurements were used as control experiments on the pH-sensitivity of the MBP coated 2DEG devices. Therefore the method with constant frequency f but varying bias potential VSa was used. Then, the flat band potential Vf b was extracted from the Mott-Schottky plots which depends on the pH. From a plot Vf b(pH) the sensitivity of the samples could be determined. To find the optimum experimental settings for the impedance measurements Cyclic Voltam- metry (CV) experiments were performed together with impedance measurements. The cyclic voltammetry data shows the leakage currents across the interface depending on the bias voltage. To obtain maximum sample stability an operation with minimum leakage current is preferable. At the same time, the conditions to obtain Mott-Schottky plots should be fulfilled, i.e., a Mott- Schottky plot should give a linear curve. Typical results are shown in figure 3.10. Concluding from the data the bias voltage VSa was chosen between approx. -0.2 and 0.2 V, usually in steps of 40mV. The amplitude of the driving voltage V0 was 10 mV. At each voltage the system was allowed to equilibrate for 20 s before a data point was taken. The impedance was recorded at four different frequencies: 10 kHz, 4 kHz, 1.6 kHz and 0.6 kHz. At all frequencies the same behavior was observed although the absolute impedance values varied slightly. 50 Experimental Techniques and Measurement Setup

main

measurement

region

] -2µ 2

9 /F 14

-4µ

8 [10 2

main 1/C 7 [A] Current

-6µ

measurement

region

-8µ

-0.4 -0.2 0.0 0.2 0.4 0.6 -1.0 -0.5 0.0 0.5

WE vs. Ag/AgCl [V] WE vs. Ag/AgCl [V]

Figure 3.10: Left: Full range capacitance voltage measurement shown in a Mott-Schottky plot. The gray shaded region is adequate for measurements as a linear curve is obtained. The dashed line is drawn to guide the eye. Right: Cyclic voltammetry data (CV) on a bare n-GaAs (dashed) and a MBP-H SAM passivated sample (dotted). The region of minimum current (grey shaded) is preferable for measurements as it ensures maximum sample stability. (“WE” denotes the potential of the work electrode). Chapter 4

Surface Electronic Structure Changes of GaAs by Molecular Adsorption

Besides an operation under wet conditions for biosensing applications it was of great interest to understand the effects of mercaptobiphenyl adsorption on the GaAs sensor. Especially, information on the surface electronic structure is valuable as it significantly influences the operation conditions of the 2DEG sensor. An excellent tool for this purpose was found in the Kelvin probe (KP) system. In combination with a light source three different parameters can be extracted from KP measurements as was introduced in section 3.2.1: the work function φW , the band bending VBB and the electron affinity χ.

4.1 Inﬂuence of Mercaptobiphenyl Deposition on Work Func- tion and Band Bending

First the inﬂuence of mercaptobiphenyl deposition on the work function and the band bending of n+- and p+-doped GaAs samples was examined. The work function is a direct observable from the KP measurement whereas the band bending can be extracted from the Surface Photo- Voltage (SPV). Please see section 3.2.1 for a detailed discussion of the experimental setup and measurement technique. The results for work function changes induced by mercaptobiphenyl adsorption are summarized in ﬁgure 4.1. A general trend of work function reduction upon molecular adsorption was observed in which the MBP-CH3 coating caused the largest reduction followed by MBP-H and MBP-OH. This phenomenological observation could not be supported by theoretical models as

51 52 Surface Electronic Structure Changes of GaAs by Molecular Adsorption molecular properties, such as the dipole moment, are mirrored directly only in the electron affinity and not in the work function. However, if the band bending is not altered to a great extent by MBP adsorption, then, the theoretical expectations on electron affinity can be transferred to the work function. This will be discussed in more detail in section 4.2. For the band bending qualitatively similar results were obtained which are illustrated in figure 4.2. Here the band bending is defined as positive if the bands are bent upwards. For both dopings a depletion of major charge carriers was observed at the surface as well before as after deposition of MBP molecules. However, the molecular deposition caused a slight increase in band bending whereat the word “increase” is used in the sense that a value is made more positive. This effect could be induced by an addition of negative charge on the surface upon adsorption, or by an energy shift of the surface states toward the valence band. This can come about because of chemisorption effects. However, a dependence of the band bending on the endgroup of the molecules is not obvious with the same reasoning as for the work function. Other groups reported similar findings for various molecules on silicon and GaAs surfaces

0.0

p-GaAs n-GaAs

-0.1 e [eV]e

-0.2 nc

-0.3 ffere i

-0.4 d n o

-0.5 ncti

-0.6 rk fu rk -0.7 Wo -0.8 Figure 4.1: Work function of bare and

bare bare MBP coated samples. The Au Kelvin

MBP-H MBP-H

MBP-OH MBP-OH MBP-CH3 MBP-CH3 probe tip is taken as reference.

bare MBP-OH MBP-H MBP-CH

400

300

200

100 Figure 4.2: Band bending of bare and

n-GaAs

0 and bending [meV] bending and MBP coated samples. The coated sam-

p-GaAs B ples show a small increase in band bending -100 compared to bare devices. 4.2 Electron Afﬁnity Changes Upon Mercaptobiphenyl Adsorption 53

[73, 71]. Ashkenasy et al. even tried to give an explanation for observed band bending changes upon adsorption of benzoic acid derivatives in terms of the LUMO energy [74]: With decreasing LUMO energy an increase of the band bending was expected due to a better interaction between LUMO and semiconductor surface states. Electronic structure calculations (see next section) on mercaptobiphenyl molecules yielded LUMO energies of -0.48 eV for MBP-CH3, -0.52 eV for MBP-H, and -0.53 eV for MBP-OH. This indeed would ﬁt the trend of the observed band bending results at least for p-GaAs. However, both the observed effects and the calculated differences in LUMO energy are comparably small hence more extensive studies are necessary to conﬁrm this speculation.

4.2 Electron Afﬁnity Changes Upon Mercaptobiphenyl Ad- sorption

The electron afﬁnity χ was determined from the work function and band bending measurements according to equation 2.1. Reproducing it here for convenience, for n-GaAs samples equation

2.1 is χ = φW − VBB − (ECB − EF ) and for p-doped samples the equivalent relation is χ = φW −Eg −VBB −(EF −EVB). Because of the high doping intensity it is reasonable to neglect the last term in the equations as the Fermi energy is very close to the band edges. Absolute values were calculated by replacing the work function φW with the measured work function difference ∆φW and the value for gold φW,Au: φW = φW,Au + ∆φW . For gold a value of φW,Au = 5.1 eV was chosen [66]. The obtained results are depicted in figure 4.3. Qualitatively the same behavior as for the work function was observed. The MBP-CH3 deposition induced the largest decrease in electron affinity followed by MBP-H and MBP-OH in descending order. The absolute value obtained for bare n-GaAs (4.57 eV) is in excellent agreement with results obtained by other groups (4,60 eV, [71]). From the simplified picture on the chemisorption of polar molecules introduced in section 2.1.2 a dependence of the electron affinity on the dipole moment can be expected. With a parallel plate capacitor model implemented in equation 2.2 the electron affinity χ should be proportional to the molecular dipole moment µ: χ ∝ µ. Unfortunately dipole moments of the MBP molecules were not found in common databases (e.g., [66, 65]). Therefore electronic structure calculations were performed for the thiol adsorbates with the Gaussian 03W package [70] (see also section 2.4.2). Following a methodology introduced by Campbell et al. [75, 76] the minimum-energy geometry of the thiol adsorbate was determined by a DFT calculation using the 6-31G+(d,p) basis set and the B3LYP functional. The thiol hydrogen atom was then removed, and the dipole for the thiol radical was 54 Surface Electronic Structure Changes of GaAs by Molecular Adsorption

p-GaAs n-GaAs

4.6 eV] 4.4 [ ity n

4.2 affi n n

3.4 ectro

3.2

El Figure 4.3: Electron afﬁnity of bare and

3.0 MBP coated samples. For the calculation a

bare bare gold work function of 5.1 eV was assumed

MBP-H MBP-H

MBP-OH MBP-OH MBP-CH3 MBP-CH3 [66]. calculated using an energy optimization at fixed geometry with the same simulation parameters as before. The hydrogen is removed without replacing it by either Ga or As atoms because the exact structure of the sulfur bond to the GaAs is not known. However, it can be expected that the sulfur - GaAs bond does not differ comparing all mercaptobiphenyls. The inclusion of polarization functions on sulfur and carbon was deemed necessary to better model the polar nature of the adsorbates [77]. The resulting dipoles were projected onto the molecular axis defined as the connecting line between the two adjacent carbon atoms of the phenyl rings. To test the reliability of the performed calculations the simulation parameters were tested on benzene derivatives whose dipole moments are listed in the Beilstein database [65]. The computational results were in very good agreement with the experimentally obtained values (see appendix A.4). However, the calculations on the MBP molecules differ from older calculations performed with the simulation software CAChe 5.0 [42]. As this simulation software was not available for additional testing the Gaussian data was chosen for a further analysis. The calculated MPB dipole moments are summarized in table 4.1 together with the values obtained for the non-radicals. Now an analysis of the electron affinity in terms of the molecular dipole moment was possible. The resulting plots are illustrated in figure 4.4. As expected, a linear relationship between electron affinity and molecular dipole moment can be drawn with slight differences in the slopes of the linear fits. Averaging both slopes results in a mean value of -0.22 eV/Dy1. The theoretical expected value can be estimated using equation 2.2 on page 16. To do this a dipole area density N ≈ 3.1 · 1018/m2 is assumed from a geometrical consideration [40]. The average tilt angle of the mercaptobiphenyls with respect to the GaAs surface normal con be concluded from NEXAFS measurements being approx. 33° [41, 37]. And for the dielectric

11 Dy = 1 Debye = 3.336 · 10−30 Cm 4.2 Electron Afﬁnity Changes Upon Mercaptobiphenyl Adsorption 55

Molecule Gaussian 03W Gaussian 03W -SH endgroup -S radical µ [Dy] µ [Dy] MBP-OH 1.39 3.32 MBP-H 1.73 3.60

MBP-CH3 2.17 4.13

Table 4.1: DFT calculated 4’-substituted 4-mercaptobiphenyl dipole moments projected on the molecular axis. The ﬁrst column shows the results for the whole molecules in gas phase. The data of the second column was calculated on molecules with the hydrogen removed from the thiol group. All dipole moments point away from the sulfur group toward the headgroup.

constant a value of ε = 4.5 was chosen as measured by Sabatani et al. for MBP-H on gold [78]. Then, the expected voltage drop across the dipole layer is

Nµ cosθ −0.22eV ∆χ = ≈ εε0 1Dy which is in surprisingly good agreement with the experimental data. However, the standard deviation for the various samples is still very high so further studies including more endgroups or other light sources are necessary to secure the obtained ﬁndings.

4.5 ty [eV] ty i

4.2 n

n-GaAs affi

p-GaAs

3.6

MBP-OH Figure 4.4: Electron afﬁnity of bare and

MBP-H MBP coated samples. Linear ﬁts are 3.3 Electron Electron MBP-CH

bare drawn for the coated samples (dashed). A comparison to bare samples seems not

3.0

0.0 3.0 3.5 4.0 4.5 valid because of the missing chemisorp-

Dipole moment [Dy] tion effects on surface dipoles. 56 Surface Electronic Structure Changes of GaAs by Molecular Adsorption

4.3 Surface Characterization by Transient Surface Photovolt- age

To gain more insight into the influence of the MBP layer grafting on GaAs surface states, transient SPV measurements were performed. These are time-resolved measurements on the material work-function with and without illumination, similar to the band bending determination. Using super-bandgap illumination, as was done in the present thesis, the population of surface states is modified via trapping of photo-induced excess carriers from valence and conduction band ([46], p.164). The final population depends mainly on the thermal cross section, which controls thermal generation and recombination, as well as the state energy position, which also influences emission rates. If the light source is switched off and the generation of carriers is stopped, the SPV relaxes to zero. In many cases this relaxation is composed of a fast component followed by a much slower “tail”. This can be explained as follows. During illumination, minority carriers, which are swept in the direction of the surface by the electric field in the space-charge region, are trapped in surface states (cf. figure 4.5B). The fast decay immediately after illumination switch-off is due to electron-hole recombination in the bulk (figure 4.5C). In its wake, the trapped minority carriers must be emitted in order to re-establish thermal equilibrium (figure 4.5D). This is a much slower process than inter-band recombination, resulting in the SPV tail. If the assumption is made, that recombination in the surface states is negligible then the process is truly exponential. This was typically found for times which are long compared to the inter-band recombination, but at which a significant re-trapping of charge has not taken place yet. However, the discard of recombination processes must be examined with caution ([46], p.164). Figure 4.6 shows the raw transient SPV data for n- and p-GaAs samples before and after deposition of a MBP-H monolayer as a representative for all measured samples. As can be seen, for n-GaAs samples the relaxation of the SPV after illumination switch-off is very fast, even faster than the response time of the Kelvin probe system. After deposition of the MBP- SAM however, the relaxation is clearly observable in the order of a few seconds. For p-GaAs samples on the other hand, the opposite trend is observed as the relaxation becomes faster after passivation. For other MBP-SAMs, the MBP-OH and the MBP-CH3 layers, the same qualitative behavior was measured. For the data of figure 4.6 a quantitative analysis of the associated time constants for the SPV tail is shown in figure 4.7. The relevant data is plotted on a logarithmic scale and from linear fits (in the logarithmic plot) time constants are extracted. The data is summarized in table 4.2 together with values for the other 4’-substituted mercaptobiphenyls. Control experiments on n-GaAs sample processed in the same manner as the other sam- 4.3 Surface Characterization by Transient Surface Photovoltage 57

A B C DE

EVL c

efW

eVBB + ------+ + Ecb EFS - EF - - - - + + +

Evb + + + + + +

Figure 4.5: Schematic of illumination effects on the band structure of an n-doped semiconductor. A) Band structure without illumination. The electrons in the surface states cause a band bending in the space charge region because their charge has to be neutralized by ionized donors. B) By illumination charge carriers are generated, minority carriers (holes) are swept to the surface and trapped in the surface states. The high charge carrier density leads to nearly ﬂat band conditions. C) After the illumination is switched off, a fast recombination in the bulk occurs causing a slight band bending. D) The trapped holes in the surface states are emitted in a slow process in order to re-establish thermal equilibrium until the initial situation is reached (E).

Laser On Laser On

-400

-300

-500

-400

-600 [mV] [mV]

-500

-700 CPD CPD n-GaAs n-GaAs -600 -800

200 250 300 0 50 100 150 200

-300 -350

p-GaAs p-GaAs

-350 -400 [mV] [mV]

-400 -450 CPD CPD

50 100 150 200 250 300 50 100 150

Time [sec.] Time [sec.]

Figure 4.6: Transient SPV measurements on MBP-H coated samples. Left: Contact potential difference before MBP-H deposition. Right: After MBP-H deposition. The illumination time is represented by the gray bar on top of the graphs. ples but using solvent without molecules in the assembly process proved the relevance of the observed effect. A typical data set is shown in ﬁgure 4.8. It is clearly visible, that the decay of the SPV signal after switching off the laser is as fast as before the treatment. Therefore it can be concluded, that the surface treatment for cleaning and oxide removal does not cause the observed changes in transient SPV data. Summarizing, for n-doped GaAs samples the interaction between surface states and the bulk is decreased which is indicated by the increase in time constant of the SPV recovery by a factor of >8. For p-doped samples the life time is reduced by approx. a factor of 2. The exact 58 Surface Electronic Structure Changes of GaAs by Molecular Adsorption

5 6

e e

bare p-GaAs bare n-GaAs

p-GaAs with n-GaAs with

MBP-H SAM e MBP-H SAM

-t/61.0s

e -t/1.4s -t/15.5s

~e ~e PD [a.u.] PD [a.u.]

-t/18.3s

3 C C e ~e

2 2

e e

0 25 50 0 50 100

Time [sec.] Time [sec.]

Figure 4.7: Logarithmic plots of transient SPV measurements on MBP-H coated samples. Left: Con- tact potential on n-GaAs samples before (solid) and after (dashed) MBP-H deposition. Right: Same measurements on p-GaAs. Dash dotted lines with respective slopes are drawn to guide the eyes.

Laser On

-400 [mV] -500

before

treatment CPD -600

200 225 250 275

-300 Figure 4.8: Control transient SPV measure-

[mV] ments on a bare n-GaAs sample. Top: Sample

-400 after 1min in HCl before any treatment. Bottom: Sample after all and 24h in Ethanol CPD -500 assembly process steps, however, using ethanol 25 50 75 100

Time [sec.] without any MBP molecules. mechanism which leads to such a phenomenon is not obvious. Probably a mixture of changes in energy, density and distribution of surface states upon MBP chemisorption is responsible for the observed behavior. An examination using Surface Photovoltage Spectroscopy (SPS) might lead to further insights. However, similar effects due to molecular coatings have been observed by other groups using photoluminescence (PL) studies. Adlkofer et al. observed a PL enhancement of InAs quantum dots embedded in GaAs samples by alkanethiol adsorption [79]. They explained this ﬁnding with a suppression of surface state density thereby reducing non- radiative recombinations. Recent PL studies performed by F. Mayer2 on a similar quantum dot system using the same mercaptobiphenyl molecules as in the present thesis showed the same effect: A PL enhancement due to MBP-H deposition by a factor of 12.

2unpublished data, 2005 4.4 Conclusion 59

Data from Mean values from Sample description ﬁgure 4.7 three different samples τ [sec] τ [sec] n-GaAs bef. treat. < 1.4 < 1.4 n-GaAs with MBP-H 15.5 13 ± 4 n-GaAs with MBP-OH - 11 ± 1

n-GaAs with MBP-CH3 - 13 ± 3 p-GaAs bef. treat. 61 70 ± 10 p-GaAs with MBP-H 18.3 26 ± 10 p-GaAs with MBP-OH - 32 ± 25

p-GaAs with MBP-CH3 - 44 ± 8 Table 4.2: Time constants τ extracted from transient SPV measurements.

4.4 Conclusion

Static and transient Kelvin probe studies were conducted on n- and p-doped GaAs samples in air before and after MBP deposition. From the static KP measurements a slight influence of monolayer grafting on the band bending was observed. The alteration in work function and electron affinity was more pronounced. For the latter a linear dependence on the molecular dipole moment of approx. -0.22 eV/Dy could be determined applying electronic structure calculations to obtain the dipole moment. This fits remarkably well with a theoretical estimation applying a simple parallel plate capacitor model. The transient SPV measurements revealed a high influence of the MBP deposition on surface charge carrier dynamics. For n-doped samples a large increase by at least a factor of 8 in minority carrier life time in the surface states was observed, whereas for p-doped samples a reduction by approx. a factor of 2 could be seen. A simple model to explain the findings could not be found, however, the experimental results are in good agreement with studies performed by other groups. 60 Surface Electronic Structure Changes of GaAs by Molecular Adsorption Chapter 5

Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices

During the second period of the present thesis the main research focus laid on the characterization of the 2DEG sensor for measurements in wet environment. For this purpose a sensor has to fulfill two important conditions: stability and sensitivity which will be treated in the first section of this chapter. Then, the influence of pH and salt concentration changes upon the sensor device are discussed.

5.1 Stability and Sensitivity

Bare GaAs devices are known to suffer an intrinsic instability in aqueous solutions which could cause sensor degradation or even device failure. The chemical surface modification with mercaptobiphenyl molecules should passivate the surface enhancing its stability by preventing contact between electrolyte and semiconductor. To test the device stability a characterization of the sensor was performed in typical conditions for biosensing applications: operation in 5mM PBS at quasi neutral pH values with 100mM NaCl background. The sample potential was kept constant with respect to the Ag/AgCl reference electrode at -400 mV because cyclic voltammetry measurements showed the lowest leakage current at that value (see figure 3.10 on page 50). Hence the best device stability was expected at that value. Comparable measurements of the coated and uncoated samples clearly demonstrated the enhanced stability of the passivated samples. As representative examples of the results obtained, figure 5.1 compares the resistance of unpassivated and MBP passivated samples as a function of time. The resistance of the unpassivated samples was found to drift rapidly with time. This is probably caused by the oxidation and/or decomposition of GaAs which easily occurs in aqueous

61 62 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices

solutions. By contrast, the coated samples were much more stable. In particular, the MBP-CH3 passivated sample exhibited a more stable response compared with the MBP-OH coated sample. For the MBP-H coating the same behavior was already observed in earlier experiments [40]. However, other material systems, such as gallium nitride or diamond, have still advantages in terms of stability as they offer stable operation for longer periods in a broad electrolyte potential range [80, 81]. With the enhanced stability by mercaptobiphenyl deposition an examination of the sensitivity of the device was possible. To do this the resistance of a device was recorded while changing the electrolyte potential. Figure 5.2 shows a representative data set obtained from a MBP-CH3 coated 2DEG sensor. The sensor was found to detect potential changes down to 100 µV without any optimization of the operation conditions. The limit is mainly set by the noise of the device. With a proper adaptation of the sensor the noise might be reduced even further to reach levels of the best sensors available, e.g., GaN based sensors are known to have extremely low noise levels with the best reported value to the knowledge of the author being 15 µV (peak-to-

3.0

bare device

MBP-OH coated

2.5 Figure 5.1: Stability of MBP-CH (trian- MBP-CH coated 3 3 gles) and MBP-OH (circles) coated sam-

2.0 ples in comparison to the faster degradation of an uncoated sample (squares). The resistance was normalized to the ini-

1.5 tial value after an equilibration of 5 min. ormalizedresistance

N in electrolyte. The measurement condi- 1.0 tions were: pH = 6.5 ± 0.2; 5mM PBS;

0 4 8 12 100mM NaCl for all measurements. The

Elapsed time [h] electrolyte was continuously pumped.

] [k

Sa R 42.60 42.61 42.590 42.600

Figure 5.2: Maximum sensitivity of the 2DEG sensor. Left: Response of the V V sample on consecutive potential steps of

300µ [mV]

100µ 300 µV. Right: Response of the sam- -399.3 -399.0 Sa

V ple on a potential step of 100 µV. The -399.9 -399.6 750 775 800 825 500 525 measurement was performed in PBS at pH

Time [sec.] Time [sec.] 5.92 ± 0.05. 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 63 peak) [27]. Silicon based devices are expected to have higher noise levels but no exact value could be found in literature. However, from experiments on the transistor recording of cell action potentials [82], which emphasize on noise optimized conditions, a minimum value of 100 - 500 µV can be estimated.

Summary

Mercaptobiphenyl coated and uncoated 2DEG sensor devices were characterized in PBS at neutral pH in terms of long term stability. The passivated devices showed a clear increase in stability compared to uncoated samples at least over 12h with MBP-CH3 yielding the best result. Furthermore, a very high sensitivity of the 2DEG device toward surface potential changes down to 100 µV was observed with the potential to reach extremely low noise levels.

5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors

The very good sensitivity in combination with the improved stability of the coated sample enabled a systematic investigation of the sensor response as the pH-value of the electrolyte was varied. The inﬂuence of the pH-value onto the surface potential of the sample was investigated by recording the resistance of the 2DEG device in a 1mM PBS solution with 100mM NaCl. The pH value was then systematically modiﬁed by titration with either HCl or NaOH. The detailed measurement procedure will be described in the following with special emphasis on the transformation from recorded resistance changes into surface potential changes. Then, the experimental data is presented followed by a comparison to theory.

5.2.1 Measurement Procedure

The 2DEG sensor in pH- and salt-sensitive transport experiments is used as an Ion Selective Field Effect Transistor (ISFET). An ISFET is usually operated in a source drain follower setup where the source drain current ISD is kept constant by adjusting the sample potential VSa with respect to the electrolyte potential [83]. If an external parameter such as the pH of the solution is changed and the ISFET is sensitive to such changes then it will respond with a shift in threshold voltage. The therefore necessary change in VSa to keep ISD constant equals the shift in surface potential ψs. However, certain electrochemical stress is exerted on the device by the enduring adaptation of the sample potential VSa which possibly induces surface oxidation. To minimize such elec- 64 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices

trochemical stress another measurement mode keeping the sample potential VSa constant and letting the source drain current change was chosen instead. This also helped to simplify the experimental setup signiﬁcantly by omitting the source drain follower. As in the experiments on device stability the sample potential was kept at VSa = −400 mV vs. the Ag/AgCl reference electrode.

The measured sample (or sheet) resistance RSa = VSD/ISD of the 2DEG sensor is a device dependent parameter. To compare the results to theoretical expectations a transformation into a device-independent parameter such as the surface potential ψs is necessary. The transformation method used throughout this thesis is schematically sketched in ﬁgure 5.3. Giving a pH sensitive measurement as example, the pH and the resistance of the device are ﬁrst recorded as a function of time (part 1). From this raw data an RSa(pH) graph can be drawn (part 2). To obtain the surface potential ψs a reference measurement of the resistance with varying sample potential RSa(VSa) is necessary (part 3). Then, the equivalent sample potential as a function of pH is obtained: VSa(pH). The change in sample potential is, in most cases, equal to a change in surface potential ψs as was explained in section 2.4. Depending on the doping type the proportionality factor between surface and sample potential is either +1 or -1. This will be discussed extensively in section 5.2.2. In the following experimental results are always plotted in terms of the sample potential VSa whereas the theoretical expectations are given in terms of the surface potential ψs.

Figure 5.3: Schematic showing the transformation of the sample resistance into sample potential. First the sample resistance RSa (and/or RSh) and the pH of the electrolyte are recorded over time. Then, both data sets are combined to get RSa(pH). Using a reference measurement RSa(VSa) it is possible to obtain the potential as a function of pH: VSa(pH). 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 65

5.2.2 Relationship between Resistance and Surface Potential Changes

The experimental data shown later will be theoretically discussed mainly in terms of the surface potential ψs which is derived from the equivalent sample potential. In this procedure the sign of the proportionality factor between the two values requires special attention. As the conven- tions for a potential reference point are somewhat different in electrochemistry and physics, a qualitative introduction will be given here to explain the sometimes confusing relationships. In the following an increase means making any value more positive, e.g., changing −10 to −5, or 3 to 7 and so on.

Applying a negative potential to an imaginary gate on the surface of the GaAs-AlGaAs heterostructure would lead to a pile-up of electrons in the gate at the surface. Thus, electrons inside the semiconductor would need more energy to come to the surface, i.e., the conduction band moves upwards. Therefore, the 2DEG channel is depleted and the resistance increases. Decreasing the gate potential even further would enhance this resistance increase. As a gate potential (Vg) change is equivalent to a surface potential (ψs) change, the following qualitative relationship can be found:

Vg ≡ ψs & ⇔ R % (5.1)

A shift of the surface potential ψs in either positive or negative direction can also be induced by a movement of the electrolyte potential Vel in the same direction. The electrolyte can be seen as the imaginary gate and in most cases even the absolute value of the movement will be the same.

The same effect is caused by moving the sample potential VSa in the opposite direction. Another possibility to move the surface potential is to change the surface charge. Here the relationship is deduced from the Grahame equation 2.16: An increase in surface charge σs leads to an increase in surface potential ψs. Summarizing, the following relationships have been deduced:

ψs & ⇔ R % (5.2)

Vel & ⇔ R % (5.3)

VSa % ⇔ R % (5.4)

σs & ⇔ ψs & ⇔ R % (5.5)

For a change in salt concentration [NaCl] the effect is not unidirectional. The relation is also determined by the Grahame equation 2.16: Adding salt leads to an improved shielding of the surface charge thereby reducing the absolute value of the surface potential. Thus, the effect on 66 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices the resistance depends on the sign of the surface charge (see also ﬁgure 2.6):

σs < 0 : [NaCl] % ⇔ ψs % ⇔ R & (5.6)

σs > 0 : [NaCl] % ⇔ ψs & ⇔ R % (5.7)

The discussion above was based on electrons as major charge carriers in the structure. If the structure is p-conducting, then certain relationships would be opposite.

5.2.3 Control Experiments

Evaluation of Measurement Modes

Control experiments, as depicted in figure 5.4, were carried out to evaluate the replacement of the traditional constant resistance mode by measurement mode chosen in section 5.2.1, denoted in the following as constant potential mode. In the first experiment shown in the left panel, the sample potential VSa (bottom) of a MBP-CH3 coated 2DEG sensor was kept at -400 mV throughout the measurement whilst the pH (middle) of the electrolyte was changed. This led to resistance changes as shown in the top graph. In a second experiment applying the constant resistance mode (right panel of figure 5.4), the sample potential was adapted manually to maintain the sample resistance constant. Both experiments showed a clear influence of the pH onto the behavior of the system, i.e., either VSa or RSa were changed upon pH changes. In order to compare the two measurement modes a reference measurement as explained in section 5.2.1 was performed (see figure 5.5). With this reference the resistance value obtained

] ] 65k 65k [ [ 64k 64k

Sa Sa

63k 63k R R

10 10

8 8 pH

6 pH 6

4 4

-0.35 -0.35

-0.40 -0.40 [V] [V]

Sa -0.45 -0.45

Sa V V

-0.50 -0.50

0 1000 2000 3000 4000 0 500 1000 1500 2000

Time [sec.] Time [sec.]

Figure 5.4: Comparison between constant potential and constant resistance mode. Left: Sample resistance RSa (top) of a MBP-CH3 passivated sample together with the pH-value of the electrolyte (middle) and sample potential VSa (bottom). In this measurement the potential was kept constant at -400 mV. Right: Here the sample potential was adapted manually in order to keep the resistance constant. 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 67

65.5k ] [ Sa

65.0k R e anc

64.5k esist

r Figure 5.5: Reference measurement in

64.0k electrolyte of the sample resistance RSa vs. mple

R = 70.3k + 14.7k * V sample potential V . With the linear ﬁt Sa Sa Sa Sa

63.5k RSa(VSa) the data from ﬁgure 5.4, left, can

-450m -425m -400m -375m -350m be processed to obtain the VSa(pH) curve

Sample potential V [V]

Sa of figure 5.6 for a certain pH in the constant potential mode experiment was transformed into a sample potential value as explained in the previous section. The resulting plot of VSa(pH) for both measurement modes, illustrated in figure 5.6, shows that the sensitivities obtained from linear fits to the data agree reasonably well.

Examination of the Leakage Current

After the validation of the measurement principle it was necessary to exclude a parasitic effect as a cause for any observed resistance changes: the leakage current ILeak flowing from the electrolyte into the semiconductor or vice versa. Any surface reactions occurring at the semiconductor-electrolyte interface could induce such a leakage current. As this parasitic current flows from the counter electrode into the 2DEG channel and alters the measured source drain current ISD, it would mimic a resistance change. However, a monitoring of the leakage current flowing through the counter electrode during all measurements in wet environment

-350m

-375m Figure 5.6: Comparison of the pH dependence of the sample potential for the two [V]

-400m

Sa measurement modes. The absolute values V obtained from both measurement modes

-425m hardly differ. Accordingly, the slope obtained from the constant potential mode (squares) is almost identical to the result

-450m

5 6 7 8 from the constant resistance mode (cir-

pH cles). 68 Influence of Aqueous Electrolytes on 2DEG Sensor Devices proved that it cannot cause the observed pH dependent change in surface potential. A typical experiment is shown in figure 5.7 where the left panel illustrates the pH variation of the electrolyte on the 2DEG sensor surface. The right panel depicts the recorded source drain characteristics together with the leakage current through the Au counter electrode at the points indicated in the left panel. From the magnification it is obvious that the pH changes indeed lead to a change in sample resistance. However, the leakage current does not change accordingly, it stays constant at values close to zero. Therefore it cannot be responsible for the differences in the source drain current.

Sensor Characterization in Air

Another reliability test of the obtained data was performed by comparing the reference measurements in electrolyte with measurements on samples with a standard titanium (Ti) - gold (Au) Schottky gate on top of the 2DEG channel. To do this the sample layout was modified in such a way that an individually addressable metal gate (10 nm Ti + 200 nm Au) could be deposited on the Hall bar like center structure of the device. Then, the sample resistance RSa and the sheet resistance RSh of the device were recorded as a function of the gate voltage Vg in a manual probe station at room temperature. A typical data set is illustrated in figure 5.8 which shows a linear dependence of the resistances and the gate voltage in the examined voltage range. This is qualitatively in excellent agreement with the reference measurements performed in electrolytes, e.g., as shown in figure 5.5. Furthermore, a characterization of the device with respect to a voltage applied to the sample

300n

200n [A]

SD 275n I

100n

270n

[A] 1n leak I

0 2m 4m 6m 8m 10m

V [V]

Figure 5.7: Control experiment to exclude leakage currents for the pH response. Left: Sample resistance RSa and electrolyte pH variation on a MBP-OH coated sample. Right: Source drain current ISD and leakage current Ileak through the counter electrode for the data points depicted in the left panel. The magniﬁcation shown in the inset demonstrates the noticeable difference in source drain currents for different pH values. 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 69

49k ]

48k [ -50.13 k /V

47k Sa R

46k

45k

3.6k ] 3.5k Figure 5.8: Front gate effect on the sam- [

3.4k -4.48 k /V Sh ple resistance RSa and sheet resistance RSh R

3.3k of a 2DEG sensor device. The resistance

3.2k is a linear function of the gate voltage Vg

-40m -20m 0 20m 40m which was applied to a standard titanium -

Front gate voltage V [V]

g gold gate on top of the Hall bar structure. backside was conducted. If the back gate voltage is able to tune the resistance of the device then an additional parameter for optimum device operation conditions, i.e., at highest sensitivity toward surface potential changes, is available. A representative back gate voltage characteristics of a sensor device is shown in figure 5.9 which was measured in nitrogen (N2) atmosphere using the flow chamber setup. Indeed for negative back gate voltages a large influence on the resistance was observed whereas for positive voltages a saturation at low resistances for back gate voltages above 0.5 V occurred. A working point of 0 V was chosen for the following measurements which at the same time simplified the experimental setup and still showed a good sensitivity of the resistances vs. potential changes.

