Photoluminescence and Resonance Raman Spectroscopy of MOCVD Grown
GaAs/AlGaAs Core-Shell Nanowires
A Thesis
Submitted to the Faculty
of
Drexel University
by
Oren D. Lea er
in partial fulllment of the
requirements for the degree
of
Doctorate of Philosophy
February 2013 © Copyright 2013 Oren D. Lea er.
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Dedications
To my family: my parents, my sister, and Bubby and Dan.
Your support made this possible. Thank you. ii
Acknowledgments
It is with great pleasure that I am able to thank and acknowledge the individuals and organizations that helped me in the course of my graduate studies. I should begin by thanking my advisor, Dr. Spanier, and my committee, Drs. Livneh, May, Shih, Taheri, and Zavaliangos for supporting me through this rather long process. Working for Dr. Spanier helped me grow as a scientist and learn things that extend well beyond the lab. And Dr. Spanier, thank you again for the opportunities for collaboration and travel. I would like to additionally thank Dr. May for allowing me to take advantage of his open o ce door and drop in and ask questions on a number of occasions. And, Tsachi, thank you for your support and advice; I don’t know how this dissertation would have been completed without your help. I would like to acknowledge my funding sources: I was supported by the GAANN fellowship from the Department of Education, the Dean’s fellowship, and the National Science Foundation (NSF) EAPSI fellowship for summer 2011. The work presented here was part of an ongoing collaboration with our Italian colleagues who I had the pleasure of visiting in Lecce, Italy. Nico Lovergine and Paola Prete supplied the nanowires that are the topic of this work. In addition to providing us with samples, they graciously shared their data and allowed me to reproduce it in gure 2.2. Adriano Cola hosted me at the lab in Lecce and made sure that I saw the lab’s fantastic surroundings. In the lab, I learned to use the FIB from Enrico Melissano. Thanks to Anna Fontcuberta i Morral and the American Physical Society for granting permission to reproduce the gure that appears in gure 5.1. I also gratefully acknowledge the help of Dr. Craig Johnson and Stephanie Johnson in acquiring the TEM micrograph presented in gure 2.4 A number of people at Drexel enriched my graduate experience. I would like to thank Dr. Barsoum for the chance to be part of the MAX-phase collaboration; I feel fortunate to have been part of such a productive collaboration. Volker Presser generously provided access to the Renishaw Raman system at the William Keck Institute; in addition to taking the time to iii
train me on the instrument, he also took the time to help nd the right conguration for the instrument. My colleagues in the lab – Chris Hawley, Jennifer Atchison, Mohammad Islam, Maria Torres, Sean Chen, Stephanie Johnson, Stephen Nonnenmann, and Terrence McGuckin – helped keep standards high and worked to keep things fun as we toiled away and I hope to collaborate with them in the future. Kevin Siegl and Alex Juskovic both taught me quite a bit when I mentored them. Judy Trachtman, Dorilona Rose, Keiko Nakazawa, Yeneeka Long, and Sarit Kunz helped me navigate the university bureaucracy. Andrew Marx provided various acts of technical support over the years. Scott Currie was a great help in building my experiments, as were Mark Shiber and the sta at the Drexel machine shop. And thank you to Dr. Knight for your continued e orts to keep our labs safe. I was fortunate to be able to take classes from Nader Engheta, Andrea Liu, and Vaclav Vitek at the University of Pennsylvania. I am grateful for how welcome I was made to feel in those classes. The highlight of my time as a graduate student was spending a few months at the Australian National Fabrication Facility’s New South Wales Node (ANFF-NSW) in Sydney, Australia as an EAPSI fellow during the summer of 2011. I would like to thank the NSF and the Australian Academy of Sciences (AAS) for the funding and logistical support. Meaghan O’Brien of the AAS did a wonderful job of helping with many of the arrangements in Australia. I am deeply indebted to my host at the ANFF-NSW Facility, Prof. Andrew Dzurak, and to Rosie Hicks for helping to arrange my visit. Dr. Fay Hudson generously shared her nanofabrication expertise with me. And it was a great experience working with the sta at the ANFF-NSW: Frank Wright, Gordon Bates, Warren McKenzie, Joanna Szymanska, and El van Zeijl. Prof. Chennupati Jagadish of the Australian National University graciously hosted me when I visited for a day. He and his team showed me great hospitality and were extremely generous with their technical knowledge. Evan Malone and the sta at NextFab Studio were a great help with building experimental equipment and also provided a pleasant work environment. Matt Blaze, Andrew, Sandy, Perry, and Sam made me feel at home in their lab. Leslie Mitts saw that I needed a place to sit
Acknowledgments iv
and write and invited me to work from the SBDC. And Babak, Dev, and Q kindly let me camp out in their lab space. A number of people helped make Sydney feel like home. I was privileged to live with Oliver and Beun who shared their home with me. Dov Rosenfeld helped me nd the ANFF and introduced me to his family in Sydney: Shula, Peter, and Ronny took good care of me while I was there. I would like to thank my friends Tim Verstynen and Jesse Engel for giving me some much-needed perspective. Dan and Ashlee, Ian and Alexis, Billy and Mimi, Micah, Cookie, Adriana, and Rich Grote hosted me at di erent times while I attended conferences. Nick Vacirca and Andrew Bohl helped keep the atmosphere at Drexel light. Linda Anderson and Howard Baker helped me get through this intact. Terrence, Amy, Zoë, and Calyx were patient with me as a housemate for an intended few months that turned into much longer. Matt Robinson and my father helped with the editing. Any mistakes that remain are mine, but there are denitely fewer thanks to their help. And I am extremely grateful to my family for not only putting up with me through my rather long periods of graduate school related crankiness, but also being consistently supportive and helping me see this through to completion. v
Table of Contents
