In-Situ Atom Probe Specimen Preparation with a Planar Reigon of Interest

IN-SITU ATOM PROBE SPECIMEN PREPARATION WITH A PLANAR REIGON OF INTEREST

by Scott E. Allen © Copyright by Scott E. Allen, 2013 All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulﬁllment of the requirements for the degree of Master of Science (Applied Physics).

Golden, Colorado Date

Signed: Scott E. Allen

Signed: Dr. Brian Gorman Thesis Advisor

Golden, Colorado Date

Signed: Dr. Thomas E. Furtak Professor and Head Department of Physics

ii ABSTRACT

Techniques for rapid preparation of atom probe specimens extracted from the surface of a bulk crystal sample are further developed with regards to samples having a planar region of interest. An atom probe specimen is a needle-shaped structure several microns long and approximately 100 nm in diameter. The conventional method for preparing these specimens maintains the sample orientation throughout the process of extracting sample segments from the bulk crystal, mounting them onto microtips, and shaping them into specimens. For samples having a planar region of interest parallel to the surface, that method produces a small disc-shaped region of interest oriented perpendicular to the specimen axis (horizontally). If the planar region of interest of the sample is composed of atoms susceptible to migrating along the curved surface of the specimen tip during atom probe tomography, this horizontal orientation makes it diﬃcult to quantify and account for any such surface migration. By reorienting the sample with a 90 degree rotation, specimens were produced with the planar region of interest oriented parallel to the specimen axis. This vertically oriented plane is up to 5 times larger than the horizontally oriented planes produced with previous specimen preparation methods. According to the model of ﬁeld-driven surface migration proposed herein, this orientation also makes it possible to quantify and account for surface migration leading to more accurate atom probe data.

iii TABLE OF CONTENTS

ABSTRACT ...... iii

LIST OF FIGURES ...... vi

LIST OF ABBREVIATIONS ...... x

ACKNOWLEDGMENTS ...... xi

DEDICATION ...... xii

CHAPTER 1 INTRODUCTION ...... 1

CHAPTER 2 BACKGROUND ...... 4

2.1 Two-Dimensional Electron Gasses ...... 4

2.2 Delta Doping ...... 5

2.3 Solid State Quantum Computing ...... 6

2.4 Focused Ion Beam ...... 9

2.5 Atom Probe Tomography ...... 12

2.6 Previous Atom Probe Experiments on Delta-Doped Silicon ...... 17

CHAPTER 3 MODELING SURFACE MIGRATION ...... 21

CHAPTER 4 EXPERIMENT ...... 24

4.1 Experimental Apparatus ...... 24

4.2 Conventional Sample preparation ...... 25

4.2.1 Feature-non-speciﬁc extration and mounting ...... 26

4.2.2 Feature-speciﬁc extraction and mounting ...... 33

4.2.3 Sharpening and low-energy cleanup ...... 33

iv 4.3 Vertical Sample Preparation ...... 34

4.3.1 Mounting ...... 34

4.3.2 Sharpening ...... 36

CHAPTER 5 RESULTS ...... 37

5.1 Reinvestigating previous APT data for signs of ﬁeld-driven surface migration . 37

5.2 Augmenting chemical resolution ...... 38

CHAPTER 6 CONCLUSION ...... 42

REFERENCES CITED ...... 43

v LIST OF FIGURES

Figure 1.1 Resolution and ﬁeld of view for various tomographic techniques. This shows that although APT has a small ﬁeld of view, it has greater resolution than other existing 3-D tomography technologies[24]...... 2

Figure 1.2 Facsimile of relative orientations of the planar ROI within an APT specimen ...... 3

Figure 2.1 Quantum well formed by a double heterojunction [28]...... 4

Figure 2.2 STM Lithography [37] ...... 6

Figure 2.3 Low dimensional features made possible by STM lithography and low temperature molecular beam epitaxy [33] ...... 6

Figure 2.4 The state of a single qubit is represented as a vector on the surface of the Bloch Sphere because it is in a superposition of the 1 and 0 states and contains relative phase information [63]...... 7

Figure 2.5 Kane quantum computer with ’A’ gates to tune individual phosphorus nuclei to respond to control pulses and ’J’ gates to perform 2-qubit logic operations[72]...... 9

Figure 2.6 Simpliﬁed graphic of ion sourcing, accelerating, and focusing in the FIB [76]...... 10

Figure 2.7 Penetration depth of gallium ions in silicon and platinum at various beam energies [77]...... 11

Figure 2.8 Various molecular processes occur during FIB deposition. Most of these are adsorption of organic precursor onto the sample surface, breakdown of precursor by secondary electrons, and deposition of platinum composite. Some sputtering and Ga implanation are undesirable yet inevitable during deposition operations [78]...... 12

Figure 2.9 Trajectories in (a) Aluminum at 10 keV (b) Aluminum at 30 keV (c) Gold at 10 keV and (d) Gold at 30 keV. In each the large interaction volume on the left is for a beam of electrons and the smaller one to the right is for a beam of FIB ions. Increasing interaction volume is shown at incresing beam energy [79]...... 13

vi Figure 2.10 This example atom probe tomogram shows layers of GaAs and GaInP with planar interfaces. This reconstruction shows Ga in blue, As in yellow, In in green and P in red [25]...... 14

Figure 2.11 Example atom probe specimen with needle-like geometry [21]...... 15

Figure 2.12 The projection of the sample surface onto the position sensitive detector is much larger than the sample tip. The trajectories of the evaporated atoms yields the high magniﬁcation needed for atomic resolution [85]. . . 15

Figure 2.13 Example specimen before and after APT shows an increase in end radius due to shank angle[86]...... 16

Figure 2.14 Local electrode geometry augments time-of-ﬂight mass spectroscopy by dominating over ion-ion interactions and other sources of energy defects [89]...... 17

Figure 2.15 (a) APT microtip array formed by DRIE and (b) bird’s-eye-view of a sample segment mounted atop a microtip [77] ...... 18

Figure 2.16 Depth proﬁle of phosphorus concentration in delta-doped Si:P [92] . . . . 18

Figure 2.17 The magnitude of the electric ﬁeld normal to the specimen surface modeled with COMSOL 4.3 by David Diercks shows that the ﬁeld is maximized at apex of the specimen tip. This is one possible explaination for the anisotropic migration of phosphorus dopant atoms in delta-doped silicon...... 20

Figure 3.1 Facsimile of relative orientations of the planar ROI within an APT specimen ...... 21

Figure 3.2 If bulk migration is not a factor, the dopant atoms will be constrainted to move on the surface of the specimen tip. As they travel toward the apex of the tip they will move up in z and toward the z-axis...... 22

Figure 3.3 This top-down view of the dopant plane within the APT specimen shows how ﬁeld driven surface migration may cause dopant atoms to move toward the z-axis of the specimen. On the left a dopant plane which is not centered in the specimen appears to bend inward. On the right a dopant plane centered in the specimen appears to narrow in the middle. These anomalies of ﬁeld driven surface migration would not be visible when the dopant plane is oriented horizontally within the APT specimen...... 23

vii Figure 4.1 Photograph from inside the chamber of the Helios 600i FIB showing the ion beam at 52º from vertical...... 25

Figure 4.2 Temperature of an APT specimen as a function of time under a single laser pulse for two energies modeled with COMOSL 4.3 by David Diercks. This shows that a 100 pJ pulse heats the specimen to a much higher temperature than a 1 pJ pulse...... 26

Figure 4.3 Protective platinum composite cap over bulk silicon sample [77] ...... 27

Figure 4.4 Trangular cross-section of sample bar formed by trench milling [77] . . . . 27

Figure 4.5 (a)First release cut and (b&c) using the manipulator for the cantilever test [77] ...... 29

Figure 4.6 Extracting the wedge-shaped sample liftout with the manipulator [77] . . 30

Figure 4.7 (a) Aligning the end of the liftout over a microtip and (b) slicing oﬀ a segment [77] ...... 31

Figure 4.8 This side view of a sample segment mounted on a mirotip shows the planar junction between the protective platinum cap and the sample surface on the top of the sample segment. The conventional extraction and mounting methods maintain the horizontal orientation of this plane...... 32

Figure 4.9 This side view of a sample segment mounted on a microtip show the planar junction between the protective platinum cap and the sample surface on the left side of the sample segment. By rotating the sample liftout 90º in-between extraction and mounting, this plane which was horizontal is now vertical...... 35

Figure 5.1 Shown is a close up view of a vertically prepared specimen containing a visable junction between two dissimilar materials. This junction is seen as a faint vertical line down the center of the specimen...... 37