Conclusion

Two measurement modes were compared for pH sensitive experiments, the constant potential and the constant resistance mode. To evaluate the constant resistance mode a reference measurement on the sample resistance as a function of the electrolyte potential was performed revealing a linear R(Vel) relationship. With this reference it could be shown that both measurement modes

60k ] [

50k Sa R

40k

6k ] 5k Figure 5.9: Back gate effect on the sample [ Sh 4k resistance RSa and sheet resistance RSh of R a 2DEG sensor device. The sample was

-2 -1 0 1 2 measured in the ﬂow chamber in nitrogen

Back gate voltage [V] (N2) atmosphere. 70 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices are equivalent giving the same pH sensitivity results. Furthermore, the leakage current could be excluded as a possible cause for the observed resistance changes upon pH variation. Mea- surements on a sample with standard TiAu Schottky gate also showed a linear dependence of the sample resistance on the front gate potential as observed in the reference measurements in electrolyte. Furthermore, a characterization of the sensor with respect to back potential changes was conducted.

5.2.4 Behavior of MBP-OH Coated Samples on pH Variations

After this verification of measurement conditions exact pH characteristics could be determined for the 2DEG sensors. The left panel of figure 5.10 shows a typical experiment on a MBP-OH coated 2DEG device where the resistance, drawn on the left axis, and at the same time the pH of the electrolyte solution, drawn on the right axis, were recorded. The electrolyte contained 1mM PBS and 100mM NaCl as in all pH sensitive measurements and the sample potential was kept at -400 mV. As can be seen an increase in pH (by titration with NaOH) always caused the resistance to increase and a pH decrease (by HCl) led to a resistance reduction. So qualitatively it can be stated following the discussion in section 5.2.2 that increasing the pH shifts the surface potential to more negative values. With the procedure described in section 5.2.1 the resistance changes were transformed into sample potential changes using a reference measurement (not shown). Before that mean resistance values were determined for every pH by taking the mean value of a 1 min long period after 2 min. equilibration time. The respective standard deviations for each data point was smaller than 40 Ω for the sample resistance. The reference showed a linear R(VSa) relationship with slopes of 25 kΩ/V for the sample resistance RSa and 1.6 kΩ/V for the sheet resistance RSh. The sheet resistance was slightly noisier than the sample resistance therefore the latter was used for analysis. Both variables are equivalent as any influence of input leads can be neglected due to the transformation into the device independent surface potential applying the reference measurement. Thereby, the constant effect of the input leads, which are not influenced by pH changes as they are isolated from the liquid by the flow chamber, is canceled out. The surface potential plot using the reference measurement is shown in the right panel of figure 5.2.1. In the measured pH range (4-8) a linear relationship between pH and surface potential was found with a sensitivity of 32 mV/pH for the shown device. This linear dependence was found for all three measured samples with a mean sensitivity of 33.4 ± 3.3 mV/pH. The observed change in surface potential can be explained in terms of the site-dissociation model introduced in section 2.3.2. The hydroxyl (-OH) group of the mercaptobiphenyl molecules pointing into the electrolyte can be either protonated or deprotonated depending on the surface 5.2 Influence of pH Changes on the Surface Potential of 2DEG Sensors 71

-375m [V]

-400m Sa l V l a

-425m

-450m

sensitivity

= mple potenti mple

-475m

32mV/pH Sa

-500m

4 5 6 7 8

Figure 5.10: Left: Resistance progression (squares, left axis) of a MBP-OH passivated sample in PBS with varying pH (circles, right axis). Right: Sample potential values as a function of pH as extracted from the left ﬁgure in combination with a reference measurement.

+ proton concentration [H ]s which in turn depends on the pH of the solution. The surface reactions determine the surface charge which then leads to a change in surface potential. An increase in pH would shift the equilibrium toward the deprotonation (MBP-O−) making the surface charge more negative. From relationship 5.5 we know that this would increase the resistance. This is in agreement with the observed reaction of the sensor device. A quantitative analysis calculating surface potential curves with the PoBoSim program (see section 2.4.1) is shown in figure 5.11. The calculations incorporate the Grahame equation for the electrolyte part of the system together with the site dissociation model for surface charges. Several parameter sets, listed in table 5.1, were found which reproduced the experimental data. In order to fit the theoretical curves the experimental data had to be shifted along the y-axis. This is justified because no absolute potential values can be measured with the experimental setup, only potential differences are accessible. As can be seen clearly, all shown theoretical curves agree excellently with the experiment. However, the used parameters can vary largely

-100 [mV] s

-50

Figure 5.11: Comparison of experimen- 0 tal data of the MBP-OH passivated sample from ﬁgure 5.10 with results of simu- 50 lations of the site - dissociation model using PoBoSim. Several parameter sets (see Surface potential potential Surface 100 table 5.1) ﬁt the experimental data rea-

3 4 5 6 7 8 9 sonably good. For clarity the curves are

pH shifted along the y-axis. 72 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices because the examined pH-range was rather small. A larger pH range was unfortunately not experimentally accessible due to the faster degradation of MBP-OH coated samples.

For the density of surface sites Ns at least a lower limit can be given. Ns determines the extent of the pH region where the surface potential depends linearly on pH: The larger Ns, the larger 13 2 the linear region. For the observed linear dependence between pH 4 and 8, Ns ≥ 5 · 10 /cm is necessary. Smaller values would cause the surface potential to saturate earlier. For the pK values such a constraint cannot be made. Only at the minimum Ns the pK values can be determined accurately as they regulate the center position of the linear response regime. So for higher Ns values several pK values can be found to ﬁt the experimental data (see dashed and dotted line of ﬁgure 5.11).

Model Line style Charging Ns pKa pKb in ﬁgure 5.11 equation [1/cm2] Site dissociation dashed 2.28 5 · 1014 8.9 -5.2 Site dissociation dotted 2.28 5 · 1014 9.9 -6.1 Site dissociation dash dotted 2.28 5 · 1013 6.6 -5.4

Table 5.1: Simulation parameters for the site dissociation model on the MBP-OH passivated sample used in ﬁgure 5.11.

Composition changes of the electrolyte due to the necessary titration can be ruled out as a cause of the observed resistance changes. Any change in ionic strength inﬂuences the surface potential as can be deduced from the Grahame equation. However, for a measurement cycle (pH 6 -> 4 -> 8 -> 6 for MBP-OH coated samples) the maximum ionic strength added by the titration with HCl and NaOH is approx. 2mM as one has to overcome twice the 1mM PBS buffer in the buffer region around pH 7. The other buffer regions at approx. pH 2 and pH 12 are hardly touched. Due to the high 100mM NaCl background the overall ionic strength stays rather constant. A strong supporting argument for this assumption is that the resistance measured at pH 6 after a full measurement cycle did not differ for more than 0.5% from the initially measured value. Also the ionic strength contributed by the H+ or OH− ions themselves at extreme pH values does not alter the ionic strength considerably. In the observed pH range (3-9) the ionic strength provided by these ions is not higher than 1mM thus negligible compared to the 100mM NaCl. 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 73

Conclusion

MBP-OH passivated samples were characterized in PBS with varying pH. A linear increase of resistance with increasing pH was observed. After a transformation using a reference measurement into sample potentials a mean sensitivity of 33.4 ± 3.3 mV/pH was determined. A comparison to calculations in terms of surface potential using PoBoSim showed that a site- dissociation model excellently explains the observed behavior. For the density of surface sites 13 2 a lower limit of Ns = 5 · 10 /cm was found which is approx. 15% of a full MBP monolayer (compare estimation in section 4.2). In this case the pK values were 6.6 and -5.4. Electrolyte composition changes could be ruled out as a cause for the observed effect.

5.2.5 Behavior of MBP-CH3 and MBP-H Coated Samples on pH Varia- tions

For the MBP-CH3 and the MBP-H coated 2DEG sensor devices a smaller response upon pH changes was expected. Due to the lack of obvious surface reactions, no -OH groups are present in the molecules, the sensitivity was supposed to be close to zero. However, experiments proved this expectation wrong. Typical recorded resistance over time curves are shown in the left panels of figures 5.12 and 5.13. Again the resistance is drawn on the left axis and the pH of the solution is drawn on the right axis. For both devices an increase in resistance, which is equal to a decrease in surface potential (relationship 5.2), was induced by an increase in pH. For an analysis in terms of sample potential a mean resistance value was extracted for every pH by letting the sensor equilibrate for 2 min after pH titration and then taking the mean value of a 1 min long period. The respective standard deviation for each data point was smaller than 50 Ω. A transformation from the resistance into sample potential was performed using reference measurements (not shown) which showed linear RSa(VSa) curves with slopes of 23.8kΩ/V for the MBP-CH3 and 17.8kΩ/V for the MBP-H passivated sample. The large difference in slopes is not surprising as the samples were taken from different wafers. The resulting sample potential vs. pH plots are illustrated in the right panels of figures 5.12 and 5.13. As was the case for MBP-OH passivated samples a linear relationship between sample potential and pH was found. For the devices shown the pH sensitivities were 39 mV/pH for the MBP-CH3 passivated sample and 28 mV/pH for the MBP-H coated device as deduced from linear fits to the data.

Surprisingly, the sensitivities for passivation layers with methyl group and hydrogen (-CH3, -H) do not differ signiﬁcantly from the value found for MBP-OH layers. The linear dependence was found for all measured samples with mean sensitivities of 33.6 ± 6.4 mV/pH for the MBP-CH3 passivation (6 measured samples) and 28.0 ± 5.5 mV/pH for the MBP-H version (3 samples). 74 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices

The experimental results for all passivation layers are summarized in table 5.2. As the protonation and deprotonation mechanism is very unlikely for the hydrophobic -H and -CH3 surface groups (e.g., see [84, 85]) another surface charging mechanism must play a dominant role. Mainly two charging mechanisms were identiﬁed as a possible cause of the found pH sensitivities: (1) As the monolayer of the deposited mercaptobiphenyl molecules is hardly perfect, oxides forming in pinholes could be charged by dissociation reactions. The oxides build -OH groups in aqueous solutions so the standard site-dissociation model is valid to describe the surface charging (see also section 2.3.2). (2) The other effect which is applicable not only to oxide but to all surfaces, be it hydrophobic or hydrophilic, is ion adsorption into a Stern layer. This was theoretically introduced in section

-300m [V] Sa

-350m l V l a

-400m

-450m

sensitivity

= mple potenti mple

-500m

39mV/pH Sa

-550m

3 4 5 6 7 8 9

Figure 5.12: Left: Resistance progression (squares, left axis) of a MBP-CH3 passivated sample in PBS with varying pH (circles, right axis). Right: Sample potential values as a function of pH as extracted from the left ﬁgure using a reference measurement. Error bars are not drawn as they are smaller than the symbol size.

-300m V] -325m [ Sa

V -350m

l a

-375m tenti

-400m po

e sensitivity

-425m

= mpl

28mV/pH

Sa -450m

-475m

3 4 5 6 7 8

Figure 5.13: Left: Resistance progression (squares, left axis) of a MBP-H passivated sample in PBS with varying pH (circles, right axis). Right: Sample potential values as a function of pH as extracted from the left ﬁgure in combination with a reference measurement. 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 75

Sensitivities from Mean values Number of Passivation ﬁgures 5.10 - 5.13 from all samples measured [mV/pH] [mV/pH] samples MBP-OH 32 33.4 ± 3.3 3 MBP-H 28 28.0 ± 5.5 3

MBP-CH3 39 33.6 ± 6.4 6 Table 5.2: pH sensitivities of MBP coated 2DEG devices.

2.3.3. An adsorption of either OH− ions or of H+ ions would result in the right change in surface potential. From the experimental data it is not possible to distinguish between the two adsorption possibilities, however, experiments performed by other groups show that OH− adsorption is preferably occurring at hydrophobic surfaces [62, 86, 87].

For a further analysis the MBP-CH3 coating was chosen as it is more hydrophobic, i.e., less polar, than the MBP-H passivation. This was concluded from contact angle measurements performed by K. Adlkofer [41]. Quantitative simulations were carried out using PoBoSim to test the applicability of both models to the experimental data. The PBS ions were explicitly taken into account as they cause a noticeable reduction in surface potential at neutral pH values. At that point the PBS composition changes from mono- to divalent ions which has a rather large effect on the surface potential. The results of calculated curves for the Stern adsorption model (dashed) and for the site- dissociation model (dotted and dash dotted) together with the experimental data are illustrated in figure 5.14. Both models, the Stern layer adsorption and the site dissociation theory, are able to reproduce the experimental data. In case of the site-dissociation model in general two different mechanisms can lead to a good agreement with the experimental data. In the first site-dissociation model only a negative charging of the surface is taken into account within the investigated pH range (dashed). This is achieved by choosing the reaction constant of the protonation reaction in such a way that it does not occur in the observed pH range. It is math- ematically equivalent to the adsorption in the Stern layer. A fixed surface charge of 0.17C/m2 had to be assumed to fit the data as was the case for the Stern adsorption model. Such a surface charge could be caused by charge transfer due to the chemisorption of the mercaptobiphenyl layer. In the second site-dissociation possibility charging of both polarity would be relevant (dash dotted). In contrast to the first site-dissociation model zero additional surface charge led to best results. Apparently the curve seems to fit more accurately to the experimental data.

However, the large values of the density of surface sites Ns, which had to be assumed in the 76 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices simulations, opposes this site dissociation model. If every atom of the GaAs crystal surface 15 2 would be available for a charging reaction, the resulting value of Ns ≈ 1.3 · 10 /cm would be a factor of approx. 4 higher than the smallest value necessary for the the model calculations1. Thus, the MBP layer would be quasi-transparent to the liquid which is opposed by the ﬁnding of improved stability due to MBP coating (see also [41]). The exact parameters used in the calculations are given in table 5.3.

Model Charging Ns pKa pKb σadd Γ Φ equation [1/cm2] [C/cm2] [mol/m2] [1/kT] Figure 5.14 Stern adsorption (- -) 2.36 2.9 · 1014 6.1 - 0.17 4.8 · 10−6 -41 Site dissociation 1 (··) 2.28 2.9 · 1014 6.1 -1.0 0.17 - - Site dissociation 2 (· -) 2.28 4.0 · 1014 8.7 -5.8 0 - - Marinova et al. [62] OH− adsorption on oil droplets 2.36 5.9 · 1012 -0.7 - 0 9.8 · 10−8 -25

Table 5.3: Simulation parameters for the Stern adsorption and site dissociation model used in ﬁgure 5.14. The experimental ﬁndings from Marinova et al. for OH− adsorption on oil droplets are also shown. For the Stern layer adsorption the equivalent values for Γ and Ns, and pKa and Φ are given according to the relationship in equation 2.37.

1 Estimated from a simple geometrical consideration for a GaAs (100) surface without surface reconstruction. The crystal structure is fcc with a two-atom basis (1 Ga and 1 As atom) and a lattice constant of 5.65Å. Therefore, there are 4 atoms (2 Ga and 2 As) per primitive cell resulting in a number density of 1.25 · 1015 atoms/cm2.

-300

-250 [mV] s

-200 Figure 5.14: Simulation of the pH dependent surface potential using PoBoSim. For -150 the Stern layer adsorption (dashed) only -100 one set of parameters ﬁtted the experi-

-50 mental data reasonably well. For the site- dissociation model two distinct parameter 0 sets were found (dotted and dash dotted). Surface potential potential Surface 50 For clarity the curves are shifted along the

3 4 5 6 7 8 9 y-axis. All parameters are given in table

pH 5.3 5.2 Inﬂuence of pH Changes on the Surface Potential of 2DEG Sensors 77

Conclusion

A characterization of MBP-CH3 and MBP-H passivated samples in 1mM PBS with varying pH was performed. Equal to the MBP-OH coated samples a linear decrease in surface potential with increasing pH was observed. Mean sensitivities were determined being -33.6±6.4 mV/pH for the MBP-CH3 passivated samples and -28.0 ± 5.5 mV/pH for the MBP-H coated samples. A site-dissociation model involving the MBP molecules as a cause of the observed effect is very unlikely. Instead a Stern layer adsorption model of OH− ions and two variations of a site-dissociation model involving surface oxides in monolayer defects were examined using PoBoSim calculations. It could be shown that all models can reproduce the observed behavior. However, an opposing argument to the better suited site dissociation model is that the necessary 14 2 density of surface sites NS ≥ 3·10 /cm is only a factor of 4 smaller than the maximum number of surface atoms (neglecting surface reconstruction and oxidation). The therefore high trans- parency to liquids of the MBP coating is opposed by the enhanced stability found in previous experiments.

5.2.6 Behavior of Bare, non-Protected Samples

To test the applicability of the site-dissociation model a measurement of the pH sensitivity of bare, uncoated 2DEG devices would be helpful. It must show sensitivities above the values measured for the passivated samples. Otherwise the charging, which can only occur in monolayer defects, would not be strong enough to cause the sensitivities of approx. 30 mV/pH. However, due to the instability of bare samples it was not possible to reproducibly measure a sensitivity value. The observed drift in resistance was too fast. Therefore another technique had to be used such as capacitance voltage measurements. This will be discussed in section 5.3.

5.2.7 Summary

Mercaptobiphenyl coated 2DEG sensor devices were characterized in 1mM PBS with varying pH. For all available passivation layers, the MBP-OH, the MBP-H, and the MBP-CH3 coating, a decrease of the surface potential with increasing pH was found. The measured sensitivities of approx. -30 mV/pH did not differ significantly between the different MBP endgroups. Bare samples could not be measured due to fast sample degradation. The changes in surface potential can be explained by a pH dependent surface charge, electrolyte composition changes could be excluded as a possible cause. For the MBP-OH passivation a site dissociation model for the protonation and deprotonation of the -OH groups 78 Influence of Aqueous Electrolytes on 2DEG Sensor Devices successfully describes the experimental findings. A minimum value for the number of surface 13 2 sites Ns = 5 · 10 /cm could be determined. For the MBP-CH3 and the MBP-H passivation a reaction of the H+ ions with the apolar endgroups of the passivation layer is highly unlikely. Instead, the adsorption of OH− groups onto a hydrophobic layer can be very probable as already shown by other groups. Simulations applying Poisson-Boltzmann theory for such a Stern layer adsorption of OH− ions and for site-dissociation models revealed that both models can reproduce the experimentally obtained data for the MBP-CH3 passivation. The very high density of surface sites necessary for the site dissociation models, which could only occur at oxides in monolayer defects, point to the Stern adsorption as the most probable charging mechanism.

5.3 Capacitance-Voltage Measurements on pH Sensitivity

As the measurement of pH sensitivities on unpassivated 2DEG devices was not successful in transport experiments another technique had to be used. In capacitance voltage (CV) measurements an appropriate method was found. The main advantage of CV measurements is that unstructured GaAs samples could be used. So even a surface degradation should not cause a significant change in sample characteristics for bare samples as it would just reproduce the initial sample configuration. In CV measurements the capacitance C is measured as a function of applied sample potential VSa. The data is analyzed in terms of Mott-Schottky plots introduced in section 2.3.4. A pH induced change in surface potential ψs would shift the flat band potential Vf b by the same value. This shift in Vf b could be observed by a shift along the x-axis in Mott-Schottky plots.

5.3.1 Bare, non-Protected Samples

The CV experiments showed that the samples needed a certain equilibration time until stable characteristics were observed. During this equilibration the samples showed a certain drift as is illustrated for a typical bare GaAs sample in the left panel of ﬁgure 5.15. It is probably caused by either removal of physisorbed molecules on the surface, by oxide dissolution, or by electrochemical surface reactions. After approx. 30 min the samples stabilized to a steady state and showed reproducible Mott-Schottky plots. The right panel of ﬁgure 5.15 shows typical experimental data obtained for unpassivated GaAs samples measured at three pH values: 5.8, 6.8, and 7.8. Two consecutive measurements are shown for each pH value which prove the reproducibility of the data. From the distance on the x-axis between the various curves a surface potential change of 60 mV/pH for bare GaAs can be extracted which is the Nernstian limit of 5.3 Capacitance-Voltage Measurements on pH Sensitivity 79 maximum sensitivity for a pH sensing device. This is in perfect agreement with values found in literature [53].

5.3.2 MBP-CH3 and MBP-OH Coated Samples

The CV technique was also used to control the results obtained in transport measurements. Un- fortunately experiments on passivated samples did suffer from certain stability limitations. The necessary cycle of sample potential during the CV measurement exhibits a large electrochemical stress on the samples. This probably leads to a removal of the mercaptobiphenyl molecules by oxidation and dissolution. Therefore it can be expected that at steady state conditions after the equilibration the samples behave similar to unpassivated samples. This was indeed observed in the experiments. Typical data is shown in ﬁgure 5.16 for MBP-

CH3 (left panel), and MBP-OH (right panel) passivated samples after an equilibration time of 30 min. During this ﬁrst 30 min no data could be reproducibly measured as the samples experienced similar drifts as for the bare sample. After equilibration the surface potential changes were either equal or close to the 60 mV/pH found for the unpassivated devices.

4.5

~120mV

4.0 ] ] 2 2 /F /F

4.0 14 14

10 pH = 7.80 [ [10 2 2

3.5 1/C 1/C

3.5 pH = 5.80 incr. measurement

duration up to 20min.

in 5min. intervals

3.0

-0.2 -0.1 0.0 0.1 0.2 -0.2 -0.1 0.0 0.1 0.2

WE vs. Ag/AgCl [V] WE vs. Ag/AgCl [V]

Figure 5.15: Mott-Schottky plots of capacitance voltage curves for a bare n-GaAs sample in 10mM PBS with 100mM NaCl. Left: Typical drift in the first cycles of a measurement during the equilibration time. Right: pH dependence of the sample capacitance. The measurement set consisted of points taken in the order as listed at pH=6.8 (circles), pH = 7.8 (triangles) and pH = 5.8 (squares). The coincidence of a second set of measurements (dashed) directly following the first set (solid) demonstrates the reproducibility of the data. The measurement frequency in all experiments was 4 kHz and a measurement took approx. 5 min to complete. 80 Influence of Aqueous Electrolytes on 2DEG Sensor Devices

5.0

~120mV

~55mV ] ] 2 2

3.0 4.5 /F /F

14 pH = 7.80 14 10 10 pH = 6.80 [

[ 2 2

4.0 1/C

1/C pH = 5.80

pH = 5.80

2.5

3.5

-0.2 -0.1 0.0 0.1 0.2 -0.2 -0.1 0.0 0.1 0.2

WE vs. Ag/AgCl [V] WE vs. Ag /AgCl [V]

Figure 5.16: Mott-Schottky plots of capacitance voltage curves of mercaptobiphenyl coated n-GaAs samples in 10mM PBS with 100mM NaCl after an equilibration time of 30 min. Left: pH dependent capacitance of a MBP-CH3 coated sample showing two consecutive measurements at each pH. Right: pH dependent capacitance of a MBP-OH coated sample. Measurement frequency was 4 kHz.

5.3.3 Summary

Unpassivated n-doped GaAs samples were measured in capacitance voltage experiments. After a certain equilibration time (≈30 min.) stable Mott-Schottky plots were obtained revealing a pH sensitivity of 60 mV/pH. This means that the site dissociation model cannot be excluded from the list of possible models for the observed pH sensitivity of MBP-CH3 coated samples. However, the objections from the theoretical side in terms of the too large surface site density remain. Passivated devices showed characteristics similar to bare devices in CV measurements with pH sensitivities close to 60 mV/pH. This is probably caused by a removal of the protecting MBP monolayer during the CV measurements.

5.4 Inﬂuence of Salt Concentration Changes

In addition to the pH, the concentration of ions in a solution is an important parameter determining the potential distribution of an electrochemical system. The salt concentration, in contrast to the pH, inﬂuences the surface potential dependent on the sign of the surface charge as was discussed in section 5.2.2. Thus, measurements employing a variation of salt concentration might give further insight into charge distributions at the surface and potentially could help to determine the right surface charging model. Therefore, experiments observing the resistance of a MBP-CH3 passivated sensor in 1mM PBS solution at constant pH but with varying NaCl concentration were conducted. 5.4 Inﬂuence of Salt Concentration Changes 81

5.4.1 Measurement Procedure

Prior to every salt concentration series, a calibration of the sensor was performed at the desired pH in the same manner as explained in section 5.2.1 for the pH sensitive measurements. All calibrations showed the expected linear relationships between resistance and electrolyte potential. The according slopes did not vary for more than 12% comparing the calibrations for all measured salt concentration series on one sample. For the data shown in ﬁgure 5.17 the calibration yielded mean sensivities of 1.79 ± 0.2kΩ/V for the sheet resistance and 18.2 ± 2kΩ/V for the sample resitance. This time the sheet resistance showed the same low noise behavior as the sample resistance, thus, it was used for further analysis. The samples were let to equilibrate up to one hour until stable conditions were reached. It was observed that a titration to smaller pH values could shorten this equilibration time. The salt was added in solid form to the electrolyte which was stirred during the whole experiment. Usually it took 5-20 s for the salt to dissolve and approx. 1 min. to reach the sample through the tubing system. This delay time was subtracted from the data. After the dissolution of the salt it was sometimes necessary to adjust the pH as the addition of salt inﬂuences the buffer of the electrolyte (see also section 2.2.3). Thus, all data points extracted from the raw data (= time evolution of the resistance) were taken at an exactly maintained pH. The PBS concentration in all experiments was 1 mM. Data points for each salt concentration were taken from the raw data by calculating the mean resistance of a 1 min. long period after letting the system equilibrate for 2 min. after the injection of the salt. The measurement setup was the same as for the pH sensitive measurements, the electrolyte was exchanged using a peristaltic pump which was pumping during the whole experiment.

5.4.2 Surface Potential Variation due to Salt Concentration Changes

Typical data of the salt concentration dependent resistance of a MBP-CH3 coated sensor is shown in figure 5.17. The first measurement series was taken at pH = 7.0 (squares), followed by pH = 3.3 (triangles), and pH = 5.1 (circles). At each pH NaCl was added to obtain salt concentrations of 3 mM, 10 mM, 30 mM, 100 mM, 300 mM, and 1 M in the electrolyte. Each salt injection is indicated by an arrow. At higher salt concentrations larger drifts were observed. However, letting the system equilibrate for 8 min. at 1 M (data not shown) proved, that the resistance indeed saturated and the error introduced by the comparably short measurement time (2 min. equilibration + 1 min measurement) is small. In the end the sample was flushed with the 1mM PBS solution of the beginning, and then the pH was titrated by adding HCl or NaOH for the next salt concentration series. It can be clearly seen that the resistance returned to its initial 82 Influence of Aqueous Electrolytes on 2DEG Sensor Devices value after the flushing, demonstrating the stability of the sample.

For all four measured MBP-CH3 passivated samples the same qualitative behavior was found. The higher the pH the larger the influence of the salt concentration on the resistance of the device. Adding NaCl to the electrolyte leads to a resistance decrease with larger effects at small salt concentrations. At high salt concentrations sometimes a very small resistance increase was observed. Often this could be related to an overall drift in device characteristics comparing the initial and final resistance values of pure 1mM PBS. The measured resistance changes could be explained by a corresponding surface potential change as was the case for the pH sensitive measurements. In principle, this change in surface potential due to the variation of NaCl concentration should even follow the same models as applied to explain the pH sensitivity: The Grahame equation 2.16 determines the potential distribution in the electrolyte, and an appropriate charging model accounts for the pH influence on surface charge. Please note that the effect of the salt concentration on the surface charge is not obvious directly from the charging equations. Its influence is rather indirect as the salt concentration influences only the surface potential in a direct way. However, this leads to an altered surface concentration of H+ ions which then influences the surface reactions, which in turn determine the surface charge. However, as can be seen in figure 5.18 neither the site-dissociation models nor the Stern layer adsorption used to fit the pH sensitive data describe the observed surface potential changes. For certain pH values even the trend is wrong which is caused by positive surface charges. This is understood from a view on the pH dependent surface charges at 1mM NaCl concentration as shown in figure 5.19 for the model calculations. Following the reasoning of section 5.2.2: At positive surface charges an increase in salt concentration causes a decrease in surface potential, but only potential augmentations were observed. Surprisingly, a far better agreement between experiment and simulation is obtained assum-

Figure 5.17: Salt dependence of the resistance of a MBP-CH3 coated 2DEG device in 1mM PBS at constant pH. The arrows indicate the addition of NaCl to the electrolyte leading to an overall concentration as written on the top of the graph. The resistance changes due to increased salt concentration are higher at pH = 7.0 (squares) than for pH = 5.1 (circles) and pH = 3.3 (triangles). 5.4 Inﬂuence of Salt Concentration Changes 83

30 30 [mV] [mV] s s

0 0

-30 -30 Surface potential potential Surface Surface potential potential Surface

-60 -60

0.01 0.1 1 0.01 0.1 1

[NaCl] [M] [NaCl] [M]

Figure 5.18: Experimental values (symbols) extracted from figure 5.17 together with simulations (lines) of the surface potential at constant pH with varying monovalent salt concentration. The same simulation models and parameters were used as to fit to the pH sensitive data (see figure 5.14 and table 5.3). Three different pH values are shown, pH = 3.3 (triangles and dotted line), pH = 5.1 (circles, dashed), and pH = 7.0 (squares, dash dotted). Left: Calculations applying the Stern layer adsorption. The results are identical to the first site dissociation model (not shown). Right: Simulation of the second site- dissociation model.

0.50

0.25

[C/m²] Figure 5.19: Calculation of the surface s charge as a function of pH at 1mM NaCl concentration for the Stern layer adsorp- 0.00 tion model (dashed) and the second site dissociation model (dotted) is drawn. The

-0.25 same parameters as used to obtain ﬁgure 5.14 were applied (see table 5.3). The re- Surface charge charge Surface sults for the ﬁrst site dissociation model

-0.50

3 4 5 6 7 8 9 are almost identical to the Stern layer ad-

pH sorption.

ing the surface charge as independent of salt concentration. The results are illustrated in ﬁgure 5.20 with corresponding surface charges. However, a mechanism that could induce such effect is not evident. A possibility would be the additional adsorption of counter-ions onto the surface. Or the voltage drop across the Stern layer, which was not accounted for in the simulations, might lead to such a salt-independent surface charge. For a comprehensive assessment further simulations and experiments will be required. 84 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices

0 [mV] s -10

-20 ti en

-30 pot

-40 Figure 5.20: Simulation according

pH = 3.3 = -1.5 mC/m

2 Poisson-Boltzmann theory assuming a

pH = 5.1 = -3.3 mC/m -50

2 salt independent surface charge together Surface

pH = 7.0 = -10 mC/m

-60 with the experimental data of ﬁgure 5.17.

0.01 0.1 1 In these simulations, the inﬂuence of the

[NaCl] [M] PBS buffer is included.

5.4.3 Summary

The behavior of a MBP-CH3 coated 2DEG sensor device was examined in 1mM PBS at constant pH but varying NaCl concentration. It was found that with increasing salt concentration the surface potential increased as well. At pH 7.0 the observed effect was higher than at 5.1 and 3.3. The absolute change in surface potential could not be reproduced with the simulation models used for the pH measurements at constant NaCl concentration. Surprisingly, a far simpler model assuming a salt independent surface charge yields excellent agreement with the experimental data.

5.5 Conclusion

GaAs based 2DEG sensor devices were characterized regarding their long term stability in 1mM PBS with 100mM NaCl at neutral pH. Mercaptobiphenyl coated devices experienced a clear increase in stability compared to non-coated devices. In sensitivity measurements it could be shown that potential steps down to 100 µV could be detected by the 2DEG sensor device. In characterization measurements in 1mM PBS with 100mM NaCl varying the pH and the salt concentration of the solution a dependence of sensor surface potential on both parameters was observed. By increasing the pH the sensor surface potential was decreased by approx. 30 mV/pH. The pH sensitivity of bare samples was determined in capacitance voltage measurements to the maximum Nernstian response of approx. 60 mV/pH. As a possible cause for the pH dependent surface potential of passivated sensor devices a site dissociation model involving -OH groups or a Stern layer adsorption of OH− ions was identiﬁed. The very high density of surface sites necessary for the site dissociation models, which could only occur at oxides in monolayer defects, point to the Stern adsorption as the most probable charging mechanism at 5.5 Conclusion 85

least for the MBP-CH3 passivated sensors. In the measurements with varying salt concentration an increasing surface potential with increasing NaCl concentration was found. The models used to explain the pH sensitivity could not reproduce the experimental data, however, a model assuming a salt independent surface charge obtained excellent agreement with the experimental data. 86 Inﬂuence of Aqueous Electrolytes on 2DEG Sensor Devices Chapter 6

Summary and Outlook

During the present work mercaptobiphenyl (MBP) passivated and uncoated gallium arsenide devices were characterized in air and in wet environment. In the first part, static and transient Kelvin probe studies were conducted on n- and p-doped GaAs samples in air before and after MBP deposition. From the static KP measurements a slight influence of monolayer grafting on the band bending was observed. The alteration in work function and electron affinity was more pronounced. For the latter a linear dependence on the molecular dipole moment of approx. - 0.22 eV/Dy could be determined applying electronic structure calculations to obtain the dipole moments. This is in excellent agreement with a theoretical estimation using a simple parallel capacitor plate model. The transient SPV measurements revealed a high influence of the MBP deposition on surface charge carrier dynamics. A simple model to explain the findings could not be found, however, the experimental results are in good agreement with studies performed by other groups. In the second part an examination of the long term stability of 2DEG sensor devices in 1mM PBS with 100mM NaCl at neutral pH was performed. The MBP passivated devices showed a clear increase in stability compared to bare devices with MBP-CH3 yielding the best result. Also a maximum sensitivity of approx. 100 µV toward surface potential changes was determined. A further characterization of passivated sensor devices was conducted in 1mM PBS with 100mM NaCl and varying pH. For all passivation layers an increasing pH led to a reduction in surface potential with mean sensitivities of approx. 30 mV/pH. Effects such as leakage currents or buffer composition changes could be excluded as a possible cause for the observed resistance changes. Capacitance voltage experiments were used to determine the pH sensitivity of bare samples being approx. 60 mV/pH. The pH induced changes in surface potential can be explained by a pH dependent surface charge. For the MBP-OH passivation a site dissociation model involving the mercaptobiphenyl -OH groups reproduces the experimental data. For the

87 88 Summary and Outlook

MBP-CH3 and the MBP-H passivation such a model is very unlikely. Instead, a Stern layer adsorption of OH− ions can explain the pH dependent surface potential. However, also a site dissociation model for surface oxides in monolayer defects ﬁts the obtained data reasonably well. The behavior of a MBP-CH3 coated 2DEG sensor device was also examined in 1mM PBS at constant pH but with varying NaCl concentration. It was found that with increasing salt concentration the surface potential increased as well. The absolute change in surface potential could not be ﬁtted with the models used for the pH sensitivity experiment but a simpler model assuming a salt independent surface charge obtained excellent agreement with the experimental data.