List of Figures ...... vii Abstract ...... xi 1. Introduction ...... 1 1.1 Semiconductor Heterostructures...... 1 1.1.1 The Double Heterostructure Laser...... 3 1.1.2 Quantum Well Devices...... 5 2. Fundamentals of Core-Shell Nanowires ...... 8 2.1 Our Samples and Hypothesis...... 8 2.2 VLS Growth of Nanowires ...... 12 2.3 Impurities and Defects ...... 15 2.3.1 Carbon...... 15 2.3.2 Wurtzite and Planar Defects...... 17 3. Photoluminescence of GaAs/AlGaAs Nanowires ...... 18 3.1 Introduction ...... 18 3.2 Experimental Procedures...... 19 3.2.1 Sample Preparation...... 19 3.2.2 Experimental Conditions...... 20 3.3 Photoluminescence Results...... 21 3.3.1 PL From GaAs Wafer...... 21 3.3.2 Bare GaAs Nanowires...... 22 3.3.3 Core-Shell Nanowires...... 23 3.4 Interpretation of Results and Relevant E ects...... 28 3.4.1 Bandgap Narrowing ...... 28 3.4.2 Donor-Acceptor Pair Luminescence...... 29 3.4.3 The Role of Hydrogen ...... 30 3.5 Conclusions from PL ...... 31 4. Resonance Raman of GaAs/AlGaAs Nanowires ...... 34 4.1 Raman Spectroscopy...... 34 4.2 Experimental Procedures...... 39 4.3 Results and Interpretation...... 44 4.3.1 Summary of Results...... 44 4.3.2 Incoming vs. Outgoing Resonance...... 47 vi
4.3.3 The Missing TO Mode ...... 49 4.3.4 Variation of the LO Peak Position...... 51 5. Single Nanowire Raman Spectroscopy ...... 55 5.1 Experimental Rationale...... 55 5.2 Procedure...... 57 5.3 Theoretical Considerations...... 59 5.4 Results and Discussion ...... 68 5.5 Conclusions ...... 71 6. Conclusions, Open estions, and Future Work ...... 72 6.1 Conclusions ...... 72 6.2 Open Questions and Future Work ...... 73 Appendix A: Finite Curvature-Mediated Ferroelectricity ...... 75 Bibliography ...... 80 Vita ...... 93 vii
List of Figures
1.1 In a semiconductor homostructure, band bending drives oppositely charged car- riers in opposite directions as shown in (a). In a heterostructure, the combination of quasi-elds and external elds can be tuned to only a ect one type of carrier as in (b), or drive both electrons in holes in the same direction as in (c)..... 2
1.2 The band diagram for a double heterostructure laser (a) under moderate forward bias and (b) under high forward bias. Under high forward bias, a well forms, enhancing the trapping of carriers helping create the necessary population inversion for lasing. Based on Kroemer [3,6]...... 3
1.3 The layer structure of the heterostructure used for the discovery of the fractional quantum Hall e ect, showing the two dimensional electron gas on the GaAs side of the GaAs/AlGaAs heterojunction [14–16]. After Lin et al. [17]...... 6
2.1 SEM image of SAGA06 nanowires still on the growth substrate. Courtesy of Enrico Melissano – CNR IMM Lecce...... 8
2.2 PL from di erent batches of core-shell nanowires, labeled by V:III precursor ratios – conditions were otherwise identical during growth. These plots reproduce plots from reference 20. Data provided courtesy of Paola Prete and Nico Lovergine.. 9
2.3 Sample output from a self-consistent Schrödinger-Poisson solver for a radial heterostructure, showing the bandstructure (top) and the calculated electron density (bottom) [Kevin Siegl, Oren Lea er, Jonathan Spanier – unpublished]. 11
2.4 TEM micrograph of SAGA06 nanowires. Courtesy of Stephanie Johnson and Craig Johnson...... 12
3.1 Some of the states and the transitions between them that contribute to the observed PL signal (based on a gure from Gilliland [91])...... 18
3.2 Photoluminescence from a semi-insulating GaAs wafer, acquired with the sample held at 78 K, showing the band edge of GaAs and carbon impurity band. . . . . 21
3.3 PL from bare GaAs nanowires (sample NW40) measured at 4.2 K with peaks labeled with tted energies. The vertical gray line is at 1.519 eV, marking the expected value for the bandgap of GaAs at 4.2 K. The annotated peak separation corresponds to the energy of an LO phonon. Excitation power was 0.023 mW. 23 viii
3.4 PL from core-shell nanowires SAGA10 measured at 4.2 K...... 24
3.5 PL from core-shell nanowires SAGA11 measured at 4.2 K...... 25
3.6 Peak position vs. power for the spectra plotted in gures 3.4 and 3.5 (blue squares correspond to the SAGA10 data and orange circles correspond to the SAGA11 data). Peak position was calculated as a weighted mean as described in the text. 27
4.1 Feynman diagram for the Raman process. Based on Fig. 7.28 in Yu and Cardona [2]. 34
4.2 A schematic of the transitions involved in incoming and outgoing resonances for a Stokes process...... 37
4.3 A schematic of the band structure of GaAs, showing the direct band gap between the conduction band and the light and heavy hole bands (Eg) and the split-o band gap (∆SO)...... 37
4.4 Initial data replotted by transforming wavenumbers to absolute energy; wavenum- ber w measured using excitation wavelength λ, E = E(λ) − E(w)...... 41
4.5 An example of the RRS data being t in OriginPro...... 42
4.6 RRS data from sample SAGA06, measured at 78 K...... 43
4.7 SAGA11 RRS data ...... 44
4.8 NW40 RRS data ...... 45
4.9 GaAs Wafer RRS...... 46
4.10 The squares show the amplitude of the RRS signal from SAGA06 measured at 78 K, plotted as a function of outgoing energy, i.e. Eex − ELO. The solid line shows the PL signal measured under the same conditions...... 47
4.11 Selected spectra showing the lack of a TO peak in the core-shell nanowire data. This e ect was independent of the excitation power used, the spectra shown were selected only because they include the full region from 250 cm−1 to 310 cm−1 in a single contiguous scan, rather than being broken up into two separate scans as was often the case...... 49
4.12 LO and TO phonons...... 50
4.13 (a) The laser line measured at a number of di erent excitation energies, measured through closed slits so as to avoid damaging the PMT. (b) The calculated o set for the laser at the di erent wavelengths...... 52
LISTOFFIGURESLISTOFFIGURES ix
4.14 Diagram of instrument...... 54
5.1 The di erence in stacking orders for (a) zinc-blend GaAs and (b) wurtzite GaAs leads to additional peaks in the Raman spectrum of wurtzite GaAs due to (c) the folding of the Brillouin zone. (Reprinted with permission from Zardo et al., Phys. Rev. B 80, 245324 (2009) Copyright 2009 American Physical Society)[ 129]. 56
5.2 Diagram of experimental setup, the line with the arrows represents the path of the laser light, which includes segments in which incoming and scattered light overlap...... 57