Figure 5.2 We divided the tomogram from previous characterizations into vertical columns and made 1-D concentration plots as a function of depth for each. The plot shown is the depth proﬁle of the column in the center about the delta-plane. Silicon is shown in grey and phosphorus is shown in pink...... 39

viii Figure 5.3 Top-down view of the tomogram shown in Figure 5.2 superimposed with peak dopant concentration of each segment in atomic percent. This shows an apparent congragation of phosphorus toward the center of the specimen...... 39

Figure 5.4 Minimum detectable dopant concentration for a 200 nm long tomogram with Si:P ratio averaged over 1 nm thick slices. This shows that due to increased ROI area, specimens prepared with thier planar ROI oriented vertically yield tomograms wich can show much smaller dopant concentrations. As the ﬁeld of view becomes nearly as wide as it is tall, this advantage diminishes...... 40

ix LIST OF ABBREVIATIONS

Atom Probe Tomography ...... APT

Scanning-Tunneling Microscope ...... STM

Density Functional Theory ...... DFT

Complementary Metal-Oxide Semiconductor ...... CMOS

Region Of Interest ...... ROI

Scanning Electron Microscope ...... SEM

Focused Ion Beam ...... FIB

Stopping Range of Ions in Matter ...... SRIM

Deep Reactive Ion Etching ...... DRIE

Two-Dimensional Electron Gas ...... 2DEG

Silicon doped with phosphorus ...... Si:P

Quantum Computer ...... QC

Quantum Bit ...... qubit

x ACKNOWLEDGMENTS

I would like to thank the members of my committee for their generosity with their time and eﬀort in helping me with this project. In particular Brian Gorman for his guidance throughout the project, Dave Diercks for his help with specimen preparation on the FIB, and Mark Lusk for introducing me to quantum computing. Rita Kirchhofer and John Chandler also provided invaluable help while I was learning to use the FIB.

xi For my ﬁrst science professor, my mentor, and dear freind, Barbara van Kuiken.

xii CHAPTER 1 INTRODUCTION

As Moore’s Law approaches its ultimate limit, the exact location of dopant atoms becomes vital in the proper functioning of semiconducting logic devices[1–13]. This is obviously the case in single-atom transistors or quantum computing devices[1–5, 14–20]. But it also holds true for any solid state logic device too small to be modeled as an infinitely periodic crystal or one that utilizes quantum confinement in one or more dimension[6, 7, 9]. Contem- porary photovoltaic technology relies on planar junctions and many promising photovoltaic devices anticipated for the future rely on quantum confining structures such as quantum wires and quantum dots. Because these, and many other devices, operate based on their atomic makeup within nanoscale regions of interest, thorough characterization requires sub- nanometer resolution achievable only with atom probe tomography (APT)[21] as seen in Figure 1.1. Just as the advent of the scanning-tunneling microscope (STM) has been a boon to nanoscience by making it possible to map surfaces of solids with atomic-scale precision[22, 23], APT extends atomic mapping capabilities to the interior of solids. This allows researchers to learn the exact atomic composition of sub-nanometer regions of interest and to obtain the lattice point locations of any element of interest[21]. We investigated a sample consisting of 9 closely stacked periods of silicon delta-doped with phosphorus[25]. These delta-doped silicon crystals could be used for ultra-fast CMOS gates[26], for ensemble quantum computing devices[27], or for experiments of fundamental physics[26]. Previous characterizations of this sample showed undesirable, anisotropic, out- of-plane displacement of dopant atoms[25]. Due to parallel anisotropies in the fabrication and characterization processes, it was unclear whether or not this displacement was a measurement defect. Therefore, re-orienting the sample crystal relative to the ATP apparatus

1 Figure 1.1: Resolution and field of view for various tomographic techniques. This shows that although APT has a small field of view, it has greater resolution than other existing 3-D tomography technologies[24]. was necessary. Orienting the planar region of interest (ROI) vertically as shown in Figure 1.2, such that the axis of the APT specimen is parallel with the delta-doped planes, led to additional benefits that may be taken advantage of in samples with similar ROI geometries. These include increased ROI volume within the atom probe field of view and the ability to re-use APT specimens, leading to more data with less sample preparation. Furthermore, it allows for reorientation of individual specimens in subsequent APT experiments. Chapter 2 provides background on the technologies used to fabricate, use, and characterize the devices we investigated. Most of the information in Chapter 2 is very basic so that it may be used as an instructional aid for new students beginning their first work on atom probe specimen preparation. Readers familiar with two-dimensional electron gases, delta-doping, solid state quantum computing, focused ion beam microscopy and atom probe tomography may prefer to skip to Section 2.6 where we discuss previous experiments on the sample we investigated. In Chapter 3 we propose a simple model for field-driven surface migration of phosphorus atoms in delta-doped Si:P, and we describe how this relates to sample orientation. According to this model,the specimen preparation methods used previously make it difficult to quantify

2 Figure 1.2: Facsimile of relative orientations of the planar ROI within an APT specimen and account for the effects of surface migration because the phosphorus plane is horizontally oriented in the specimen. Chapter 4 describes the conventional FIB method for atom probe specimen preparation used in previous experiments. We then detail our refinements to this method, in particular how to rotate the sample in order to re-orient the planar ROI vertically. In Chapter 5 we report the advantages of our method of vertical specimen preparation. We provide evidence that field-driven surface migration has been a factor in previous experiments. We also give a quantitative description of increased ROI volume as a function of specimen geometry.

3 CHAPTER 2 BACKGROUND

The samples we investigated are silicon delta-doped with phosphorus. Delta-doping is a method of confining dopant atoms, and therefore charge carriers, into a single plane. By confining charge carriers to a two-dimensional electron gas, quantum confinement effects give the device properties relevant to quantum computing technology among other things. Because these devices require atomically precise fabrication, atom probe tomography is an ideal characterization technique.

2.1 Two-Dimensional Electron Gasses

A 2D Electron Gas (2DEG) forms when electrons are strongly quantum conﬁned in one dimension and free in the other two. This planar feature is most commonly observed in heterojunctions between layers of semiconducting materials with unequal bandgaps. Figure 2.1 shows a quantum conﬁned well formed by a double heterojunction.

Figure 2.1: Quantum well formed by a double heterojunction [28].

They also have been observed on the surfaces of topological insulators such as bismuth an- timonide and on the surface of liquid helium. 2DEGs are what give graphene[29] many of it’s

4 exciting electronic properties[30, 31]. More recently, 2DEGs have been made with a several- nanometer thick planar distribution of n-type dopants in a semiconducting crystal[32]. Be- cause the dopant concentration along the z-direction (normal to the dopant plane) is a Delta function, this technique is known as delta-doping[1, 32, 33]. One exceptional feature of 2DEGs is their electron mobility. In certain devices, 2DEGs have achieved mobility of over 3x107cm2/V s [26]; four orders of magnitude above what can be regarded as high. This extraordinary mobility makes them candidates for use in ultrafast, high eﬃciency CMOS devices[33–36]. It also provides an interesting environment for the probing of fundamental physics.

2.2 Delta Doping

To make a delta-doped plane of phosphorus in silicon (Si:P), p-type silicon is placed in a high vacuum and heated to 1200 C to remove the native oxide from the surface[25]. The silicon is cooled to room temperature and phosphine gas is then injected into the chamber to adsorb onto the surface of the silicon[37, 38]. A 60 s annealing at 350 C incorporates the phosphorus into the surface of the silicon without allowing it to diffuse too deeply[25, 37, 39– 41]. To prevent phosphorus migration during silicon overgrowth, low-temperature molecular beam epitaxy is used[25, 37]. Molecular beam epitaxy is the slow growth of crystal (<3000 nm per hour) in an ultra high vacuum with no molecular precursor[42–44]. Metallic or semimetallic elements are heated in effusion cells until they begin to evaporate via thermal excitation. Flux of ballistic atoms is kept low enough to prevent them from interacting until they reach the crystal surface. To make a delta-doped plane with confined edges or lower-dimensional features, STM lithography[23] is used before phosphine adsorption. After oxide removal, the surface of the silicon is passivated with hydrogen gas[37, 45]. Anywhere phosphorus is to be added, the surface is patterned via hydrogen desorption using an STM tip[37, 46, 47]. A small quantity of phosphine gas is injected into the system and will adsorb as a monolayer on any exposed surface of the silicon[37, 48]. Hydrogen atoms that remain outside of the pattern desorb

5 during annealing[37, 49, 50]. Encapsulating silicon is grown via low temperature molecular beam epitaxy. This process is shown in Figure 2.2. Depending on the STM patterning, any feature conﬁned to a plane such as 1D wires, tunnel gaps, and even single dopant sites can be made with this technique. Some of these features are shown in Figure 2.3. STM lithography and low temperature molecular beam epitaxy can be used on germanium as well with excellent results[32–34, 37, 46, 47].