For the future a further insight into the adsorption effects of molecules onto the GaAs surface could be gained by advanced Kelvin probe measurements using a monochromatic light source. Then, the energy of the surface states could be determined by Surface Photovoltage Spectroscopy (SPS) and a more detailed analysis of the surface electronic structure would be possible. Interesting would be also an examination of other molecules with larger dipole to obtain more information about its inﬂuence on electron afﬁnity.

For measurements in wet environment a further improvement in stability would be helpful, e.g., the crosslinking of the mercaptobiphenyl monolayer might enhance the passivation [91]. This would enable a larger pH variation helping to identify the right surface charging model. Apart from this a further step toward real biosensing application should be done. A possible model system for such applications are proteins in solid supported membranes which could mimic important interaction mechanisms in cell biology. These membranes are a very flexible and robust system to measure specific reactions on surfaces. As a first testbed experiments on

Figure 6.1: Schematic of the charging of NTA headgroups in a lipid monolayer supported on a hydrophobic solid. The binding of Ni2+-ions to the NTA groups makes the surface charge more positive. Adding EDTA removes the Ni2+- ions from the NTA. The change in net surface charge is one electron charge [88, 89, 90]. 89 a lipid monolayer consisting of DMPC1, cholesterol and DOGS-NTA2 were conducted. The membrane can be deposited on hydrophobic surfaces by a technique called solvent-exchange. For a detailed description of this process see e.g. [90]. The functional NTA headgroups can be charged with divalent nickel ions and decharged by removing the nickel ions from the headgroups by EDTA3 [92]. The whole procedure is schematically sketched in ﬁgure 6.1. Please note that the change in net charge corresponds to only one electron due to the intricate formation of the octahedral nickel - NTA complex [88, 89, 90].

First measurements on a lipid monolayer on MBP-CH3 passivated samples providing the necessary hydrophobic surface were performed as illustrated in ﬁgure 6.2. The left panel shows the reaction of the 2DEG sensor upon injection of the Ni2+ and EDTA containing buffer before the deposition of the lipid layer. Here the Nickel buffer consisted of 10mM PBS buffer with

1mM NiCl2 and 150mM NaCl, and the EDTA buffer contained 50mM EDTA in 10mM PBS. Both buffers were adjusted to pH = 7.5 and simply injected into the ﬂow chamber. As can be seen after a certain equilibration time the sensor had the same resistance for both buffers. Then, the lipid monolayer was deposited on the sensor device via solvent exchange. After that, the sensor showed a clear response on the different buffers as is depicted in the right panel of ﬁgure 6.2. The direction of the observed resistance change agrees excellently with the behavior expected from the discussion in section 5.2.2: Decreasing the surface charge by adding EDTA increases the resistance. This experiment clearly demonstrates the potential of the 2DEG sensor device in biosensing applications.

11,2-dimyristoyl-sn-glycero-3-phosphocholine 21,2-dioleoyl-sn-glycero-3-[N(5-amino-1-carboxypentyl) iminodiaceticacid]succinyl) 3EthyleneDiamineTetraaceticAcid

52k 42k 2+ 2+ ] ] Ni Ni [ [ 2+ EDTA Sa Sa

51k 41k EDTA Ni EDTA

50k 40k stance R stance i

39k 49k Sample resSample Sample resistance R resistance Sample

38k 48k

1000 2000 3000 4000 5500 6000 6500

Elapsed time [sec.] Elapsed time [sec.]

Figure 6.2: Experiment on the charging of a lipid monolayer containing chargeable DOGS-NTA on a MBP-CH3 passivated sensor device. Left: Response of the sensor on the Ni- and EDTA buffer before the deposition of the lipid monolayer. Right: Response of the sensor after the lipid deposition by solvent exchange. 90 Summary and Outlook Part II

III-V Semiconductor Devices for Molecular Electronics

Chapter 7

Introduction

The second part of the present thesis deals with the application of III-V semiconductor heterostructures for molecular electronics. A convenient definition for molecular electronics is “the set of electronic behaviors in molecule-containing structures that are dependent upon the characteristic molecular organization of space” [7]. Research in molecular electronics in the last years was driven mainly by the ongoing miniaturization in todays silicon technology which manifests itself in the often cited empirical Moore’s law [8]. A popular formulation of Moore’s law is “the doubling of the number of transistors on integrated circuits every 18 months” [93]. Naturally, this continuing miniaturization will encounter severe problems as device dimensions approach physical limits, although it might proceed for another 25 years [9]. E.g., if the device dimensions reach the mean free path of charge carriers the bulk description of current transport used to design most current circuit elements breaks down [10, 11]. Or, regarding the doping of semiconductors, statistical effects lead to drastically changing device characteristics as the number of dopant atoms in shrinking device volumes decreases [10, 11]. Therefore, molecular electronics goes one step beyond this top-down approach, and features the use of molecules as functional units in an electrical circuit in a bottom-up approach [94, 95]. Molecules show inherent advantages over inorganic devices as, e.g., the statistical doping problem can be circumvented by the mostly easy and cost-effective mass fabrication of identical molecules with required current transport characteristics. Additionally, molecules promise to solve leakage problems known from bulk silicon devices as they are a natural confinement to electrons. Fur- thermore, chemist might synthesize custom-tailored molecules according to the specific needs of circuit designers [12, 13, 14]. The “birth” of molecular electronics is often attributed to the visionary paper of Ari Avi- ram and Mark Ratner published in 1974, in which they proposed a molecular rectifier [96]. However, seminal ideas from which molecular electronics emerged can even be followed back

93 94 Introduction to the 1940s to Robert S. Mulliken and Albert Szent-Gyorgi [97] but a thorough treatment of molecular electronics history would exceed this introduction. In their imaginative work, Avi- ram and Ratner proposed the molecular analogue to an inorganic pn-junction. The suggested molecule comprises a donor and an acceptor moiety which are connected by a bridge (see left panel of figure 7.1). Aviram and Ratner have been able to show that such a molecule would, in principle, be an insulator for applied voltages below a critical threshold, followed by a sudden switch-on in current for higher voltages (right panel of figure 7.1). The general idea took quite a long time to be demonstrated experimentally, this occurring 25 years later by Metzger et al. [98] (using different molecules). Nowadays, molecular structures for all necessary elements for logic circuits have already been proposed and, in part, experimentally verified. This includes wires, insulators, transistors, logic gates, adders,... and many more [7, 95, 14, 99, 100, 101]. On the way toward fully mono-molecular electronic (MME) devices, where all aspects such as wiring and electrical function of an electrical circuit are fulfilled only by molecules, hybrid molecular electronic (HME) devices, consisting of molecules connected to inorganic electrodes, are promising candidates to gain more insight into molecular conduction mechanisms [14]. One of the major challenges in these HME systems is the reproducible fabrication of contacts, often termed nanogap electrodes, which allow for a reliable contacting to molecules with a predetermined spacing. A diversity of methods has already been used to build contacts to single molecules, molecular layers, or other nanoparticles the most prominent being scanning probe based techniques [102, 103, 104, 105], mechanically controlled break junctions (MCBJ) [106, 107, 108], electromigration [109, 110, 111], electrodeposition [112, 113], electrochemical etching [114, 115], and electron beam nanolithography [116, 117]. Other fabrication methods include shadow evaporation over various template structures [118], etched nanopores [119, 120], and trenches on the side wall of mesa etched heterostructures [121], us-

NC CN

S S

NC CN

AcceptorBridge Donor

Figure 7.1: Left: Schematic of the molecular rectifier proposed by Aviram and Ratner [96]. The molecule is composed of a donor moiety, tetrathiafulvalene, connected by a methylene bridge to an acceptor moiety, tetracyanoquinodimethane. Right: Calculation of the IV characteristics of the rectifier molecule connected to metal electrodes. Reprinted from [96]. 95 ing an approach related to the technique presented in this thesis. A further interesting method to access single molecule measurements was recently reported by the same group (T. Dadosh and coworkers, [122, 123]): hybrid gold nanoparticle - molecule - gold nanoparticle units are first fabricated which are then electrostatically trapped between nanogap electrodes made by electron beam lithography. In the following, the very popular MCBJ method to fabricate nanogap contacts is discussed in more detail to elucidate the advantages of the technique followed during this thesis. First attempts to measure molecular conductance using MCBJ electrodes were put forth by the groups of Tour and Reed [106], and Bourgoin and co-workers later considerably improved the technique [124]. In the MCBJ approach, a notched metal wire glued onto a flexible substrate is fractured by bending of the substrate (cf. left panel of figure 7.2). During the rupture the electrodes are exposed to a surface active (usually a dithiolated) molecule1 containing solution. The gold surfaces are soon covered with strongly adhering self-assembled monolayers (SAM) of the dissolved molecules. The solvent is then allowed to evaporate and the tips are slowly moved together until the onset of conductance is achieved (cf. right panel of figure 7.2). Non-linear I-V curves were measured repeatedly for a great variety of molecules using this method [14]. Its advantages are the suitability to contact single-molecules, the preparation of fresh and clean contacts due to the breakage already in solution, and the aptness to adjust the electrode distance. However, in MCB junctions it is not possible to predetermine the distance, furthermore, no microscopic technique is available to observe the molecules in the junction due to the fabrication process, and a parallelization to include many electrode pairs in one device seems hardly feasible. In a similar way, all other existing fabrication methods inherently combine certain advantages with a varying number of shortcomings. Most of the techniques have been demonstrated to be very well suited for contacting nanoscale objects. However, applications which require at the same time macroscopically flat surfaces with a pre-designed gap separation and symmetric, coplanar electrodes can hardly be addressed. Such properties are particularly important for the manipulation, positioning and electrical investigation of molecules on or between electrodes by, e.g., scanning probe techniques [125, 126]. This includes the directed assembly and electrical study of even more complex molecular circuits, eventually using a probe tip as a third electrode [102]. In this thesis, novel fabrication methods are presented that combine the benefits of using only conventional process technology for lateral patterning with the precision, clean- ness and smoothness of cleaved heterostructures grown by molecular beam epitaxy (MBE). As the crystallographic cleavage is done after finishing the micropatterning of the device, the

1dithiolated molecule: molecule with thiol (-SH) end groups at both sides. Thiol groups readily bind to most noble metals, such as gold, platinum or palladium. 96 Introduction

Figure 7.2: Left: Schematic of a mechanically controlled break junction (MCBJ) Right: Close-up of the sensitive electrode region after moving the contacts together until the onset of conductance is achieved. Reprinted from [106]. sensitive nanogap region is protected from any organic contamination during all lithographic process steps. This provides for very flat and clean electrodes with a well defined separation predetermined by the accuracy of MBE growth, and readily accessible to topological characterization using surface probe techniques. Due to a groove-like electrode separation, molecules under study can be freely suspended between the contacts avoiding disturbing influences that may arise from electrostatic, van der Waals or other interactions with supporting substrates.

GaAs Based Systems In the first approach, denoted in the following as planar electrode method, the nanogap electrodes are fabricated on a AlGaAs-GaAs heterostructure that is not electrically active but instead acts as a supporting template structure for metal electrodes. To do so, a few nanometers thin GaAs layer is embedded between two thick AlGaAs layers by MBE growth. After a lateral patterning by optical lithography and wet chemical etching, a clean and atomically flat surface is exposed by crystallographic cleavage. Then, the GaAs layer is selectively etched and a thin metal film is evaporated perpendicular to the cleavage plane. This metal film ruptures at the etched trench and thereby forms the two nanogap electrodes (see left panel of figure 7.3). After that, the device is ready for functionalization with molecules and their electrical characterization. By using the advanced cleaved-edge overgrowth (CEO) MBE technique2, it is even possible to fabricate several nanogap electrodes of varying width down to a few nanometers on one device. In this approach, denoted in the following as the CEO electrode method, the MBE

2The CEO technique consists of a second MBE growth step perpendicular to the first growth direction. Prior to the second growth, the samples are cleaved in-situ in the MBE chamber. More details are given in chapter 12. 97 grown structure consists of several very thin AlGaAs layers embedded in between thick GaAs layers. Then, in contrast to the previously described approach, a second MBE growth step consisting of a thin GaAs layer followed by a thick AlGaAs layer is performed perpendicular to the first growth direction. Subsequently, the device is cleaved, selectively etched, and a thin metal film is evaporated perpendicular to the cleavage plane. In the same manner as before, the film rips off at the trench edges, and several nanogap electrodes with different thicknesses are obtained, as is schematically sketched in the right panel of figure 7.3. In principle, such a device would allow for the simultaneous characterization of single molecules, and molecular layers. Thereby, it would give insight in the influence of molecular environment on the current carrying properties of molecules.

InAs Based Systems In a further development step, it is desirable to actively use the supporting semiconductor structure. This would establish a connection to part I of this thesis where molecules have been assembled directly on semiconductor (GaAs) layers. On one hand, the electrically active usage of the semiconductor structure would omit the metal evaporation process, which inﬂuences the electrode distance due to non-perfect perpendicular evaporation. And on the other hand, new insight into fundamental interactions could be gained as most research in molecular electronics so far concentrated on metallic electrodes and still little is known about the interaction between

Figure 7.3: Schematic of the experimental configuration for molecular conductance measurements using nanogap electrodes on AlGaAs-GaAs heterostructures. Left: Coplanar electrodes on the cleaved facet of a MBE grown AlGaAs-GaAs heterostructure. A thin metal film evaporated perpendicular to a cleaved facet ruptures at the trench formed by a selectively etched GaAs layer embedded between two AlGaAs layers. The inset illustrates molecules connecting the nanogap electrodes. Right: Electrodes based on the cleaved plane of a CEO grown AlGaAs-GaAs heterostructure. The adjustable width of one set of electrodes (1 and 2) allows, in principle, for the combined measurement of single molecules (electrodes 1 and 3) and molecular layers (electrodes 2 and 3). 98 Introduction semiconductors and molecular functional units. However, it is doubtful that a GaAs based structure even with high density doping could be used for such a purpose due to the depletion region at GaAs surfaces. Therefore a doped GaAs - molecule - doped GaAs system inherently includes two relatively large tunneling barriers at the semiconductor - molecule interface, hence, making a determination of the electrical characteristics of the molecule at least difficult, if not impossible. A solution to this systematic problem is the use of semiconductors which show an surface charge accumulation layer instead of a depletion layer. A prominent example for such a material is Indium Arsenide (InAs) which possesses a very conductive two dimensional electron gas at surfaces of various orientations [15, 127, 128, 16, 129]. E.g., Kajiyama and coworkers showed that Au/n-In(x)Ga(1−x)As diodes experience a negative Schottky barrier for high In contents [130] (see figure 7.4). This can be explained by a conduction band edge lying below the Fermi level, thus, an electron accumulation layer is formed. Even superconducting behavior of such layers was reported [131]. Conductive surface charge accumulation channels exist (or can be obtained by surface treatments) not only in InAs, but also in other material systems such as InP [132], InSb [133], GaSb [134, 135] or even diamond [136]. One possible structure realization for active semiconductor nanogap electrodes is a heterostructure consisting of two thick surface conducting material layers (e.g., InAs) with a thin (typically 1-5 nm) embedded intermediate layer. This intermediate layer must interrupt the electrical connection between the two surface conducting layers of the outer material. For this purpose, it could consist either of another semi-conducting material having a surface conducting layer of opposite charge polarity, or, of an insulating material. The outer layers serve as electrical source and drain contacts to nanoscale objects like π-conjugated molecules, DNA- oligonucleotides, or others that electrically bridge the separating inner layer, thereby, forming a hybrid nanoelectronic unit.

1.4 Schottky barrier

Band gap

1.2

1.0 eV]

0.8 gy[

0.6 Ener 0.4 Figure 7.4: Band gap (dotted) and Schot- 0.2 tky barrier (dashed) of Au/n-In(x)Ga(1-x)As

0.0 diodes for varying indium concentrations.

x = 0 0.2 0.4 0.6 0.8 1.0 For high indium contents the Schottky

nAs In Ga As Composition barrier becomes negative. Adapted from

x 1-x

GaAs [130]. 99

Figure 7.5: Band gaps (left panel) and band offsets (right panel) of common III-V semiconductors. Left: Lowest forbidden bandgap as a function of lattice constant for non nitride III-V compound semiconductors (points) and their random ternary alloys (lines) at zero temperature. The materials with Γ-, X-, and L-valley gaps are indicated by solid, dotted, and dashed lines, respectively. Reprinted from [137]. Right: Conduction band edge and valence band edge energies plotted as a function of the lattice constant of semiconductors. The ﬁlled circles indicate the band edges of the binary semiconductors and the lines show the band edges of the ternary alloys. The zero energy point represents the approximate gold Schottky barrier position in the band gap of any given alloy. Reprinted from [138].

However, the intermediate layer is also the major difficulty in the semiconductor electrode approach. InAs, having a lattice constant of 6.1 Å, does not have a “partner” material to form unstrained ternary alloys suited for MBE growth as it is the case the GaAs-AlAs system. As can be seen from figure 7.5, the closest materials in terms of lattice constant are GaSb and AlSb. However, problems arising from the band offsets shown in the right panel of figure 7.5 can be expected: InAs-GaSb heterojunctions form broken, or type III, energy band lineups which probably leads to large leakage currents through the semiconductor structure. Also InAs-AlSb heterojunctions are not perfectly suited for nanogap electrodes, as they do not impose a barrier to hole currents due to the staggered, or type II, band lineups. From a band engineering point of view, the InAs-InP or the InAs-AlAs system would be preferable. However, the large difference in lattice constants imposes major problems in the fabrication of such heterostructures. One solution would be the step from bulk growth to nanowire structures which enables the fabrication of heterostructures with large lattice misfits because the structure can laterally relax. With such a technique, InAs-InP-InAs structures were already grown successfully, and proved electrically working [139, 140, 141]. For the connection of molecules to the semiconductor electrodes, also thiol groups could be used preserving the surface accumulation channel as was already reported for indium containing semiconductors [142]. 100 Introduction Chapter 8

Fundamentals of Molecular Conduction

In this chapter an overview of the different theoretical aspects of current transport in molecules will be given, followed by an introduction to molecules relevant to this thesis.

8.1 Molecular Conductance Theory

Historically, the broad field of molecular electronics was explored starting from two different bases. On one side there have been chemists and biologists working on the transfer of electrons inside or in between molecules. The comprehension of this electron transfer is important to understand the cycle of many prominent reactions such as photosynthesis. On the other side there have been solid state physicists, who worked on transport in mesoscopic structures and applied their expertise to molecular systems. Due to this evolution of the molecular electronics research field there are many different theoretical approaches on the description of current transport in molecular systems. However, as one can imagine, they are closely related as all of them describe the same system. This section is the attempt to show the connections between different system descriptions and to give the reader the possibility to compare experiments on molecular conduction with different scientific background. However, in order to understand the present work it is sufficient to start with section 8.1.5 and to skip the next subsections. Various parts of this section are based on excellent information sources including textbooks on transport in molecular and mesoscopic systems [143, 144, 145, 101, 146, 147], and various review articles on electron transfer and molecular current transport [148, 149, 150], as well as research articles [124].

101 102 Fundamentals of Molecular Conduction

8.1.1 Introduction

The focus of interest in the field of molecular electronics is to describe the transmission of electrons from one site, the donor D, to another site, the acceptor A, via a bridge B. This bridge will be either a whole molecule, a part of a molecule, or a layer of many molecules in parallel. Usually, the bridge is hindering the electron transmission being an energetic barrier. A first classification of all terms occurring in molecular electronics can be made by distinguishing the nature of the donor or acceptor. In so called electron transfer (ET) experiments both, the donor and acceptor, are a part of a molecule and the electron transmission occurs via the intermediate part of the molecule. Therefore, the observable in the system is the rate kD→A of electron transmission. However, if donor and acceptor are solid state devices like metals or semiconductors, one speaks of molecular conduction experiments, and the observable is a current. One major difference between these two types of experiments is the method to create an excess of electrons in the donor. In ET experiments electrons are usually created by irradiation or chemical reactions. The electron transmission then takes place without any voltage drop across the bridge. However, in molecular conduction experiments an electron excess is created by applying a bias voltage to the leads what naturally also influences the molecular bridge. Another major classification of electron transmission can be made in terms of classical and quantum mechanical events. Classical transmission in this context means that the electron gains enough energy to overcome the energetic barrier to the acceptor. This could either happen by applying a bias voltage to the donor-acceptor system, or by thermal activation as in thermoionic emission. Quantum transmission on the other hand involves all types of tunneling events. There is the “standard” tunneling through a rectangular barrier as known from quantum mechanics together with a variety of enhancements of this process which either lower the effective barrier (e.g., Fowler-Nordheim tunneling) or improve the coupling between the donor and the acceptor (e.g., superexchange mechanism). Then, the electron transmission can be further subdivided by the number of transmission events which are necessary for the current flow. In sequential tunneling or hopping conduction the electron experiences several transmission events on the way from the donor to the acceptor materializing on a site of the bridge after each event. Whereas in direct tunneling or in superexchange there is only one transmission event. Furthermore, there are other distinguishing features as whether the transmission involves no loss of energy (elastic transmission) or scattering events (inelastic transmission) which also influences whether the phase information of the electron wave function is conserved (coherent process) or not (incoherent process). 8.1 Molecular Conductance Theory 103

8.1.2 Landauer Formula

In the Landauer approach, a current through a structure is expressed in terms of the probability of single electron transmission through the conductor. It will be used in the simple one level model of section 8.1.5 to explain the shape of molecular conductance measurements. The Lan- dauer approach is able to describe ballistic conductors, i.e., where the size of conductor is small compared to the mean free path. Surprisingly, in this case one observes only finite currents although no resistance is expected due to the lack of scattering events! Furthermore, it also accurately describes the current flow in degenerate conductors at low temperatures in terms of a single particle transmission coefficient. One might expect that many particle effects should influence the current, however, for coherent transport the exclusion principle indeed does not influence the current flow. For the following discussion zero temperature is assumed so that there is current flow only in the energy range µl > E > µr where µl and µr denote the Fermi energies of the left and right contacts, respectively. Furthermore, the transmission characteristics are assumed to be independent of energy.

The resistance in a ballistic conductor arises from the fact that the current in the contacts carried by infinitely many transverse modes has to be redistributed to “fit” into the conductor. The current density j on the conductor from the left contact due to particles in a infinitesimal volume of momentum space d~kl around ~kl may be written:

jl = −eD(~kl) fl(~kl)vz(~kl)d~kl (8.1) where fl is the distribution function on the left side of the barrier. If we reduce the problem to the one dimension perpendicular to the barrier (=conductor) then D(~kl) = 2/(2π) is the density of states in 1D k-space, and the velocity vz perpendicular to the barrier from the left is ∗ vz(~kl) = hk¯ z,l/m . The overall current from the left Il is then the sum over all k-space weighted by the transmission Tt(E) of the conductor. Z 2e ∞ Il = − dkl(kl) fl(kl)v(kl)Tt(E) (8.2) 2π 0

An equivalent expression can be written for the right contact and the overall current is then the difference of the currents from both contacts. With the common transformation into an energy integral kdk = m∗dE/h¯ 2 and the substitution v = hk¯ /m∗ one obtains: ·Z Z ¸ 2e ∞ ∞ I = dE fl(E)Tt(E) − dE fr(E)Tt(E) (8.3) h 0 0 104 Fundamentals of Molecular Conduction

In the simplest approximation f (E) is the equilibrium Fermi distribution which is characterized by the Fermi level µ. For zero temperature the integral then is (Tt(E) = const.):

2e I = · T · (µ − µ ) (8.4) h t l r Therefore the conductance yields the Landauer formula:

2 I I 2e Tt G = = = · Tt = (8.5) V (µl−µr) h 12.9kΩ e

For molecules one would split the overall transmission Tt into the transmission from the left contact into the molecule Tt,l, the transmission through the molecule Tt,m and the transmission from the molecule into the right contact Tt,r [151, 152]:

Tt = Tt,l · Tt,m · Tt,r (8.6)

One can roughly approximate coherent, non-resonant1 tunneling through molecules as tunneling through a rectangular barrier, in which case

Tt,m = exp(−βl) (8.7) where l is the width of the barrier, i.e., the length of the molecule, and β is the tunneling decay parameter given by: s ¡ ¢ 2m∗ · α φ − eV β = 2 2 (8.8) h¯ 2

Here φ is the barrier height for tunneling through the LUMO level, φ = (EF − ELUMO) or ∗ through the HOMO level, φ = (EHOMO − EF ), EF is the Fermi level of the electrode, m is the effective mass, V = (µl − µr) is the bias that is applied, and α is a parameter used to describe the asymmetry in the potential proﬁle across the electrode-molecule-electrode junction.

8.1.3 Electron Transfer and its Connection to Molecular Conductance

Electron transfer (ET) is a process by which an electron moves from one molecular part D to another molecular part A via a mediating bridge B inside a molecule. ET is usually described in terms of transfer rates kD→A, and it arises out of nature’s need to move electrons (reducing equivalents) or holes (oxidizing equivalents) from one site to another. Numerous essential

1i.e. no molecular level lies inside the potential window opened by the two electrodes 8.1 Molecular Conductance Theory 105 processes in biology require ET, including oxygen binding / transport, photosynthesis / respira- tion, and many more. Usually, an ET system is described by a nuclear coordinate which lumps together all the distances in all involved bonds, and the energy dependence of the system is described by a parabola. This description is adapted from a simple picture of the energy of a biatomic molecule in which the bond joining the two atoms vibrates. The change in energy with bond length is a parabola according to Hooke’s law. In figure 8.1, an electron transfer reaction is schematically illustrated. The donor-bridge- acceptor (D-B-A) system is represented in two states, that before electron transfer (R the reactant state: D*-B-A), and that after electron transfer (P the product state: D+-B-A−). It is important to realize that these represent two different states of the same system. The electron jumping from R to P has to occur at cross-over point (C) because of: a) the Franck-Condon principle. Electron transfer occurs so rapidly (compared to atomic vibrations) that no change in nuclear configuration can occur during the transfer. This requires that the transfer is a vertical transition in the diagram. b) Conservation of energy requires that the transition is a horizontal line on the diagram. The only place where both conditions are fulfilled is where the nuclear energy profiles cross (point C). The crossing point represents the energy level to which the reactant state must be raised before progressing to the product state. ET processes can be classified according to a possible anti-crossing between states R and P. A diabatic or non-adiabatic electron transfer is a quantum jump from one curve to the other and the curves actually cross. An adiabatic process in thermodynamics is one in which no exchange of heat with the environment occurs. In the electron transfer context, an adiabatic process is one in which no quantum jump occurs, there is an interaction at the barrier and anti-crossing of

D+ -B-A - D*-B-A

D-B-A u h Figure 8.1: Schematic of an electron transfer process. y g r

e First the system is excited usually by irradiation. Then, n E it relaxes to point A. After that it has to overcome

nuclearcoord. ACB the barrier at the crossing point C and subsequently, it reaches the product state at point B. The electron prob- electron ability density at the different transition states is also probability density D-B- A illustrated at the bottom of the graph. 106 Fundamentals of Molecular Conduction the curves representing the two states occurs to form a a quasi-state at the top of the activation barrier (see ﬁgure 8.2, and [153] for further information).

In standard electron transfer theory, the rate constant kD→A which describes a non-adiabatic transfer event is based on a Golden-rule expression [148]:

2π k = |V |2F (8.9) D→A h¯ D→A where VD→A is the coupling between the donor and acceptor electronic states, and where F is the thermally averaged and Franck-Condon weighted density of nuclear states. According to A.

Nitzan [148], this transfer rate kD→A can be related to molecular conduction G by a comparison to the Landauer conduction formalism:

e2 k 8h¯ G = D→A (8.10) πh¯ F πΓDΓA

Here, ΓD and ΓA is the broadening of the molecular bridge level through which the transmission or transfer occurs with respect to the donor or acceptor. It can be related to the life time τ of an electron on the bridge before it escapes to the donor or acceptor ΓA,D = τA,D/h¯.

8.1.4 Classical and Quantum Mechanical Transmission

In the following, a brief overview of several transmission types is given, which frequently appear in publications on molecular electronics. Table 8.1 on page 110 at the end of this subsection might help the interested reader to estimate temperature or ﬁeld effects on the various conduction mechanisms. The barrier height in this subsection is given in energy units!

Thermoionic emission Effect that due to the non-discrete Fermi distribution at T 6= 0, a small part of electrons have high enough energies to overcome a potential barrier. The current due to thermoionic emission over a barrier of height φ is:

2 I = A(1 − r)T exp[−φ/kBT] (8.11)

Diabatic Adiabatic

R P P

= R = =

D = D D *

D +

- - - + B B * B - - - B -

A A A

- - - A Figure 8.2: Schematic of diabatic and adiabatic y g r e

n electron transfer. In adiabatic processes an inter- E action between the two states occur whereas in ACBACB Nuclearcoordinate Nuclearcoordinate diabatic processes the curves actually cross. 8.1 Molecular Conductance Theory 107

2 3 2 −2 where A = 4πmkBe/h = 120 A/cm K is a fundamental constant, r is the reﬂection coefﬁcient of the electrons, and T is the temperature. This is called the Richardson- Dushman equation [154].

Schottky emission Process in which carriers overcome a barrier by thermoionic emission, taking into account the barrier lowering due to image charges caused by an electric ﬁeld |~E|. One gets the modiﬁed current density [155]: · µ q ¶ ¸ 2 I = A(1 − r)T exp − φ − e e|~E|/4πε /kBT (8.12)

Frenkel-Poole conduction is due to ﬁeld-enhanced thermal excitation of trapped electrons into the conduction band, a process similar to Schottky emission. Instead of the metal- dielectric barrier height found in Schottky emission, the barrier height in Frenkel-Poole conduction represents the depth of the trap potential with respect to the edge of the conduction band. As seen from its characteristics, the barrier lowering is twice that observed in Schottky emission, because of the immobility of the positive charge associated with the trap, e.g. see [155, 156].

Hopping conduction refers to the process in which thermally excited electrons hop from one isolated state to the next, whose conductance also depends strongly on temperature. Dif- ferent from Schottky emission, there is no barrier lowering effect.

Fowler-Nordheim tunneling Tunneling through a potential barrier whose thickness is sub- stantially decreased with an externally applied high electric ﬁeld, allowing electrons to tunnel across the potential wall. One could imagine it as a kind of extreme direct tunneling.

Direct or coherent tunneling “Normal” tunneling as known from quantum mechanics. Tak- ing electrons as wave functions, coherent tunneling means they do not loose their phase information during the tunneling process [144]. The electrons have no time to be completely relocalized in the molecule after the initial tunneling step at the metal-molecule electronic contact. The current can be calculated using Z e2 +∞ I(V) = Tt(E,V)[ f (E − µl) − f (E − µr)]dE (8.13) πh¯ −∞

in which Tt is the transmission coefﬁcient of the structure, µl,r is the chemical potential of the left and right electrode, respectively, and f (ε) denotes the Fermi function at the 108 Fundamentals of Molecular Conduction

temperature of the experiment. For the special case of a rectangular barrier, J. Simmons found an approximate expression for equation 8.13 [157]. According to the approxima- tions and calculations made by him, the tunneling current density J through a barrier of height φ and width d is given by: p " p # (2m∗φ) ³e´2 2d (2m∗φ) J = e V exp − e (8.14) 4π2d h¯ h¯ for V ' 0 µ ¶ " s µ ¶# ³ e ´ eV 2d eV J = φ − exp − 2m∗ φ − − 4π2hd¯ 2 2 h¯ e 2 µ ¶ " s µ ¶# ³ e ´ eV 2d eV φ + exp − 2m∗ φ + (8.15) 4π2hd¯ 2 2 h¯ e 2 φ for V < e

∗ where me is the effective electron mass, and V the bias potential. Putting all known constant, one obtains for d already expressed in [nm] and all potentials in [V] for the case φ for 0 < V < e : · ¸ µ ¶ " sµ ¶# A eV eV J = 6.166 · 1012 · φ − exp −10.246 · d φ − − m2 2 2 µ ¶ " sµ ¶# eV eV 6.166 · 1012 · φ + exp −10.246 · d φ + (8.16) 2 2

The results for a bias voltage of 1 and 2V are illustrated in ﬁgure 8.3 on page 110. Tun- neling is an elastic process, hence, for a conducting (molecular) state coupled to the electrodes only electrons in the Fermi sea of the metal electrode with energies equal to the molecular level can tunnel into the molecule. Therefore, the current through a molecular level stays constant once the level is inside the potential window opened by the electrodes. This results in a sharp peak in the conductance.

Sequential tunneling In the case of weak coupling to the electrodes electrons can relocal- ize completely on the molecule. Taking an analogue from semiconductor physics, the molecule can be considered as a quantum dot weakly coupled to both electrodes through tunnel junctions. Thus, sequential tunneling considers the tunneling of an electron through the metal-molecule-metal junction as a sequential process, the molecule being succes- 8.1 Molecular Conductance Theory 109

sively charged and discharged. Electron tunneling rates through both metal-molecule junctions can be obtained from a golden rule calculation, whereas the current can be calculated by solving a master equation connecting the different charge states of the molecule (e.g., see appendix of [124].

Superexchange mechanism Superexchange and sequential (charge hopping) mechanisms can both contribute when an electron or hole is transferred from a donor to an acceptor via a bridge with the assistance of an intermediate or “midway” group where the charge carrier can localize. In the superexchange process, direct, long-distance electron transfer is enhanced by indirect mixing of the donor and acceptor wave functions through the orbitals located between the donor and acceptor. So the molecular part between the donor and acceptor facilitates tunneling by increasing the size of quantum state space for the charge transfer. In sequential charge transfer, the charge temporarily resides on the midway group, while in superexchange, this intermediate state only participates by providing a virtual state [150].