5.3 Polarized Raman spectra from a single nanowire, grouped by the position of the polarization analyzer, with the angle of the λ/2-waveplate labeled, less a constant o set of 50°...... 58
5.4 Schematic showing the scattering conguration and illustrating the vectors used in the calculation of the expected Raman scattering intensity...... 60
5.5 Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = eˆi, where φ is the angle between the [211¯ ] and xˆ1...... 65
5.6 Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration where eˆs is set orthogonal to eˆi, where φ is the angle between the [211¯ ] and xˆ1...... 66
5.7 Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = xˆ3, where φ is the angle between the [211¯ ] and xˆ1...... 67
5.8 Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = xˆ2, where φ is the angle between the [211¯ ] and xˆ1...... 67
5.9 (a) Raman from a single SAGA06 nanowire. (b) Image of the nanowire from the microscope’s CCD...... 68
5.10 Zoomed in plot of the single SAGA06 Raman data, showing an apparent luminescent background, and a clearly resolved TO phonon peak, but no sign of the LO phonon peak...... 69
5.11 Solid lines are cos4(θ ) ts to the data measured in the (a) parallel and (b) perpendicular congurations...... 70
LISTOFFIGURESLISTOFFIGURES x
A.1 Polarization vs. distance from inner radius for the size nanowires used in the study, illustrating the e ect of strain in increasing the polarization of thin ferroelectric shells...... 75
A.2 Waterfall plot of the polarization across the thinnest shell, with color representing the temperature used in the calculation of the polarization...... 76
LISTOFFIGURESLISTOFFIGURES xi
Abstract Photoluminescence and Resonance Raman Spectroscopy of MOCVD Grown GaAs/AlGaAs Core-Shell Nanowires Oren D. Lea er Jonathan E. Spanier, Ph.D.
This work describes experiments conducted on GaAs/AlGaAs core-shell nanowires. The
GaAs/AlGaAs materials system has been a major platform in the development of heterostruc-
ture devices. Heterostructure nanowires grown using bottom-up growth techniques are a
means to creating high quality nanoscaled heterostructures with a variety of potential
uses, most notably in optoelectronics. The GaAs/AlGaAs nanowires that were the subject
of this study were provided to us by partners in Italy, who specialize in MOCVD growth
of heterostructures. These nanowires were hypothesized to have elds at the interface
between core and shell that were in uencing the bandstructure. We used low temperature
photoluminescence (PL), resonance Raman, and polarized Raman spectroscopies to character-
ize the nanowires and understand the in uence of the shell on the electronic structure of
the nanowires. The PL and resonance Raman experiments were carried out on a custom
instrument constructed as part of carrying out this study.
PL gave us a more complete picture of the in uence of defect states on the electronic
properties and the signicance of donor-acceptor-pair (DAP) luminescence in the previously
observed spectral character. The contrast in spectral character between bare GaAs nanowires
and the core-shell nanowires led to an alternative hypothesis that the role of the shell in
determining the spectral characteristics was largely through the thermal history imparted xii
on the cores when they were heated to the shell’s growth temperature; at the elevated
temperatures, hydrogen incorporated into the cores as they were grown di used out.
Hydrogen and carbon are impurities that are di cult to avoid in MOCVD growth, because
they are byproducts of the precursor breakdown and may be incorporated into the nanowires
during growth. Prior to exposure to the elevated temperatures, hydrogen compensated the
carbon which is useful as a p-type dopant in GaAs.
Further investigation of the nanowires using resonance Raman spectroscopy showed
strong coupling between the LO-phonon and the bound exciton state, particularly in the
core-shell nanowires, supporting the new hypothesis. Polarized Raman spectroscopy was
used to investigate the possibility of wurtzite GaAs being present in what were otherwise
zinc-blende GaAs structures.
Abstract
1
Chapter 1: Introduction
The principal applications of any su ciently new and innovative technology have always been – and will continue to be – applications created by that technology.
Kroemer’s Lemma of New Technology [1]
1.1 The Signicance of Semiconductor Heterostructures
Heterostructure nanowires, the subject of our research, fall under the broader category
of semiconductor heterostructures; so to contextualize our research, some description of
semiconductor heterostructures is in order. To illustrate some of the properties that make
heterostructures useful and the AlGaAs-GaAs material system particularly attractive to work with, we will discuss the double heterostructure (DH) laser and the quantum well
heterostructure. Both of these examples also share the features that the heterostructure
is used to control the spatial distribution of carriers in the device and that they were
breakthroughs enabled by improved control of semiconductor growth, which were achieved
using GaAs/AlGaAs in both cases.
GaAs/AlGaAs heterostructures have been of particular importance in the development of
heterostructure devices, largely because there is such a close match in lattice constant
between GaAs and AlAs, reducing the e ect of strain as an issue to contend with during
crystal growth. Because the lattice spacings of the family of ternary Alx Ga1−x As compounds vary so little, while the bandgaps vary signicantly, heterostructures based on GaAs/AlGaAs 2 have often been the rst grown for various types of devices [2, 3]. Most other combinations of III-V compounds have a signicant lattice mismatch that if not accounted for in the design, may lead to the formation of defects in the material.
-qF (a)
+qF
(b)
+qFh -qFe
(c)
+qFh
Figure 1.1: In a semiconductor homostructure, band bending drives oppositely charged carriers in opposite directions as shown in (a). In a heterostructure, the combination of quasi-elds and external elds can be tuned to only a ect one type of carrier as in (b), or drive both electrons in holes in the same direction as in (c). (This gure is based on Kroemer [4].)