Figure 2.2: STM Lithography [37]

Figure 2.3: Low dimensional features made possible by STM lithography and low temperature molecular beam epitaxy [33]

2.3 Solid State Quantum Computing

The combination of STM lithography and low-temperature molecular beam epitaxy provides a fabrication method with suﬃcient atomic precision for the construction of solid state

6 quantum logic devices[10–13, 17, 37, 46, 47, 51–56]. It is diﬃcult to overstate the impact that a scalable quantum computer (QC) will have on science as a whole[33, 57–60]. The advantage of quantum computing over classical computing is that the fundamental unit of quantum information, the quantum bit (qubit), contains relative phase information (see Figure 2.4) and may entangle with other qubits. Qubit states that couple too strongly with their environment quickly lose their relative phase information; a process known as decoherence[61]. Those that couple too weakly with their environment cannot exhibit entanglement with other qubit states[62].

Figure 2.4: The state of a single qubit is represented as a vector on the surface of the Bloch Sphere because it is in a superposition of the 1 and 0 states and contains relative phase information [63].

Just as classical computers became highly scalable with the development of solid state logic devices( i.e. the transition from vacuum tube diodes to semi-conductor diodes) many researchers believe that QCs will be most scalable in the solid state[61]. Two emerging solid state quantum computing schemes show promise and are excellent candidates for APT characterization. These are the 2DEG electron spin QC [59, 60, 64–67]and the Kane nuclear

7 spin QC[37, 68]. The Kane QC uses the nuclear spin states of individual phosphorus atoms in a matrix of diamond-structured silicon as qubit states[37, 68]. Because decoherence is considered the primary obstacle in QC technology, nuclear spin states, with their low environmental coupling, have been an attractive option for qubit states. On the other hand, nuclear spin states have the chronic problem of non-entanglement. The nuclear spins states of phosphorus dopant atoms couple with one-another through the spin of an intermediary electron while still having decoherence times on the order of 10ˆ18 seconds[62, 69, 70]. This intermediary electron is the donor electron at room temperature but at cryogenic temperatures (˜ 100 mK) it becomes weakly bound to the phosphorus atom[37]. Phosphorus atoms are placed ˜20 nm apart, and coplanar ˜20 nm below the crystal surface. Above each phosphorus atom on the crystal surface is an electrode labeled the ‘A’ gate. In between each ‘A’ gate is another electrode labeled the ‘J’ gate. As in other nuclear spin schemes, a finely tuned radio pulse is used to flip spin state. The ‘A’ gate can control which qubit will be flipped by influencing the spin interaction between the weakly bound donor electron and its host nucleus. This spin interaction alters the energy difference between the up and down nuclear spin states thereby tuning a single atom to respond to a particular radio frequency. The ‘J’ gate is used for two-qubit logic operations by influencing the tunneling of donor electrons between phosphorus atoms[37, 71]. The 2DEG electron spin QC is an example of ensemble quantum computing[59, 60, 64], as opposed to the Kane QC which uses individual particle states for qubits. As with any other 2DEG, they are made by strongly confining electrons to a planar region using double heterostructures or delta-doped planes. One of the major challenges in this scheme is that optical pulses which can control electron spin states also easily excite undesirable electron, exciton, and trion resonances. The use of ultrafast off-resonant laser pulses have been shown to be successful in coherent control of electron ensemble spin states by inducing a stark shift in the trion resonance[64, 73].

8 Figure 2.5: Kane quantum computer with ’A’ gates to tune individual phosphorus nuclei to respond to control pulses and ’J’ gates to perform 2-qubit logic operations[72].

Both of these QC schemes require atomically precise construction within an ultrapure silicon matrix[10–13, 68]. This makes them excellent candidates for APT characterization with special consideration during specimen preparation for a planar ROI.

2.4 Focused Ion Beam

In order to characterize any solid state device in the atom probe, sections of it must first be extracted, mounted on a microtip array and formed in to thin needle-shaped specimens. The ideal tool for APT specimen preparation is the Focused Ion Beam (FIB). The FIB is a precision milling, deposition, and imaging instrument similar to the Scanning Electron Microscope (SEM)[74, 75]. As the name implies, the difference between the two is that the beam rastered over the sample surface by the FIB is a beam of ions, usually Ga+, as opposed to a beam of electrons in the SEM. Gallium ions are sourced by a Liquid Metal Ion Source (LMIS)[76] wherein metallic gallium is heated to a liquid state and subjected to a strong electric field. Under the influence of this field, a liquid metal will form into a cone shape known as a Taylor Cone with an end radius as small as 2 nm. The sharp tip magnifies the electric field to the point where Ga+ ions are field evaporated. Ga is ideal for this application due to it’s low melting point and low ionization energy. Furthermore, gallium is not highly reactive and has enough atomic mass for milling operations. After ions

9 are sourced, the processes of electrostatic lensing, rastering over the sample, and collection of resultant secondary electrons for imaging are like those in the SEM. Figure 2.1 shows a simpliﬁed representation of how ions are accelerated and focused after they are sourced.

Figure 2.6: Simpliﬁed graphic of ion sourcing, accelerating, and focusing in the FIB [76].

While imaging, the FIB does alter the sample in three ways that the SEM does not. As mentioned, Ga is heavy enough to mill a sample and will do so even at low beam current and beam energy used for imaging. The user can literally watch a sample erode away in real time. The FIB also implants Ga into the sample surface. The exact depth of implantation depends on the beam energy and sample material. A type of Monte Carlo simulation known as the binary collision approximation is the base for the Stopping and Range of Ions in Matter (SRIM) program which calculated these penetrations depths shown in Figure 2.7 [78]. Within the penetration depth, the FIB can also turn the surface of a crystalline sample amorphous. The primary use for FIB instruments is precision milling with nanometer resolution[74, 75]. As the sample is bombarded with heavy gallium ions, atomic scale erosion (aka sputtering) occurs. The higher the beam current and/or energy the faster the sample will mill. Unless the milling process is chemically assisted, atoms milled from the sample can easily

10 Figure 2.7: Penetration depth of gallium ions in silicon and platinum at various beam energies [77]. re-deposit nearby. Re-deposition is especially noticeable with rapid milling that produces a large ﬂux of sputtered sample atoms or when milling deep, narrow cuts which sputtered sample atoms cannot easily escape. Redeposition is the primary limiting factor in making ultrahigh aspect-ratio features via FIB milling. Another major use of the FIB is precision deposition with nanometer resolution. FIB deposition is often done to make a protective layer over a sample or for adhering micro- structues together. The latter is often refered to as “welding” although “gluing” would be the more accurate word. To do this, a gaseous organic compound containing platinum is injected into the vacuum chamber to settle on the sample surface. As seen in Figure 2.8, when Gallium ions strike the sample surface they create a shower of secondary electrons. These secondary electrons rend the gas molecules into volatile and nonvolatile species. The volatile species evaporate away while the nonvolatiles deposit onto the sample surface as a solid composed of approximately 55% Pt, 20% C, and 25% Ga [78]. The same process can be done with an electron beam but is much slower due to much deeper penetration depths and greater interaction volumes in the sample and fewer total secondary electrons per incident particle . Neither electron nor ion beams travel in straight lines within the

11 sample but follow convoluted trajectories (see Figure 2.9) as they lose energy to various atomic processes including electron emission. Ion beams lose more of their kinetic energy in the small volume near the sample surface compared to electron beams. Therefore, more of the secondary electrons they produce are allowed to escape the sample and interact with the gas molecules leading to faster deposition rates.

Figure 2.8: Various molecular processes occur during FIB deposition. Most of these are adsorption of organic precursor onto the sample surface, breakdown of precursor by secondary electrons, and deposition of platinum composite. Some sputtering and Ga implanation are undesirable yet inevitable during deposition operations [78].

For both milling and deposition operations, the user deﬁnes an area over which the ion beam will raster. This is done with a graphical user interface (GUI) which allows the user to draw a shape superimposed over the FIB-produced images. The high resolution of the FIB conﬁnes the ion bombardment tightly within the boundary of the shape drawn by the user.

2.5 Atom Probe Tomography

Atom Probe Tomography is the only technique currently capable of characterizing materials with near atomic spatial resolution and near atomic chemical resolution simultaneously[21]. Typical spatial resolution is 0.2nm in the x and y directions and 0.05nm in the z direction

12 Figure 2.9: Trajectories in (a) Aluminum at 10 keV (b) Aluminum at 30 keV (c) Gold at 10 keV and (d) Gold at 30 keV. In each the large interaction volume on the left is for a beam of electrons and the smaller one to the right is for a beam of FIB ions. Increasing interaction volume is shown at incresing beam energy [79].