Inelastic effects Two phenomena, decoherence and relaxation, limit the capability of a molecular wire to exchange information between metallic electrodes. Both phenomena increase with increasing temperature and length of the wire [158]. Decoherence is the lost phase information during transmission of a wave packet through the molecular wire. This can be due to scattering effects but also due to dispersive propagation inherent to the transmission. The scattering is often caused by vibronic coupling of electrons on the molecule to molecular vibrations. It gives birth to the Inelastic Electron Tunneling Spectroscopy (IETS), first developed at the Ford Laboratories [159], which consists of observing vibrational bands in the IV characteristics of a transport medium. The experiment examines the dependence of the transport current on the voltage, the first derivative (conductance), and, more specifically, the second derivative of the current. In these second-derivative IETS spectra, one sees peaks that correspond to excitation of a vibrational mode on the wire [158, 160].

8.1.5 Simple Model for Molecular Conduction Including Charging Ef- fects

In the following a simple model, extracted from ref. [146], is presented to illustrate the role of determining factors on the shape of molecular IV characteristics. This model was used in this 110 Fundamentals of Molecular Conduction

Mechanism Current T dep. V dep. Ã q ! φ−e eV 2 4πεd I 1 1/2 Schottky emission I ∝ T exp − kT ln( T 2 ) ∝ T ln(I) ∝ V Ã q ! φ−e eV 2 πεd I 1 I 1/2 Frenkel-Poole conduction I ∝ VT exp − kT ln( T 2 ) ∝ T ln(V ) ∝ V ³ ´ φ I 1 Hopping conduction I ∝ V exp − kT ln(V ) ∝ T I ∝ V ³ √ ´ 3 2 4d 2m 2 I 1 Fowler-Nordheim tunneling I ∝ V exp − 3ehV¯ φ none ln(V 2 ) ∝ V ¡ 2d √ ¢ Direct tunneling (eV ¿ φ) I ∝ V exp − h¯ 2mφ none I ∝ V Table 8.1: Conduction mechanisms through a barrier of height φ and thickness d, and their temperature and bias dependence. Mainly extracted from [161, 155]. The direct tunneling relationship is taken from the Simmons model [157] for small bias voltages compared to barrier height: V ¿ φ/e.

Figure 8.3: Current density due to direct tunneling between inﬁnitely extended parallel electrodes through a rectangular barrier according to the Simmons model [157]. The dependence on barrier height and width is shown. Left: Tunneling at a bias of 1V. Right: Tunneling at a bias of 2V. thesis to estimate the right parameters for a proper simulation of experimental IV characteristics as will be presented in chapter 11. The basic features of molecular conductance are in most cases easily understood in terms of three factors:

(1) Distance |EF − EMol| from the Fermi Energy EF to the nearest molecular level EMol, (2) broadening Γl, Γr of the molecular levels due to the coupling to the contacts and (3) charging energy Uch per electron.

To understand the inﬂuence of these factors on the current transport through molecules, three basic topics have to be addressed: 8.1 Molecular Conductance Theory 111

(1) An energy level diagram showing the molecular energy levels relative to the Fermi energy in the metallic contacts (see below), (2) an estimate of the broadening of the molecular levels due to the coupling to the contacts (see page 111), and (3) the spatial proﬁle of the applied potential under bias (see page 112).

Energy Level Diagram

The first step in understanding the IV curve for a molecular conductor is to draw an energy level diagram and locate the Fermi energy. Considering first a molecule sandwiched between two metallic contacts, but with very weak electronic coupling, one could line up the energy levels as shown in the left panel of figure 8.4 using the metallic work function (WF) and the electronic affinity (EA) and ionization potential (IP) of the molecule. The picture changes qualitatively if the molecule is chemisorbed directly on the metallic contact, see right panel of figure 8.4. Then, the molecular levels are broadened significantly by the strong hybridization with the delocalized metallic wavefunctions (not illustrated), making it possible to transfer fractional amounts of charge to or from the molecule. Indeed, there is a change in the electrostatic potential inside the molecule due to the charge transfer and the energy levels of the molecule are shifted by a contact potential (CP). It is now more appropriate to describe the transport in terms of the HOMO-LUMO levels associated with incremental charge transfer rather than the affinity and ionization levels associated with integer charge transfer.

Fermi Energy Location

The location of the Fermi energy EF relative to the HOMO and LUMO levels is probably the most important factor in determining the current vs. voltage characteristics. Usually, it lies

vacuumlevel CP

WF -EA WF LUMO E E -IP F F HOMO

metal molecule metal metal molecule metal Figure 8.4: Energy level diagram for a metal-molecule-metal sandwich. Left: Weakly coupled molecule. Right: Strongly coupled molecule. The broadening of the molecular levels due to hybridization is not illustrated. 112 Fundamentals of Molecular Conduction

somewhere inside the HOMO-LUMO gap [146]. EF is located by the requirement that the number of states below EF is equal to the number of electrons in the molecule which depends on the amount of charge δn transferred to the molecule by chemisorption. δn is driven by the difference between the contact Fermi energy, and the charge neutrality level of the molecule

ECNL which denotes the location of the Fermi energy for a neutral molecule. It furthermore depends on the charging energy Uch, and the density of states D, assumed constant over this energy range: D δn = (EF − ECNL) (8.17) 1 +Uch · D

Level Broadening, Potential Proﬁle and η-Model

It is evident that the strength of coupling of the molecule to the contacts is important in determining the current flow - the stronger the coupling, the larger the current. A useful quantitative measure of the coupling is the resulting broadening Γ of the molecular energy levels, which can also be related to the life time τ of an electron in the molecular level: Γ = τ/h¯. The broadening from the two contacts add to the total broadening: Γ = Γl + Γr. Another very important factor is the voltage profile across the molecular conductor. At equilibrium, the entire system has a common Fermi energy EF which is equal to the electrochemical potentials µl and µr in the two contacts. Applying a voltage Vappl across the structure causes the levels µl and µr to split by Vappl: µl −µr = Vappl. However, the position of µl,r with respect to the molecular level and the exact potential profile remains unknown. It is often convenient to do a one-parameter characterization of the profile of the applied potential inside the molecule using a voltage division factor η. This method is sometimes denoted as the η-Model. Then, taking the molecular level as reference, the chemical potentials can be written as: µl = EF − ηeVappl and µr = EF − (1 − η)eVappl. If the molecule is (energetically) halfway between the contacts it seems appropriate to choose η = 0.5. If furthermore the molecule is highly polarizable, then the potential profile could be flat inside the molecule (cf. figure 8.5). Throughout this thesis η = 0.5 was assumed with a potential profile of figure 8.5 A.

h =0.5 eVappl h =0 eVappl

0 0 metal molecule metal metal molecule metal

Figure 8.5: Illustration of the voltage division factor η for a highly polarizable molecule. 8.1 Molecular Conductance Theory 113

One-Level Model

A current through a molecule can be calculated from a simple sequential picture with one molecular energy level EMol (cf. ﬁgure 8.6). If this energy level EMol was in equilibrium with the left contact then the number of electrons Nl occupying the level would be given by:

Nl = 2(for spin) f (EMol, µl) (8.18) while if it was in equilibrium with the right contact the number would be:

Nr = 2(for spin) f (EMol, µr) (8.19) where: 1 f (EMol, µ) = ³ ´ (8.20) 1 + exp EMol−µ kBT Under non-equilibrium conditions the number of electrons N will be somewhere in between

Nl and Nr and we can write the net current at the left junction as:

eΓ I = l (N − N) (8.21) l h¯ l and that of the right junction as: eΓ I = r (N − N) (8.22) r h¯ r The current is the rate of an electron transfer from the contact into the level times the free

“space” for the electron. Steady state requires Il = Ir so that:

Γ f (E , µ ) + Γ f (E , µ ) N = 2 l Mol l r Mol r (8.23) Γl + Γr 2e ΓlΓr Il = Ir = I = ( f (EMol, µl) − f (EMol, µr)) (8.24) h¯ Γl + Γr

rate:electr./sec.

Gl/h Gr/h ml

E Mol m r Figure 8.6: Illustration of the one level conduction model. The molecular level is ﬁlled from the left side metal molecule metal and empties into both sides. 114 Fundamentals of Molecular Conduction

This is nothing else than the Landauer conductance formula (equation 8.4) where the transmission Tt is identiﬁed as the coupling to the contacts ΓlΓr/Γl + Γr, and including the energy of the molecular level.

Charging Effects To treat charging effects, i.e. a (partial) “materialization” of electrons on the molecule leads to a shift in molecular orbital energy, a potential USC due to the change in number of electrons on the molecule from the equilibrium value 2 f (EMol,n,EF ) has to be added:

USC = Uch(N − 2 f (EMol,N,EF )) (8.25)

Then the molecular level EMol is let to ﬂoat up or down by this potential: EMol = EMol,N +USC. This has to be done in a self-consistent manner as the number of electrons depends on the molecular level energy and hence also USC.

Level Broadening

The broadening of the discrete level EMol can be included by replacing the discrete level with a Lorentzian density of states D(E):

1 Γ D(E) = 2 2 (8.26) 2π (E − EMol) + (Γ/2)

This modiﬁes equations 8.23 and 8.24 to: Z ∞ Γ f (E , µ ) + Γ f (E , µ ) N = 2 dE D(E) l Mol l r Mol r (8.27) −∞ Γl + Γr Z ∞ 2e ΓlΓr I = dE D(E) ( f (EMol, µl) − f (EMol, µr)) (8.28) h¯ −∞ Γl + Γr

Coulomb Charging and Coulomb Blockade To include a qualitative picture of Coulomb charging in this one-particle picture it is necessary to distinguish between spin-up (↑) and spin-down (↓) electrons. This can be viewed as the splitting of the molecular level into two levels, one for spin-up, one for spin-down. The charging then applies separately to both levels, so equation 8.25 has to be replaced by:

EMol,↑ = EMol,equ +Uch(N↓ − f (EMol,equ,EF )) (8.29)

EMol,↓ = EMol,equ +Uch(N↑ − f (EMol,equ,EF )) (8.30) 8.1 Molecular Conductance Theory 115

Whether the molecule-metal coupling is strong enough for this to occur depends on the relative magnitudes of the single electron charging energy (U) and energy level broadening Γ. As a rule of thumb, if Uch >> Γ, we can expect the structure to be in the Coulomb Blockade (CB) regime characterized by integer charge transfer; otherwise it is in the Self-Consistent Field (SCF) regime characterized by fractional charge transfer [146].

Shapes of Molecular Current Voltage Characteristics

Conductance Gap Usually, molecular current voltage characteristics show a more or less pronounced conductance gap at low bias voltages followed by a strong increase in current at higher voltages. From the simple model described in the previous section, the conductance gap can be understood qualitatively. As is shown in ﬁgure 8.7, a larger distance from the molecular level to the metal Fermi energy results in a larger conductance gap. It is important to understand that the conductance gap cannot be identiﬁed with the HOMO-LUMO gap, as is often done in literature, but with the distance from the closest molecular level to the Fermi energy of the electrodes.

Inﬂuence of Temperature and Broadening The coupling of the molecule to the electrodes, and an increase in temperature lead to a broadening of the molecular level. This in turn causes a “smearing out” of IV- and GV-characteristics, as is illustrated in ﬁgure 8.8.

Inﬂuence of Charging

30µ

400µ

20µ

300µ

10µ

0 200µ

-10µ Current [A] Current 100µ

-20µ Conductance [A/V] Conductance

-30µ

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

Bias Voltage [V] Bias Voltage [V]

Figure 8.7: Inﬂuence of the molecular level energy on IV- (left) and GV-characteristics (right). The two curves are calculated for EF −EMol = 0.5 eV (dashed), and EF −EMol = 1 eV (dotted). Other parameters were: Γl = Γr = 0.1, T = 77 K, and Uch = 0 eV. 116 Fundamentals of Molecular Conduction

30µ 150µ

20µ

100µ

10µ

50µ

-10µ Current [A] Current

-20µ Conductance [A/V] Conductance

-30µ

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

Bias Voltage [V] Bias Voltage [V]

Figure 8.8: Inﬂuence of temperature and broadening on IV- (left) and GV-characteristics (right). The curves are calculated for T = 77 K (dashed), and T = 300 K (dotted and solid). In the solid curve the broadening of the level was explicitly taken into account with an Lorentzian energy proﬁle. Other parameters were: Γl = Γr = 0.1, EF − EMol = 0.5 eV, and Uch = 0 eV.

The charging of the molecule due to electron transfer from or to the electrodes causes the molecular level to shift in energy, thereby, hampering a further electron transfer. The effect of the charging is comparable to the broadening discussed above, however, it changes the shape of IV- and GV-characteristics in a different manner. Figure 8.9 illustrates one example.

8.1.6 NEGF Formalism and Extended Hückel Theory

In contrast to the above described one-level model, real molecules typically have multiple levels that often broaden differently and overlap in energy. Therefore, a formalism is needed that can

30µ 150µ

20µ

100µ

10µ

50µ

-10µ Current [A] Current

-20µ Conductance [A/V] Conductance

-30µ

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

Bias Voltage [V] Bias Voltage [V]

Figure 8.9: Influence of charging effects on IV- (left) and GV-characteristics (right). The two curves are calculated for Uch = 0 eV (dashed), and Uch = 1 eV (dotted). Other parameters were: EF −EMol = 0.5 eV, Γl = Γr = 0.1, and T = 300 K. The broadening of the coupling was not taken into account. 8.2 Molecules of Interest and Deposition Technique 117 do justice to multiple levels with arbitrary broadening and overlap. Such a formalism can be found in the Non-Equilibrium Green’s Function (NEGF) method. A description of the NEGF formalism is beyond the scope of this thesis, please refer to literature for a proper introduction (e.g., [146, 147, 162]). A simple, yet powerful technique to determine the energy levels of molecule, electrodes and their broadening and overlap is the Extended Hückel Theory (EHT). In section 2.4.2 a short introduction into the calculation of molecular properties was already given. The standard Hückel theory (HT) is a semi-empirical method based on the LCAO2 approach. It applies some heavy simplifications on the multiple particle Schrödinger equation which is the starting point for all quantum chemical methods: (1) The Born-Oppenheimer approximation, which assumes the behavior of electrons can be studied in a field of frozen nuclei. (2) Then, HT only takes the π-electrons into account. To do so, the molecule is constructed using the nuclei which are connected by σ-bonds. The π-orbitals which are suitable to build π-bonds are then used for the LCAO-method. (3) A further simplification is the disregard of overlap integrals. In EHT, which is an extension to the standard Hückel theory, overlap integrals are taken into account, as well as the σ-orbitals. See [163] or standard textbooks on quantum chemistry for further details. EHT is known to shift energy levels to negative values, e.g., for the biphenyldithiol molecule by approx. 5-6 eV [146]. However, the relative distances of electrode and molecular levels seem to be consistent with advanced techniques [146], therefore, a use of EHT seems justified to obtain a first guess of molecular conduction characteristics. All calculations on IV characteristics of molecules presented in this thesis were done with HückelIV3 which applies EHT and the NEGF formalism [164].

8.2 Molecules of Interest and Deposition Technique

A major advantage of molecular electronics compared to standard silicon technology is the “perspective that the electronic properties of a device may be adjusted by design of the chemical structure” [14]. Both, chemical structure and electronic transport properties strongly depend on each other, and might further be tuned by external stimuli, e.g., electric or magnetic ﬁelds. Thereby, a whole set of functions could be embedded in a circuit by an appropriate choice of active molecules. This section gives a short introduction into the required molecular structure for conductance measurements performed in this thesis.

2Linear Combination of Atomic Orbitals, e.g., see [163] 3freely available at www.nanohub.org 118 Fundamentals of Molecular Conduction

8.2.1 Required Molecular Structure

A molecule suitable for conductance measurements in hybrid molecular electronic (HME) devices has to fulﬁll mainly two requirements: (1) It must connect to the inorganic electrodes either by covalent bonds or by van der Waals interaction, and (2) it must comprise an electronic function, the simplest being just a conducting wire. For good current carrying properties of the hybrid electrode - molecule system a covalent link is desirable to allow for maximum overlap of molecular and electrode wave functions: If the molecule of interest comprises a conductive inner part, and is connected to metal electrodes, then a short distance between molecule and electrode yields a hybridization of inner and outer extended wave functions, hence, a common electronic wave function which extends over the whole junction. The most prominent, and most investigated link so far is the bond between a thiol (sulfur) group on the molecule and a gold substrate ([14], and chapter 1.2), which was also present on the molecules used for this thesis.

8.2.2 Molecular Wires: Oligophenylenevinylene

For the electronic function of the molecule the most basic one was chosen: a molecular wire. This should result in a maximum effect comparing nanogap electrodes before and after placing the conductive molecules. Furthermore, rigid rod-like structures are of particular interest as their rigidity helps to place them between the electrodes [165]. Electron transport is expected to take part through the frontier orbitals of a molecule, i.e., highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO), as these should be closest to the Fermi levels of the electrodes. As was shown in the previous chapter, the conductance gap heavily depends on the distance between the electrode Fermi level and the closest molecular orbital. Therefore, it can be expected that for molecules with small HOMO-LUMO gaps good current carrying properties are observed. Promising candidates for such molecules are large, delocalized π- systems as the HOMO-LUMO gap decreases with increasing size of the delocalized system. Such π-systems can be built on carbon atoms with alternating sequences of single and double bonds, or aromatic building blocks such as phenyl rings. A prominent example for such a structure is polyphenylenevinylene (PPV) as shown in figure 8.10 [14]. Their shorter relatives are oligophenylenevinylenes (OPVs). The molecules used in this thesis were all-trans configured undecamers of 2,5-disubstituted p-phenylenevinylene with p-thioacetylphenyl endgroups, in the following denoted as OPV11. In addition, trimers (OPV3) and heptamers (OPV7) have been available (cf. bottom of figure 8.10), however, they have not been used for conductance measurements due to their smaller size. The 8.2 Molecules of Interest and Deposition Technique 119

Figure 8.10: Chemical structure of poly- phenylene-vinylene (PPV, top) and 2,5- disubstituted oligo-p-phenylenevinylene with p-thioacetylphenyl endgroups (OPV, bottom). Due to the alternating sequence of phenyl rings and single and double carbon bonds, electrons in π-bonds can extend over the whole molecule (= delocalized π-system). molecules have been synthesized by Dr. F. Scheliga in the group of Prof. Dr. E. Thorn-Csányi at the university of Hamburg who conducted a thorough investigation on substituted OPVs varying type and conformation of substituents and endgroups (e.g., [166, 167, 168]). For the present requirements of a long, rigid, and conducting molecule, they provided the undecamer which combines a defect-free structure, high solubility in organic solvents, rod-like structure, and mono-dispersity (equal length of all molecules). The solubility is mainly achieved by the additional side groups with distinguishes them from “normal” oligo-p-phenylenevinylenes. That these molecules indeed are able to build up a delocalized electron system was tested by extended Hückel simulations using HyperChem [169] (see ﬁgure 8.11). Thereby, also the length of the OPV11 molecule could be estimated being 8.5 nm measuring from sulfur to sulfur atom. The link to electrodes is accomplished by thiol groups at both ends which have been protected from oxidation by acetyl groups (R-C2H3O). These protection groups can either be removed before assembly, or left at the molecule during the assembly process, which was done during this thesis. Naturally, the adsorption characteristics are thereby changed to a certain extent.

8.2.3 Deposition of Oligophenylenevinylene Molecules

As deposition method the self-assembly technique already describe in chapter 1.2 was used. The deposition parameters for OPV assembly on gold and InAs surfaces were optimized by Dr. A. Hansen at the Walter Schottky Institut. He varied the solvent composition, concentration of solution, deposition duration, and deposition temperature. More details of the deposition parameters will be given at relevant positions in the text. 120 Fundamentals of Molecular Conduction

Figure 8.11: Chemical structure (top), HOMO (middle), and LUMO (bottom) of OPV11 molecules with simplified phenyl side chains. The molecule was first geometry optimized in HyperChem [169] with the built-in MM2+ force field. Then, it was energy optimized using the extended Hückel theory option. For HOMO and LUMO the orbital wave functions are visualized. Chapter 9

Experimental Techniques and Measurement Setup

The present work deals with the fabrication and characterization of nanometer spaced electrodes. This implies certain requirements on experimental setup and sample fabrication. In contrast to the ﬁrst part on GaAs biosensors, the sample layout which had to be developed for the nanometer spaced electrodes will be described at the appropriate position in the following chapters. In this chapter, the methods used for surface and electrical characterization will be brieﬂy introduced. Then, the examination tools suited for molecular layers will be presented, and in the last part the electrical setup which was built during this thesis will be explained.

9.1 Surface Characterization Methods

For the topographical characterization mainly two instruments were used during this thesis, the atomic force microscope (AFM), and the scanning electron microscope (SEM), which will be explained in the following.

9.1.1 Atomic Force Microscope

The AFM is an important tool to examine the surface of nanogap electrodes because of its height resolution down to the Ångstrom scale. It belongs to the family of Scanning Probe Microscopes (SPM). The central component of all SPM microscopes is basically the same: the height of a microscopic tip interacting with the sample surface is adjusted by piezoelectric elements. Images are taken by scanning the sample relative to the probing tip and measuring the deﬂection of the tip-carrying-cantilever as a function of the lateral position (see ﬁgure 9.1).

121 122 Experimental Techniques and Measurement Setup

In contrast to scanning tunneling microscopes, AFMs do not require conducting samples as no current is forced through tip and sample. The AFM key element is its microscopic force sensor, the cantilever, which is usually formed by one or more beams of silicon or silicon nitride. On one end of the cantilever is the atomically sharp tip pointing toward the surface. Tips can be obtained commercially with various aspect ratios and in different grades of sharpness, the best having tip end diameters down to 4 nm (e.g., SuperSharpSiliconTM tips from NanoWorld AG, CH). The lateral resolution of the AFM depends mainly on this tip radius whereas the piezo elements determine its vertical resolution reaching values better than 1 Å. For topographical imaging in the so called contact mode, the tip is brought into continuous contact with the sample and scanned over the surface. As the cantilever approaches the surface, it is bent by attractive and repulsive forces (van der Waals, electrostatic, magnetic or capillary forces). Usually, a laser beam combined with a multi segment photodetector detects the deflection of the cantilever (see figure 9.1). The deflection is then translated by a feedback loop to the piezoelectric scanner which moves in z-direction to keep the deflection constant. Typical forces experienced by the cantilever are between 0.1 and 100 nN. In the so-called TappingModeTM or non-contact mode, that can also be applied in liquid environments, the cantilever oscillates close to its resonance frequency, typically ≈ 300 kHz, and slightly “taps” the surface during scanning. Its advantage with respect to contact mode is the elimination of lateral shear forces. This enables TappingMode to image soft, fragile, and adhesive surfaces without damaging them. Fur- thermore, it is not as sensitive to contamination and distortions from the usually present water film on the sample surface. The interpretation of AFM images is not as straight-forward as desired. A rich variety of artifacts arise from the tip-sample interaction: An AFM image is produced by the convolution

Photo- Cantilever/Tip Figure 9.1: Schematic of the AFM op- detector Assembly erational principle. The tip on the can- Laser tilever scans across the sample and is deflected by surface forces. This is detected by the offset of a laser beam on a two- or multi-segment photodetector. The sig- Sample Feedback- nal is transmitted in a feedback loop to Loop Threeaxis the piezo element to modify the sample’s Piezoelectric elevation in order to maintain a constant Scanner cantilever deflection. The piezoelectric element also performs the x- and y- movement. 9.1 Surface Characterization Methods 123 of the real surface with the tip geometry. Therefore, an infinitely sharp peak on a surface would appear as a “round-shaped hill” in the topographical image. Figure 9.2 illustrates this effect of the tip-surface convolution and the consequences of varying tip radius on the obtained topographical image of a deep trench. Such a structure resembles the devices which were examined throughout this thesis. A comparably blunt tip of 10 nm diameter is not able to enter a deep 10 nm wide trench, therefore, it only produces a V-shaped image of the channel. However, a sharp tip enters the trench producing a U-shaped image. Nevertheless, the real topography is blurred by the tip scanning. As one can imagine, the extraction of the trench width from AFM images deems extremely difficult if the exact tip extensions are not known. Unfortunately, this is the situation one usually experiences in reality. A further complication is that the trenches observed in this thesis are expected to have rounded edges which makes a distinction between tip-induced “blurring” and real blunt structures almost impossible. All AFM measurements were conducted using a Nanoscope IIIa from Digital Instruments, Inc. (Santa Barbara, USA) in TappingMode. For most applications, SuperSharpSiliconTM can- tilevers purchased from NanoWorld AG, CH, were used. Their initial tip diameter is approx. 4 nm according to the supplier. However, the demanding task to measure structures at sample edges requires several tip-sample approaches until the desired region is found. This leads to a slight damaging of the tip, therefore, it must be expected that most images were produced with altered tip extensions, i.e., bigger tips. Few measurements were also carried out using standard tips with typical tip diameters of 10 nmThe˙ cantilever eigenfrequency was about 300kHz, scan sizes ranged from 10 µm x 10 µm down to 200 nm x 200 nm and typical scan rates were 0.5-1.5 Hz. All images were processed with a flattening algorithm using either the Nanoscope

10nm 5nm

10nm 10nm Figure 9.2: Schematic illustrating the AFM tip-surface convolution. The left part demonstrates the imaging of a deep, 10 nm wide trench by a semicircular tip of 10 nm diameter. The full circles depict the measured topographical image resulting in a V-shape. The right part shows the effect of a 5 nm diameter tip which results in a U-shape image. 124 Experimental Techniques and Measurement Setup software or the freely available WSxM software1. Devices thought for AFM measurements were never mesa patterned as it was impossible to find the nanogap region in AFM as the distance between fingers was large compared to the finger width.

9.1.2 Scanning Electron Microscope

The operational principle of a SEM is comparable to an optical microscope. A beam is emitted from a source, collected by a combination of condenser aperture and lens, and then focused on the sample by an objective lens. The main difference, of course, is the use of an electron beam instead of optical light (see figure 9.3). Therefore, the lenses have to work electromagnetically: electrons are deflected by specially designed magnets. The focal lengths of the lenses are tunable via the currents driving the magnets. An additional device which is used in an SEM is a deflecting coil which can move the beam on the sample surface. SEMs can be classified according to their source type: There are instruments using heated

filaments as an electron source, such as tungsten filaments or LaB6 tips, whereas more advanced SEMs use field emission sources, where the work function for electrons to leave the source crystal is reduced by an external electrical field. The latter type reaches the best resolution as the source size is as small as 5-20 nm [163]. When the electron beam hits the sample, several processes occur: Electrons are backscat- tered elastically or inelastically, by the electron beam ionized atoms emit characteristic X-rays while filling up their core shells, part of them transfer their energy to Auger electrons which are also highly element specific, and furthermore, so-called true secondary electrons are excited by the initial electron beam. These electrons are usually used for the spatial imaging. As electrons are used to illuminate the sample and also to create the image, major difficulties arise when the sample is becoming charged. Especially for semiconductors or insulators the energy of the primary electrons (usually 1-30 keV) has to be adapted cautiously. Sometimes a deposition of a very thin metal film alleviates the situation, however, the surface structure might be altered by the deposition process. All SEM observations during this thesis were conducted using a Hitachi S-4000 field emission SEM. With the S-4000 magnifications up to 300’000x are possible. Typical acceleration voltages for the primary electrons were 20-30 keV and typical working distances between sample and detector were 5-20 mm. Samples were usually mechanically mounted on aluminum holders thereby ensuring good electrical contact. A peculiar characteristic of the available SEM was the presence of varying noisy electromagnetic fields which led to wave-like distortions at

1http://www.nanotec.es/download.htm 9.2 Characterization of Molecules and Molecular Layers 125

Figure 9.3: Schematic beam path of a SEM. high magniﬁcations. However, by rotating the image before starting the data acquisition, most distortions could be avoided. Nevertheless, this averaging process resulted in a loss of certain details (see ﬁgure 9.4).

9.2 Characterization of Molecules and Molecular Layers

For a fully functional hybrid molecular electronics device it is essential to deposit molecules of interest on and between the nanogap electrodes. The necessary optimization of the grafting process for the OPV11 molecules used in this thesis was performed by Dr. A. Hansen at the Walter Schottky Institut. As his studies are of great inﬂuence for the present thesis, part of his work will be presented in chapter 11 and the tools used to characterize the molecules and their layers on substrates will be introduced in the following.

Figure 9.4: Illustration of the inﬂuence of external ﬁelds on the SEM characterization. The right image was taken after turning the scan direction by 90°. The focus was also slightly altered. 126 Experimental Techniques and Measurement Setup

9.2.1 Ellipsometry

Ellipsometry is a versatile tool to determine layer thicknesses of multilayer systems, and it was used to examine the success of the assembly process of OPV molecules on planar substrates. As it is an optical measurement method the layers under examination have to be at least partially transparent. For thin (<10 nm) layers this is always the case, even for metallic layers. An ellipsometer consists of a light source, a polarizer P and an analyzer A which measures the polarization after reflexion of the light beam on a sample (see figure 9.5). The beam hits the sample under an angle φ with respect to the surface normal, and is then reflected at the surface and all interfaces inside the sample (provided the beam is not absorbed). The reflection is polarization dependent, i.e., the polarization of the reflected beam is changed with respect to the incident beam. This change depends both on thicknesses and refractive indexes of each layer. This makes a determination of the components of a multi-layered structure possible. Naturally, the more complex the structure is, the more theoretical multilayer constructions exist that could explain the observed polarization change. The polarization is measured using an analyzer - detector combination in terms of ellipsometric angles ∆ and Ψ which are defined by the complex reflection coefficients R for p-, and s-polarized light: tanΨ · exp(i∆) = Rp/Rs. Various methods to measure the polarization exist. E.g., in the often used null ellipsometry, the angles of polarizer, compensator, and analyzer are adjusted in such a way that the reflected light intensity in the detector vanishes. As light sources lasers or white light sources are available. Lasers are usually used in single wavelength ellipsometry, whereas white light sources are necessary for spectroscopic ellipsometry. The polarizer is an optical element which transforms a light beam of arbitrary polarization into a linear polarized beam. When a beam passes the polarizer, the field component parallel to the optical axis is not influenced whereas the component perpendicular to the optical axis is eliminated. A polarizer which is used to analyze the polarization of a light beam is called an analyzer. A compensator is often found in ellipsometers. It is an anisotropic optical element with a fast and a slow optical axis. Therefore, the phase of one polarization component is changed

Laser

Detector ll u n P C f A Figure 9.5: Schematic operational principle of null-ellipsometry. A: Analyzer, C: Compensator, Sample P: Polarizer. 9.2 Characterization of Molecules and Molecular Layers 127 with respect to the other. A 90° compensator or λ/4 element shifts the phase of the s-polarized light component by 90° without altering the p-component phase. Thereby, a linear polarized beam with equal p- and s-polarized components is transformed into a circular polarized light beam and vice versa. Compensators are critical elements of an ellipsometer. Due to heating caused by the passing laser beam the compensator properties might change which introduces systematic errors in the measurement. Various ellipsometer types try to eliminate this problem with different techniques. E.g., the “Minsearch Algorithm” implemented in the EL X-02C ellipsometer from “Dr. Riss Ellipsometerbau” avoids the compensator and instead uses an analyzer mounted on a high precision stepping motor. Measurements were performed using ﬁrst a standard null-ellipsometer and later the EL X- 02C. Both ellipsometers apply HeNe lasers (632.8 nm) as light sources, and the incident angle in all measurements was 70°.

9.2.2 UV-VIS Spectroscopy

UV-VIS spectroscopy measures the absorption or transmission of a substance of interest for light in the visible (VIS) or near UV range. It can be used to gain insight into the electronic structure of materials and was used to estimate the HOMO-LUMO gap of OPV molecules which have been available for molecular conductance measurements. In UV-VIS spectroscopy valence electrons in the illuminated molecules of interest are moved to an excited state. Electrons in closed shells or σ-bonds require too high excitation energies to absorb in the UV-VIS region. Non-binding electrons or electrons participating in π-bonds can be excited more easily. The corresponding excitations are summarized in ﬁgure 9.6. UV absorption bands are usually not sharp lines but broad bands due to included vibrational or rotational states. Furthermore, interactions with the surrounding solvent and hydrogen bonds effectively broaden the absorption band. In highly conjugated systems such as OPV molecules, the HOMO-LUMO transition is the most prominent low-energy peak in the adsorption band as it is the easiest excitation of an electron in a ground-state molecule.

p* n-p* n E p-p*

p Figure 9.6: Schematic illustrating the excitation of a non- bonding (n) and a π-Orbital to the ﬁrst excited state (π∗). 128 Experimental Techniques and Measurement Setup

9.3 Electrical Setup

9.3.1 Low-Temperature Conductance Measurements

All nanogap electrodes presented in this thesis use a semiconductor structure either as a support for metal electrodes or as the functional unit to contact molecules. At room temperature semiconductors show relatively high charge carrier densities, hence, leakage currents have a significant influence on high impedance measurements. As the resistance of molecules can be in the GΩ range a minimization of leakage currents through the semiconductor structure is mandatory, therefore, measurements should be carried out at low temperatures. This also helps to sharpen molecular features, although, the influence of temperature on the broadening of molecular levels is small compared to charging effects or broadening due to the contacts (see section 8.1.5). Further requirements for the measurement setup were: (1) Suitability for a subsequent characterization of multiple nanogap devices, (2) low noise, and (3) temperature control. To fulfill all requirements, a new measurement setup appropriate for helium and nitrogen dewars was designed and built together with S. Strobel (see figure 9.7, and [170]). The design was mainly adapted from the group of M. Grayson at the Walter Schottky Institut. It consists of a long tube with a sample stage at one end and its other end connected to a cross piece with standard iso flange. The other openings of the cross piece are used for an electrical feedthrough and for a connection to a rotary evacuation pump. For evacuation the whole tube is encap- sulated by another tubing. The requirement of multiple device measurements was fulfilled by implementing 16 separate, individually addressable channels. Low noise measurements were enabled by maintaining a shielding as close as possible to the sample in combination with a

Figure 9.7: Photograph of the electrical measurement setup. The magnification shows the sample stage with built-in sample. 9.3 Electrical Setup 129 highly flexible grounding architecture. This included the design of a “switch box” which allows for the separate grounding of signal and shield leads (see figure 9.8). Temperature control was implemented using a LakeShore 331 temperature controller in combination with a high power resistor on the sample stage. However, manual temperature control by inserting or extracting the measurement tube from the dewar proved to be more efficient. A calibrated Si diode was used to measure the temperature. And to maintain maximum versatility, most setup components were built as easily exchangeable modules. The nanogap devices itself were connected to the measurement setup by bonding them to standard chip carriers as shown in the magnification of figure 9.7.