Nanowire heterostructures are a progression in the continued development of semicon- ductor heterostructures, so before attempting to describe semiconductor heterostructure nanowires, it will be helpful to rst describe semiconductor heterostructure thin lms.
Semiconductor heterostructure devices in use today are built around thin lms. The growth techniques used for nanowires are based on those developed for thin lms [5]. Of particular relevance for nanowire growth are molecular beam epitaxy (MBE) and metal organic chemical
Chapter1: Introduction 1.1SemiconductorHeterostructures 3 vapor deposition (MOCVD).
The feature that denes a semiconductor heterostructure is that the composition of the
semiconductor changes as a function of position – in other words, it includes two or more
semiconductors grown in contact with each other. This is in contrast to homostructures, which can have varied doping, but consist of a single material throughout [3].
1.1.1 The Double Heterostructure Laser
Electrons Electrons
Donors Donors Light Light
Acceptors Acceptors
Holes Holes (a) (b)
Figure 1.2: The band diagram for a double heterostructure laser (a) under moderate forward bias and (b) under high forward bias. Under high forward bias, a well forms, enhancing the trapping of carriers helping create the necessary population inversion for lasing. Based on Kroemer [3,6].
Ideas for devices based on heterostructures signicantly predate their realization. For
example, Shockley was issued a patent in 1951 that mentions the idea of using a wide bandgap
material emitter in a transistor to improve device performance [7], an idea that was more
fully developed by Kroemer [8]. The barrier to their realization was the challenge of growing
lms that combined di erent materials without creating defects [3,9].
In a semiconductor homostructure, i.e. a single semiconductor material, an electric eld
can be externally applied or develop from a doping gradient, but either way the bands remain
parallel. This means that any electrons or holes are acted on with equal and opposite forces,
Chapter1: Introduction 1.1SemiconductorHeterostructures 4
so electrons are subjected to a force Fe = −qE and holes are accelerated by Fh = +qE.A
gradient in the composition has the e ect of creating a “quasi-electric eld” arising from the
gradient of the bandgap. The important thing about the quasi-electric eld is that it is
inherently di erent for the valence and conduction bands, thus the forces are now described
by Fe = −qEc and Fh = +qEv [4].
This important feature, illustrated in gure 1.1, is key to the function of a variety of
devices because it allows independent control of electrons and holes. An important application
of this concept was the double heterostructure (DH) laser [3,9, 10].
The DH laser is a particularly compelling historical example of semiconductor heterostruc-
tures, because it was the rst device that achieved something using a heterostructure that
couldn’t be achieved using conventional semiconductor devices. In 1963, Herbert Kroemer
conceived of the DH laser as a means of defeating the limitations of solid state lasers – at the
time, solid state lasers needed to be operated at low temperatures and in short pulses, because
they would otherwise melt due to the high injection current required. He had been thinking
for some time about using heterostructures as a means of controlling the drift of carriers in a
semiconductor device. He was not the rst to think about using heterostructures to improve
transistor performance, but his in-depth analysis enabled him to propose the DH laser as a
means of building a solid state laser that could operate at room temperature continuously
(CW) [1,3].
Kroemer’s general insight about heterostructures was that they are a means of producing what he called “quasi-electric elds.” The DH laser was devised as a means of achieving a
room temperature operating CW solid-state laser by overcoming the need for extremely high
injector current required by previous designs in order to create a population inversion; the
Chapter1: Introduction 1.1SemiconductorHeterostructures 5
high current necessitated their operation at liquid nitrogen temperatures or in short low
duty-cycle pulses [1, 6]. The DH laser design has been extremely important technologically;
it is the basis of the lasers used in CD and DVD players, ber optic communications, as well as other applications [3]. One of the interesting details of the history of the DH laser
is the lack of interest from his management Kroemer received in response to his initial
proposal to attempt to fabricate a DH laser; it is in part in reference to this history that
Kroemer formulated his lemma [1]. The wider bandgap regions around the active region of
the DH laser are used to prevent the carriers from escaping the active region into opposing
contacts [6, 11].
Much of the early heterostructure literature focused on the Ge-GaAs system because their
lattice constants are quite close to each other. It turns out that the Ge-GaAs system has
complications that arise from the interface between a polar and non-polar materials making it
challenging to create device quality heterostructures using the Ge-GaAs system [12].
In addition to optoelectronic devices, heterostructures have been extremely valuable for
use in high-speed electronic devices. The heterostructure bipolar transistor (HBT), for
example, is used in a variety of RF applications. The HBT uses gradients in the bandgap of the
device to in uence the drift of minority carriers in the device to decrease their transit times,
leading to a faster device [13].
1.1.2 Quantum Well Devices
Quantum structures are a further development in the progress of heterostructure devices. In
these structures, carriers are conned to a well that is smaller in at least one dimension than
the Bohr exciton radius [2]. Carriers conned in a quantum well take on a set of discrete
Chapter1: Introduction 1.1SemiconductorHeterostructures 6
AlGaAs (Si-Doped)
AlGaAs (Undoped)
GaAs (Undoped)
GaAs (Substrate) Ef
Figure 1.3: The layer structure of the heterostructure used for the discovery of the fractional quantum Hall e ect, showing the two dimensional electron gas on the GaAs side of the GaAs/AlGaAs heterojunction [14–16]. After Lin et al. [17]. states resulting from the particle-in-a-box like nature of the connement [18]. Additionally, their density of states is modied by the dimensionality of their connement, making their physics distinctly di erent from carriers in bulk.
Quantum well structures are also particularly useful for the creation of high mobility devices because they allow the separation of carriers from dopants through the technique of modulation doping [19]. High mobility carriers conned in quantum wells show additionally interesting physics, in particular, the fractional quantum Hall e ect was discovered using a
GaAs-AlGaAs heterostructure [14–16]. One quantum well structure in particular is of interest to us here, because its band structure was the basis for the band structure originally proposed for the nanowires we studied.