(where the z direction is defined as parallel with the axis of the specimen)[21, 81]. It differs from other microscopy and tomography techniques in that the specimen is destroyed in a controlled fashion and a virtual reconstruction is made.Figure 2.10 shows a virtual reconstruction of layers of GaAs and GaInP. Atom probe specimens are extremely thin, needle-like structures with end radius 25-100 nm[82, 83] (see Figure 2.11 ). Like the Taylor Cone in the LMIS, this sharp tip greatly magnifies an applied voltage and creates a highly curved electric field. Atoms are then field evaporated, one atomic layer at a time, from the surface of the specimen either by a strong pulse above the standing bias above of the specimen voltage or by a UV laser pulse[78, 84, 85]. Each of these ions follows a trajectory normal to the specimen tip surface, resulting in the high magnification necessary for atomic resolution. As the ions strike a position-sensitive detector they form a flat, two-dimensional image (see Figure 2.12) . From this, they are virtually mapped onto the the curved surface from which they originated. This process is

13 Figure 2.10: This example atom probe tomogram shows layers of GaAs and GaInP with planar interfaces. This reconstruction shows Ga in blue, As in yellow, In in green and P in red [25]. repeated for subsequent layers which are then virtually stacked one on top of another to form a three-dimensional map. In a typical contemporary APT apparatus, the position-sensitive detector will only detect roughly 60 percent of the atoms. The resulting tomogram will have a random 40 percent missing within the field of view compared to the actual specimen. Although an ideal atom probe specimen is cylindrical with a hemispherical tip, most get wider further from the tip. As these specimens are evaporated, the end radius gets larger which reduces the magnification and increases the width of the field of view because the specimen tip acts much like a spherical emitter where the magnification is inversely proportional to the end radius. The length of the field of view is limited by the maximum specimen voltage of the atom probe; as the specimen is blunted too much by the evaporation process, greater voltage is required for subsequent evaporations than the instrument is capable of producing. Figure 2.13 shows a specimen before and after evaporation in the atom probe. The chemical identity of each ion is determined via time-of-flight mass spectroscopy by recording the time between the evaporation pulse and the time each ion strikes the detector.

14 Figure 2.11: Example atom probe specimen with needle-like geometry [21].

Figure 2.12: The projection of the sample surface onto the position sensitive detector is much larger than the sample tip. The trajectories of the evaporated atoms yields the high magniﬁcation needed for atomic resolution [85].

15 Figure 2.13: Example specimen before and after APT shows an increase in end radius due to shank angle[86].

Time-of-flight spectroscopy determines the mass-to-charge ratio of ions traveling under the influence of a known electric field. To produce a known electric field with adequate precision, newer atom probe designs include a local electrode[78, 88, 89] which creates a strong electric field focused at the tip of the specimen. This field not only decreases the voltage required to field evaporate the specimen and reduces contamination from any nearby tips. It also dominates over ion-ion interactions and other sources of energy defects thereby eliminating the need for energy-compensating lenses which would reduce the field of view and would filter out the majority of ions in transit[81]. Because APT experiments are done at ultrahigh vacuum, it would be inconvienent if the atom probe chamber could hold only one specimen at a time and have to be vented and re-pumped for each one. To expedite the testing of multiple specimens consecutively, specimens are mounted on a 2D array of microtips (see Figure 2.15) made specifically for APT. Older atom probe systems that held only one specimen at a time were, by comparison, impractical. APT microtip arrays are made with a common microelectromechanical systems (MEMS) technique[91], similar to chemically assisted FIB milling, known as deep reactive ion etching (DRIE)[92]. On top of a silicon wafer, the surface is masked with circles of photoresist. These masks protect the silicon from etching where the microtips are to be formed. Just as in gas-

16 Figure 2.14: Local electrode geometry augments time-of-flight mass spectroscopy by dominating over ion-ion interactions and other sources of energy defects [89]. assisted FIB deposition, chemicals adsorb on the the surface of the silicon and are broken up by a shower of secondary electrons produced by ion bombardment. The difference is that the resultant volatile species bond with and passivate atoms sputtered from the surface, vastly increasing the rate of erosion. The silicon underneath the protective photoresist is formed into an array of tall, thin posts with a flat circular top 2 um in diameter.

2.6 Previous Atom Probe Experiments on Delta-Doped Silicon

The focus of our experiment is a sample of 9 closely stacked periods of delta-doped Si:P fabricated by phosphine adsorption and low temperature molecular beam epitaxy[25]. In previous APT characterizations of this sample it appeared that the delta-doped layers were not perfectly planar, but were instead dopant gradients that exponentially decay above the original plane and cut off abruptly below it. In other words, the phosphorus atoms appar- ently underwent anisotropic migration and “floated” upwards but did not “sink” downwards significantly. The conventional definition of the boundary of the dopant layer is where the dopant concentration is equal to 5x108atoms/cm3[25]. By this definition, the dopant layer extends 1.3 nm below the original plane of Phosphine adsorption and ˜8 nm above. Because the

17 Figure 2.15: (a) APT microtip array formed by DRIE and (b) bird’s-eye-view of a sample segment mounted atop a microtip [77]

Figure 2.16: Depth proﬁle of phosphorus concentration in delta-doped Si:P [92]

18 dimensionality of an electron gas is defined by the quantum confinement of free charge carriers only, this distribution may be adequately planar for 2DEG applications in CMOS devices and spintronics [94]but may fall short of the atomically precise fabrication necessary for some QC applications[51, 68, 95–97]. In these experiments the delta-doped planes were not re-oriented from construction to characterization in the atom probe. Therefore it was unclear if this undesirable out-of -plane movement of the phosphorus dopant atoms was a genuine failure to construct planar dopant distributions or if it was a measurement defect. Two prevailing explanations are as follows. As silicon was epitaxially grown layer-by-layer on top of the dopant layer, phosphorus from the layer below could migrate into the new growth above. Alternatively, dopant migration could occur in the atom probe as high laser energy can cause surface mobility of specimen atoms immediately before evaporation[25]. The anisotropy in surface migration is due to the magnification of the field at the tip; phosphorus atoms have a higher affinity for the high field region (see Figure 2.17) than silicon atoms. It is unclear when the dopant migration occurred because the direction of migration is parallel to the only major anisotropies of the fabrication and characterization processes. These are the direction of the epitaxial growth and the gradient of the APT evaporation field.

19 Figure 2.17: The magnitude of the electric ﬁeld normal to the specimen surface modeled with COMSOL 4.3 by David Diercks shows that the ﬁeld is maximized at apex of the specimen tip. This is one possible explaination for the anisotropic migration of phosphorus dopant atoms in delta-doped silicon.

20 CHAPTER 3 MODELING SURFACE MIGRATION

One solution to the issue of parallel anisotropies is reorienting the sample crystal within the atom probe apparatus by milling the atom probe specimen with the planar ROI oriented vertically (such that the axis of the atom probe specimen was parallel to the planar ROI as shown in Figure 3.1).

Figure 3.1: Facsimile of relative orientations of the planar ROI within an APT specimen

Should field-driven surface mobility be an issue with a vertically oriented ROI it is easier to identify it and differentiate it from fabrication defects. For the vertical specimen, let us define the z-axis as the axis of the APT specimen, the x-axis as normal to the planar ROI, and therefore the y-axis is parallel to the ROI. If the dopant plane is perfectly centered in the APT specimen at x=0, it will intersect the apex where the field is greatest. Field effects will hold any P atoms at this point in place. Any dopant atoms that lay on the y-axis (because they stayed on the delta plane where they are supposed to be) will migrate in the

21 y-z plane along the curved surface of the specimen tip. This will cause an anomalous in- plane congregation of P atoms along the z-axis. Any dopant atoms that lay on the x-axis at x0(due to out-of-plane migration during fabrication) will migrate in the x-z plane along the curved surface of the specimen tip. This will cause an anomalous narrowing of the dopant plane which is most pronounced along the z-axis. In short any P atoms will migrate along the surface toward the z axis.

Figure 3.2: If bulk migration is not a factor, the dopant atoms will be constrainted to move on the surface of the specimen tip. As they travel toward the apex of the tip they will move up in z and toward the z-axis.