9.3.2 Electrostatic Trapping

Electrostatic trapping is a powerful method to place nanosized objects between nanogap electrodes. It was first introduced by Bezryadin et al. [171], and later modified by Amlani and co-workers [172]. To trap a particle between two nanometer separated electrodes, the nanogap device is immersed in a diluted colloidal solution of metallic or polarizable particles. Then, an oscillating voltage is applied to the electrodes with a large series resistor included in the circuit (compare figure 9.9). The non-uniform alternating electric field between the electrodes attracts the particles due to a dielectrophoretic force toward the field maximum. This maximum is usually on the shortest connection line between the electrodes. Once a particle is trapped between the electrodes electrically bridging the gap, the trapping process should self-terminate as the voltage drop now occurs mainly at the series resistor and the electric field between the electrode vanishes. However, it is recommendable to monitor the trapping to be able to stop the process manually to prevent the agglomeration of further particles. This can be accomplished by an

tosample toinstruments signal channel1 channel1 shield channel2 channel2

BNC switchable connector channel

channel ground selector switches

Figure 9.8: Schematic of the switch box. It allows for the separate grounding of shield and signal lead for each of the 16 channels (only two are shown). Furthermore, a selector may be used to switch each channel-shield combination to a separate output. 130 Experimental Techniques and Measurement Setup oscilloscope as was done in this thesis, which at the same time can act as the series resistor [110]. Electrostatic trapping was used to test the electrical functionality of the nanogap device. It was expected to observe a clear change of the IV characteristics of a device before and after trapping a conducting gold nanoparticle. Certain problems were caused by the leakage currents which are driven through the colloidal particle solution due to the necessary applied frequencies in the kHz range. However, by optimizing trapping conditions a successful capture of single gold particles was possible (see section 10.5 on page 145). The optimization included the design of a special electrical switch box with very short cable lengths to minimize stray capacitances. Furthermore, it provided shielding by a Faraday cage like environment and allowed for trapping experiments in darkness to minimize leakage currents through the supporting semiconductor structure.

Figure 9.9: Illustration of the trapping process. First, the voltage drops between the nanogap electrodes (indicated by the wide arrow in the left image), and a polarizable particle is attracted toward the maximum ﬁeld strength. After the particle is trapped electrically bridging the gap (right image), the voltage drop occurs at the series resistor (indicated by the arrow), and the trapping stops. Chapter 10

Fabrication and Characterization of a Co-Planar Nanogap Device

As was already introduced in section 7, nanogap electrodes based on supporting AlGaAs-GaAs heterostructures are fabricated making use of a metal film rupture at a selectively etched trench. The trench width is defined by a preceding MBE growth. In this chapter a more extensive description of the nanogap electrode fabrication process will be given, however, to achieve a better comprehensibility, too specific technical details are omitted and instead listed in appendix A.5. After the description of electrode fabrication, several optimization processes are presented, followed by a topographical and electrical electrode characterization. This includes the test of electrical functionality by electrostatic trapping of gold nanoparticles. Typical device failure mechanisms are discussed as well, and the chapter is concluded by the work on nanogap electrodes with electrically active semiconductor layers.

10.1 Nanogap Electrode Fabrication

The whole fabrication process of co-planar metallic nanogap electrodes based on AlGaAs-GaAs heterostructures is schematically illustrated in ﬁgure 10.1. Roughly six process groups can be distinguished: MBE growth, mesa etching, contact pad metalization, cleavage, selective etching, and electrode metalization. For low temperature measurements a further packaging step would be required, and a possible molecule deposition process will be described in the next chapter. In the following, each process step is explained in detail:

MBE Growth Starting material for the AlGaAs-GaAs heterostructure are epi-ready (001) GaAs wafers. For

131 132 Fabrication and Characterization of a Co-Planar Nanogap Device

Figure 10.1: Schematic of the fabrication process for planar nanogap electrodes. a) Molecular Beam Epitaxy (MBE) grown AlGaAs/GaAs heterostructure with nanometer thin GaAs layer. b) Finger like structure obtained by conventional microstucturing applying optical lithography and mesa etching. c) Device with metallic leads deﬁned by a standard lift-off process. d) Atomically smooth cleavage along crystal plane. e) Selective etching of the GaAs layer (marked by arrows). f) Full device after thin ﬁlm metalization for a following deposition of molecules bridging the gap region (sketched in the inset). The two metallic leads connected to bottom and top electrode allow for an electrode operational test.

the lower electrode a 500-1000 nm thick Al0.3Ga0.7As layer is MBE grown on the semi-insulating substrate followed by a thin GaAs layer which later defines the electrode distance. In this thesis layers of 5, 6, 10, 20 and 50 nm thickness were used. Then, a 300-500 nm thick Al0.3Ga0.7As layer is deposited which later acts as a support for the top electrode. The whole MBE grown structure is illustrated as figure 10.1(a). Usually, the MBE stack is covered by a 10 nm thick GaAs cap layer to prevent AlGaAs oxidation (not drawn in the figure as it will be removed in the next process step). The thicknesses of the AlGaAs layers are set by design needs: The thick bottom layer is necessary to reliably stop the mesa etching process in the AlGaAs layer (see below). And the only slightly thinner top electrode layer prevents a bridging of the nanogap by the contact pad metalization which tends to overlap the sample edge after cleavage.

Mesa Etching After MBE growth, the wafer is cleaned from the gallium on its backside1, and it is cut into approx. 6 x 4 mm large pieces. Then, a lateral patterning of the heterostructure is carried out by conventional optical lithography. This step is necessary for an integration of a larger number of nanogap devices on one chip. To do so, narrow (approx. 30 µm wide) ﬁnger-like structures are

1gallium is used to fix the wafers to the tantalum holder in the MBE chamber. 10.1 Nanogap Electrode Fabrication 133 patterned using standard optical lithography and wet chemical etching. First, the thin GaAs cap layer (not shown in figure 10.1) is removed by a citric acid based solution (CAS, please refer to appendix A.5 for details). Then, the sample is spin coated with photoresist, soft baked, and the desired structure transferred via UV illumination. After development and a further hard bake, the mesa etching is performed applying a phosphoric acid based etch (compare figure 10.1(b)). The etch is stopped in the second AlGaAs layer, usually in a depth of approx. 850 nm from the wafer surface. This is controlled by profilometer (Dektak) measurements.

Contact Pad Deposition As connection to an external electrical circuit metallic contact pads are deposited on the sample using optical lithography and a standard lift-off process. The contact pads comprise a thick gold layer (100-200 nm) on a thin titanium (sometimes also chromium) adhesion layer (≈10 nm). As deposition technique standard electron beam evaporation is applied. A schematic of the device after these process steps is illustrated in figure 10.1(c). The deposition of two contact pad fingers on one mesa finger allows for the electrical testing of both top and bottom electrodes as will be explained later. In contrast to various other nanogap fabrication techniques, the later electrode region is still protected inside the heterostructure from any possible contamination!

Cleavage and Selective Etching By cleaving the substrate, an atomically flat and perfectly clean (110) surface of the AlGaAs- GaAs sandwich structure is exposed as shown in figure 10.1(d). This is usually done by scribing a mark at one end of the sample with a diamond needle and then applying a shear force with two tweezers. The size of the samples after cleavage is approx. 3 x 4mm which is suitable for standard chip carriers. After that, the embedded GaAs layer is etched selectively versus the outer AlGaAs layers using the CAS etch for 10-40 s as is depicted in figure 10.1(e). The necessary etching duration heavily depends on the width of the sacrificial GaAs layer. For 20 nm layers, an etching time of 10-30 s proved sufficient to reproducibly fabricate working samples. However, for 5 nm GaAs layers, the etching duration had often to be increased up to 40 s to obtain a reasonable yield of working devices. To minimize any contamination sources the cleavage can even be done in-situ in the etching solution. The selectivity of the etch is very high (115:1 for Al0.3Ga0.7As vs. GaAs; [173]), therefore the roughening of the AlGaAs surface due to etching is comparably small maintaining the advantages of the smooth cleavage facet. 2 E.g., AFM characterizations revealed a root mean square (RMS) roughness RRMS for a freshly cleaved GaAs plane of 0.08 nm, and for a 30 s CAS etched AlGaAs layer of 0.18 nm. q N 2 2 ∑i (zi−z¯) RRMS is a measure for the roughness of a surface having N points of height zi: RRMS = N−1 with the N ∑i=1 zi mean height defined as z¯ = N . 134 Fabrication and Characterization of a Co-Planar Nanogap Device

Nanogap Electrode Deposition After etching, the electrode forming thin film metal layer is evaporated perpendicularly to the cleaved surface as is illustrated in figure 10.1(f). The electrical contact between the top and the bottom electrode is interrupted by the rupture of the metal film at the etched trench edges. Thereby, the two nanogap electrodes are separated. The two contact pad fingers on the mesa allow for a check of electrode operation: As the metal is evaporated perpendicular to the cleavage plane, a good conduction among top contact pads (or bottom pads) can only be caused by a proper working thin metal film of top (or bottom) electrode on the cleavage facet. A good conduction is therefore a strong argument for proper working electrodes. The gap size between the electrodes is mainly determined by the layer sequence set during MBE growth, the minor roughening and widening of the AlGaAs-GaAs interface due to non-perfect selective etching, and the lateral roughness of the thin film metal layer. A change in the electrode distance by the metal thickness itself seems negligible as the evaporation is perpendicular to the cleavage facet. In the present thesis electrodes could be fabricated on heterostructures with thicknesses of the embedded GaAs layer down to 5 nm.

Bonding and Packaging After a successful electrical test of electrode operation the samples were glued into standard 8-pin or 20-pin chip carriers, usually, by double side adhesive tape (see also appendix A.5.6). This is necessary for measurements in the low temperature experimental setup (see ﬁgure 9.7). The electrical contact from sample to chip carrier was accomplished by standard gold wire ball bonding.

10.2 Optimization of Process Parameters

Besides MBE growth, the two most critical process steps in nanogap electrode fabrication (based on AlGaAs-GaAs heterostructures) are the selective etching process and the electrode metal deposition. The etching process in great part determines the yield of working samples as etch depth and etch profile influence the rupture of the metal film. Furthermore, due to a small widening of the gap because of non-perfect selective etching it affects the final distance of the nanogap electrodes. For the metal deposition, a minimum thickness of a few nanometer is obligatory to ensure proper conducting behavior. However, regarding the film rupture, the metal layer should be as thin as possible. Furthermore, the lateral roughness of the metal film at the trench edges determines the final electrode distance and influences the yield of working samples. Therefore, a large part of the invested work dealt with the optimization of these two process steps. 10.2 Optimization of Process Parameters 135

10.2.1 Choice of Electrode Materials

As electrode material, three different metal systems were examined: a palladium - gold alloy (PdAu, 20:80), a titanium - gold structure (Ti/Au), and a chromium - gold system (Cr/Au). In the following, the process of material selection and thickness optimization will be described. For pure gold layers it was assumed that during evaporation the metal atoms start to cluster resulting in rough surfaces. For thin PdAu films better characteristics in terms of roughness were expected3. Therefore, the PdAu system was examined first. As an initial step, thin PdAu layers were characterized in terms of roughness using AFM measurements on PdAu coated cleavage facets, and in terms of electrical conductivity by standard Hall-bar structures. The Hall-bar like structures were patterned with optical lithography and a standard lift-off process on epi-ready GaAs wafers. The AFM was also used to determine the thickness of the PdAu layers as the evaporation machine was not calibrated for this alloy. The roughness analysis was performed on 1 µm x 1 µm large regions. Results for thin PdAu films of various thicknesses are summarized in figure 10.2. For the electrical conductivity it was found that a film thickness greater than 6 nm results in sheet resistances in the order of 200-300Ω/¤. Hence, the resistance in a nanogap device which is caused by the electrodes itself can be estimated being in the 10kΩ range. This is sufficiently conductive for electrical measurements on molecules as the expected resistance for

3These assumptions were mainly based on private communications, however, similar remarks are also found in various publications [174, 175, 35, 176].

1.0

15 ] 2

0.8 /squ.]

5 m

0.6 4 100/µ

0.4

10 0.2 RMSroughness [nm] Peakdensity [

1 SheetResistance [

0.0

0 5 10 15 20 0 5 10 15 0 5 10 15

Thickness [nm] Thickness [nm] Thickness [nm]

Figure 10.2: Surface and electrical characterization of thin PdAu layers on epi-ready GaAs wafers. Left: Sheet resistance of thin PdAu layers measured on Hall-bar like structures patterned by optical lithography and lift-off on standard GaAs wafers in 4-point geometry. The error bar of the left data point exceeds the lower graph boundary. Middle: RMS roughness of 1 µm x 1 µm large regions on PdAu coated cleavage planes analyzed by AFM. Right: Peak density of peaks higher than 1 nm above the surface mean in 1 µm x 1 µm large areas. 136 Fabrication and Characterization of a Co-Planar Nanogap Device molecules or molecular layers typically exceeds 1MΩ as reported in literature [151, 152, 177]. For the surface roughness however, the results were not as good as expected. For all PdAu layers a RMS roughness close to 0.5 nm was measured with a minimum for 10 nm thick films. A possible explanation for this minimum might be that for thinner layers the metal film is still non- continuous whereas for thicker layers already grain formation occurs. Also the peak density, illustrated in figure 10.2 for peaks higher than 1 nm above the surface mean, was unexpectedly high. This peak density was taken as a guess for the expected lateral roughness of the electrodes at the trench edges which influences the yield of working samples and the electrode separation. Because of the poor roughness outcome for PdAu the next material system was examined: Ti/Au. Another reason to switch to Ti/Au was its success in trapping experiments (see section 10.5) where PdAu did not give reproducible results. Topographical AFM characterizations on thin Ti/Au films surprisingly showed better roughness values than PdAu. The best values were found for 3 nm/7 nm Ti/Au with a typical example displayed in figure 10.3. Here, the RMS roughness of the Ti/Au coated cleavage plane (left panel) was RRMS = 0.13 nm which is very close to the value obtained for a freshly cleaved surface of RRMS = 0.08 nm (right panel). The maximum corrugation of the Ti/Au film was below 1.1 nm. Typically, RMS roughness values varied between 0.1 and 0.5 nm for layers between 2 nm/6 nm and 5 nm/15 nm Ti/Au. The conductance was not tested by 4-point measurements on Hall-bar like structures, but measurements on nanogap devices showed lead resistances of 0.5-30kΩ similar to the values estimated for the PdAu devices. The Cr/Au system was rarely used, however, some AFM characterizations showed similar roughness values as for the Ti/Au system. E.g., for 1 nm/4 nm Cr/Au a roughness of RRMS = 0.2 was determined.

Figure 10.3: AFM characterization of a thin titanium - gold system. Left: Topographical image of a cleaved surface after deposition of 3 nm Ti and 7 nm Au. The RMS roughness is 0.13 nm. Right: For comparison, a topographical AFM image of a freshly cleaved facet. RMS roughness was 0.08 nm. 10.2 Optimization of Process Parameters 137

10.2.2 Etching Duration and Metal Layer Thicknesses

As was already briefly mentioned, the fabrication of working nanogap devices becomes more and more demanding with decreasing electrode separation. Therefore, a proper adjustment of selective etching duration in combination with the choice of electrode metal layer thickness was obligatory. To do so, etching durations and film thicknesses were varied and subsequently nanogap devices were classified in electrical tests as illustrated in figure 10.4: The resistance between top electrodes (left panel), bottom electrodes (center panel), and between top and bottom electrodes (right panel) was measured at room temperature. A device was defined as working if the resistance between either top or bottom electrodes was below 10kΩ, and if the resistance between top and bottom electrode exceeded 10MΩ at room temperature. This lead to resistances higher than 10GΩ at liquid helium temperature (4.2 K), i.e., currents were below 100 pA at 1 V bias voltage which is the limit of the experimental setup.

The results for devices with 5 nm GaAs layer and 10 s selective etching in CAS are summarized in the column plot of ﬁgure 10.5. On one hand, for very thin metal layers (2.5 nm/5 nm Ti/Au) no sufﬁciently good conductivity was measured in between top, and in between bottom electrodes. On the other hand, for comparably thick layers (5 nm/15 nm Ti/Au), the conductivity of bottom and top electrodes was satisfactory, however, the devices failed due to short circuits between top and bottom electrode. For 3 nm/10 nm Ti/Au all three requirements were met by some devices on one sample. Unfortunately, these parameter settings drifted over time and an increasing number of short circuited devices was observed. Therefore, the etching duration was prolonged, and at the same time the metal thickness decreased. Lately, best results were obtained for etching times of 30-40 s, and metal layers of 2 nm/6 nm - 3 nm/7 nm Ti/Au.

Figure 10.4: Experimental conﬁguration for the electrode operational test. a) Test of the upper electrode. b) Bottom electrode testing. c) Check of insulating behavior between electrodes. 138 Fabrication and Characterization of a Co-Planar Nanogap Device

Figure 10.5: Optimization of the electrode metal layer thickness. The percentage of working devices on one sample after 10 s selective etching in CAS and deposition of the electrode metal layer (Ti/Au) of given layer thicknesses. “Working” is deﬁned according to three categories as listed in the legend.

10.2.3 Summary

PdAu and Ti/Au as electrode materials were tested. Both showed very good conductivities already for very thin layers. Surprisingly, the Ti/Au layers were superior to PdAu layers in terms of smoothness, therefore, they were used for further device processing. Cr/Au layers were not tested systematically but seemed to have similar characteristics to the Ti/Au layers. Furthermore, metal layer thickness and selective etching durations were optimized. With decreasing sacriﬁcial GaAs layer thickness an increasing sensitivity of yield upon parameter settings was found. Lately, best results were obtained for etching times of 30-40 s, and metal layers of 2 nm/6 nm - 3 nm/7 nm Ti/Au.

10.3 Electrode Separation

A determination of the real electrode separation is very important as it determines whether molecules are able to bridge the gap region or not. The electrode separation is mainly influenced by the thickness of the sacrificial GaAs layer set during MBE growth, the widening of the etched trench due to non-perfect selective etching, and the lateral roughness of the thin film metal layer.

10.3.1 Surface Characterization

As surface characterization methods mainly AFM and SEM were available. Figure 10.6 displays a SEM micrograph of a device with 5 nm intermediate GaAs layer after a full process cycle which included 30 s selective CAS etching and the deposition of 3 nm/7 nm Ti/Au. The sample was tilted by 30° with respect to the surface normal during image capture to enhance the contrast between the gap and the electrodes. Both electrodes appear as smooth and flat 10.3 Electrode Separation 139 surfaces, and the electrode separation seems constant in the observed range. The gap region was identified as the horizontal bar in the image, and from its vertical extension an electrode separation of 8 ± 3 nm was calculated. The error is composed of the instrument specifications and an estimate value of the effect of a round-shaped edge on the contrast. An AFM characterization revealed more insight into the surface roughness of the electrodes. Figure 10.7 shows two typical images of devices with 20 nm GaAs layer (left panel), and 5 nm GaAs layer (right panel). Naturally, the characterization became increasingly difficult with decreasing GaAs layer thickness due to the AFM tip size: The smaller the gap becomes, the sharper the tip has to be in order to “see” the trench. As expected, the gap of the 5 nm device appears narrower than for the 20 nm device. Both samples show comparably flat surfaces with the 20 nm device having a smoother electrode surface with a RMS roughness of only 0.1 nm and a maximum corrugation below 1.2 nm on both sides of the gap. The 5 nm device is rougher with an RRMS value of 0.4 nm and a maximum corrugation of 3.4 nm. On one hand this is due to the increased etching duration of 40 s compared to 30 s for the 20 nm device, and the thinner metal layer thickness. On the other hand the AFM tip appears to be sharper in the 5 nm characterization which can be deduced from the comparable depth which is measured for the trench. A further reason for the rougher surface could be impurities embedded during MBE growth. Such impurities could be more easily attacked by the CAS leading to rougher surfaces. Due to the smooth surface of the 20 nm device it is reasonable to extract an electrode separation from the topographical image by taking the mean surface as a lateral limit. This gives a gap size of 22.5 nm with a standard deviation of 0.8 nm, and a maximum lateral deviation from the mean value of 2.1 nm. The lateral roughness value is slightly overestimated as any vertical corrugation is translated into a lateral roughness in the AFM characterization. For the 5 nm device an extraction of electrode separation was not made due to the rougher surface. However,

Figure 10.6: SEM characterization of a device with 5 nm GaAs layer after selective etching in CAS (30 s) and electrode metalization (3 nm Ti, 7 nm Au). The perspective is tilted by 30°. The gap width can be estimated from the image being 8 ± 3 nm. 140 Fabrication and Characterization of a Co-Planar Nanogap Device the 8 nm obtained from the SEM characterization are drawn in the cross sectional proﬁle as a guide to the eye.

In conclusion, devices with 20 nm and 5 nm GaAs layer were characterized showing an electrode separation which was approx. 3 nm larger than the GaAs layer thickness. This is due to the non-perfect selective etching in combination with the metal deposition. Here, it can be expected that mainly the etching is responsible for the widening, and the metalization is canceling part of this widening due to lateral growth during evaporation. A topic which could not be resolved by neither SEM or AFM is the question of material composition: It is not clear at which position the metal ﬁlm exactly ruptures. Therefore, the real electrode separation might be smaller than the above estimations as the metal ﬁlm could follow the surface topography mimicking the etched trench.

Figure 10.7: AFM characterization of coplanar nanogap electrodes after selective etching and metalization. Left: Device with 20 nm embedded GaAs layer after 30 s etching in CAS, and deposition of 3 nm Ti and 7 nm Au. Right: Sample with 5 nm GaAs layer after 40 s CAS etching and 2 nm Ti + 6 nm Au metalization. The bottom of each graph illustrate a cross-sectional proﬁle as indicated in the topographical image. For the 20 nm device the gap width is approx. 23 nm. For the 5 nm device the electrode separation is hardly determinable. The 8 nm estimated from the SEM image are indicated in the proﬁle. 10.3 Electrode Separation 141

10.3.2 Estimation of the Minimum Possible Electrode Separation

An estimation of the minimum possible electrode separation is interesting as a rich variety of molecules exist at lengths of 2-3 nm. Longer molecules are increasingly harder to synthesize as the solubility decreases with increasing molecular length. This is also the reason for adding side groups at the OPV molecules used in this thesis which increases solubility. As was discussed in the previous section a widening of the etched trench after etching and metalization in the order of 3 nm seems reasonable. Therefore, a limiting parameter would be the thinnest MBE layer which still could be selectively etched. In this context, etch tests were performed on multi-layered structures: The ﬁrst “positive” structure comprised two 20 nm, two 10 nm, two

5 nm, one 2 nm, and one 1 nm GaAs layer separated by 50 nm Al0.3Ga0.7As layers each. Here, every second 20 nm, 10 nm, and 5 nm layer was highly silicon doped as a possible extension of the nanogap device is the use of the sacriﬁcial layer as a gate electrode. The second, in the following “negative” denoted, structure consisted of one 20 nm, 10 nm, 5 nm, 2 nm, 1 nm

Al0.3Ga0.7As layer separated by 50 nm GaAs each. Typical topographical images obtained by AFM of samples etched for 5 s in CAS are displayed in ﬁgure 10.8. For the positive structure the 2 nm layer seems to be affected by the etching although hardly visible in the AFM image (marked by arrows in the left panel of ﬁgure 10.8). For the 1 nm layer it is not clear whether no etching occurs, or whether the trench is too narrow to be resolved by the bigger AFM tip. However, the negative structure reveals that 1 nm thick layers can be grown still affecting the surface of a device after etching. Nevertheless, the selectivity is decreased, probably due to the native oxide found at semiconductor surfaces which is usually more easily dissolved in aqueous solutions. From these AFM characterization it is also possible to distinguish between the effect of widening due to non-perfect selective etching, and the narrowing effect of metal deposition. The trenches in the positive structure are approx. 5 nm wider than the GaAs layer independent of the exact thickness. For longer etching durations even greater widening values up to 10- 15 nm were observed. The metal deposition on the other hand then led to re-closing of the gap down to electrode separations only 3 nm wider than the GaAs layer thickness as was observed in the previous chapter. Assuming, that 1 nm GaAs layer devices can be successfully fabricated, a minimum electrode distances of 4 nm seems therefore achievable. If the selectivity could be improved and thereby the widening of the gap reduced, the limiting parameter would be the lateral roughness of the metal layer. Taking the 2.1 nm from the 20 nm device characterized in the previous section devices with electrodes as close as 2-3 nm might be possible. 142 Fabrication and Characterization of a Co-Planar Nanogap Device

Figure 10.8: AFM characterization of selectively etched (5 s in CAS) multilayer systems. Left: A structure comprising two 20 nm, two 10 nm, two 5 nm, one 2 nm, and one 1 nm GaAs layer (left to right) separated by 50 nm Al0.3Ga0.7As layers each. For the 5-20 nm layers every second layer was highly silicon doped. The 2 nm GaAs layer is indicated by arrows in the topographical and cross-sectional image. Right: Layer stack consisting of one 20 nm, 10 nm, 5 nm, 2 nm, 1 nm Al0.3Ga0.7As layer (right to left) separated by 50 nm GaAs each. The bottom of both graphs illustrates cross-sections as indicated by the dashed line in the height image.

10.3.3 Etch Selectivity and Inverted Structure

From the discussion above it is understandable that an improvement of selectivity is desirable. It is a big advantage of the presented technique that the nanogap width can be predetermined by the MBE growth. However, due to the etching process and metal deposition the initial monolayer precision is reduced. Therefore certain methods to improve the selectivity or the etching profile were examined. These included etching tests at various temperatures, ultrasonication during etching, and increased aluminum content of the AlGaAs layers. Unfortunately, neither of these tests showed a significant improvement. A decreased temperature led to smaller etch rates but not to significantly changed selectivities. Ultrasonication seemed to reduce etch defects and gave hope of sharper etch profiles but also damaged a large amount of devices. And AlGaAs layers with higher aluminum content showed an increased defect density in MBE growth. Therefore, a new acid with superior etch characteristics for the GaAs-AlGaAs system was searched, and found in HF based etchants. It is reported in literature that HF is able to etch 10.3 Electrode Separation 143

AlGaAs layers for aluminum contents > 50% with complete selectivity [178]. In order to make use of this property the design of the nanogap device had to be inverted as is sketched in figure 10.9. Etch tests indeed showed promising results with a reduced widening of the gap in the order of 1-3 nm for devices with 10 nm thick sacrificial Al0.66Ga0.34As layers etched for 30 s in 5% HF (see left panel of figure 10.10). However, after metal deposition all devices suffered from short circuits between top and bottom electrodes. This was confirmed by a topographical AFM characterization as shown in the right panel of figure 10.10: The metal seems to accumulate at the trench edges thereby bridging the nanogap. This effect might be due to a different mobility of metal atoms on the semiconductor surface which could lead to such a material pile up. Because of these difficulties no further attempts were done in this direction. Furthermore, the successful fabrication of samples with the initial design having estimated electrode separations of 8 nm decreased the necessity to look for other options: The 8 nm electrode separation allows for the characterization of OPV11 molecules having a length of approx. 8.5 nm as they are able to successfully bridge the nanogap.

Figure 10.9: Illustration of the inverted nanogap structure. The sacriﬁcial layer consists of an AlGaAs layer with high aluminum content (> 50%) suitable for selective etching with HF based etchants. It is embedded in two thick GaAs layers.

Figure 10.10: AFM characterization of coplanar inverted nanogap electrodes. The Al0.66Ga0.34As layer thickness was 10 nm. Left: Device after 30 s etching in 5% HF. Right: Same device after perpendicular deposition of 3 nm titanium, and 7 nm gold. Clearly, the metal accumulated at the trench bridging the gap. 144 Fabrication and Characterization of a Co-Planar Nanogap Device

10.3.4 Summary

Nanogap electrodes based on AlGaAs-GaAs heterostructure were characterized with AFM and SEM revealing clean and smooth electrode surfaces. The electrode separation was estimated to be approx. 3 nm larger than the sacriﬁcial GaAs layer thickness, probably due to non-perfect selective etching in combination with the metal deposition process. A minimum electrode separation achievable with the present technique of 3-4 nm was guessed. An improvement by switching to the better selective HF etch could not be implemented successfully.

10.4 Device Failure Mechanisms

The overall yield of working samples was very low, on one chip usually one or maximum two nanogap devices met the requirements of the electrical operational test. Many of these samples then were destroyed during the bonding process, the cooling to helium temperature, or simply by time. Unfortunately, these three problems could not be solved successfully. An optimization of bonding parameters and a chip design for bonding gave only a slight relieve. A further small improvement was obtained by the slowing down of the cooling procedure, and all devices were held in darkness at low pressure (<10 mbar) in order to prevent oxidation and to prolong the life time. In order to further improve the yield certain effort was spent on an evaluation of other possible failure mechanisms. Few non-working samples could be explained by a failed MBE growth as shown exemplarily in ﬁgure 10.11 for a 5 nm device. The cross sectional TEM image apparently demonstrates that the growth of the AlGaAs layers did not work properly resulting in the irregular GaAs layer. The magniﬁcation displayed in the inset furthermore shows suspicious super lattices in contrast. Non-surprisingly, an AFM characterization of the wafer surface revealed an extremely rough surface with holes as deep as 75 nm in the wafer. Nevertheless, for most devices this failure mechanism could be excluded by a wafer surface

Figure 10.11: TEM micrograph (left) and AFM surface characterization (right) of a device with failed MBE growth. The TEM magnification indicates superlattice growth which might explain the unusual etching profile. 10.5 Electrical Characterization - Trapping of Gold Nanoparticles 145 characterization. Other mechanisms must be responsible in this case for device failure. One was identified in etch defects as illustrated in figure 10.12. The device which incorporated a 20 nm GaAs layer suffers from both un-etched regions after CAS etching (marked by circles) and over-etched regions. Such etch defects might be caused by a failed MBE growth, however, other groups reported similar etching problems [179]. As solution a soft ultrasonication during CAS etching was tried but a significant improvement could not be demonstrated. Probably, most devices failed due to a bridging of the nanogap region by (1) non-perfect etching: Either the etch profile was not sharp enough to lead to a rupture of the metallic film, or part of the nanogap region was not etched at all, or (2) the metal deposition led to a closure of the gap. Unfortunately, it was impossible to make a single effect responsible for all observed device failures. Apparently various mechanisms interacted in destroying the samples. Therefore, no real improvement of yield was achieved and all measurements involved the fabrication of a large amount of samples. However, such low yields seem to be common in the fabrication of nanogap electrodes as is obvious from publications (e.g., [118]) or presentations (e.g., [180]) from other groups.

10.5 Electrical Characterization - Trapping of Gold Nanopar- ticles

To illustrate the application of the nanogap device to contact nanoscale objects single gold colloid particle were positioned on the gap. This was accomplished by using the electrostatic trapping method which was already introduced in section 9.3.2. It makes use of the dielectrophoretic force a polarizable particle experiences in an alternating electrical ﬁeld due to induced dipoles. The alternating ﬁeld can be produced simply by applying an oscillating voltage to the nanogap electrodes. In addition, a series resistor included in the circuit should prevent the trapping of

Figure 10.12: SEM micrograph of typical etch defects. Part of the nanogap region is only partially or not at all etched (marked by circles). Graph adapted from [170]. 146 Fabrication and Characterization of a Co-Planar Nanogap Device more than one conducting nanoparticle. To monitor the trapping process it is advisable to use the internal resistance of an oscilloscope as this series resistor. The advantage of trapping metal nanoparticles between the nanogap electrodes for a functional electrode test are rather obvious: As the particles are highly conductive a large difference comparing IV characteristics before and after trapping the particle can be expected. Hence, it was important to obtain nanoclusters without a protecting organic shell which is often used to prevent an agglomeration of particles to bigger units. This requirement was met by particles obtained from Polysciences, Inc., which are delivered with intrinsic negative charge in de-ionized water to prevent agglomeration due to Coulomb interaction. Trapping experiments were performed with 30 nm large gold particles (according to the supplier) on devices with 20 nm intermediate GaAs layer. Prior to any modification the electrodes showed a fairly good insulating behavior at room temperature with non-linear IV characteristics. The attributed resistances ranged from 5 MΩ to 500 MΩ. By cooling the device to liquid helium temperature (4.2 K) the resistances exceeded 10 GΩ i.e. currents were below 100 pA at 1 V indicating a diminishing leakage current through the semiconductor. After that the trapping of single gold nanoparticles was performed: The initial highly concentrated colloidal solution was diluted with deionized water to 1mM. Then, in order to diminish leakage currents through liquid and semiconductor structure, only a small droplet of the solution was released on the active part of the device. The whole trapping was performed by applying an AC voltage to the device in darkness in a Faraday-cage-like trapping box until a successful trapping event was indicated in the oscilloscope. Various trapping parameter settings were tested and subsequently the gap area was examined in a scanning electron microscope. Depending on the choice of parameters in some cases gold particles adsorbed to the surface but did not bridge the gap. In other cases a large number of particles accumulated on and between the electrodes. Optimum conditions for the particular experimental setup were found for voltage amplitudes in the range of 3-4 VRMS and frequencies between 10 and 40 kHz. This resulted in the trapping of a single gold particle between the electrodes after typically 5-10 s until indicated in the oscilloscope. Typical electrical characterization data of a sample with a 20 nm GaAs layer before and after the successful trapping are displayed in figure 10.13. Clearly, the IV characteristics change from very good electrode isolation (≈11GΩ) to a clean short-circuit, as indicated by a decrease of the resistance over more than six orders of magnitude (at T=4.2 K). A SEM micrograph of a single colloidal gold particle trapped between the electrodes is shown in figure 10.14.