The layered structure in gure 1.3 is a schematic of the modulation doped structure
Chapter1: Introduction 1.1SemiconductorHeterostructures 7
used by Tsui et al., which was grown with a 1 µm base of undoped GaAs, 500 Å of undoped
AlGaAs, and 600 Å of Si doped AlGaAs. In some of their structures, they also used a thin layer
of doped GaAs on top as a protective layer. The higher electron a nity of GaAs leads to
the carriers from the ionized dopants in the AlGaAs accumulating in GaAs side of the
undoped GaAs/AlGaAs heterojunction. The resulting structure achieved very high mobility
by having a high quality interface and separation of carriers from dopants [14]. It was with
this structure in mind that we formulated our hypothesis about our nanowires that had no
intentional doping of their cores and Si in their AlGaAs shells.
Chapter1: Introduction 1.1SemiconductorHeterostructures 8
Chapter 2: Fundamentals of Core-Shell Nanowires
Figure 2.1: SEM image of SAGA06 nanowires still on the growth substrate. Courtesy of Enrico Melissano – CNR IMM Lecce.
2.1 Our Samples and Hypothesis
The samples we studied were GaAs-core—AlGaAs-shell nanowires grown using metal organic
chemical vapor deposition (MOCVD), which is also sometimes referred to as metal organic vapor phase epitaxy (MOVPE). They were provided to us by Nico Lovergine and Paola Prete who run a lab in Lecce, Italy, that specializes in MOCVD growth of III-V semiconductors. The
nanowires we studied were part of a series of nanowires grown with varying V:III precursor
ratios, from which we were able to use core-shell nanowires from three di erent batches
and bare GaAs nanowires from one growth. The parameters used for the growths of the 9 ) s t
i 5 : 1 n U
y r a r t i
b 1 0 : 1 r
A (
y t i s n
e 2 0 : 1 t n I
3 0 : 1
1 . 4 0 1 . 4 5 1 . 5 0 1 . 5 5 1 . 6 0 E n e r g y ( e V )
Figure 2.2: PL from di erent batches of core-shell nanowires, labeled by V:III precursor ratios – conditions were otherwise identical during growth. These plots reproduce plots from reference 20. Data provided courtesy of Paola Prete and Nico Lovergine. nanowires are listed in table 2.1. As will be explained below, at the point that we became involved, it was hypothesized that the interface between core and shell a ected the electronic properties of the nanowires.
The signicant di erence between these nanowires and MOCVD grown GaAs/AlGaAs nanowires described in the literature is in the choice of arsenic precursor. Arsine (AsH3) is the precursor used for most MOCVD grown nanowires in which arsenic is the group V element [21, 22]. For the nanowires we studied, tertiarybutylarsine (TBA, C4H11As) was used instead [20, 23, 24]. TBA has a lower decomposition temperature than arsine, so it is utilized more e ciently allowing growth at lower temperatures and with a lower V:III ratio. TBA is
Chapter2: Fundamentals 2.1OurSamplesandHypothesis 10
also safer than arsine; the LC50 (median lethal concentration) for arsine is 20 ppm at four
hours exposure time, while for TBA it is over 500 ppm and it has a lower vapor pressure – a
signicant reason to prefer it if the quality of growth products is not adversely a ected [25].
TBA has been used successfully as a precursor for MOVPE growth of high quality GaAs
lms with low densities of incorporated impurities [26–29]. In optimized growth conditions
using TBA, it has been shown that the lower bound for the inclusion of carbon acceptor
doping is limited by the breakdown of the trimethylgallium (TMG) [30]. Thus, based on the
growth of GaAs lms, there is no reason to assume that the additional carbon from the TBA would necessarily be incorporated into the growth product.
Table 2.1: Excerpt from sample growth log, growth times are specied in minutes [Lovergine and Prete, private comm.]
Sample Core T(◦C) time V:III Shell T(◦C) time V:III Cap T(◦C) time V:III NW40 GaAs 400 90 5 ------SAGA06 GaAs 400 60 20 AlGaAs 650 4 20 GaAs 650 1 20 SAGA10 GaAs 400 60 20 AlGaAs 650 10 20 - - - - SAGA11 GaAs 400 60 5 AlGaAs 650 4 5 GaAs 650 1 5
The hypothesis for this work was predicated on the knowledge that carbon from the
breakdown of the precursors can result in p-type GaAs and that there was Si contamination
of Al source that could lead to n-type shells. It was hypothesized that these impurities created
the conditions for band bending and possibly a quantum well. The plan for our experiments was developed based largely on accounts such as Jiang et al. [31], Lauhon et al. [32], Lu et al.
[33], and Li et al. [34], which focus on the heterostructure properties of the nanowires, rather
than emphasize the challenges of nanowire growth.
Self-consistent Schrödinger-Poisson calculations suggested that with su ciently high
doping of core and shell, it was possible for a quantum well to form at the interface. These
Chapter2: Fundamentals 2.1OurSamplesandHypothesis 11
Figure 2.3: Sample output from a self-consistent Schrödinger-Poisson solver for a radial heterostructure, showing the bandstructure (top) and the calculated electron density (bottom) [Kevin Siegl, Oren Lea er, Jonathan Spanier – unpublished]. calculations were performed using a solver for a radially symmetric heterostructure written by Kevin Siegl, an REU summer student in our lab, based on a published description of such a solver [35, 36]. Figure 2.3 shows the output of one such calculation, with an assumed doping of 1 × 1017 cm−3 in the core and 2 × 1018 cm−3 in the core.
The remainder of this chapter will provide more detail about nanowires and their growth, followed by a more in-depth discussion of some of the related issues to provide context for the following chapters where we discuss our experimental results.
Chapter2: Fundamentals 2.2VLSGrowthofNanowires 12
Figure 2.4: TEM micrograph of SAGA06 nanowires. Courtesy of Stephanie Johnson and Craig Johnson.
2.2 VLS Growth of Nanowires
Nanowires are structures that are on a scale of tens of nanometers or less in cross section with lengths of hundreds of nanometers up to many microns. Semiconductor nanowire
heterostructures are nanowires composed of more than one semiconductor material.