In practice, the dopant plane is likely to be situated somewhat to the side of the apex of the specimen intersecting the x-axis at a point which we will call x’. P atoms at x>x’ will migrate toward the delta plane and P atoms with x

22 Figure 3.3: This top-down view of the dopant plane within the APT specimen shows how field driven surface migration may cause dopant atoms to move toward the z-axis of the specimen. On the left a dopant plane which is not centered in the specimen appears to bend inward. On the right a dopant plane centered in the specimen appears to narrow in the middle. These anomalies of field driven surface migration would not be visible when the dopant plane is oriented horizontally within the APT specimen. specimen geometry, this increase is a factor of 3-5. Second, the specimens are reusable. The length of the field of view is limited by the maximum specimen voltage of the atom probe; as the specimen is blunted by the evaporation process, greater voltage is required for subsequent evaporations. Vertically aligned specimens can be re-sharpened in the FIB for multiple atom probe experiments, whereas horizontally aligned specimens will have had their entire ROI evaporated. Specimen reuse allows for more data with fewer FIB operations. It also creates the opportunity, with a single specimen, to confirm that any interesting structural features are oriented relative to the sample crystal and not a measurement defect oriented relative to the atom probe apparatus. After resharpening, the specimen can be rotated about its axis inside the atom probe for subsequent measurements.

23 CHAPTER 4 EXPERIMENT

Using the FIB sections of the sample are extracted from the bulk crystal and mounted atop a prepared microtip array to be shaped into sharp, needle-like APT specimens[78]. If the ROI is confined to particular features or structures within the sample, sections are extracted one at a time with the ROI at the center. This feature-specific extraction would likely be the prefered method for the characterization of Kane QC devices. If the ROI covers at least a few hundred nanometers, a large bar is extracted all at once from the sample from which individual sections are cut. This feature-non-specific method is used for our characterization of delta-doped Si:P.

4.1 Experimental Apparatus

Our apparatus consisted of the Helios 600i FIB from the FEI company[75] with an Oxford Instruments Omniprobe 400 manipulator[98], and the Cameca Instruments LEAP4000XSi atom probe[81]. The Helios 600i is a dual beam instrument with an electron beam primarily used for SEM imaging and a gallium ion beam primarily used for FIB milling and deposition. The axis of the electron beam is aligned vertically so to have a 90º angle of incidence with a horizontal sample surface. The axis of the ion beam is aligned 52º from the vertical electron beam so to have a 38º angle of incidence with a horizontal sample surface. The e-beam has a landing voltage range of 20 eV - 30 keV and a current range of 0.7 pA - 22 nA. The ion beam has a landing voltage range of 500 eV - 30 KeV and a current range of 0.1 pA- 65 nA. The piezo-controlled sample stage has an XY range of motion of 150 mm and a Z range of motion of 10 mm. It can tilt between -10º and +60º and has full 360º rotation capability.

24 Figure 4.1: Photograph from inside the chamber of the Helios 600i FIB showing the ion beam at 52º from vertical.

Both the tilt and rotations are compucentric, meaning that the axis of rotation is about the focal point in the center of the ﬁeld of view of the user. The Omniprobe 400 is a piezo controlled in-situ manipulator with omnidirectional movement and 4 degrees of freedom (x,y,z,r). Its axis is constant at 45 degrees from vertical. The Cameca Instruments LEAP 4000XSi uses a local electrode and pulsed UV laser to evaporate the specimen as opposed to a pulsed voltage. It has 0.1-.03 nm resolution in the Z-direction and 0.3 nm -0.5 nm resolution in X and Y. Its laser has a pulse energy range of 1 nJ - 2 fJ. The minimum pulse energy of the LEAP 3000X is 200 pJ. This may have the problem over overheating the specimen leading to surface mobility of the sample atoms. The use of the low-energy laser pulses with the 4000XSi should avoid this problem altogether. Figure 4.2 shows the eﬀects of laser pulse energy on specimen temperature.

4.2 Conventional Sample preparation

Before any FIB operations (including imaging) can begin, the sample surface should be protected from the milling, Ga implantation, and amorphization eﬀects of ion bombardment[78]. This is done by depositing a ˜50 nm thick protective layer of platinum composite with the electron beam. 50 nm was chosen because at 30 keV gallium ions can penetrate at least 10

25 Figure 4.2: Temperature of an APT specimen as a function of time under a single laser pulse for two energies modeled with COMOSL 4.3 by David Diercks. This shows that a 100 pJ pulse heats the specimen to a much higher temperature than a 1 pJ pulse. nm into platinum and the protective cap is not pure platinum so we made the assumption that ions may be able to penetrate deeper in to it. To do this, a reduced area scan is defined such that the e-beam will raster over the area above the sample crystal from which APT specimens will be made while injecting gaseous platinum precursor. Beam energy was reduced to 2 keV in order to minimize the interaction volume and maximize the flux of secondary electrons through the sample surface. This thin layer should be sufficient to protect the sample from Ga+ ions while depositing a thick (˜200 nm) layer of platinum composite with the FIB. The dimensions of this thick layer will become the dimensions of the sample liftout. An example is shown in Figure 4.3.

4.2.1 Feature-non-speciﬁc extration and mounting

For the feature-non-speciﬁc procedure we chose dimensions of 4 µm by 40 µm for the platinum composite cap. With the sample protected, a process known a trench milling can be done in preparation for extraction. On both sides of the cap, angular cuts are made to form a 40 µm long bar with a triangular cross-section. The stage is tilted 22º toward the ion column to form a 30 degree angle of incidence. Using high beam currents of 5-11 nA

26 Figure 4.3: Protective platinum composite cap over bulk silicon sample [77] to reduce milling time, the mill is made 45 µm long by 0.5 µm wide by 5 µm deep. The stage is then compucentrically rotated 180º and an identical cut is made on the other side. Sputtered atoms from the second cut will redeposit on the fresh surfaces made by the first cut. To clean them off, the stage is again compucentrically rotated 180º and the first cut is repeated. This forms a bar with a trangular cross-section connected at both ends to the bulk sample as shown in Figure 4.4.

Figure 4.4: Trangular cross-section of sample bar formed by trench milling [77]

At this point, the bar is still connected to the bulk sample at the two ends. The next step is to release one end, forming the sample bar into a cantilever. This is done by ﬁrst setting the stage to a position of 0º tilt relative to the ion beam (90º angle of incidence).

27 A cut is made at one end of the bar which slightly overlaps the trench cuts ( Figure 4.5 (a)). This will free one end, forming the bar into a cantilever. Next, we return the stage to its original horizontal position, insert the manipulator and align the major axis of the bar with the projection of the manipulator axis onto the sample surface such that the free end of the liftout is closest to the manipulator tip ( Figure 4.5 (c)). To test if the bar is free from the bulk sample, gently press down on the free end with the manipulator. If the bar bends downward ala the cantilever effect ( Figure 4.5 (b)), the trench milling procedure was successful. If instead, the tip of the manipulator slides across the surface of the bar without bending it, the bar is still attached somewhere. In the latter case, the trench milling procedure is repeated with slightly larger cuts to make sure all the cuts overlap and with somewhat lower beam currents to reduce redeposition. This is repeated until the cantilever test is successful. With the stage in its original horizontal position, we then weld the tip of the manipulator to the free end of the bar with a deposition pattern approximately 3 x 3 µm wide by 0.5 µm thick. The manipulator is now connected to the stage via the sample, so the stage must not be moved until the sample bar is disconnected and lifted out. Therefore it is prudent to avoid redeposition at the expense of some milling time for this final cut. We do this with milling overlaps of about ˜1 um and lower beam currents. With both ends of the bar free from the bulk sample, the manipulator is free to move about the chamber with the sample bar (now referred to as the sample liftout) in tow. Extraction is shown in Figure 4.6. The triangular cross-section of the liftout is not just the result of a convenience in the trench milling process, but is a vital part of properly mounting the sample to an APT microtip array. If the bottom of the sample liftout were a flat surface and it was mounted flush to the flat top of the microtip, the gaseous platinum precursor could not adsorb onto these surfaces. Therefore the weld, being confined outside the edge of the junction between the two, would be milled away during the sharpening process as the sample and the top of the microtip are reduced to a narrow needle. We make the bottom of the liftout a well

28 Figure 4.5: (a)First release cut and (b&c) using the manipulator for the cantilever test [77]

29 Figure 4.6: Extracting the wedge-shaped sample liftout with the manipulator [77] defined point so that the contact between the sample and the microtip is vanishingly small, the platinum precursor can adsorb onto all the surfaces, and the weld fills the gap between sample and microtip. Thus, sample and the microtip can be milled arbitrarily narrow and still contain a platinum composite weld attaching the two. To mount a sample onto a microtip, we first align the end of the liftout with the top of the microtip using the bird’s-eye-view from the e-beam to make x and y alignments. The angle of the Ion beam makes it useful for the lowering the liftout (in the z direction) onto the microtip. Only the top face of the liftout has a protective layer of platinum composite, so it is good practice to minimize its exposure to the ion beam. To that end, a rough z alignment can be made from the bird’s-eye-view of the e-beam. With e-beam focused on the top of the microtip, the liftout high above will be out of focus. As the liftout is lowered, it will come into focus when it nears the z coordinate of the top of the microtip but before it collides with it. Using the angled view of the ion beam for the final alignment, we gently touch the bottom of the liftout to the top of the microtip array as seen in Figure 4.7 (a). The weld is formed with deposition pattern about 2 x 2 µm wide by .3 µm thick centered over the junction between the sample and the microtip. Once the sample is welded, it can be sliced from the liftout with a 0.2 µm wide mill as seen in Figure 4.7 (b). This process repeated on subsequent microtips with the remainder of the liftout.