Summary AlGaAs-GaAs heterostructure based nanogap electrode devices were electrically tested by positioning single gold nanoparticles between the electrodes. The applied positioning method was 10.5 Electrical Characterization - Trapping of Gold Nanoparticles 147

Figure 10.13: IV characteristics at 4.2 K of a device before (dashed) and after (dotted) trapping a single gold particle. The resistance of the device before trapping exceeds 10 GΩ, after trapping it decreases to approx. 1.5 kΩ. The insets in the left part of the graph sketch the experimental conﬁguration, and the magniﬁcation in the right part demonstrates the high impedance behavior before trapping.

Figure 10.14: SEM micrograph of a single gold nanoparticle trapped between nanogap electrodes. Reprinted from ref. [181].

electrostatic trapping using an alternating electrical ﬁeld. It was possible to successfully trap single particles electrically bridging the nanogap region which decreased the resistance between the electrodes by six orders of magnitude. This demonstrates the applicability of the presented nanogap fabrication method for molecular electronics applications. 148 Fabrication and Characterization of a Co-Planar Nanogap Device

10.6 Omitting the Metal: Nanometer-Spaced Semiconductor Electrodes

In the previous sections it became clear that the electrode metal deposition itself alters the electrode separation and is a probable failure mechanism. Therefore, a method is desirable which avoids the metal at all, and instead makes active use of the semiconductor structure which only acted as a support for the metal electrodes so far. It was already explained in the introduction that InAs is a promising candidate for such structures as it experiences an electron accumulation layer at the surface (see pages 97 - 99). An exemplary design adapted to an InAs based nanogap device is shown in figure 10.15. Two InAs layers acting as electrodes are separated by a nanometer thin barrier material. Molecules could be positioned between the InAs layers and then be electrically characterized or used as functional units in an electrical circuit. By patterning the sample into mesa plateaus, e.g., by optical lithography and wet chemical etching, it would be possible to integrate a large number of devices on one chip. The main difficulty in InAs based systems is the choice of barrier material. Problems could either arise from growth, as possible barrier materials like GaAs or InP have highly different lattice constants, or from electrical properties as many materials experience unusual band offsets in combination with InAs. A further requirement for the barrier material was a suitability for selective etching. This seemed necessary because it is advisable to use a known system as a test bed for the semiconductor electrodes such as the trapping of gold nanoclusters. Otherwise it would be hard to distinguish between the influence of molecules and the influence of the InAs itself on IV characteristics. For the trapping experiment however, a trench like structure is necessary.

10.6.1 InAs-InAlAs-InAs System

The ﬁrst material system examined was the InAs-In0.8Al0.2As-InAs system. The idea was to use an aluminum containing compound to make the structure suitable for HF based selective

Figure 10.15: Schematic of a semiconductor nanogap electrode device based on InAs. Molecules bridging the barrier material are illustrated as white bars. 10.6 Omitting the Metal: Nanometer-Spaced Semiconductor Electrodes 149

4 etchants, and to stay as close as possible to the lattice constant of InAs: In0.8Al0.2As has 5.98 Å , and InAs 6.06 Å.

Indeed it was possible to grow In0.8Al0.2As layers up to 20nm on InAs substrates without causing signiﬁcantly more growth defects than for InAs epi-layers on InAs substrates. Figure

10.16 displays a typical cross-sectional AFM image of a InAs-In0.8Al0.2As-InAs structure with 20nm In0.8Al0.2Aslayer, capped by 100nm InAs. The growth direction in the AFM image is from left to right. The In0.8Al0.2As layer can be identiﬁed as the depression which appears as a vertical dark bar in the topographical AFM image. This is due to the tensile stress caused by the In0.8Al0.2As with the smaller lattice constant of 5.98 Å compared to the 6.06 Åof the InAs.

Unfortunately, the In0.8Al0.2As layer proved not electrically insulating at room temperatures. Resistances measured vertically through InAs-In0.8Al0.2As-InAs stacks did not differ from resistances measured on pure InAs layers of the same dimensions (data not shown). Fur- thermore, an immersion in 5% HF did not show any etching effect. The electrical data was surprising because from a view on the band gaps itself, In0.8Al0.2As having 0.77 eV and InAs 0.35 eV at room temperature, and an assumed type-I band offset a certain inﬂuence on the IV charavcteristics was expected. However, from simulations with nextnano3 taking the strain into account, it was found that the hole band is shifted upwards due to the strain. Thereby the energetic barrier is changed into a potential well. Thus, hole currents short circuit the whole stack (at least at higher temperatures). As the task was to allow for electrostatic trapping experiments which have to be carried out at room temperature, the aluminum content was increased to 40% in order to allow for better current blocking behavior in combination with HF sensitivity. However, the lattice misﬁt in

4Lattice constants for binary alloys are extracted from [137], lattice constants for ternary alloys are linearly interpolated as suggested in the same publication.

Figure 10.16: Cross-sectional AFM image of a InAs-In0.8Al0.2As-InAs heterostructure. The In0.8Al0.2As layer can be identiﬁed by the depression which is due to the smaller lattice constant of In0.8Al0.2As (5.98 Å) compared to InAs (6.06 Å). 150 Fabrication and Characterization of a Co-Planar Nanogap Device

Figure 10.17: Cross-sectional AFM image (amplitude) of a InAs-In0.6Al0.4As- InAs heterostructure. The sample was capped with photoresist (PR) to simplify the measurement. this case was too large (5.90 Å of In0.6Al0.4As compared to 6.06 Å of InAs), and MBE growth resulted in highly strained layers with three dimensional growth and large defects. A typical example is shown in ﬁgure 10.17 for a 20 nm thick In0.6Al0.4As layer embedded in InAs, again with the growth direction from left to right. Clearly, ﬁshbone like defects starting from the

In0.6Al0.4As layer can be identiﬁed. The subsequently grown InAs layer only partly covers the In0.6Al0.4As, hence, an electrical working device cannot be fabricated from this system.

10.6.2 InAs-GaSb-InAs System

Another possible barrier material for the InAs system which was examined is GaSb. With a lattice constant of 6.10 Å it is very close to InAs (see also figure 7.5 on page 99) so MBE growth was expected to be less problematic. This could be verified on InAs-GaSb-InAs heterostructures with GaSb layers of various thickness: 5 nm, 10 nm, 15 nm, and 20 nm. All wafers did show normal MBE growth with normal defect densities. As an example figure 10.18 shows a SEM micrograph of a mesa etched InAs-GaSb(20 nm)-InAs(200 nm) wafer. The GaSb and the top InAs layers can be clearly identified. Due to this promising growth results an electrical characterization was performed on patterned devices. The samples were etched through the GaSb layer to a depth of 700-1000 nm leaving 250 µm x 250 µm large plateaus. In the etched regions and on the plateaus at least two Ti/Au (10 nm/200 nm) contact pads were deposited. This allows for a characterization of the InAs surface accumulation channel by measuring the resistance between the pads on the plateau, and for a characterization of the current blocking behavior of the GaSb layer by measuring the resistance between a pad on the plateau and in the etched region. Typical results 10.6 Omitting the Metal: Nanometer-Spaced Semiconductor Electrodes 151

Figure 10.18: SEM micrograph of a InAs-GaSb-InAs heterostructure with 20 nm GaSb layer. The right part of the graph illustrates the cross section of the mesa-edge shown in the SEM image. The perspective angle is 60° with respect to the surface normal. for measurements at room temperature and liquid helium temperature (4.2 K) are illustrated in ﬁgure 10.19. At room temperature as well as at helium temperature the IV characteristics of the InAs layer shows an ohmic behavior with typical resistances of only 25-75 Ω at room temperature, and 100-200 Ω at 4.2 K. For the examples illustrated the resistances are 55 Ω (r.t.) and 180 Ω (4.2 K). The room temperature resistance is smaller because the bulk InAs adds to the conductivity due to the small energy gap of InAs (0.35 eV at room temperature [137]). The measurements through the GaSb layer indicate a non-linear IV characteristic at both temperatures with attributed resistances (at 100 mV) of 70 Ω (r.t.) and 580 Ω (4.2 K). The good conductivity for measurements on the InAs plateaus demonstrates the existence of a charge accumulation layer in the InAs even at very low temperatures. Unfortunately, the GaSb layer does not block current transport to such an extent that neither trapping experiments or measurements on molecules are possible. This is probably due to the staggered band line up

room

0.5

mA] through

temperature

GaSb layer

0.0

-0.5 urrent [ urrent

C on plateau Figure 10.19: IV characteristics

-100m -50m 0 50m 100m of an InAs-GaSb-InAs heterostruc-

liqu. helium ture at room (top) and liquid he- 0.5 mA] temperature (4.2K) lium (4.2 K) temperature (bottom).

0.0 At each temperature the current was through

GaSb layer measured between two pads on the -0.5 urrent [ urrent

on plateau C same plateau (squares), and through

-100m -50m 0 50m 100m the GaSb layer between pads on the

Bias voltage [V] plateau and in the etched region. 152 Fabrication and Characterization of a Co-Planar Nanogap Device of GaSb and InAs as electrons might move from the conductance into the valence band and vice versa.

10.6.3 Summary

InAs based devices with various intermediate layers were fabricated, electrically characterized and the growth of the device examined. The InAs itself shows a very promising electrical behavior at low temperatures promising great applications to molecular electronics. However, the barrier materials tested were either not suitable for bulk MBE growth, or failed in electrical characteristics. Recently, examinations on a new material system, InAs-InP-InAs, were started which will be brieﬂy discussed in the outlook (see chapter 13).

10.7 Conclusion

In this chapter the nanogap fabrication process was described in detail. As electrode material several metals were examined: PdAu, Ti/Au, and in part Cr/Au. All systems were very conductive for layers thicker than 6-8 nm. In terms of smoothness the Ti/Au system was superior to PdAu, and Cr/Au seemed similar to Ti/Au. Furthermore, the surface of processed nanogap electrodes was characterized by AFM and SEM revealing clean and smooth electrode surfaces. The electrode separation seemed to be approx. 3 nm larger than the sacriﬁcial GaAs layer thickness. Working samples with electrodes separated by approx. 8 nm could be fabricated reproducibly although with very low yield (< 5%). This allows for the measurement of IV characteristics on OPV11 molecules. A minimum possible electrode separation of 3-4 nm achievable with the present technique was guessed. Inverted structures suitable for HF etching with higher selectivity were also examined but did not work electrically. As most probable failure mechanisms the bridging of the nanogap region due to either non-perfect etching or lateral growth during metal deposition were supposed. Unfortunately, no real improvement in yield was achieved probably due to the interaction of multiple failure mechanisms and drift of process parameters. The applicability of the presented nanogap fabrication method for molecular electronics applications was tested by successfully positioning single gold nanoparticles of 30 nm diameter between approx. 22.5 nm separated electrodes. Accordingly, the IV characteristics of the nanogap device changed from high impedance behavior by six orders of magnitude to good conductance, demonstrating its potential. As an extension to the AlGaAs-GaAs heterostructure based devices, nanogap electrodes built on InAs heterostructures were examined. The InAs itself showed very promising electrical behavior, however, the barrier materials tested were either not suitable for bulk MBE growth, or failed in electrical characteristics. Chapter 11

Conductance of Oligophenylenevinylene Molecules

As was explained in the previous chapter, nanogap electrodes with a distance of approx. 8 nm could be successfully fabricated. This allows for the electrical characterization of OPV11 molecules which are able to bridge the gap region being approx. 8.5 nm long. Even for devices with slightly larger electrode separation, e.g. 10 nm, conductance measurements on OPV11 molecules seem possible due to the, although small but existing, lateral corrugation of the electrodes of 2 nm: Certain regions of the gap should therefore be separated by less than 8.5 nm.

In the beginning of this chapter, the characterization of OPV11 molecules on gold surfaces is described, followed by OPV11 conductance measurements using nanogap devices. The second part deals with a theoretical treatment of OPV11 current-voltage characteristics and is concluded by a comparison between calculation and experiment.

11.1 Electrical Measurements on Planar Nanogap Electrodes

11.1.1 Deposition of Oligophenylenevinylene Molecules

For an electrical characterization of OPV11 molecules it is essential to control their deposition on the electrodes. As experimental technique the deposition from solution, often leading to self- assembled monolayers, was chosen as described in sections 8.2.3 and 1.2. In principle, such a molecule grafting could lead to several situations as is sketched in ﬁgure 11.1: The desired conﬁguration is the bridging of the nanogap by the molecules which are chemically bound to the electrodes. However, a non-bridging situation is also possible driven either by chemisorption

153 154 Conductance of Oligophenylenevinylene Molecules or physisorption. To achieve the bridging conﬁguration it is recommendable to have a high density of molecules on the electrodes in order to force the molecules to stand up, but leaving the molecules still enough space to bend over and bridge the gap. To ﬁnd the right parameter settings, OPV11 molecules were deposited on gold surfaces and subsequently characterized by ellipsometry (method described in section 9.2).

Mainly two parameters were varied: the OPV11 concentration in the solvent, and the incubation time of the gold samples in the molecule containing solution. As solvent a 2:1 mixture of dichloromethane (DCM: CH2Cl2) and isopropanol (IPA) showed best capabilities to dissolve the original OPV11 powder. The samples were 1 cm x 1 cm large pieces of standard epi-ready GaAs wafers coated with 5 nm/50 nm Ti/Au. After immersion in the molecule containing solution, the samples were washed several times in DCM and IPA to remove physisorbed molecules. A typical washing procedure consisted of six cycles: 4x 1 min. immersion in DCM followed by 2x 1 min. immersion in IPA. Subsequently, the samples were purged dry using a filtered low pressure N2 blow. Then, the thickness of the molecular layer was determined by ellipsometry. To do so the obtained ellipsometric angles were fitted using a two layer model consisting of a molecular layer with refractive index n=1.55 on a gold layer. Layer thicknesses extracted from the ellipsometric data as a function of immersion time, and molecular concentration are illustrated in figure 11.2. As can be expected, an increase in molecular concentration at constant immersion times of 20±1 h leads to an increased measured thickness of the molecular film (see left panel of figure 11.2). This can be interpreted by either a standing up of the molecules, or by filling up of holes in an already standing but non-perfect monolayer of molecules. At concentrations above 40 µM the thickness seems to saturate between values of 7 nm - 7.5 nm. This can be interpreted by a full OPV11 monolayer with the molecules tilted by 30°-35° with respect to the surface normal. Thicknesses larger than the molecular length were never measured indicating that multilayer formation does not occur. A test using only IPA as solvent for the molecule did not produce significantly thick OPV11 layers even for longer immersion times. In the right panel of figure 11.2 both immersion time and

S S S S Au S S Au S S S S Au Au Figure 11.1: Three possible binding modes of thiol termi- S S nated conjugated oligomers between gold probes. Chemisorp- SH HS tion can either lead to molecules bridging the gap (top), or to Au Au a non-bridging configuration (center). This could also happen SH HS by physisorption (bottom). Adapted from [165]. 11.1 Electrical Measurements on Planar Nanogap Electrodes 155 concentration were varied. Again, higher concentrations lead to thicker layers as well as do longer immersion times. For the experiments on nanogap devices a concentration of 20-30 µM and an incubation time of approx. 20 h were selected which should give already dense OPV11 films with still sufficient space for the molecules to bend.

11.1.2 Current-Voltage Characteristics

For the measurement of current-voltage (IV) characteristics on OPV11 molecules nanogap devices with 5nm GaAs layer were fabricated. As was shown in section 10.3 this results in an approximate electrode distance of 8 nm making a bridging of the gap by OPV11 molecules possible. Prior to molecule deposition on the electrodes each sample was electrically tested at liquid helium temperature (4.2 K). Working devices showing the typical high impedance behavior (I < 100 pA at 1 V) were then immersed in a molecule containing solution as described in the previous section. After 20 h incubation time the samples were removed from the solvent, washed several times and purged dry. Then, they were cooled down again to 4.2 K, and electrically characterized. In 2 of approx. 20 examined samples a change in the IV characteristics was observed. The other samples did either not show any effect upon immersion in the molecule containing solvent or a subsequent SEM examination showed metal or dirt particles on the gap region. Three consecutively, at 4.2 K and on the same sample recorded IV curves after molecule deposition are

[

e 4

4 i

100

75 Incubation Time [h]

50 Ellipsometry Thickness [nm] Thickness Ellipsometry 0 10 25

0 10 20 30 40 50 0 0

Concentration [µM] Concentration [µM]

Figure 11.2: Ellipsometry measurements on OPV11 molecular layers on gold. Left: Variation of the molecular concentration at constant immersion time of 20±1 h in DCM/IPA solution (squares). The use of isopropanol alone as solvent did not produce significantly thick layers (circle). The dashed line is drawn to guide the eye. Right: Both, the incubation time, and the concentration of molecules in the DCM/IPA solvent mixture were varied. 156 Conductance of Oligophenylenevinylene Molecules illustrated in figure 11.3 indicated by the right inset. For comparison the low leakage currents measured on the same sample before the treatment are shown as indicated by the left inset. As can be seen, the IV curves show a clear change after molecular deposition having a conductance gap at voltages below approx. 0.3 V followed by an exponential-like increase in current at higher bias. Typical values at 1 V were 0.5 - 1 nA. This current increase can be attributed to resonant transmission through molecular orbitals. Qualitatively, the behavior of the system can be understood by a look on the energy levels of its components as was introduced in section 8.1.5 (see page 109): In a simplification, the electrode - molecular layer - electrode system can be seen as one molecule, represented by its molecular orbital energies, spanned between two metallic leads which are characterized by their Fermi energy. Bringing the molecule and the electrodes together charge transfer between the components occurs and their Fermi levels align. Often, the resulting Fermi energy of the system lies in the energy gap between the HOMO and the LUMO of the molecule. In the example illustrated in the left panel of figure 11.4 the potential window at low bias opened by the two electrodes still leaves out any molecular orbitals. Therefore, the main current transport mechanism is off-resonance tunneling from electrode to electrode which is extremely small due

Figure 11.3: Current-Voltage characteristics of OPV11 molecules assembled on planar nanogap electrodes at 4.2 K. Three consecutively, on the same sample recorded IV curves are shown (dashed, vertically translated by 1nA each) in comparison to the high impedance IV characteristics before molecular assembly (dotted). The insets contain schematics of the experimental configuration; in addition the lower part of the graph illustrates the chemical structure of the assembled OPV molecules. 11.1 Electrical Measurements on Planar Nanogap Electrodes 157 to the comparably large electrode separation. Hence, a conductance gap is observed. For higher bias voltages, the energy window crosses molecular levels, in the example shown in the right panel of figure 11.4 it is the HOMO level, and resonant transmission through the orbital leads to a strong increase in current. To exclude any effects of the solvent itself control experiments were performed on working devices which passed the normal molecule deposition procedure, however, using an immersion solvent without molecules. It was found that no sample out of 6 showed any effect upon this procedure. A typical result of this control experiment is summarized in figure 11.5 in comparison to the average IV curve of figure 11.3.

11.1.3 Summary

In conductance measurements on OPV11 molecules a change of the IV characteristics comparing before and after molecular deposition was observed for part of the samples: A conductance

Figure 11.4: Schematic energy diagram of a metal-molecule-metal structure. The molecule is represented by its molecular orbitals and the electrodes by the equilibrium Fermi energy EF . Left: Situation at low bias voltage V assuming an equal voltage drop at both electrodes. No molecular orbital lies in the potential window eV opened by the electrodes. Right: System at high bias. Resonant transmission through the HOMO occurs.

0.5 Figure 11.5: Control experiment for molecular conductance measurements. A device which was immersed for 20 h in

0.0 a DCM/IPA solution without molecules still shows the typical high impedance IV

Current [nA] Current curve (dotted). For comparison a typical curve for a measurement after immer-

-0.5 sion in OPV11 containing solvent is shown (dashed). The bias voltage was limited to

-1.0 -0.5 0.0 0.5 1.0 1 V to prevent damage to the device as it

Bias Voltage [V] was used for further experiments. 158 Conductance of Oligophenylenevinylene Molecules gap for low bias voltages is followed by an exponential like increase in current. Control experiments on devices which were immersed in pure solvent without molecules did not show any change in IV characteristics. The results could be interpreted by the model introduced in section 8.1.5: The current increase is attributed to starting resonant transmission through molecular orbitals.

11.2 Comparison to Model Calculations Employing EHT and NEGF

A more detailed expectation for current-voltage characteristics of electrode-molecule-electrode systems can be obtained from calculations applying extended Hückel theory (EHT) in combination with the Non-Equilibrium Greens Function (NEGF) formalism which was introduced in section 8.1.6. However, a proper treatment of long molecules is difficult due to the increasing computational effort with increasing number of involved atoms, and the demanding task to find the correct molecular configuration. Therefore, model calculations have to be performed on simplified OPV molecules as a representative of the measured molecular layer.

11.2.1 Molecular Electronic Structure

As a first step extended Hückel calculations were carried out on isolated OPV molecules of different length using HyperChem [169]. The purpose of this task was to get insight into the electronic structure of the OPV molecules and to estimate how accurate a description of the molecule with EHT is. To do so, the geometry of the molecules was first optimized using MM2+ force fields [182]. Then, the molecular orbital energies were calculated using the EHT routine implemented in HyperChem. It was found that it is very difficult to find the optimum geometrical configuration of the OPV molecules due to the forked side chains (see figure 8.10 on page 119 for the chemical OPV structure). Therefore, the side chains were reduced from forked O-C8H18 groups to linear O-C3H7 chains to simplify the calculations. The calculated molecular orbital energies for the simplified OPV molecules with 1-11 phenyl rings1 in a range between -9.25 eV and -11.75 eV together with the HOMO-LUMO gaps are illustrated in figure 11.6. The HOMO-LUMO gap experiences a 1/x like decay with increasing molecular length, and at the same time the density of molecular orbitals in the observed energy

1Only phenyl rings with side groups are counted. By increasing this number by two one gets the total number of phenyl rings (see also figure 8.10 on page 119). 11.2 Comparison to Model Calculations Employing EHT and NEGF 159 window increases. This behavior is due to the narrowing of the HOMO-LUMO gap with increasing size of the π-conjugated system. It can be understood by looking at the molecule as a potential well for electrons with infinitely high walls [183]. From visualizations of HOMO and LUMO wavefunctions, as illustrated in figure 11.7, it can be seen that such an assumption of a

π-system confined to the whole molecule seems indeed justified. The energy eigenvalues En for a potential well, i.e. the molecule consisting of N units separated by a distance d, are2 [184]: h¯ 2π2 2 En ≈ ∗ 2 · n . By filling the eigenstates with electrons according to the Pauli principle an 2me·(Nd) expression for the HOMO-LUMO gap Egap can be found:

2 2 h¯ π −1 Egap ≈ const. ∗ 2 · N (11.1) 2me · d

The solid line in the left panel of figure 11.6 is a fit according to this expression modified by a constant offset, and taking N as the total number of phenyl rings in the molecule. In section 8.1.6 it was already stated that EHT calculations tend to underestimate the absolute molecular orbital energies, however, yielding fairly good relative results. To check this assumption, the energy calculations were compared to UV-VIS absorption spectra taken from OPV molecules in solution. The absorption maximum at lowest energy can be identified with the HOMO-LUMO transition (see also section 9.2.2). Normalized spectra of OPV3, OPV7,

2The potential well length (N − 1)d can be approximated for large N as: (N − 1)d N−→→∞ Nd

3.2

OPV OPV OPV

1 3 5

1.6

LU eV]

-10 -10 -10 LU [

3.0

1.4

-11 -11 -11 HO

HO Energy

2.8

1.2

OPV OPV OPV

7 9 11

2.6 eV]

-10 -10 -10 LU [ LU LU

1.0 HOMO-LUMO gap [eV] gap HOMO-LUMO

2.4 HO -11 -11 HO -11 HO Energy

0 2 4 6 8 10 12

# Phenyl rings with side groups

Figure 11.6: Extended Hückel calculations on OPV molecules using HyperChem [169]. Left: The HOMO-LUMO gap of OPV molecules vs. number of phenyl rings (squares) is drawn on the left hand axis. The solid line represents a ﬁt to the data according to equation 11.1 adding a constant offset. Additionally, the adsorption maxima from UV-VIS measurements are shown (circles, right hand axis). Right: Molecular orbital energies between -9.25 eV and -11.75 eV for OPV molecules of varying length. The subscripted numbers denote the counted phenyl rings with side chains. LUMO and HOMO are highlighted by “LU” and “HO”, respectively. 160 Conductance of Oligophenylenevinylene Molecules

Figure 11.7: Representations of HOMO and LUMO wave functions of selected OPV molecules with simplified phenyl side chains. The molecules were first geometry optimized in HyperChem applying MM2+ force fields [169]. Then, they were energy optimized using EHT. For the OPV7 part of the molecule is hidden by the label.

and OPV11 are displayed in ﬁgure 11.8. They are in very good agreement to measurements on similar molecules by other groups [185]. It can be seen that the absorption maximum shifts to longer wavelengths with increasing molecule length which corresponds to the EHT calculations. However, the calculated absolute HOMO-LUMO gap energies are underestimated by approx. 1.5 eV comparing them to the measured absorption energies (see left panel of ﬁgure 11.6). From the UV-VIS data an estimation of the effective conjugation length is also possible. It is a measure of the maximum extension a π-electron wave function can have in the OPV molecules. According to ref. [185] the effective conjugation length is reached if the wavelength of the absorption maximum changes by less than 1 nm while increasing the number of phenyl units by one. Fitting the UV-VIS data with expression 11.13 as derived above would result in an effective conjugation length of 17-18 phenyl units. This is far larger then the 4-5 phenyl units which are usually assumed for unsubstituted PPV molecules [186, 185]. However, it was already shown that for substituted OPV molecules large effective conjugation lengths in the order of 10-17 phenyl units can be expected (see page 25 in [185]).

3 The ﬁt gives Egap = 2.357eV + 1.5952eV/N with N being the total number of phenyl units. 11.2 Comparison to Model Calculations Employing EHT and NEGF 161

= 400nm 450nm 500nm 550nm

1.0

0.8 nce

0.6

OPV OPV OPV

3 7 11

0.4 Absorba Figure 11.8: UV-VIS absorption spectra

0.2 of OPV molecules in DCM/IPA solution. The absorption maximum shifts toward

0.0

3.2 3.0 2.8 2.6 2.4 2.2 lower energies with increasing molecular

Energy [eV] length.

11.2.2 IV Curve Calculations on Simpliﬁed Molecules with Hückel-IV

The underestimation of the HOMO-LUMO gap by the EHT calculations opens the question whether a theoretical calculation of OPV IV-characteristics by EHT, and a subsequent comparison to experimental results is reasonable or not. It is obvious that for bias voltages larger than the HOMO-LUMO gap the theoretical calculation must fail, because at such voltages the Fermi energies of the electrodes cross either LUMO or HOMO. As they are energetically too close together in the calculation any features obtained at such high voltages in the calculated IV characteristics are at least shifted to lower voltages or even totally wrong. However, there is the justified hope that EHT calculations give a first guess of the expected IV characteristics for small applied voltages below the HOMO-LUMO gap: In this regime mainly the overlap of the orbitals with the electrodes determines the IV characteristics by influencing the molecule - electrode coupling. Thus the shape of the wave function is the main influencing parameter for the IV characteristics. And it is reported that for model molecules, such as benzenedithiol, EHT yields a fairly good description of the orbital wave functions [146]. This assumption was tested by comparing wave function representations of HOMO and LUMO obtained by EHT with more elaborate calculations employing density functional theory with STO-3G basis set and B3LYP functional. The accuracy of the DFT calculation becomes evident from the obtained HOMO-

LUMO gap of 2.90 eV for the OPV1 which is very close to the value obtained from the ﬁt of the UV-VIS data giving 2.89 eV. A plot of HOMO and LUMO wave functions comparing EHT and DFT is displayed in ﬁgure 11.9 demonstrating the good description of the wave function by EHT. Unfortunately, DFT could not be used to calculate IV characteristics during this thesis. As program to calculate IV characteristics based on EHT in combination with the NEGF formalism the freely available tool Hückel IV 2.0 was used [164]. A calculation of the whole 162 Conductance of Oligophenylenevinylene Molecules

Figure 11.9: Representations of HOMO and LUMO wave functions of OPV1 molecules with simpliﬁed phenyl side chains. Calculations employing EHT coincide very well with more elaborate DFT calculations. Differences in brightness of the wave functions and size variations of atoms and chemical bonds are mainly due to the different visualization programs implemented in the quantum chemical calculation programs.

OPV11 molecule was not successful due to limitations of Hückel IV, therefore the smaller OPV1 was used as a representative of the long molecule. This has the additional advantage that the

HOMO-LUMO gap is closer to the measured value for the OPV11. Calculated HOMO and LUMO energies were -11.3 eV and -9.7 eV, respectively. In Hückel IV the molecule is attached via the sulfur to gold (111) surfaces with a distance of 1.9 Å of the sulfur to the gold (111) plane. This is equivalent to a sulfur-gold bond length of 2.53 Å [187]. The hydrogen atoms on the sulfur have to be removed in order to bind the molecule to the gold electrodes. A schematic of the simulated structure is sketched in ﬁgure 11.10. As was explained in section 8.1.5 three parameters are important in the determination of the IV-characteristics: The coupling Γ to the electrodes, the Fermi energy of the system, and the charging energy Uch. The coupling was chosen symmetrically Γl = Γr = 1. For the Fermi energy and the charging energy various values were examined. Figure 11.11 illustrates the IV- characteristics (left panel) together with the conductance (right panel) calculated for the OPV1 molecule connected to gold electrodes and a charging energy of Uch = 1eV. Selected Fermi

Figure 11.10: Au electrode - molecule - Au electrode structure used for IV characteristics calculations with Hückel IV. 11.2 Comparison to Model Calculations Employing EHT and NEGF 163

energies were calculated with EF = −11eV being the energy at which the molecule has net zero charge at zero bias. The same calculations but for a charging energy of Uch = 2eV are shown in ﬁgure 11.12. These charging energies are in the range of typical values found for aromatic molecules [188]. All IV characteristics have qualitatively a shape similar to the experimental results: At low bias voltages a conductance gap is observed followed by a strong increase in current. Here different shapes can be observed: either linear, exponential like or step like fashions. At the charging energy of Uch = 1eV the current increases faster than for charging energies of Uch = 2eV. This is understandable as the higher charging energy leads to a stronger “escape” of the molecular orbital from the electrode potentials. The extension of the conductance gap is mainly determined by the difference between the Fermi energy and the HOMO energy EF − EHOMO

10 30

E = -11.0eV

25 V] E = -10.8eV

5 E = -10.6eV

E = -10.0eV 20

F [µA/ e [µA]

0 15 ent

E = -11.0eV Curr

-5 E = -10.8eV

E = -10.6eV Conductanc 5 F

E = -10.0eV

-10 0

-2 -1 0 1 2 -2 -1 0 1 2

Bias Voltage [V] Bias Voltage [V]

Figure 11.11: Left: Theoretical IV characteristics of OPV1 connected to gold (111) electrodes with a charging energy of 1 eV. Right: Conductance-Voltage plot of the same structure.

30 10

E = -11.0eV

25 V]

E = -10.8eV

E = -10.6eV

20 E = -10.0eV [µA/

F e [µA]

0 15 ent

E = -11.0eV Curr

-5 E = -10.8eV

E = -10.6eV Conductanc 5

E = -10.0eV

-10 0

-2 -1 0 1 2 -2 -1 0 1 2

Bias Voltage [V] Bias Voltage [V]

Figure 11.12: Left: Theoretical IV characteristics of OPV1 connected to gold (111) electrodes with a charging energy of 2 eV. Right: Conductance-Voltage plot of the same structure. 164 Conductance of Oligophenylenevinylene Molecules as can be understood from the simple model presented in section 8.1.5. Surprisingly, this is even true for a Fermi energy of -10.0 eV although in this case the LUMO is energetically closer than the HOMO, therefore, current transport through the LUMO would seem more favorable. However, the individual coupling of the LUMO to the electrodes might be weaker than for the HOMO, hence, an electron transfer through the LUMO is made more difficult. Another interesting feature appears in the conductance plots: a more or less pronounced peak occurs at bias voltages close to the HOMO-LUMO gap of 1.6 eV. This behavior becomes understandable from a look on the quasi Fermi levels of left and right electrode while increasing the bias as is shown in figure 11.13. When one electrode Fermi levels comes close to a molecular level it seems to “wait” for the other electrode to reach the neighboring molecular level. This is not surprising if one thinks of the dependence between charging of the molecule and its density of states. As was explained in the one level model of section 8.1.5 the current transport can be understood by electron transfer rates implying a fractional charge transfer on the molecule, i.e. a charging of the molecule. If the DOS in a certain energy range is very small then a charge transfer to or from the molecule leads to a strong shift in molecular orbital energy. For a large DOS however, the shift is comparably small. Naturally, the DOS of a molecule is highest at its molecular orbital energies, and usually, this relation is also valid for the molecule connected to electrodes. At least for the examined OPV1 this is the case as can be seen from figure 11.14.

11.2.3 Comparison between Theory and Experiment

Comparing the Hückel IV calculations shown in the previous section with the experimental data illustrated in ﬁgure 11.5 a very good qualitative agreement can be found for a charging energy

-8.5 -8.5 [eV] [eV]

-9.0 -9.0 F F left right left right

electrode electrode electrode electrode

-9.5 -9.5

-10.0 -10.0

E = -11.0eV E = -11.0eV

F F

E = -10.8eV E = -10.8eV

F F

-10.5 -10.5

E = -10.6eV E = -10.6eV

F F

E = -10.0eV E = -10.0eV

F F -11.0 -11.0

-11.5 -11.5

-12.0 -12.0 ElectrodeFermi Energy E ElectrodeFermi Energy E

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

Bias Voltage [V] Bias Voltage [V]

Figure 11.13: Theoretical Fermi energies of left and right electrode depending on bias voltage calculated for charging energies of Uch = 1 eV (left), and Uch = 2 eV (right). The vertical dashed lines indicate the molecular orbital energies of the isolated molecule. 11.2 Comparison to Model Calculations Employing EHT and NEGF 165

.u.] 10

0.1 Figure 11.14: Density of states (dotted) and

0.01 transmission (dashed) of a OPV1 molecule con-

Transmission, DOS [a DOS Transmission, nected to gold electrodes. The molecular orbital

-12 -11 -10 -9 energies of the isolated molecule are indicated by

Energy [eV] vertical lines at the bottom. of Uch = 1eV and a Fermi energy of -10.8 eV. A plot comparing experimental and theoretical results demonstrating this remarkable coincidence is displayed in ﬁgure 11.154. The absolute values however, are far higher for the calculation than for the experiment, especially, by taking into account that in the experiment not single molecules but molecular layers are characterized: By a simple geometrical consideration the maximum number of molecules in the gap can be estimated regarding a closed packed monolayer to be in a range of 15000 - 5 150000 molecules . But as the simulated molecule OPV1 is shorter than the measured molecule

4Features observed in the calculated curve above a bias voltage of 1.6 V are not valid due to the underestimation of the HOMO-LUMO gap as explained in section 11.2.1. 5From quantum chemical programs the width and height of the molecule were estimated being approx. 2 nm and 0.2 nm, respectively. From a typical electrode width of 30 µm the number of molecules is calculated.