Nanowires can be produced by either top-down or bottom-up methods. Top-down methods
start with bulk material of the desired composition and remove material leaving behind
the nanowires; bottom-up methods follow nature’s method of building structures up
by self-assembly. The semiconductor industry uses top-down methods and the rapid
improvement of semiconductor devices has been closely tied to advancement fabrication
methods. Bottom-up methods o er potential advantages over what can be achieved through
Chapter2: Fundamentals 2.2VLSGrowthofNanowires 13
top-down fabrication; at the nanoscale, bulk materials are no longer especially uniform, and
bottom-up methods can be used to fabricate structures with geometries not achievable using
top-down methods [5, 37].
Nanowires have been demonstrated in a variety of applications including: p-n junctions [38,
39], LEDs [40, 41], lasers [42–44], photodetectors [45], single molecule detectors [46], and
photovoltaics [47–52]. Nanowire heterostructures have been fabricated to contain quantum wells [32, 33, 53], tunnel diodes [54], and work as high-mobility transistors [31, 34].
Most nanowires, including the nanowires that were the subject of this study, are grown
from the vapor phase starting with seed particles, which are most often Au [5]. One of the
drawbacks to the use of a catalyst is the possibility of contamination by the catalyst materials;
this has been documented with the contamination of Si nanowires by their Au catalyst
particles. Au in Si acts as a deep level trap, degrading the performance of the material for any
device applications [5, 55]. There are methods for growing nanowires from vapor without the
use of a catalyst; these methods avoid the issues associated with catalysts, but generally
require some element of top-down control, such as lithographically patterning a substrate
before nanowire growth [56–60]. Other methods of growing nanowires include solution
phase epitaxy (SPE) and liquid phase epitaxy (LPE), but they are applicable to a limited range
of materials and not widely used for nanowire growth [5].
The origins of nanowire growth techniques lie with observations of spontaneous BeO
microwhisker formation in the presence of metal droplets reported by Edwards and Happel
in 1962[ 61]. Application of this method to Si was reported by Wagner and Ellis in 1964 with the rst proposed mechanism, which they named the Vapor–Liquid–Solid (VLS)
mechanism [62].
Chapter2: Fundamentals 2.2VLSGrowthofNanowires 14
For a single component material, like Si, with a Au seed, the VLS mechanism is relatively
simple. It assumes that precursor molecules in the vapor phase (SiCl4 in the case of Wagner
and Ellis) preferentially stick to the liquid droplet formed from the melted seed particle and
breakdown forming a solution of Si-Au. The Si-Au solution becomes super saturated with Si
as more precursors breakdown and the temperature of the growth system is lowered towards
the Si-Au eutectic point. The super saturated solution then spontaneously precipitates out
Si leading to the one-dimensional growth, with the seed particle taking on the eutectic
composition [62].
There is some complication to the model, because the role played by the seed particle is
not actually that of a catalyst, thought it is often discussed as if it were. A catalyst raises
a reaction rate by lowering the activation energy through its presence, while not being
consumed itself. There have been several studies that have shown that the activation energy
for the breakdown of the precursors in the presence of the seed is approximately the same as without it [5, 23, 62].
Additionally, the role of the phase of the seed particle is unclear, but it may be unimportant
because the Vapor–Solid–Solid (VSS) mechanism has been observed in which the seed
particle remains solid. The VSS mechanism was observed using in-situ TEM by Kodambaka
et al. where they observed nanowires growing via VLS and VSS simultaneously in the same
growth environment [63].
The VLS model becomes more complex in dealing with binary compounds; in part
because the solubility of the components can be vastly di erent from each other, making the
explanation of supersaturation driven growth less plausible [5, 64]. The solubility of the
group V elements tends to be negligible in a Au seed particle, while the low melting points of
Chapter2: Fundamentals 2.2VLSGrowthofNanowires 15
Ga and In are generally below the growth temperature leading to the issue that there is no
solubility limit for the two liquid materials. The insoluble elements can be assumed to reach
the growth surface through surface di usion. However the explanation of why the soluble
element precipitates out is unclear [5].
After axial growth, during which the VLS (or similar) mechanism dominates, the growth
conditions may be changed to promote epitaxial growth of material on the surface of the
nanowire [32, 37, 65]. This is the technique used to grow the nanowires that we studied.
There have been a number of papers in the last few years detailing methods for growing
high quality nanowires using MOCVD; although, because arsine is the generally preferred
precursor, nearly all the papers describe the use of arsine rather than TBA. For our purposes,
a high quality nanowire is one that is straight (unkinked), untapered, free of planar defects, a
controlled crystal structure, and with a controlled dopant concentration [22].
2.3 Impurities and Defects in MOCVD Grown Nanowires
2.3.1 Carbon
Carbon is a byproduct of the MOCVD precursor chemistry, making it a challenging impurity to
eliminate from growth product; but it can be a desirable impurity in controlled concentrations,
because it is a good p-type dopant in GaAs: it has low di usivity compared to other p-type
dopants, it can achieve high doping concentrations, and it can be included just by changing
growth conditions [66–71]. For the nanowires in our study, tertiarybutylarsine (TBA) was
chosen over the more commonly used AsH3, introducing more carbon to the reaction. But
this shouldn’t necessarily lead to large amounts of carbon in the nanowires: in lm growth,
TBA has been used to produce high quality GaAs with low carbon content, and there is
Chapter2: Fundamentals 2.3ImpuritiesandDefects 16
evidence that use of TBA does not signicantly increase the carbon content of lms nearly as
much as the choice of TMG as a Ga precursor [26, 27, 72, 73]. In lm MOCVD growth, carbon
doping can be controlled by using a combination of gallium precursors, such as TMG with
triethylgallium (TEG) [74–76].
The growth rate of the nanowires in our study provides good reason to expect that carbon
is incorporated into the nanowires; it is low enough that the nanowires are tapered as seen in
gure 2.4. Tapering is evidence of sidewall growth, which occurs during slow growth of GaAs
nanowires; and sidewall deposition is the route by which carbon is incorporated into GaAs
nanowires; it doesn’t enter through the catalyst particle because the solubility of carbon in
gold is very low [77–79]. There are also a number of possible planar defects visible in the
gure 2.4, but without further imaging, it is impossible to distinguish them from other
phenomena, such as strain, that can appear as imaging artifacts.