30 Figure 4.7: (a) Aligning the end of the liftout over a microtip and (b) slicing oﬀ a segment [77]

31 Figure 4.8: This side view of a sample segment mounted on a mirotip shows the planar junction between the protective platinum cap and the sample surface on the top of the sample segment. The conventional extraction and mounting methods maintain the horizontal orientation of this plane.

32 After about 12 samples are mounted and none of the liftout remains on the manipulator, the samples are secured with a backside weld. The stage is compucentrically rotated 180º and an identical weld is made on the opposite side of each.

4.2.2 Feature-speciﬁc extraction and mounting

For the feature-speciﬁc extraction procedure we use dimensions of 4 x 4 µm for the protective platinum composite cap. Trench mill about the cap with cuts 9 µm long by 0.5 µm wide by 5 µm deep at 30º angle of incidence. Omit the cantilever test and proceed with extraction and mounting as in the feature-non-speciﬁc procedure.

4.2.3 Sharpening and low-energy cleanup

To form a sample mounted on a microtip into an APT specimen, tilt the stage to 52º so that the ion beam has the bird’s-eye-view over the microtip array. Some time can be saved by rough shaping the sample to have a 1-0.5 µm square profile using the cleaning cross section at 0.43 nA and 30 keV before annular milling. For the final shaping of the specimen, a series of annular mills is made with the outer radius being just larger than the profile of the sample and inner radius of 400 nm, then 200 nm, then 150 nm, each done at 80 pA and 30 keV. The final step is to clean the surface of the specimen with a low energy ion beam to remove damage done from previous high energy bombardment. After setting the beam to 72 pA and 2 keV, it will need to be carefully refocused. The sharper the focus is, the more collumnated the beam will be and the narrower the shank angle of the specimen will be. Rather than drawing a milling pattern, we simply imaged the specimen at 50 k x for ˜60 s. At these low energies it possible image with the e-beam while milling with the ion beam. The remainder of the platinum composite cap must be removed entirely before the specimen is suitable for APT. Since the e-beam images have a sharp contrast between silicon and platinum composite, it is best to watch the specimen on the e-beam and stop the ion beam as soon as the cap has eroded away. If the ion beam is allowed to mill too far below the Si-Pt

33 junction, it could mill away the ROI. If any of the cap remains, the specimen will likely fail during APT.

4.3 Vertical Sample Preparation

In samples containing heterojunctions, deta-doping, or an array of STM-aranged atoms, the ROI most likely has a planar geometry. When the planar ROI is parallel to the surface of the bulk sample, the conventional extraction/mounting procedure will produce APT specimens containing a small disc-shaped ROI oriented perpendicular to the specimen axis. It is best to orient a planar ROI vertically within the APT specimen as.

4.3.1 Mounting

With a planar ROI that is parallel to the sample surface, three options exist for preparing vertically oriented atom probe specimens.

Option 1

Use the FIB stage tilt if the diﬀerence between the maximum positive stage tilt and maximum negative stage is nearly 90º or greater. (1) Align the major axis of your sample bar with the axis of rotation for FIB stage tilt. (2) Tilt the stage in the negative direction (3) Attach the manipulator to the sample liftout and disconnect the liftout from the bulk sample. (4) With the manipulator at a safe height, tilt the stage the other direction a total of 90º (or nearly 90º if that is the maximum stage tilt). (5) Attach slices of the liftout to an appropriate microtip array.

Option 2

Use the manipulator rotation and stage rotation. (1) With the plane of the sample surface orthogonal to the axis of rotation of the stage (stage tilt 0 degrees), align the major axis of the sample bar parallel with the projection of the manipulator axis onto the plane of the sample surface. (2) Attach the sample lift out to the manipulator and disconnect the liftout from the bulk sample. (3) Rotate the manipulator about its axis 180º such that the

34 major axis of the sample liftout is normal to the plane of the sample surface. (4) Attach the sample liftout to the surface of the bulk sample or another stable surface parallel to the sample surface. (5) Rotate the stage 90º. The side of the liftout facing the manipulator will be facing up when mounted (6) Re-attach the sample liftout to the manipulator and detach it again from the bulk sample surface. (7) Rotate the manipulator about its’ axis 90º such that the major axis of the sample liftout is again parallel to the the bulk sample surface. (8) Attach slices of the liftout to an appropriate micro-tip array.

Option 3

Begin with the microtip array mounted within the FIB chamber such that the axes of the microtips are parallel with the bulk sample surface. No tilts or rotations are necessary.

Figure 4.9: This side view of a sample segment mounted on a microtip show the planar junction between the protective platinum cap and the sample surface on the left side of the sample segment. By rotating the sample liftout 90º in-between extraction and mounting, this plane which was horizontal is now vertical.

Which options are available will depend of course on the limitations of the FIB apparatus being used, but the ﬁnal decision may very well come down to personal preference. We,

35 for example, can achieve a maximum diﬀerence between negative and positive stage tilt of 70º. We deemed 70º to be suﬃcient for a nearly vertical ROI and began using option 1 because it requires fewer milling/depositing operations than option 2 and we were not equipped for option 3. We later changed to option 2 because performing the lift-out and mounting procedures with a non-zero stage tilt was somewhat disorienting for us. This led to more failures in properly navigating the manipulator, making the whole procedure ultimately slower. With proper equipment and adequate practice, options 1 and 3 may be faster but the advantage of option 2 is that it should not require more practice than any other extraction/mounting procedure.

4.3.2 Sharpening

Both FIB and SEM imaging show excellent contrast between the silicon and the platinum composite cap, which is now on the side of the sample. This allowed us to precisely locate the delta-doped plane by measuring the distance from the Si-Pt junction. Knowing that our sample had 70 nm of silicon epitaxially grown above the delta-doped plane, we could easily place the center of an annular mill pattern 70 nm from the junction. Thus we could ensure that our specimens contained the ROI. With the ROI occupying entire length of the APT specimen, and the platinum composite cap on the side instead of the top, there is a much greater margin of error in the low-energy clean up. If the ion beam is left on longer than necessary, the specimen will still contain the ROI. If it is left on too breiﬂy, damage from Ga bombardment may be visable but the specimen will still be usable. This step is otherwise identical as in the conventional method.

36 CHAPTER 5 RESULTS

By the methods described herein, we succesfully prepared APT specimens of delta-doped Si:P having the delta-doped plane vertical with respect to the specimen axis. Shown below is a closeup view of a fully prepared specimen containing a planar junction between two dissimilar materials. The junction is visible as a faint vertical line down the center of the specimen.

Figure 5.1: Shown is a close up view of a vertically prepared specimen containing a visable junction between two dissimilar materials. This junction is seen as a faint vertical line down the center of the specimen.

5.1 Reinvestigating previous APT data for signs of ﬁeld-driven surface migration

Our method of vertical preparation is most valuable when anisotropic surface migration is present, because these eﬀects will be manifested more obviously on a vertical sample as

37 shown in Figure 3.3. Our analysis of previous APT charactarizations of delta-doped Si:P indicate that field-driven surface migration is a likely contributor to the undesirable out-of- plane displacement of phosphorus atoms. Surface migration differs from bulk migration in that it occurs in a constrained path. As phosphorus atoms travel toward the apex of the specimen along it’s surface, they approach the center of the specimen in x and y as well as being displaced from the delta-plane in z. Therefore, surface migration during APT could cause an apparent increase in the dopant concentration about the center of the specimen that bulk migration would not. The 1-D concentration plot shown in Figure 2.16 is averaged over the entire profile of the specimen. In Figure 5.2 we took the tomogram from previous experiments and divided it into vertical columns. As we would expect from field-driven surface migration, the section in the center shows the highest peak concentration (see Fig- ure 5.3). This demonstrates that the vertical preparation method may improve future APT charactarizations of delta-doped Si:P by making measurement defects more visable as shown in Figure 3.3.