Figure 11.15: Comparison between the IV curve for a single simpliﬁed OPV1 molecule embedded between two gold electrodes as calculated with Hückel IV [164]. For comparison the averaged measured IV characteristics is also illustrated. 166 Conductance of Oligophenylenevinylene Molecules

OPV11 an overestimation of current in the calculation is not surprising. Furthermore, inelastic scattering effects which probably decrease the current especially through long molecules are not taken into account in the Hückel-IV tool. In addition, experiments from other groups indicate that the conductance of a molecular layer is not equivalent to the conductance of a single molecule multiplied with the number of molecules in the layer [177]. Moreover, qualitative agreement with at the same time large quantitative discrepancies between theory and experiment were also observed from other groups for similar systems such as phenyldithiol [189].

11.2.4 Summary

The electronic structure of OPV molecules of varying length was examined using extended Hückel theory. With increasing length a decrease in HOMO-LUMO gap was found which could be explained by a comparison to a potential well with infinitely high walls. From UV- VIS absorption measurements it could be demonstrated that EHT underestimates the HOMO- LUMO gap. Nevertheless, a calculation of IV characteristics as a qualitative guess for the experimental situation using EHT in combination with the non-equilibrium Greens function method seems justified by comparing HOMO and LUMO wave functions to DFT calculations. Then, IV characteristics of simplified and shortened OPV molecules were calculated showing a qualitative agreement to experiment: A conductance gap at low bias is followed by a strong increase in current. Explanations for quantitative deviations from the experiment were proposed.

11.3 Conclusion

In this chapter the current carrying properties of OPV molecules were examined experimentally and theoretically. In conductance measurements on OPV11 molecules IV characteristics consisting of a conductance gap for low bias voltages followed by an exponential like increase in current were observed for part of the samples. Strong experimental arguments were found to exclude the solvent as a possible cause for the change in IV characteristics. The current increase could be qualitatively explained with starting resonant transmission through molecular orbitals. By applying extended Hückel theory to simpliﬁed OPV molecules more insight into the behavior of the electrode - OPV molecule - electrode system was gained, and a qualitative agreement to experiment was found for typical parameter settings. During this process the limitations of using EHT to describe the system by underestimating the HOMO-LUMO gap became evident. Explanations for existing quantitative deviations in the simulated IV characteristics from the experiment were proposed. Chapter 12

Fabrication and Characterization of a CEO Nanogap Device

An interesting, and still not fully answered question in molecular electronics is: How is the conductivity of a junction containing an individual molecule related to the conductivity of a junction containing a large ensemble of molecules [177]? Presently it is not clear how to make such quantitative comparisons, since this relies on the normalization of measured currents to a single molecule [151, 152]. On one hand there are experiments on junctions with individual or small ensembles of molecules indicating that the current scales with the number of molecules in the junction, i.e. N molecules carry N times as much current as an individual molecule [103, 190, 191]. On the other hand experiments based on large and highly dense ensembles of molecules show normalized currents which vary by orders of magnitude [151]. It is unlikely that uncertainties in the number of measured molecules alone are able to explain such discrepancies. Instead, theoretical examinations suggest that the local environment of the measured molecules deeply inﬂuence their current carrying properties. Effects can be attributed to the potential proﬁle across the molecular junction [192, 193] as well as to heat conduction [194, 195], and vibronic coupling [196, 160]. The biggest deviation from the linear scaling can be expected for a densely packed monolayer junction in comparison to an individual molecule junction. To examine such deviations a structure which allows for the simultaneous characterization for molecular layers and single molecules is needed.

12.1 Electrode Fabrication by Cleaved Edge Overgrowth

Such a structure can be achieved using the Cleaved Edge Overgrowth (CEO) method: A remarkable property of III-V semiconductors, which was already used in the planar nanogap approach,

167 168 Fabrication and Characterization of a CEO Nanogap Device is their ability to cleave atomically ﬂat along a crystal plane. This property can be used to fabricate a totally new class of semiconductor structures by performing a second MBE growth step on an in-situ cleaved heterostructure. Such a growth on cleaved facets was ﬁrst realized by L. Pfeiffer and coworkers at Bell Labs who fabricated a two-dimensional electron gas on a cleaved (110) edge of a GaAs wafer [197]. With such a CEO method the fabrication of broken T-shaped structures is accessible [198] which would allow for the shrinkage of one of the two nanogap electrodes to a width of only a few nanometers. This, in principle, would enable a simultaneous measurement on single molecules and one dimensional molecular layers, as will be explained in the following.

12.1.1 CEO Nanogap Electrode Fabrication

The whole fabrication process of broken T-shaped nanogap electrodes based on CEO grown AlGaAs-GaAs heterostructures is schematically illustrated in ﬁgure 12.1. It differs in three process steps from the fabrication of planar electrodes: A second MBE growth step, the CEO growth, is added which includes a second cleavage procedure. And the patterning into ﬁnger- like structures is only optional as it causes additional problems in the structure. This will be elucidated in section 12.1.2. In the following, each process step is explained in detail:

1st MBE Growth As for the planar electrode approach, the starting material for the AlGaAs-GaAs heterostructure are epi-ready (001) GaAs wafers. However, the grown layer structure differs: If the structure is designed for selective etching by CAS then a nanometer thin Al0.3Ga0.7As layer is embedded by MBE growth between two thick GaAs layers. The Al0.3Ga0.7As layer thickness later defines the electrode width. In principle, the capping GaAs layer could also be omitted, however, it is essential for the finger approach described in section 12.1.2. Then, it should have a thickness of several hundred nanometers. The whole structure after the 1st growth is illustrated as figure 12.1(a).

Wafer Thinning For CEO, samples have to be cleaved in-situ in the MBE chamber after the first growth. The cleavage is a crucial step in sample fabrication as an atomically flat surface must be obtained to ensure a proper second MBE growth. Cleavage defects such as step like structures should be avoided. To facilitate the cleavage it is recommendable to thin the wafers after the first MBE growth from the initial thickness of 400-500 µm down to 100-120 µm. To do so, the wafer is removed from the chamber, and the gallium (Ga), which is used as a glue in the MBE chamber, is washed from the wafer backside by immersion in concentrated HCl (37%). The wafer front 12.1 Electrode Fabrication by Cleaved Edge Overgrowth 169

Figure 12.1: Schematic of the fabrication process for CEO nanogap electrodes. a) First MBE growth of an AlGaAs/GaAs heterostructure with nanometer thin AlGaAs layer. The AlGaAs layer thickness determines the later electrode width. b) In-situ cleavage for the second MBE growth step. c) Cleaved Edge Overgrowth (CEO) of a nanometer thin GaAs layer followed by a thick AlGaAs layer, perpendicular to the first growth direction. The GaAs layer thickness later defines the electrode separation. d) Selective etching for contact pad deposition applying optical lithography. e) Contact pad deposition via a standard lift-off process. The right contact pad might also be deposited by directed evaporation omitting the optical lithography on the cleavage facet. f) Second cleavage to provide an atomically flat and clean surface exposing the sensitive electrode region. g) Selective etching of GaAs layers to obtain the trench between the electrodes. h) Device after thin film metalization for a following deposition of molecules bridging the gap region (marked by an arrow, molecule is sketched). The metal deposited on the GaAs layers is not shown in order to avoid confusion. i) Device implementing two electrodes of different width suitable for simultaneous measurements on single molecules (electrodes 1 and 3), and molecular layers (electrodes 2 and 3). 170 Fabrication and Characterization of a CEO Nanogap Device can be protected by photoresist during this step. After the Ga removal, the thickness of the wafer is determined using a micrometer. Then, the wafer is fixed to a quartz glass with the epi layer facing the glass surface using an acetone soluble wax. After that, the wafer is thinned by continueous movement on a clean room tissue soaked with 12% bromine-methanol solution (50 ml methanol und 6 ml bromine) and interrupted by a thickness control using the micrometer. Subsequently, the wafer is removed from the quartz glass and cut into 7.1 x 7.1mm large pieces using a computer controlled scribe table. Furthermore, a 0.95mm long mark is scribed starting at a point 1mm inside the wafer and at 3.3mm from one sample corner. This is the target point which should induce the in-situ cleavage necessary for the CEO growth (see figure 12.2). After a thorough cleaning in boiling acetone and methanol, the samples are built on a special sample holder as is illustrated in figure 12.2.

Cleavage and 2nd MBE Growth (CEO) Once in the MBE chamber and after growth preparations such as substrate heating, a solid cleavage bar is used to induce a cleavage at the target cleavage point by brute mechanical force (see figures 12.1(b) and 12.2). Then, the CEO-MBE growth can be started. In this step a nanometer thin GaAs layer is grown, followed by a thick (approx. 500 nm) Al0.3Ga0.7As layer. The structure is often capped by a 10 nm thin GaAs capping layer (not shown). The thickness of the first CEO-GaAs layer defines the electrode separation in analogy to the thin GaAs layer in the planar electrode approach. An illustration of the device after CEO growth is displayed as figure 12.1(c).

Figure 12.2: CEO sample holder. The cleavagebar [110] CEOsamples samples suited for CEO growth are fixed on the holder using gallium and a moni- [001] targetcleavage point(scribedby tor wafer. The monitor wafer is necessary diamondneedle) for temperature measurements and growth rate calibration. Before CEO growth starts, the samples are in-situ cleaved us- 3.3mm ing a bar which should induce cleavage at the target point by mechanical force. Fig- sampleholder monitorwafer ure adapted from [199]. 12.1 Electrode Fabrication by Cleaved Edge Overgrowth 171 of the capping GaAs layer has to be removed prior to contact pad evaporation as is shown in figure 12.1(d). This can be achieved by performing a selective etching process with CAS after the development step in the optical lithography procedure for the lift-off process. Then, the left contact pad is deposited by standard electron beam evaporation. The right contact pad does not require a lift-off process. Instead, a directed metal evaporation can be used with the source located at a distant point on the right side and below the sample. This leads to a coverage of the right sample side, i.e. the CEO grown layers, and the sample bottom without deposition on any other sides. Thereby, the right electrode can be contacted simply by putting the sample on a conducting surface. The contact pads, as usual, comprise a thick gold layer (100-200 nm) on a thin titanium adhesion layer (10 nm). A schematic of the sample at this process stage is shown in figure 12.1(e).

2nd Cleavage and Selective Etching To this point the sensitive nanogap region is still protected inside the sample. In order to make it accessible the substrate has to be cleaved again. This exposes an atomically flat and perfectly clean (110) surface of the AlGaAs-GaAs sandwich structure as illustrated in figure 12.1(f). After that, the GaAs layers are etched selectively versus the AlGaAs layers using the CAS etch as is depicted in figure 12.1(g). Now the broken T-shaped, electrode forming AlGaAs layers can be clearly identified.

Nanogap Electrode Deposition After etching, the electrode thin film metal layer is evaporated perpendicularly to the cleaved surface as is illustrated in figure 12.1(h). Similar to the planar nanogap approach, the electrical contact between left and right electrode is interrupted by the rupture of the metal film at the etched trench separating the two electrode supporting AlGaAs layers. The gap size between the electrodes is mainly determined by the layer sequence set during MBE growth, the minor roughening and widening of the AlGaAs-GaAs interface due to non-perfect selective etching, and the lateral roughness and lateral growth during deposition of the thin film metal layer. Subsequently, molecules could be assembled on the electrodes as functional units in an electrical circuit. For the desired simultaneous characterization of individual molecules and molecular layers1 it is necessary to embed more AlGaAs layers of different thicknesses separated by thicker GaAs layers during the 1st MBE growth. This would result in a device layout as sketched in figure 12.1(i) for two AlGaAs layers. Accordingly, the contact pad deposition process involves an additional etching step with optical lithography in order to obtain the staircase structure shown

1Molecular layers in the present context refers to a one dimensional, densely packed array of molecules as visualized in ﬁgure 12.1(i). The interaction between the molecules might be different compared to two dimensional SAM layers. 172 Fabrication and Characterization of a CEO Nanogap Device in the ﬁgure.

12.1.2 Integrating Multiple Devices on One Sample

From the planar nanogap electrode approach it is known that a large integration of nanogap devices on one sample chip is advisable due to the low yield in fabrication. The finger like structure used in the planar approach can be adapted to the CEO approach as is shown in figure 12.3. For the structuring a mesa patterning has to be carried out using optical lithography and wet chemical etching. In principle, this etching process could be performed either after the first MBE growth step, or after the CEO growth step. Both options were examined. Though, a patterning of the device after the CEO growth step could not be achieved because of large difficulties in the optical lithography: The finger like structure is touching the edges of the sample, however, due to interference effects it was impossible to obtain a defect-free patterning reaching the very end of the sample. By doing the etching before the CEO growth step this problem was circumvented

Figure 12.3: Schematic of the finger-like CEO nanogap electrode fabrication. a) Device after both MBE growth steps and a mesa patterning applying wet chemical etching and optical lithography. b) Selective etching of the GaAs layers. c) and d) Device after electrode metalization and deposition of contact pads seen from two different perspectives. The nanogap electrode regions are marked by arrows. In d) the position of the evaporation source is also illustrated. 12.2 Electrode Characterization and Failure Mechanisms 173 as the nanogap region is located in the middle of the sample at this stage. Yet, additional problems arose as a deposition of material during the CEO growth on the mesa side walls must be prevented. This imposed serious problems as will be shown later. Figure 12.3(a) illustrates the device after both MBE growth steps and the mesa etching process. A subsequent selective etching process (see figure 12.3(b)) makes the device ready for electrode metalization. In contrast to all previously described methods on AlGaAs-GaAs heterostructures, the finger CEO approach does not require a cleavage to expose the nanogap region. This is certainly a drawback as the sensitive region is not protected inside the wafer once the mesa patterning is performed. The electrode metal deposition has to be carried out in a certain direction to avoid short circuits between the electrodes. This is a very demanding task in CEO electrode fabrication as many possible leakage paths by non-interrupted metal films exist. A possible location for the evaporation source is indicated in figure 12.3(d). Figure 12.3(c) illustrates a different view on the metalized structure.

12.2 Electrode Characterization and Failure Mechanisms

For the finger CEO approach the main difficulty was to find the optimum MBE growth settings to avoid any material deposition on the finger flanks and on the finger top surface. Material deposition on the finger side walls would destroy the broken T-shaped growth structure, hence, no nanogap electrodes could be fabricated. Material deposition on the finger plateau would lead to short circuit paths as the shadow effect illustrated in figure 12.3(c) and (d) depends on a sharp edge from the CEO growth. Usually, during MBE growth the samples are rotated for a homogeneous material deposition. For the present task however, a directed growth with fixed sample position is preferable. Two different sample orientations were tested as shown in figure 12.4. The material cells are positioned on a circle on one side of the MBE chamber and the cells are numbered according to their position on an analog clock. Arsine (As) is always present as a background gas whereas aluminum and gallium are grown by a directed beam of atoms toward the device. The sample itself can be freely rotated with respect to the cells. In configuration A the sample normal is centered between the aluminum and the gallium cell. Therefore, one side of the mesa etched finger is exposed to the aluminum cell during growth, and the other one to the gallium cell. In configuration B the sample is rotated in order to hide one finger wall from the cells. In both configurations the deposition comes from a point below the sample bottom in order to prevent material deposition on the sample surface. After CEO growth the samples were characterized by SEM. For samples grown in configu- 174 Fabrication and Characterization of a CEO Nanogap Device

sample sample

Figure 12.4: Illustration of directed MBE growth for the finger CEO approach. In option A one side of the finger is exposed to the aluminum cell, and the other side to the gallium cell. In configuration B one side is exposed to both cells whereas the other one is hidden from material deposition. ration A it was found that material was indeed deposited on both finger walls in a curtain like shape as shown in the left panel of figure 12.5. The opposite finger side is not shown, but a similar structure was observed. Unfortunately, these “defects” could not be removed by citric acid solution. Non-surprisingly, a subsequent electrode metal deposition produced only short circuited devices. For devices grown in configuration B the material deposition occurred only on one mesa wall, as expected. Representative SEM micrographs are illustrated in the center and right panel of figure 12.5. The hidden mesa wall was protected from material deposition which instead accumulated on the opposite wall. Nevertheless all devices but one exception also experienced short circuits after electrode metal deposition. A trapping experiment on this single working device failed. The short circuits could mostly by traced back to metallic bridges still caused by the contamination on one side of the mesa wall. This material could not be removed during the selective etching process, hence, destroying the shadow effect necessary for proper electrode fabrication. In addition to the problems from material deposition on the mesa walls mainly two other failure mechanisms could be identified. They are illustrated by typical SEM micrographs in figure 12.6. On part of the samples the CEO MBE growth lead to a material deposition on the wafer surface as shown in the left panel of figure 12.6. Naturally, such wafers could not be used any further as the electrode metal deposition would easily produce short circuits. Another mechanism which might cause a metal bridge between left and right electrode were defects in the CEO grown “shadow wall”. An example for such a defect is shown in the right panel of figure 12.6 for a device after CAS etching. Due to this problems the “standard” CEO approach was tested in parallel to the finger CEO approach. It omits the mesa patterning and instead exposes the broken T-shaped electrode structure by cleavage. However, this implies that only one device can be integrated on one sample. An SEM image of a device after CEO growth is displayed in figure 12.7 illustrating the 12.2 Electrode Characterization and Failure Mechanisms 175

Figure 12.5: SEM micrograph of typical failure mechanisms for the CEO finger approach. Left: Curtain like material deposition on the finger side walls due to directed MBE growth in configuration A (see also figure 12.4). Center and Right: Effects of directed CEO growth in configuration B. One mesa wall seems free from contamination (center) whereas on the opposite wall of the same finger clearly material was deposited (right).

Figure 12.6: SEM micrograph of typical failure mechanisms. Left: Device after 30s etching in CAS. Clearly, material at the wafer / CEO layer interface can be seen which was probably deposited during CEO growth. Right: Defect in the “shadow wall” after selective etching. Such defects might lead to metal bridges connecting left and right electrode. layers grown in the first and the second MBE step. Due to the fresh cleavage the problematic material deposition known from the finger approach could be prevented. A further advantage of this approach is the accessibility of the nanogap region to AFM characterization. Typical topographical images of samples after selective etching and after a subsequent electrode deposition are displayed in figure 12.8. The devices shown comprise one

30 nm thick Al0.3Ga0.7As layer as the thin electrode, separated by a 25 nm thick GaAs layer from the thick electrode. The thin electrode is located at the right side of each topographical image. The AFM images together with the cross sections shown at the bottom of the ﬁgure demonstrate that a fabrication of broken T-shaped electrodes is indeed possible by using the CEO method. This emphasizes the large potential of CEO grown electrodes for molecular electronics applications! 176 Fabrication and Characterization of a CEO Nanogap Device

Figure 12.7: SEM micrograph of a CEO grown nanogap device. The brighter horizontal line visible in the epi layer is the 30nm thin AlGaAs layer which later transforms into the left electrode. The direction of growth becomes apparent from the tilted cleavage edge of the CEO grown layer.

Figure 12.8: AFM characterization of CEO nanogap electrodes. Left: Device with 30nm wide electrode layer and 25nm separation after 10s etching in CAS. Right: Same device after deposition of 3nm Ti and 10nm Au. At the bottom of both graphs two cross-sections are shown as indicated in the picture. The color palette was adjusted to blacken all structures which are more than 2nm below the maximum elevation (see lower right corner of both graphs). The blurred appearance of the right graph is either due to a smoothing effect of the metal deposition, or due to a blunter tip although for both AFM measurements fresh super-sharpened tips were used. 12.3 Conclusion 177

However, the proper electrical operation could not be demonstrated as all fabricated devices (approx. 20) suffered from short circuits. Part of this short circuits could be attributed to cleavage defects which frequently occur. A further part of the samples suffered from material deposition on the wafer surface. For the rest of the devices a possible connection between the electrodes by a non-working metal film rupture at the walls of the thin AlGaAs layer was identified. Therefore, the design of the device was improved: GaAs-AlGaAs superlattices were embedded below the “active” AlGaAs layer. This should lead to a metal film rupture in the same manner as for the planar electrode approach. Nevertheless the few samples which could be processed still suffered from short circuits.

12.3 Conclusion

In this chapter the fabrication of broken T-shaped electrodes using the CEO method was presented. Such electrodes would allow for the simultaneous characterization of single molecules and one-dimensional molecular layers. Two approaches were examined, a ﬁnger like structure integrating many devices on one sample, and a cleavage approach with the advantage of maximum electrode protection but the drawback of only one device per sample. For the ﬁnger approach the problem of material deposition on the mesa walls during MBE growth could not be solved. Based on the cleavage approach however, electrodes could be fabricated and AFM examinations demonstrated its large potential. However, the demonstration of proper electrical function could not yet be achieved. 178 Fabrication and Characterization of a CEO Nanogap Device Chapter 13

Summary and Outlook

During the work on the present thesis nanometer spaced electrodes based on III-V semiconductor structures were fabricated, characterized, and used to measure the conductance of oligophenylenevinylene (OPV) derivatives. In the first part the nanogap fabrication process based on the cleavage of AlGaAs-GaAs heterostructures was explained, and process parameters such as electrode material, electrode thickness, and selective etching duration were optimized. Best results were obtained for Ti/Au as electrode material, metal layer thicknesses of 2 nm/6 nm - 3 nm/7 nm Ti/Au, and etching times of 30-40 s. Furthermore, the surface of processed nanogap electrodes was characterized by AFM and SEM revealing clean and smooth electrode surfaces with electrode separations being approx. 3 nm larger than the sacrificial GaAs layer thickness. Structures with electrode separations down to 8 nm could be fabricated reproducibly although with low yield. As most probable failure mechanisms the bridging of the nanogap region due to either non-perfect etching or lateral growth during metal deposition were supposed. In addition to the AlGaAs-GaAs heterostructure based devices, nanogap electrodes based on InAs were examined with promising results for further research. The applicability of the presented nanogap fabrication method to molecular electronics was tested by successfully positioning single gold nanoparticles of 30 nm diameter between approx. 22.5 nm separated electrodes. This led to a resistance change by six orders of magnitude. The next step toward a hybrid molecular electronics device was performed by examining the current carrying properties of OPV molecules experimentally using AlGaAs-GaAs heterostructure based nanogap electrodes. In current voltage measurements on OPV derivatives a conductance gap for low bias voltages followed by an exponential like increase in current was observed. By applying extended Hückel theory and the non-equilibrium Greens function formalism to simplified OPV molecules a qualitative agreement between theory and experiment could be demonstrated. Explanations for existing quantitative deviations in the simulated IV character-

179 180 Summary and Outlook istics from the experiment were proposed. Furthermore, the fabrication of broken T-shaped electrodes using the CEO method as an extension to the previous technique was examined which would allow for the simultaneous characterization of single molecules and one-dimensional molecular layers. AFM examinations demonstrated the large potential of the CEO nanogap fabrication technique, however, a proper electrical function hast still to be investigated.

13.1 Implementation of a Gate Electrode

An important advantage of the presented nanogap electrode fabrication technique compared to competing methods is the comparably simple integration of a third electrode acting as a gate. The sacrificial GaAs layer, which was only necessary to define the trench for electrode rupture, could be actively used as a gate in case of high doping. An adaption of the device layout to separately contact this gate electrode can be easily implemented. Such a three electrode setup would allow for a deeper insight into the electronic structure of the examined molecules and the role of the molecular orbitals in current transport phenomena: The gate could be used to shift the orbital energies with respect to source and drain Fermi energies, thereby, moving them into or out of the energy window opened by the electrodes. This would furthermore allow for a transistor operation of the molecule similar to common solid state devices. However, problems arise from the electrostatic shielding of the gate potential by the source and drain electrodes. To evaluate this, model calculations were performed on a semiconductor nanogap device similar to a real device layout. Results for a silicon based device with 7.5 nm thick source and drain electrodes separated by 5 nm are illustrated in figure 13.1. Such a structure is comparable to typical AlGaAs-GaAs heterostructure based semiconductor electrodes. Source and drain electrode are held at -1 V and +1 V, respectively, whereas the gate potential is set to +5 V. The potential distribution in the whole structure is color coded as shown at the right side of each graph. As can be seen for a gate located at 10 nm below source and drain, i.e. left and right, electrodes the bright regions around the gate, which represent potentials of 2-3 V, do not reach the space between source and drain electrode. Molecules lying on the electrodes at point A, or even attached below the electrodes at point B, would almost not “feel” the gate, instead their potential is determined effectively only by source and drain electrodes. Even for a hardly achievable gate location of only 2.5 nm below source and drain electrode, molecules at point A would not be affected by the gate potential. Only at point B a slight variation in the potential distribution can be observed. The reason for this very small gate effect is the electrostatic shielding of the potential by the comparably large source and drain electrodes. 13.2 InAs-InP-InAs System 181

Figure 13.1: Electrostatic simulation of a gate electrode beneath semiconductor based nanogap electrodes. The source and drain, i.e. left and right, electrode metal layer thickness is 7.5 nm, and the electrode separation 5 nm. Both electrodes were held at -1 V and +1 V, respectively. The potential distribution in the structure is color coded as indicated at the right side of each graph. Left: The gate electrode, represented by a 5 nm x 5 nm large square held at +5 V, is located at 10 nm below the source and drain electrodes. Right: Same as left graph but with a distance between gate and left / right electrode of 2.5 nm.

These ﬁndings imply that the layout of three electrode nanogap devices must be improved to attach molecules not on top of source and drain electrode but somehow locate them below the electrodes closer to the gate. A possible starting point might by an underetching of the electrodes to open a microﬂuidic channel between source and drain, and gate electrode. Never- theless, processing would become more complicated and unwanted effects like the assembly of molecules between either source and gate, or drain and gate must be addressed.

13.2 InAs-InP-InAs System

A further promising extension to the present system is the step from metal electrodes to semiconductor electrodes as was already introduced in section 10.6 for InAs based electrodes. Here the main difficulty was to find an appropriate barrier material to electrically insulate the surface conducting InAs layers and at the same time provide for a proper MBE growth. For bulk MBE growth this resulted in serious problems, however, by switching to nanowire growth new material systems such as InP could be tested. Although bulk growth of InAs-InP-InAs is not possible due to the high strain, nanowires allow for the lateral relaxation of the InP layers which enables a controlled and ordered growth of InAs-InP heterostructures with monolayer precision [200, 201]. In collaboration with the group of Prof. Lars Samuelson at the university of Lund, Sweden, first tests on InAs-InP nanowire devices were started. A schematic for such a device suitable for molecular electronics applications is illustrated in figure 13.2. By locating the nanowires on a conducting substrate with a thin insulating layer, e.g., SiO2 on Si, a gate could be implemented even more easily than with the “standard” AlGaAs-GaAs heterostructure based approach (not 182 Summary and Outlook illustrated in the figure). However, even InP might not show sufficiently good insulating properties at the required layer thicknesses of only 3-5 nm for typical bias voltages of 1-2 V. Such values would be necessary for a proper characterization of molecules. Therefore, it was tried to selectively etch the InP layer to obtain a InAs-vacuum-InAs system which would show superior insulating properties. As acid, HCl based solutions were chosen which are known to readily etch InP layers and at the same time leave InAs layers almost untouched [178, 202]. On nanowires, this behavior could be verified for thick InP layers embedded in InAs wires as is shown in figure 13.3. In the approx. 60 nm thick InAs nanowires various InP layers of different thickness were implemented as observable in the TEM micrograph: one very thick layer measuring approx. 150 nm in length and three, only 3-4 nm thin InP layers closer to the end of the nanowire on the right side of the graph. After 30 s etching in concentrated HCl the thick InP layer was indeed removed, however, for the thin InP layers no etching could be observed as shown in the SEM micrograph at the bottom of figure 13.3. Even for layers up to 20 nm thickness no effect was observable which excludes the limited resolution of the SEM as cause for the missing observation. A probable explanation might be a strain induced change in etching characteristics, a dependence of etch selectivity on crystal orientation, or InAs impurities left in the InP layer which could stop the selective etching. Nevertheless, the InAs structure is a very promising system for future molecular electronics applications due to its interesting electronic properties. Furthermore, a working InAs device would open the door to a broad research field regarding molecule - semiconductor interactions

Figure 13.2: Schematic of an InAs nanowire device.

Figure 13.3: (A) TEM micrograph of a InAs nanowire with embedded InP layers before treatment. (B) SEM micrograph of identical nanowires after etching them for 30 s in concentrated HCl (37%). The 3-4 nm thin InP layers are indicated by arrows in the TEM micrograph. Graphs taken by C. Thelander (Univ. Lund, Swe- den). 13.2 InAs-InP-InAs System 183 and gate induced conductance changes. Therefore, further efforts in this direction are highly recommended. 184 Summary and Outlook Bibliography

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A.1 List of Abbreviations

2D 2-Dimensional 2DEG Two Dimensional Electron Gas AFM Atomic Force Microscope AlGaAs Aluminum-Gallium-Arsenide AlSb Aluminum-Antimonide Au Gold CAS Citric Acid Solution, i.e., C6H8O7 dissolved in water, and mixed with H2O2 (5:1) CB Coulomb Blockade CEO Cleaved Edge Overgrowth CP Contact potential CV Cyclic Voltammetry DCM Di-Chloro-Methane (H2-C-Cl2) DNA Desoxy-Ribonucleic-Acid EA Electron Afﬁnity EHT Extended Hückel Theory ET Electron Transfer FET Field-Effect Transistor FTIR Fourier Transform Infrared Spectroscopy GaAs Gallium-Arsenide GaN Gallium Nitride GaSb Gallium-Antimonide GC Gouy-Chapman HME Hybrid-Molecular Electronic device HOMO Highest Occupied Molecular Orbital HRXPS High Resolution Xray Photoelectron Spectroscopy HT Hückel Theory IETS Inelastic Electron Tunneling Spectroscopy IHP Inner Helmholtz Plane continued on next page ...

201 202 Appendix

InAs Indium-Arsenide IP Ionization Potential IPA IsoPropAnol IS Impedance Spectroscopy ISFET Ion-Selective Field Effect Transistor KP Kelvin Probe LUMO Lowest Unoccupied Molecular Orbital MBE Molecular Beam Epitaxy MBP 4-mercaptobiphenyl (H-(C6H4)2-SH) MBP-CH3 4’-methyl-4-mercaptobiphenyl (CH3-(C6H4)2-SH) MBP-H 4-mercaptobiphenyl (H-(C6H4)2-SH) MBP-OH 4’-hydroxy-4-mercaptobiphenyl (HO-(C6H4)2-SH) MCBJ Mechanically Controlled Break Junction MDSI Modulation Doped Single Interface device MME Mono-Molecular Electronic device NEGF Non-Equilibrium Green’s Function formalism NEXAFS Near Edge Xray Adsorption Fine Structure ODT OctaDecaneThiol OHP Outer Helmholtz Plane OPV OligoPhenyleneVinylene PB Poisson-Boltzmann PBS Phosphate Buffered Saline PPV PolyPhenyleneVinylene RMS Root Mean Square (roughness) SAM Self-Assembled Monolayer SCF Self Consistent Field SDOS Surface Density Of States Si Silicon SPM Scanning Probe Microscope SPR Surface Plasmon Resonance SPV Surface Photo Voltage STM Scanning Tunneling Microscope vdW van der Waals WF Work Function

A.2 List of Symbols

[] Concentration in mol/litre Xi Property X of an ion of type i Xs Property X at the surface continued on next page ... A.2 List of Symbols 203

Xl,Xr Property X at left or right electrode, respectively X∞ Property X in inﬁnity

β Tunneling decay parameter χ Electron affinity δ Thickness of the compact Stern layer ε Dielectric constant −12 2 ε0 Permittivity of free space: 8.854 · 10 C /Jm η Voltage division factor: one-parameter characterization of the profile of the applied potential inside a molecule Γ0 Saturation adsorption ΓD,ΓA Broadening of donor and acceptor level, respectively Γl,Γr Broadening of a molecular level due to coupling to the left and right electrode, respectively ∞ Infinity κ Debye length µ Chemical potential or Fermi energy µl, µr Fermi energy of left and right electrode, respectively φ Barrier height φW Work function Φ Energy gained by adsorption ψ Electrostatic potential in V ψs Electrostatic surface potential in V ψδ Electrostatic potential at the outer Helmholtz plane in V ρ Concentration in 1/m3 σ Charge density in C/m2 2 σadd Additional fixed surface charge used in simulations in C/m 2 σads Surface charge density caused by adsorbed molecules in C/m σads,max Maximum surface charge density caused by adsorbed molecules in C/m2 2 σs Surface charge density in C/m τ electron life time in a certain energy state

c Concentration in mol/litre CDL Double layer capacitance Csc Space charge layer capacitance D(~k) Density of states in k-space e Elementary charge: 1.6022 · 10−19 C ~E Electric ﬁeld ECB Conduction band edge energy continued on next page ... 204 Appendix

ECNL Charge neutrality level, which denotes the Fermi energy of a neutral molecule EF Fermi energy Eg Band gap energy EHOMO Energy of Highest Occupied Molecular Orbital ELUMO Energy of Lowest Unoccupied Molecular Orbital EMol Energy of a molecular level E~S Surface electric ﬁeld EVB Valence band edge energy EVL Local vacuum level fl, fr Distribution function for left and right electrode, usually the Fermi distribution fε Fermi distribution function at energy ε G Conductance in A/V I Ionic strength (1st part), or current (2nd part) ISD Source drain current j Current density in A/m2 kD→A Rate of electron transfer from donor D to acceptor A in 1/s −23 kB Boltzmann constant: 1.381 · 10 J/K ~kl,~kr,kl,kr k-vectors and their absolute values for left and right electrode, respectively Keq Reaction constant Ka Reaction constant, considering the water concentration as constant l Hall bar length m∗ Effective electron mass N Number of electrons, atoms, or molecules 23 NA Avogadro number: 6.022 · 10 /mol Nads,bulk Absolute number of adsorbant molecules in the bulk solution Nall,bulk Absolute number of all molecules in the bulk solution 3 ND Donor concentration in 1/m 2 Ns Density of surface sites in 1/m pHpzc pH of the point of zero charge T Absolute temperature in K Tt Transmission RRMS Root mean squareq roughness: For an AFM image with N datapoints of N 2 N ∑i=1(zi−z¯) ∑i=1 zi height zi:RRMS = N−1 , with the mean value z¯ = N RSa Sample resistance measured in 2-point geometry: RSa = VSD/ISD in Ω RSh Sheet resistance measured in 4-point geometry: RSh = V4P/ISD in Ω/¤ Uch Charging energy a molecule gains by an transfer of one electron onto it 3 Uel Electrolyte potential used for nextnano simulations continued on next page ... A.3 Processing Details for Biosensor Fabrication 205

3 USa Sample potential used for nextnano simulations −28 3 v0 Volume of a hydrated hydroxyl ion in solution v0 = 1.1 · 10 m v,vz Absolute velocity, velocity in z-direction V4P Voltage drop along Hall bar in 4-point geometry VBB Band bending VB Backing potential in V VC Contact potential in V Vf b Flat band potential VSa Sample potential Vsc Voltage drop across space charge layer VSD Source drain voltage VDL Voltage drop across double layer w Hall bar width z Valency of an ion

A.3 Processing Details for Biosensor Fabrication

A.3.1 Standard Photolithography and Mesa Etching Step

First, the samples were cleaned by subsequent sonication in acetone and isopropanol (IPA) and purged dry by nitrogen (N2). Then, thin photoresist was deposited (Shipley S1805) for 40 s at 6000 rpm. After that, a soft bake was done for 30 min in a 90°C oven. Subsequently, the mask layout was transferred to the photoresist by UV exposure for approx. 5s with a Karl Suss MJB-3 mask aligner. This was followed by a developing step for approx. 10-30 s in a mixture of AZ 351B developer and deionized (DI) water (1:4). In the following, the developing was stopped in DI water and the sample was dried by N2. Then, a hard bake at 120°C for another 30 minutes was performed. After that, the mesa was etched in a solution containing orthophosphoric acid (H3PO4), hydrogen peroxide (H2O2) and water (H2O) in a ratio of 1:1:38 for about 60 s. Typical etch depths have been measured by proﬁlometer (DekTak) being ≈ 100 nm. The quality of all process steps was controlled by optical microscopy.