In growth of GaAs using AsH3 and TMG as precursors, carbon in the growth product is a
byproduct of TMG – the only C containing precursor – which is obvious from the chemical
equation describing the growth,
AsH3 + Ga(CH3)3 −−→ GaAs + 3 CH4. (2.1)
Subtler is how carbon is incorporated in the GaAs, because it is via an intermediary product
of the breakdown of TMG, which explains how the carbon comes to be incorporated into the
As-sites. In what is believed to be the primary route for carbon incorporation, as the TMG
undergoes pyrolysis, Ga-bound carbene (GaCH2) forms as a reaction product, which can be
adsorbed from both ends – the carbon can occupy an As-site or the gallium can occupy its
Chapter2: Fundamentals 2.3ImpuritiesandDefects 17 own site [80–82].
2.3.2 Wurtzite and Planar Defects
Planar defects are in part related to the issue that wurtzite GaAs is a possible growth product,
rather than only zinc blende GaAs as is the case for bulk GaAs. Wurtzite is a crystal structure
that di ers from zinc blende only in the stacking order of the layers, so a single plane of wurtzite in zinc blende would essentially be a stacking fault.
One of the complications of growing GaAs as a nanowire is that unlike in the bulk case where GaAs only forms in the zinc blende structure, GaAs can form a wurtzite (WZ) or zinc
blende (ZB) structure when it is nanoscaled [83–85]. In fact, GaAs nanowires can have WZ
and ZB segments mixed along the length of a single nanowire [86, 87]. Control over which
phase nanowires grow in has been a recent theme in several recent publications [88–90].
Chapter2: Fundamentals 2.3ImpuritiesandDefects 18
Chapter 3: Photoluminescence of GaAs/AlGaAs Nanowires
3.1 Introduction
Conduction Band Free Exciton
Donor Levels
CB-A Band to Band Hot Electron D-A (F,X)
Acceptor Level
Valence Band
Figure 3.1: Some of the states and the transitions between them that contribute to the observed PL signal (based on a gure from Gilliland [91]).
Photoluminescence spectroscopy (PL) – like cathodoluminescence, thermoluminescence,
or electroluminescence – is an emission spectroscopy where carriers are excited from the valence band to the conduction band and the radiative recombination of carriers is observed.
In the case of PL, the carriers are excited into the conduction band by light, but otherwise, the
physics are the same as in other luminescence processes. Luminescence processes can
be viewed as having three steps: excitation, thermalization, and radiative recombination. 19
Thermalization means that the excited carriers reach thermal equilibrium and relax to the
lowest energy states available to them, thus “forgetting” their histories, meaning that the
resulting spectrum should be essentially independent of the energy of the excitation used –
the exception to this is hot luminescence, where carriers that are not fully thermalized
recombine [2, 92].
Because of the thermalization, PL spectra can contain a signicant amount of information
about defect states lying within the bandgap of a material. In a perfect sample of direct
bandgap material, where the transition is allowed, we would expect carriers to accumulate at
the band edges and then recombine radiatively. At low temperatures, when dopants are not
ionized, the excited carriers can interact with the dopants, creating peaks in the spectrum that
can dominate the band edge luminescence [2, 91, 92].
Though our initial hypothesis was that the interface plays a role in the electronic
properties of the nanowires, we will interpret the results in this chapter as being due to the
impurity content of the GaAs. As we will explain below, high concentrations of dopants can
also modify the band structure of a material, causing the bandgap to shrink or renormalize. We will show that most of the features in our PL spectra are accounted for by donor-acceptor pair
(DAP) luminescence, a defect band due to carbon, and the renormalization of the bandgap.
3.2 Experimental Procedures
3.2.1 Sample Preparation
Nanowires were removed from growth substrates by brief ultrasonic agitation while immersed
in isopropyl alcohol (IPA). Nanowires were then deposited on substrates by placing drops of
IPA-nanowire suspension on SiOx on degenerately doped Si substrates that were placed
Chapter3:PL 3.2ExperimentalProcedures 20
on a hot plate set at ≈100 ◦C to evaporate o the IPA. Substrates were then placed on the
cryostat’s cold nger with a thin layer of Apezion-N thermal grease holding them in place.
All data was collected in a back scattering conguration. Laser power was measured
using a calibrated sensor (Newport 883-SL) that was placed at one leg of a beam-splitter.
Samples were aligned using a camera that was placed in the optical train for alignment
purposes and then the sample position and focus were optimized by maximizing the collected
PL intensity. See gure 4.14 for a diagram of the instrument.
3.2.2 Experimental Conditions Temperature Selection
At room temperature, the PL from GaAs nanowires is strongly quenched by thermally
activated defects. Early on in our experiments, we observed this e ect anecdotally, nding it
much easier to measure PL from nanowires cooled to 78 K using liquid nitrogen; therefore we
conducted all our experiments at below room temperature. Titova et al. investigated this
e ect in detail, showing that the strong quenching occurred above 120 K [93].
For PL, it is preferable to cool samples to 4.2 K using liquid helium. This improves PL
in several ways: thermal broadening is reduced, non-radiative relaxation mechanisms
(e.g. phonons) are suppressed, and carriers are frozen on impurities [2]; thus, we conducted
some of our PL experiments at 4.2 K. The reason not all experiments were carried out at 4.2 K was that we had limited access to liquid helium.
Laser Line Selection
The main selection requirement for the excitation energy used for the PL experiments was that it was above the bandgap energy of the core and below that of the shell. At low
Chapter3:PL 3.2ExperimentalProcedures 21
temperature, the bandgap of the AlGaAs shell is approximately 2 eV, thus any laser line over
1.52 eV from the Ti:Sa laser meets this requirement [24].