5.2 Augmenting chemical resolution

By preparing the planar ROI vertically we increase the chemical resolution of the resulting tomogram. The number of atoms detectable in an atom probe tomogram, and therefore the chemical resolution, is proportional to the area of the ROI within the ﬁeld of view. The area of a vertical cross-section of an atom probe tomogram can be approximated as a rectangle topped with a half-circle 1 A = πr2 + 2r(H − r) 2

Where H is the length of the ﬁeld of view and r is the end-radius of the specimen tip. Concentration gradients are measured by averaging the dopant concentration over a thin slice of the tomogram. The more atoms a slice contains the smaller the dopant concentration detectable. Two methods are possible for decreasing the minimum detectable concentration within a slice: increasing the area of the slice and averaging over a thicker slice. The

38 Figure 5.2: We divided the tomogram from previous characterizations into vertical columns and made 1-D concentration plots as a function of depth for each. The plot shown is the depth proﬁle of the column in the center about the delta-plane. Silicon is shown in grey and phosphorus is shown in pink.

Figure 5.3: Top-down view of the tomogram shown in Figure 5.2 superimposed with peak dopant concentration of each segment in atomic percent. This shows an apparent congragation of phosphorus toward the center of the specimen.

39 former is only possible by changing specimen geometry or widening the ﬁeld of view. The latter reduces the spatial resolution of the concentration gradient. The following ﬁgure demonstrates the geometric advantage of a vertically alligned ROI in terms of minimum detectable concentration.

Figure 5.4: Minimum detectable dopant concentration for a 200 nm long tomogram with Si:P ratio averaged over 1 nm thick slices. This shows that due to increased ROI area, specimens prepared with thier planar ROI oriented vertically yield tomograms wich can show much smaller dopant concentrations. As the ﬁeld of view becomes nearly as wide as it is tall, this advantage diminishes.

For a field of view only 50 nm wide and 200nm long, the vertical cross-section of the tomogram has 5 times the area as the horizontal cross-section and therefore the vertical orientation can detect 1/5 the concentration. As the field of view gets wider, the horizontal cross-section increases in area faster than the vertical and they are nearly equal when the tomogram is just as wide as it is long. The above figure does not account for resharpening and reuse of vertically aligned specimens. The effective area of the cross-section increases by an additional factor equal to the number of succesful uses. Therefore a vertically alligned specimen which produces a tomogram with twice the ROI area of an identical horizontal specimen will have effectively 4 times

40 the ROI area if used a total of twice, 6 times the ROI area if used a total of three times, and so on.

41 CHAPTER 6 CONCLUSION

Techniques for rapid preparation of atom probe specimens extracted from the surface of a bulk crystal have been further developed with regards to samples having a planar region of interest. By rotating the sample 90º in-between extracting and mounting on an APT microtip array, we produced specimens with the planar ROI oriented vertically. This technique disaligns the anisotropies of the molecular beam epitaxy and atom probe tomography processes. We have shown that it also increases the ROI volume within the ﬁeld of view of the atom probe by as much as a factor of 5 and produces specimens that can be resharp- end and reused. These advantages make it ideal for the characterization of photovoltaics, and logic devices containing heterojunctions or delta-doping. It may also aid in the APT characterization of several emerging quantum computing logic devices.

42 REFERENCES CITED

[1] D.W. Drum, L.C.L Hollengerg, M.Y. Simmons, M. Freisen, Phys. Rev B 85, 155419 (2012)

[2] M. Xaio, I. Martin, E Yanblonovitch, and H.W. Jiang, Nature (London) 430, 435 (2004)

[3] A. Morello, J.J. Pla, F.A. Zwanenburg, K.W. Chan, K.Y, Tan, H. Huebl, M. Mottonen, C.D. Nugoroho, C. Yang, J.A. van Donkelaar, A. D.C. Alves, D.N. Jamieson, C.C. Escott, L.C.L. Hollengerg, R.G. Clark, and A.S. Dzurak, Nature (London) 467, 687 (2010)

[4] G.P. Lansbergen, R. Rahman, C.J. Wellard, I. Woo, J. Caro, N. Collaert, S. Biesemans, G. Klimeck, L.C.L Hollengerg, and S Rogge, Nat. Phys 4, 656 (2008)

[5] H. Huebl, C.D. Nugroho, A. Morello, C.C. Escott, M.A. Eriksson, C. Yang, D.N. Jamieson, R.G. Clark, and A.S. Dzurak, Phys. Rev. B 81, 235318 (2010)

[6] M. Fuechsle, J. A. Miwa, S. Mahaptra, H. Ryu, S. Lee, O. Warschkow, L.C.L Hol- lengerg, G. Klimeck, and M.Y.Simmons, Nat. Nanotech. 7, 242-246 (2012)

[7] S. Roy and A. Asenov, Science 309, 388-390 (2005)

[8] T. Shinada, L. Okamoto, and I Ohdomari, Nature 437, 1128-1131 (2005)

[9] V.V. Zhirnov, R.K. Cavin, J.A. Hutchby, and G.I. Bourianoﬀ, Proc IEEE 91, 1934-1939 (2003)

[10] G.P. Lansbergen et al, Nature Phys. 4, 656-661 (2008)

[11] L.E. Calvet, J.P. Snyder, and W. Wernsdorfer, Phys. Rev. B 78 195309 (2008)

[12] K.Y. Tan, et al, Nano Lett. 10, 11-15 (2010)

[13] M. Pierre et al, Nature Nanotech, 5, 133-137 (2010)

[14] B.E. Kane, Nature (London) 393, 133 (1998)

[15] R. Crijen, E. Yablonobitch, K. Wang, H.W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, and D. Divincenzo, Phys. Rev. A 62, 012306 (2000)

43 [16] A.J. Skinner, M.E. Davenport, and B.E. Kane, Phys. Rev Lett. 90, 087901 (2003)

[17] M. Friesen, P. Rugheimer, D.E. Savage, M.G. Legally, D.W. van der Weide, R. Joynt, and M.A. Eriksson, Phys Rev B 67, 121301R (2003)

[18] S. R. Schoﬁeld, N.J. Curson, M.Y. Simmons, F.J. Ruess, T. Hallam, L. Oberbeck, and R. G. Clark, Phys. Rev. Lett. 91, 136104 (2003)

[19] L.C.L Hollenberg , A.S. Dxurak, C.J. Wellard, A.R. Hamilton, D.J. Reilly, G.J Mil- burn, and R.G. Clark, Phys. Rev. B 69, 113301 (2004)

[20] C.D Hill, L.C.L Hollenberg, A.G. Fowler, C.J. Wellard, A.D. Greentree, and H.-S Goan, Phys. Rev. B 72, 045350 (2005)

[21] B.P. Gorman, A.G. Norman, and Y. Yan, Microsc. Microanal. 13, 493–502 (2007)

[22] G. Binnig, H. Roher, C. Gerber and E. Weibel, Appl. Phys. Lett. 40, 178-180 (1982)

[23] D.M. Eigler and E.K. Schweizer, Nature 344, 524-526 (1990)

[24] http://dierk-raabe.com/atom-probe-tomography/

[25] C.M. Polley, W.R. Clarke, J.A. Miwa, G. Scappucci, and M. Y. Simmons, J.W. Wells, B.P. Gorman, Submited

[26] A. Kumar, G. A. Cs´athy, M. J. Manfra, L. N. Pfeiﬀer, and K. W. West, Phys. Rev. Lett. 105, 246808 (2010)

[27] A.S. Dzurak, M.Y. Simmons, A.R. Hamilton, R.G. Clark, et al. Quant. Inf. Comput. 1, 82 (2001)

[28] http://physicsmadeeasy.wordpress.com/physics-made-easy/condensed-matter-v

[29] B. Joualt, B. Jabakhanji, N. Camara, W. Desrat, C. Consejo, J. Camassel, Phys. Rev. B 83, 195417 (2011)

[30] G.M. Minkov, O.E. Rut, A.V. Germanenko, A.A. Sherstobitov, V.M. Daniltsev, Phys. Rev. B 64, 235327 (2001)

[31] K.E.J. Goh, M.Y. Simmons, A.R. Hamiltion, Phys. Rev. B 77, 235410 (2008)

[32] E. Shubert, Delta-doping of semiconductors, Cambridge University Press: Cambridge (1996)

44 [33] G. Scappucci, W.M. Klesse, A.R. Hmiltion, G. Capellini, D.L. Jaeger, M.R. Bischof, R.F. Reidy, B.P. Gorman, M.Y. Simmons, Nano Lett. 12, 4953-4959 (2012)

[34] G. Scappucci, G. Capellini, W.M. Klesse, M.Y. Simmons, Nanotechnology 22, 495302 (2011)

[35] Y. Kamata, Mater. Today 11, 30 (2008)