A.3.2 Standard Lift-Off Step

The Lift-Off procedure is similar to the standard photolithography step. Usually another type of photoresist (Shipley 1818) was used and the soft-bake was shortened to 15 min. The exposure time was slightly longer and the hard bake was omitted. To improve the slope of the photoresist for better lift-off results certain tests were done with a 60 s dip in phenyl-chloride (C6H5Cl) prior to UV exposure to harden the surface of the photoresist. However, no signiﬁcant change in process yield could be observed. After the developer step the sample was build into the evaporation chamber and the desired metals were evaporated. If an Ohmic contact was desired, 206 Appendix then the native oxide of the sample was removed by a dip in concentrated HCl shortly before mounting them into the evaporation chamber. After the removal from the chamber the sample was immersed into acetone for at least 1h. Then, the metal was lifted-off by an acetone ﬂow generated by pipette pumping. Subsequently, the sample was cleaned again. Sometimes a soft ultrasonication or mechanical force exerted by a wooden toothpick helped to lift-off the metal from the substrate.

A.4 Evaluation of Gaussian 03W Electronic Structure Cal- culations

To test the reliability of the Gaussian 03W calculations [70] employing DFT theory with the 6-31G+(d,p) basis set and the B3LYP functional for dipole moment calculations a comparison to values listed in the Beilstein database [65] was made. No value for mercaptobiphenyls was found, therefore other molecules were chosen for comparison. To check the correct calculation of the endgroup influence various benzene derivatives were simulated. The results are listed in table A.3. Furthermore, the reliable simulation of the thiol influence on the molecular dipole moment was tested with several alkanethiols. For all tested molecules the calculated dipole moments are in very good agreement with the experimentally obtained values. In few cases a slight overestimation, especially for the thiol influence, of the dipole moment by Gaussian 03W was observable.

A.5 Nanogap Device Processing Details

A.5.1 Preparation of Citric Acid Based Solution (CAS) Organic acid based solutions are common selective etchants for III-V semiconductors [178]. For the GaAs-AlGaAs system a citric acid (C6H8O7) - hydrogen peroxide (H2O2) mixture was chosen with a reported selectivity of 115:1 for GaAs vs. Al0.3Ga0.7As [173]. It was prepared by mixing 1.094 g of monohydrate citric acid (C6H8O7·H2O) with 0.906 ml DI water and then diluting 5 parts of the resulting solution with 1 part H2O2.

A.5.2 Mesa Etching First, the cap layer was removed by 5 s etching in CAS. Then, the etching was stopped in DI water for at least 20 s, the sample cleaned with IPA1, and purged dry with nitrogen. After that, a standard cleaning procedure was performed (subsequent 1 min bath in acetone and IPA, followed by rinsing) and purged dry with nitrogen. Subsequently, the sample was coated with

1isopropanol A.5 Nanogap Device Processing Details 207

Structural Molecule Beilstein Gaussian 03W formula name database [65] results [70] µ [Dy] µ [Dy] Benzene derivatives H-C6H5 benzene 0.0 0.0 OH-C6H5 phenol 1.3-1.6 1.6 CH3-C6H5 toluene 0.3-0.4 0.4 F-C6H5 ﬂuorobenzene 1.6 1.7 CF3-C6H5 triﬂuoromethyl-benzene 2.2-2.8 3.1 H-C6H4-SH benzenethiol 1.4 1.8 Alkanethiols CH3-C5H10-SH hexane-1-thiol 1.6 1.9 H-C4H8-SH butane-1-thiol 1.5 1.8 CH3-C4H8-SH pentane-1-thiol 1.5 1.9

Table A.3: Comparison between Gaussian 03W results and Beilstein database listed dipole moments for various benzene derivatives and alkanethiols. For the OH terminated benzene the direction of the dipole moment is opposite compared to the other benzene derivatives. However, dipole moment directions are not listed in the database therefore only absolute values were compared.

Shipley S1805 photoresist for 40 s at 8000 rpm. Then, the sample was soft-baked for 30 min in a 90°C oven. In the following, the sample was given time to cool down, and the desired structure was transfered by UV illumination for approx. 5 s (exact time varied with lamp power). Subsequently, the structure was developed for approx. 10 s in developer solution (AZ400:H2O = 1:4). The development was stopped by DI water (> 30 s) and the sample purged dry. Then, the sample was hard baked for 30 min in a 120°C oven. After letting the sample cool down, the mesa structure was etched in phosphoric acid solution (H3PO4:H2O2:H2O = 1:1:38). Etch rate is approx. 100 nm/min. The etching was stopped in DI water, the photoresist removed by acetone (>30 s bath + rinsing) and a standard cleaning procedure performed. Etch depths were controlled by proﬁlometer (Dektak). (see also section A.3.1)

A.5.3 Contact Pad Deposition

For contact pad deposition a lift-off process is used as was already described in section A.3.2. Sometimes also an additional oxygen plasma step prior to metal evaporation was applied to remove photoresist residues on the sample surface in the exposed areas. 208 Appendix

A.5.4 Cleavage and Selective Etching Cleavage is done by scribing a mark at one end of the sample with a diamond needle and then applying a shear force with two tweezers. After that, the embedded GaAs layer is etched selectively versus the outer AlGaAs layers using the above described CAS etch for 10-40 s. The etching is stopped with DI water (>30 s), then the sample is washed with IPA, and purged dry by N2. The IPA step helps to remove remaining water and etch residues on the sample as it is water soluble but easier to evaporate.

A.5.5 Nanogap Electrode Deposition After etching, the electrode forming thin ﬁlm metal layer is evaporated perpendicularly to the cleaved surface. To do so, the sample is built in a specially designed sample holder for the evaporation machine which allows for perpendicular evaporation. An increase in yield was observed by building the sample in upside-down, i.e. with the contact pad side on the sample holder. Then, after evacuating the evaporation chamber to pressures below 4 · 10−7 mbar, titanium and gold layers were evaporated at rates of approx. 1Å/s.

A.5.6 Bonding and Packaging The samples were usually glued to standard 8-pin or 20-pin chip carriers by double side adhesive tape. Sometimes, also standard two-component glue or wax was used. All methods were able to survive the later molecule deposition process which implies a long time immersion in strong organic solvents. However, a slight contamination of the molecule containing solution by dissolution of tape, glue or wax could not be excluded. Therefore, freshly prepared molecule solutions were used. The electrical contact of the device to the chip carrier was accomplished by standard gold wire ball bonding on a Hybond 522A machine. Unfortunately, many devices broke down during this process, probably due to the ultrasonication during the bonding. Especially the adhesion of bottom electrode pads was not satisfactory. Therefore, it is recommendable to start the ﬁrst bond on the sample, and not on the chip carrier: If the bond is not successful, at least no wire has to be removed from the chip carrier. Best results were obtained with the settings listed in table A.4.

1st bond 2nd bond (on sample) (on chip carrier) Ultrasonic power 2 4 Time 4 10 Force 5 4

Table A.4: Bond parameters yielding best results on a Hybond 522A gold wire ball bonder. List of Publications

In preparation:

x High-Aspect Ratio Nanogap Electrodes for Molecular Electronics Applications. S. Luber, S. Lingitz, F. Zhang, A. G. Hansen, F. Scheliga, E. Thorn-Csányi, M. Bichler, M. Tornow; accepted by small

y Characterization of a Chemically Passivated GaAs Based Sensor Device in Electrolytes. S. Luber, D. Gassull, D. Schuh, M. Tanaka, M. Tornow, G. Abstreiter;

Peer reviewed journal articles:

z Silicon-on-Insulator Microﬂuidic Device With Monolithic Sensor Integration for µTAS Applications. S. Sharma, K. Buchholz, S. Luber, U. Rant, G. Abstreiter, M. Tornow; IEEE Journal of Microelectromechanical Systems 15, 308-313, (2006)

{ Nanometre spaced electrodes on a cleaved AlGaAs surface. S. Luber, S. Strobel, H-P. Tranitz, W. Wegscheider, D. Schuh, M. Tornow; Nanotechnology 16, 1182-1185, (2005)

| Liquid Phase Sensors Based on Chemically Functionalized GaAs/AlGaAs Heterostruc- tures. S. Luber, K. Adlkofer, U. Rant, A. Ulman, M. Grunze, D. Schuh, M. Tanaka, M. Tornow, G. Abstreiter; Physica E 21, 1111-1115, (2004)

209 210 List of Publications

} Silicon-on-Insulator Based Thin-Film Resistor for Chemical and Biological Sensor Ap- plications. M. G. Nikolaides, S. Rauschenbach, S. Luber, K. Buchholz, M. Tornow, G. Abstreiter, A. R. Bausch; ChemPhysChem 4, 1104-1106, (2003)

Non-reviewed journal articles:

~ “Nano-Engineering” auf ultra-glatten Halbleiteroberﬂächen - Neue Konzepte für die molekulare Nanoelektronik. M. Tornow, S. Luber, F. Zhang, A. Hansen, M. Bichler, E. Thorn-Csányi, F. Scheliga; Nanotechnologie in Bayern, Magazinreihe “Zukunftstechnologien in Bayern”, media mind Verlag, München, (2006)

Chemically Passivated GaAs/AlGaAs Heterostructure HEMTs for Biosensor Applica- tions. S. Luber, K. Adlkofer, U. Rant, A. Ulman, M. Grunze, D. Schuh, M. Tanaka, M. Tornow, G. Abstreiter; Proceedings of the 26th ICPS, IoP Conference Series 171, P277, (2002)

Patents:

Semiconductor Based Nanoelectronic Device Structure. O. Dier, S. Luber, M. Tornow; Technische Universität München, European patent application, EP06000250, (2005)

Silicon-on-Insulator Biosensor Device. G. Abstreiter, A. R. Bausch, K. Buchholz, S. Luber, M. G. Nikolaides, S. Rauschenbach, E. Sackmann, M. Tornow; Fujitsu Laboratories Ltd., international patent, DE-10221799-A1, GB-2390938-B, JP- 2003329638-AA, US-6870235-B2, (2002) Acknowledgement

Diese Arbeit wäre ohne den Beistand vieler Personen nicht möglich gewesen, bei denen ich mich an dieser Stelle herzlich bedanken möchte. Dabei reichte die Unterstützung vom fachli- chen Bereich bis in den privaten Bereich, in dem vor allem meine Familie und Freunde beim Überstehen anstrengender Phasen geholfen haben. Im Folgenden werde ich versuchen, die mei- sten Personen, die zum Gelingen dieser Arbeit beigetragen haben, namentlich zu nennen. Prof. Gerhard Abstreiter gebührt mein größter Dank, für die Aufnahme als Doktorand an seinen Lehrstuhl und für die hervorragenden Rahmenbedingungen, die er für meine wissenschaftliche Arbeit am WSI geschaffen hat. Außerdem bedanke ich mich für sein großes Interesse am Fortgang der Arbeit, vor allem die in schönstem Bayerisch geäußerten Fragen haben maßgeblich die Richtung der Dissertation beeinflusst. Als nächster ist Dr. Marc Tornow zu nennen, der mich in seine Arbeitsgruppe aufgenommen hat und meine Arbeit ausgezeichnet in vielfältiger Weise betreut hat. Vor allem auch seine Unterstützung in schwierigeren Situationen hat mir sehr geholfen. Des Weiteren hat mein Trauzeuge Dr. Uli Rant großen Anteil an meiner Arbeit. Durch Motivation in allen Bereichen und vielfache wissenschaftliche Diskussionen hat er mich immer weiter vorangetrieben. Am Erfolg des ersten Teils der Arbeit war auch die Gruppe um Dr. Motomu Tanaka maß- geblich beteiligt, die für die Passivierung der Biosensoren verantwortlich war. Insbesondere ist Daniel Gassull zu nennen, der die Arbeit von Dr. Klaus Adlkofer weitergeführt hat, und mit vielen Diskussionen die GaAs Sensoren angetrieben hat. Auch war er der erste Katalane, der den Münchener Winter in kurzen Hosen überstanden hat! Den zweiten Teil der Arbeit haben zu einem großen Teil die Diplomstudenten, die ich betreuen durfte, bearbeitet und beeinflusst. Den Anfang bildete Sebastian Strobel, der u.a. das experimentelle Setup mit aufgebaut, und die Ex- perimente zum elektrostatischen Trapping durchgeführt hat. Dabei hat er ausgezeichnete Arbeit geleistet, selbst wenn es menschlich zwischen uns manchmal hakelte. Sein Nachfolger war Fan Zhang, der erste Molekülmessungen durchführen konnte, und asiatischen Flair in die Arbeits- gruppe einbrachte. Danach, bis zum Ende der Dissertation, unterstütze mich Simone Lingitz als hervorragende Allrounderin, die sowohl in der Simulation als auch in den Experimenten ausgezeichnete Arbeit geleistet hat. Die Messungen an den Molekülen wären auch ohne die Hilfe von Dr. Allan Hansen nicht möglich gewesen, der mit dänischer Gelassenheit den OPV Molekülen die besten Abscheideparameter abgerungen hat. Die dabei gesammelten Messdaten hat er mir dankenswerterweise für diese Arbeit zur Verfügung gestellt. Die OPV Moleküle wurden dabei von Dr. Felix Scheliga in der Arbeitsgruppe von Prof. Dr. Emma Thorn-Csányi synthetisiert, 211 212 Acknowledgement der in mühevoller Arbeit Moleküle herstellen konnte, die für unsere Zwecke geeignet waren. Ohne ihn wären keine direkten Messungen an Molekülen möglich gewesen. Für das GaAs Probenwachstum darf ich mich vor allem bei Max Bichler bedanken, der immer ein offenes Ohr für zumeist dringende Probenwünsche hatte. Außerdem haben auch Dr. Dieter Schuh, Prof. Werner Wegscheider, und Dr. Peter Tranitz Proben gewachsen. Weiterhin ist bei den Versuchen mit InAs besonders Oli Dier hervorzuheben, der mit wirklich beispielhaftem Engagement das Projekt unterstützt und vorangetrieben hat. Bei den theoretischen Berechnungen zum Stromtransport bekam ich sehr große Unterstützung durch Luca Latessa und Prof. Paolo Lugli. Und auf der Biosensor Seite wurde ich bei den Simulationen hervorragend durch Stefan Birner, dem nextnano3 Produzenten, unterstützt. Vie- len Dank auch fürs Korrekturlesen und die Implementierung neuer Features in nextnano3 (“ab morgen ist es drin...”). Bei den Dipolmoment-Berechnungen stand mir außerdem Dr. Georg Heimel beratend zur Seite. Euch allen vielen Dank dafür! Auf technischer Seite wurde mir ebenfalls Hilfe von vielen Seiten zu teil: In der Technologie von Angelika Stumpf, Claudia Paulus und Sonja Matich, in der Werkstatt von Wolfgang Bendak, Fritz Sedlmeir, Michi Fischer und Hubert Riedl, und in allen Belangen vom her- ausragenden Ade Ziegltrum. Für Hilfe bei verzwickten bürokratischen Belangen möchte ich mich auch besonders bei Irmgard Neuner, der “guten Seele des Lehrstuhls”, bedanken. Für die Beratung in internationalen Belangen, insbesondere während meines Aufenthaltes in Japan, bin ich auch besonders Kenji Arinaga zu Dank verpflichtet, der mir half, die Eigenhei- ten der japanischen Mentalität verstehen zu lernen. Außerdem waren viele weitere Personen am Erfolg meiner Arbeit beteiligt, u.a. Dr. Karin Buchholz, die mich auch bei der Jobsuche unterstützte, Dr. Michael Nikolaides und Stephan Rauschenbach mit ihrer Zusammenarbeit bei den Biosensoren, Dr. Claes Thelander und Prof. Lars Samuelson durch ihre Arbeit zu den InAs Nanowires, und viele mehr. Für die gute Atmosphäre im Büro möchte ich bei Dominic Dorfner, Shivaji Dasgupta, Dr. Claus Ulbrich, und Dr. Joel Moser bedanken. Des Weiteren möchte ich einige weitere Kollegen namentlich nennen, die durch tatkräftige Hil- fe, kritische Fragen und/oder gute Atmosphäre die Arbeit beeinflusst haben: Dr. Erika Prings- heim, Michael Huber, Olaf Weidemann, Thomas Wassner, Andreas Härtl, Dr. Frank Fi- scher, Miro Kroutvar, Matthias Herbst, Dr. Matt Grayson, Sebastian Roth, Dr. Dominique Bougeard, Dominik Heiss, Barbara Baur, ... Finanzielle Unterstützung erfuhr diese Arbeit aus dem Sonderforschungsbereich 563 der Deut- schen Forschungsgemeinschaft, durch Fujitsu Laboratories Europe und vor allem auch durch das BMBF mit der Nano-Nachwuchsgruppe 03N8713. Und nun darf ich noch meiner Familie danken, vor allem meiner Frau Nicola, für ihre Unter- stützung und noch vieles mehr, meiner Tochter Maja Carlotta, die den Rhythmus der Schreib- phase mitgestaltet hat, meinen Eltern, die meine Ausbildung und soviel anderes ermöglicht haben, und meiner Schwester Andrea. Außerdem meinen Ex-Kommilitonen Silvester Kuhar und Tilo Steinmetz für den Spaß am Studium. In der Schriftenreihe des Walter Schottky Instituts der Technischen Universität München sind bisher folgende Bände erschienen:

Vol. 1 Vol. 7 Cornelia Engel Markus Sexl Si/SiGe basierende Phototransistoren Verspannte und gitterrelaxierte 131 Seiten In(GaAl)As Heterostrukturen ISBN 3-932749-01-4 144 Seiten ISBN 3-932749-07-3

Vol. 2 Vol. 8 Peter Schittenhelm Christian Obermüller Selbst-Organisation und Selbst-Ordnung Photolumineszenszspektroskopie mit in Si/SiGe-Heterostrukturen optischen Nahfeldmethoden an GaAs- 151 Seiten Nanostrukturen ISBN 3-932749-02-2 140 Seiten ISBN 3-932749-08-1

Vol. 3 Vol. 9 Andreas Nutsch Edilson Silveira Selektive Epitaxie von (GaIn)(AsP) Inelastische Lichtstreuung an niedrig- Schichtstrukturen dimensionalen Halbleiterstrukturen 129 Seiten 104 Seiten ISBN 3-932749-03-0 ISBN 3-932749-09-X

Vol. 4 Vol. 10 Peter Baumgartner Eberhard Christian Rohrer Optische und elektronische Eigenschaften Photoleitungs-Spektroskopie von lasergeschriebener GaAs-Nanostrukturen Diamant 180 Seiten 153 Seiten ISBN 3-932749-04-9 ISBN 3-932749-10-03

Vol. 5 Vol. 11 Walter Franz Rieger Thomas Wimbauer Untersuchung der elektronischen und Magnetische Resonanz-Untersuchungen an strukturellen Eigenschaften von modernen Halbleitermaterialien GaNAlN und deren Legierungen 125 Seiten 158 Seiten ISBN 3-932749-11-1 ISBN 3-932749-05-7

Vol. 6 Vol. 12 Markus Hauser Herbert Verhoeven Oberflächenemittierende Laserdioden Thermische Eigenschaften von mit Mehrfachepitaxie CVD-Diamantschichten 148 Seiten 154 Seiten ISBN 3-932749-06-5 ISBN 3-932749-12-X

Vol. 13 Vol. 20 Hans-Christoph Ostendorf Christoph Martin Engelhardt Trennung von Volumen- und Zyklotronresonanz zweidimensionaler Oberflächenrekombination in Silizium Ladungsträgersysteme in Halbleitern, 128 Seiten Effekte der Elektron-Elektron-Wechsel- ISBN 3-932749-13-8 wirkung und Lokalisierung 317 Seiten Vol. 14 ISBN 3-932749-20-0 Martin Städele Dichtefunktionaltheorie mit exaktem Vol. 21 Austausch für Halbleiter Eduard Neufeld 202 Seiten Erbium-dotierte Si/SiGe-Lichtemitter und ISBN 3-932749-14-6 -Wellenleiter 136 Seiten Vol. 15 ISBN 3-932749-21-9 Helmut Angerer Herstellung von Gruppe III-Nitriden mit Vol. 22 Molekularstrahlepitaxie Gert Schedelbeck 144 Seiten Optische Eigenschaften von Halbleiter- ISBN 3-932749-15-4 nanostrukturen hergestellt durch Über- wachsen von Spaltflächen Vol. 16 154 Seiten Wolfgang Heller ISBN 3-932749-22-7 Spektroskopie einzelner Quantenpunkte in magnetischen und elektrischen Feldern Vol. 23 128 Seiten Jürgen Zimmer ISBN 3-932749-16-2 Optoelektronisches Verhalten von Dünn- schichtbauelementen aus amorphem und Vol. 17 mikrokristallinem Silizium Molela Moukara 171 Seiten Pseudopotentiale mit exaktem Austausch ISBN 3-932749-23-5 117 Seiten ISBN 3-932749-17-0 Vol. 24 Berthold Schmidt Vol. 18 Leistungsoptimierung abstimmbarer Ralph Oberhuber InGaAsP/InP Halbleiterlaser Elektronische Struktur und Transport in 85 Seiten verspannten Halbleiterschichtsystemen ISBN 3-932749-24-3 110 Seiten ISBN 3-932749-18-9 Vol. 25 Jianhong Zhu Vol. 19 Ordering of self-assembled Ge and SiGe Reiner Pech nanostructures on vicinal Si surfaces High-Energy Boron-Implantation into 120 Seiten Different Silicon Substrates ISBN 3-932749-25-1 158 Seiten ISBN 3-932749-19-7 Vol. 26 Vol. 33 Gerhard Groos Martin Rother Herstellung und Charakterisierung von Elektronische Eigenschaften von Silizium-Nanostrukturen Halbleiternanostrukturen hergestellt durch 168 Seiten Überwachsen von Spaltflächen ISBN 3-932749-26-X 196 Seiten ISBN 3-932749-33-2

Vol. 27 Vol. 34 Uwe Hansen Frank Findeis Theorie der Reaktionskinetik an Optical spectroscopy on single self- Festkörperoberflächen assembled quantum dots 119 Seiten 156 Seiten ISBN 3-932749-27-8 ISBN 3-932749-34-0

Vol. 28 Vol. 35 Roman Dimitrov Markus Ortsiefer Herstellung und Charakterisierung Langwellige Vertikalresonator-Laser- von AlGaN/GaN-Transistoren dioden im Materialsystem InGaAlAs/InP 196 Seiten 152 Seiten ISBN 3-932749-28-6 ISBN 3-932749-35-9

Vol. 29 Vol. 36 Martin Eickhoff Roland Zeisel Piezowiderstandsmechanismen in Optoelectronic properties of defects in Halbleitern mit großer Bandlücke diamond and AlGaN alloys 151 Seiten 140 Seiten ISBN 3-932749-29-4 ISBN 3-932749-36-7

Vol. 30 Vol. 37 Nikolai Wieser Liwen Chu Ramanspektroskopie an Gruppe III- Inter- und Intraband Spektroskopie an Nitriden selbstorganisierten In(Ga)As/GaAs 161 Seiten Quantenpunkten ISBN 3-932749-30-8 124 Seiten ISBN 3-932749-37-5

Vol. 31 Vol. 38 Rainer Janssen Christian Alexander Miesner Strukturelle und elektronische Intra-Valenzbandspektroskopie an SiGe- Eigenschaften amorpher Silizium-Suboxide Nanostrukturen in Si 275 Seiten 100 Seiten ISBN 3-932749-31-6 ISBN 3-932749-38-3

Vol. 32 Vol. 39 Martin W. Bayerl Szabolcs Kátai Magnetic resonance investigations Investigation of the nucleation process of of group III-nitrides chemical vapour deposited diamond films 155 Seiten 178 Seiten ISBN 3-932749-32-4 ISBN 3-932749-39-1

Vol. 40 Vol. 46 Markus Arzberger Jan Schalwig Wachstum, Eigenschaften und An- Feldeffekt-Gassensoren und ihre wendungen selbstorganisierter InAs- Anwendung in Abgas- Quantenpunkte nachbehandlungssystemen 236 Seiten 125 Seiten ISBN 3-932749-40-5 ISBN 3-932749-46-4

Vol. 41 Vol. 47 Markus Oliver Markmann Christopher Eisele Optische Eigenschaften von Erbium in Novel absorber structures for Si-based Si/Si1-xCx, Si/Si1-xGex und Si/SiOx thin film solar cells Heterostrukturen 126 Seiten 182 Seiten ISBN 3-932749-47-2 ISBN 3-932749-41-3

Vol. 42 Vol. 48 Rainer Alexander Deutschmann Stefan Hackenbuchner Two dimensional electron systems in Elektronische Struktur von Halbleiter- atomically precise periodic potential Nanobauelementen im thermodynamischen 210 Seiten Nichtgleichgewicht ISBN 3-932749-42-1 213 Seiten ISBN 3-932749-48-0

Vol. 43 Vol. 49 Uwe Karrer Andreas Sticht Schottky-Dioden auf Galliumnitrid: Herstellung und Charakterisierung Eigenschaften und Anwendungen in der von dünnen Silizium/Siliziumoxid- Sensorik Schichtsystemen 182 Seiten 166 Seiten ISBN 3-932749-43-X ISBN 3-932749-49-9

Vol. 44 Vol. 50 Günther Anton Johann Vogg Giuseppe Scarpa Epitaxial thin films of Si and Ge based Design and fabrication of Quantum Zintl phases and sheet polymers Cascade Lasers 169 Seiten 193 Seiten ISBN 3-932749-44-8 ISBN 3-932749-50-2

Vol. 45 Vol. 51 Christian Strahberger Jörg Frankenberger Vertikaler Transport und extreme Optische Untersuchungen an zwei- Magnetfelder in Halbleitern dimensionalen Ladungsträgersystemen 167 Seiten 158 Seiten ISBN 3-932749-45-6 ISBN 3-932749-51-0

Vol. 52 Vol. 58 Doris Heinrich Po-Wen Chiu Wavelength selective optically induced Towards carbon nanotube-based molecular charge storage in self-assembled electronics semiconductor quantum dots 116 Seiten 144 Seiten ISBN 3-932749-58-8 ISBN 3-932749-52-9

Vol. 53 Vol. 59 Nicolaus Ulbrich Tobias Graf Entwurf und Charakterisierung von Spin-spin interactions of localized Quanten-Kaskadenlasern und electronic states in semiconductors Quantenpunktkaskaden 194 Seiten 133 Seiten ISBN 3-932749-59-6 ISBN 3-932749-53-7

Vol. 54 Vol. 60 Lutz Carsten Görgens Stefan Klein Analyse stickstoffhaltiger III-V Halbleiter- Microcrystalline silicon prepared by hot Heterosysteme mit hochenergetischen wire CVD: preparation and characteri- schweren Ionen sation of material and solar cells 116 Seiten 157 Seiten ISBN 3-932749-54-5 ISBN 3-932749-60-X

Vol. 55 Vol. 61 Andreas Janotta Markus Krach Doping, light-induced modification and Frequenzverdreifacher mit Anti-Seriellem biocompatibility of amorphous silicon Schottky-Varaktor für den Terahertz- suboxides bereich 180 Seiten 156 Seiten ISBN 3-932749-55-3 ISBN 3-932749-61-8

Vol. 56 Vol. 62 Sebastian Tobias Benedikt Gönnenwein Ralph Thomas Neuberger Two-dimensional electron gases and AlGaN/GaN-Heterostrukturen als ferromagnetic semiconductors: chemische Sensoren in korrosiven materials for spintronics Medien 198 Seiten 153 Seiten ISBN 3-932749-56-1 ISBN 3-932749-62-6

Vol. 57 Vol. 63 Evelin Beham Sonia Perna Photostromspektroskopie an einzelnen Wasserstoff-Passivierung von tri- Quantenpunkten kristallinem Silizium durch hydro- 186 Seiten genisiertes Siliziumnitrid ISBN 3-932749-57-X 136 Seiten ISBN 3-932749-63-4

Vol. 64 Vol. 71 Oliver Schumann Andreas Florian Kreß Einfluss von Stickstoff auf das Manipulation of the Light-Matter-Inter- Wachstum und die Eigenschaften action in Photonic Crystal Nanocavities von InAs-Quantenpunkten 185 Seiten 148 Seiten ISBN 3-932749-71-5 ISBN 3-932749-64-2

Vol. 65 Vol. 72 Gerhard Rösel Markus Grau Entwicklung und Charakterisierung von Molekularstrahlepitaktische Herstellung Typ-II-Heterostrukturen für die Abstimm- von antimonidischen Laserdioden für region in abstimmbaren Laserdioden die Gassensorik 101 Seiten 138 Seiten ISBN 3-932749-65-0 ISBN 3-932749-72-3

Vol. 66 Vol. 73 Angela Link Karin Buchholz Zweidimensionale Elektronen- und Löcher- Microprocessing of silicon on insulator Gase in GaN/AlGaN Heterostrukturen substrates and biofunctionalisation of 156 Seiten silicon dioxide surfaces for sensing ISBN 3-932749-66-9 applications in fluids 170 Seiten Vol. 67 ISBN 3-932749-73-1 Matthias Sabathil Opto-electronic and quantum transport Vol. 74 properties of semiconductor nanostructures Dominique Bougeard 156 Seiten Spektroskopische Charakterisierung von ISBN 3-932749-67-7 Germanium-Quantenpunkten in Silizium 154 Seiten Vol. 68 ISBN 3-932749-74-X Frank Fischer Growth and electronic properties of two- Vol. 75 dimensional systems on (110) oriented GaAs Jochen Bauer 139 Seiten Untersuchungen zum kontrollierten ISBN 3-932749-68-5 Wachstum von InAs-Nanostrukturen auf Spaltflächen Vol. 69 140 Seiten Robert Shau ISBN 3-932749-75-8 Langwellige oberflächenemittierende Laser- dioden mit hoher Ausgangsleistung und Vol. 76 Modulationsbandbreite Ingo Bormann 198 Seiten Intersubband Spektroskopie an Silizium- ISBN 3-932749-69-3 Germanium Quantenkaskadenstrukturen 124 Seiten Vol. 70 ISBN 3-932749-76-6 Andrea Baumer Structural and electronic properties of hydrosilylated silicon surfaces 163 Seiten ISBN 3-932749-70-7 Vol. 77 Hubert Johannes Krenner Coherent quantum coupling of excitons in single quantum dots and quantum dot molecules 160 Seiten ISBN 3-932749-77-4

Vol. 78 Ulrich Rant Electrical manipulation of DNA-layers on gold surfaces 249 Seiten ISBN 3-932749-78-2

Vol. 79 René Todt Widely tunable laser diodes with distributed feedback 152 Seiten ISBN 3-932749-79-0

Vol. 80 Miroslav Kroutvar Charge and spin storage in quantum dots 150 Seiten ISBN 3-932749-80-4

Vol. 81 Markus Maute Mikromechanisch abstimmbare Laser-Dioden mit Vertikalresonator 170 Seiten ISBN 3-932749-81-2

Vol. 82 Frank Ertl Anisotrope Quanten-Hall-Systeme, Vertikale Ultrakurzkanal- und Tunneltransistoren 170 Seiten ISBN 3-932749-82-0

Vol. 83 Sebastian M. Luber III-V semiconductor structures for biosensor and molecular electronics applications 212 Seiten ISBN 978-3-932749-83-4