[36] D. Liang, J.E. Bowers, Nat. Photonics 4, 511 (2010)

[37] M.Y. Simmons, S. R. Schoﬁeld, J.L. O’Brien, N.J. Cuson, L. Oberbeck, T. Hallam, R.G. Clark, Surf. Sci. 1209-1218 (2003)

[38] N.J. Curson, S.R. Schoﬁeld, M.Y. Simmons, L. Oberbeck, R.G. Clark, Surf. Sci. 687, 532-535 (2003)

[39] D.P. Adams, T.M. Mayer, B. Swartzentruber, J. Vac. Sci. Technol. B 14, 1642 (1997)

[40] H.F Wilson et al, Phys Rev B 74 195310 (2006)

[41] H.F. Wilson, O. Warschkow, N.A. Marks,S.R. Schoﬁeld, N.J. Curson. P.V. Smith, M.W. Randy, D.R. McKenzie, and M.Y. Simmons, Phys. Rev lett. 93, 226102 (2004)

[42] H.-J. Gossman, L.C. Feldman, Phys. Rev B 32, 6 (1985)

[43] D.S. Lin, T.S. Ku, T.J. Sheu, Surf. Sci. 424, 7 (1999)

[44] L. Oberbeck, N.J. Curson, M.Y. Simmons, R. Grenner, A.R. Hamilton, S.R. Schoﬁeld, R.G. clark, Appl. Phys. Lett. 81, 3197(2002)

[45] K. Oura, V.H. Lifshits, A.A. Saranin, A.V. Zotov, M. Katayama, Surf. Sci. Rep. 35, 1 (1999)

[46] C Thirstrup, M. Sakurai, T. Nakayama, M. Aono, Surf. Sci. 411, 203 (1998)

[47] J.R. Tucker, T.-C. Shen, Solid State Electron. 42, 1061 (1998)

[48] J.L. O’Brien, S.R. Schoﬁeld, M.Y. Simmons, R.G. Clark, et al., Phys. Rev. B 64, R161401 (2001)

[49] T.C. Shen, C. Wang, G.C. Abeln, J.R. Tucker, J.W. Lyding, Science 268, 1590-1592 (1995)

[50] D.S. Lin et al., Phys Rev. B 61, 2799 (2000)

45 [51] P.M. Koenraad and M.E. Flatte, Nature Mater. 10, 91-100 (2011)

[52] G.P. Lopinski, D.D. Wayner, R.A. Wolkow, Nature 406, 48-51 (2000)

[53] Y. Wda Surf. Sci. 386, 265 (1997)

[54] J.R. Tucker and T.C.Shen, Solid Stat Electron. 42, 1061 (1998)

[55] F. J. Ruess, L. Oberbeck, M.Y. Simmons, K.E.JGoh, A.R. Hamilton, T. Hallam, S.R. Schoﬁeld, N.J. Curson, and R.G. Clark, Nano Lett. 4, 1969 (2004)

[56] T.-C Shen, J.S. Kline, T. Schenkel, S.J. Robinson, J.-Y Ji, C. Yang, R.-R. Du, and J.R Tucker, J. Vac. Sci. Technol. B 22, 3182 (2004)

[57] R. Pilarisetty, Nature 479, 7373 (2011)

[58] R. Vrigen, E. Yablonovitch, K. Wang, H.W. Jiang, A. Bladin, V.Roychowdhury, T. Mor, D. Divincenzo, Phys. Rev. A 62, 012306 (2000)

[59] Semiconductor Spintronics and Quantum Computation, edited by D.D Awschalom, D. Loss, and N Samarth (Springer-Verlag, Berlin, 2002)

[60] A. Sutic, J. Fabian, and S. Sas Sarma, Rev. Mod. Phys, 76, 323 (2004)

[61] D.P. DiVincenzo, D. Loss, Superlattices Microstruct. 23, 419 (1998)

[62] A.M. Tyryshkin et al, Nature Mater. 11 143-147 (2012)

[63] http://bradrubin.com/quantum-computing-blog/2008/12/29/the-bloch-sphere-part- 1-see-the-qubit.html

[64] C. Phelps, T. Sweeney, R.T. Cox, and H. Wang, Phys. Rev. Lett.102, 237402 (2009)

[65] J. M Elzerman, R Hanson, L.H.W van Beveren, B. Witkamp, L.M.K. Vandersypen, and L.P. Kouwenhoven, Naature (London) 430, 431 (2004)

[66] J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, and A.C. Gossard, Science 309, 2180 (2005)

[67] N Shaji, C.B. Simmons, M. Thalakulam, L.J. Klein, H. Qin, H. Luo, D.E. Savage, M.G Lagally, A.J. Rimberg, R Joynt, M. Friesen, R.H. Blick, S. N. Coppersmith and M.A. Eriksson, Nat. Phys. 4, 540 (2008)

[68] B.E. Kane Nature 393, 133-137 (1998)

46 [69] G. Ferher, E.A. Gere, Phys. Rev 114, 1217 (1959)

[70] A. Morello et al, Nature 467, 687-691 (2010)

[71] A.S.Dzurak, M.Y. Simmons, A.R. Hamilton, R.G. Clark, et al., Quant. Inf Comput. 1, 82 (2001)

[72] http://www.physics.ohio-state.edu/˜hammel/ssqc.html

[73] J.A. Gupta, R. Knobel, N. Samarth, and D.D. Awschalom, Science 292, 5526 (2001)

[74] J. Orloﬀ, M. Utlaut and L. Swanson (2003). High Resolution Focused Ion Beams: FIB and Its Applications. Springer Press. ISBN 0-306-47350-X. (2003)

[75] http://www.fei.com

[76] L.W.Swanson, Nucl. Instrum. Methods Phy

[77] http://www.taka.jaea.go.jp/tiara/663/nanobeam/index e.html

[78] K. Thompson, D.Lawrence, D.J. Larson, J.D. Olson, T.F. Kelly, B. Gorman, Ultrami- croscopy 107, 131-139 (2007)

[79] http://commons.wikimedia.org/wiki/File:FIB Deposition.jpg

[80] R. Ramachandraa, B. Griﬃnb, D. Joy, Ultramicroscopy 109 (6), 748-757 (2009)

[81] http://www.cameca.com

[82] D.J. Larson, B.D. Wissman, R.L. Martens, R.J. Vielliux, T.F. Kelly, T.T. Gribb, G.F. Erskine, N. Tabat, Microscopy Microanal. 7 (1), 24 (2001)

[83] D.J. Larson, D.R. Foord, A.K. Petford-Long, H. Liew, M.G. Blaminre,A. Cerezo, G.D.W. Smith, Ultramicroscopy 79, 287 (1999)

[84] B. Gault, F. Vurpillot, A. Vella, M. Gilbert, A. Menand, D. Blavette, B. Deconigout, Rev. Sci. Instrum. 77, 043705 (2006)

[85] B. Gault, F. Vurpillot, A Bostel, A. Menand, B. Deconihout, Appl. Phys. Lett. 86 (9), 094101 (2005)

[86] http://www.nonmet.mat.ethz.ch/people/phds/henningg/AtomProbe/index

[87] L. Viskari, K. Stiller,Ultramicroscopy 111 (6), 652–658 (2011)

47 [88] D.J. Larson, P.H. Clifton, N. Tabat, A. Cerezo, A.K. Petford-Long, R.L. Martens, T.F. Kelly, Appl. Phys. Lett. 77 (5), 726 (2000)

[89] T.F.Kelly, P.P. Camus, D.J. Darson, L.M.Holzman, S.S. Bajikar, Ultramicroscopy 62, 29 (1996)

[90] http://www-ﬁm.materials.ox.ac.uk/techniques.html

[91] G.T.A Kovacs, N.I Maluf, K.E. Petersen, Proceedings of the IEEE 86 (8), 1536 (1998).

[92] J.Yeom, Y. Wu, J.C Selby, M.A.Shannon, J. Vac. Sci. Technol. B ( 2005)

[93] C.M. Polley, W.R. Clarke, J.A. Miwa, G. Scappucci, and M. Y. Simmons, J.W. Wells, B.P. Gorman, Submited to Nanolett. (2013)

[94] D. J. Frank et al. Proc. IEEE 89, 259-288 (2001)

[95] R. Vrijen et al. Phys. Rev. A 62, 012306 (2000)

[96] L.C.L Hollenberg, A.D. Greentree, A.G. Fowler, and C.J. Wellard, Phys. Rev. B 74, 045311 (2006)

[97] J.J. Morton, D.R. McCamey, M.A. Eriksson, and S.A. Lyon, Nature 479, 343-353 (2011)

[98] http://www.oxford-instruments.com