3.3 Photoluminescence Results
3.3.1 PL From GaAs Wafer
7 8 K ) s t i n U
y r a r t
i b r A (
y t i s n
e 1 . 4 9 0 5 7 t n I
1 . 4 6 1 . 4 8 1 . 5 0 1 . 5 2 1 . 5 4 1 . 5 6 E n e r g y ( e V )
Figure 3.2: Photoluminescence from a semi-insulating GaAs wafer, acquired with the sample held at 78 K, showing the band edge of GaAs and carbon impurity band.
In order to conrm the operation of the instrument, we used a piece of GaAs wafer as a
reference sample. The PL spectrum from the GaAs wafer (gure 3.2) shows two main peaks:
the band edge at 1.508 eV and the peak at 1.491 eV which we attribute to the carbon impurity
band [94].
Chapter3:PL 3.3PhotoluminescenceResults 22
A common approximation for the bandgap of GaAs is the Varshni equation,
aT2 E = E(T=0 K) − , (3.1) g T + b with E(T=0 K) = 1.519 eV, a = 5.405 × 10−4 eV/K, and b = 204 K (for the Γ transition) [94,
95]. With the given values, at 78 K, equation (3.1) predicts a bandgap of 1.507 eV, which
agrees well with the peak in gure 3.2.
Measuring a bulk wafer sample was a means to conrm the operation of our instrument with a sample that was somewhat similar to the samples of interest (the nanowires), but also
much easier to measure by virtue of giving a very strong signal and being large enough that it was easy to align to. After we conrmed the operation of the instrument, we continued onto
measuring the nanowire samples.
3.3.2 Bare GaAs Nanowires
PL from the bare nanowires (NW40) measured at 4.2 K resolved three peaks in the spectrum,
as shown in gure 3.3. The highest energy peak appears at 1.512 eV, while the strongest
peak is at 1.494 eV. The expected position for the band edge is 1.519 eV, which we interpret
as meaning that the band edge has been depressed to 1.512 eV. The peak at 1.494 eV, we
interpret as being carbon impurity band, which also helps account for the energy of the band
edge. A large carbon content helps account for the depressed band edge energy, because the
band edge can be reduced by su ciently high p-doping by carbon [96]. The peak at 1.457 eV
is a LO phonon replica of the band-edge peak [97]. Phonon replicas arise from a coupling
between excitons and phonons, in this case between a bound-exciton and the LO phonon,
Chapter3:PL 3.3PhotoluminescenceResults 23
1 . 4 9 4 4 e V
) 4 . 2 K s t
i 7 9 6 n m e x c i t a t i o n n U
y r a r t
i 3 6 . 5 m e V b r
A (
y t i s
n 1 . 4 5 7 9 2 e V e t X 1 0 1 . 5 1 1 7 1 e V n I
1 . 4 2 1 . 4 4 1 . 4 6 1 . 4 8 1 . 5 0 1 . 5 2 1 . 5 4 1 . 5 6 E n e r g y ( e V )
Figure 3.3: PL from bare GaAs nanowires (sample NW40) measured at 4.2 K with peaks labeled with tted energies. The vertical gray line is at 1.519 eV, marking the expected value for the bandgap of GaAs at 4.2 K. The annotated peak separation corresponds to the energy of an LO phonon. Excitation power was 0.023 mW. where the exciton scatters a phonon before recombining [98]. This consistent with strong
coupling between LO phonons and carbon acceptors, which has been documented before in
GaAs as noted in the discussion below [97, 99].
3.3.3 Core-Shell Nanowires
Figures 3.4 and 3.5 show low temperature PL from nanowires SAGA10 and SAGA11. Data was normalized by dividing by product of the excitation power and signal integration time,
and the minimum value was subtracted o to reference the curves to a common baseline.
Chapter3:PL 3.3PhotoluminescenceResults 24
3 80x10 Power (mW) 0.0058 0.0059 0.0062 60 0.0072 0.017 0.024 0.036 0.065 0.070 0.10 40 0.118 0.15 0.19 counts/mW/s 0.20 0.290
20
0 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 Energy (eV)
Figure 3.4: PL from core-shell nanowires SAGA10 measured at 4.2 K.
Because not all of the spectra covered the same energy range, the normalization is imperfect, but the alternative of not removing the background amplies the e ect of the constant background (dark signal) in the spectra measured with lower power excitation, making the comparison between spectra worse.
The peak of the PL from the core-shell nanowires varies as a function of the excitation power and it is consistently lower energy than the band-edge of bulk GaAs at 4.2 K. The power dependence of the peak position shows the trend of increasing peak energy with increasing power. Figure 3.6 plots the peak position as a function of the excitation intensity for the data plotted in gures 3.4 and 3.5. The peak position was calculated as a weighted
Chapter3:PL 3.3PhotoluminescenceResults 25
Power (mW) 120x103 0.0055 0.011 0.035 0.152 100 0.22 0.24 0.25 80 0.27 0.28 0.36 0.38 60 0.47 counts/mW/s 0.56 0.76 1.19 40
20
0 1.40 1.42 1.44 1.46 1.48 1.50 1.52 1.54 Energy (eV)
Figure 3.5: PL from core-shell nanowires SAGA11 measured at 4.2 K.
P ξ ξ · I (ξ ) mean of the data, i.e. P where ξ is the energy and I (ξ ) is the intensity of the PL at ξ I (ξ ) that energy. It seems worth highlighting that the data presented in gure 3.6 is consistent for the most part, showing a fairly consistent trend over more than two orders of magnitude of excitation intensity – especially considering that the data was taken on two separate days, on di erent samples, with some inherent uncertainties about the actual power and number of nanowires in the spot due to the drift associated with the instrument.
The PL from SAGA11 (gure 3.5) shows a peak at approximately 1.44 eV. We only found this peak in PL from the SAGA11 nanowires. It is likely that this is signicant; SAGA11 were the core-shell nanowires grown with the lowest V:III precursor ratio among the samples of
Chapter3:PL 3.3PhotoluminescenceResults 26 core-shell nanowires we studied here. The lower ratio increases the likelihood of wurtzite growth, leading us to hypothesize that the peak at 1.44 eV is a result of the heterojunctions that form between zinc blende and wurtzite sections [89].
Chapter3:PL 3.3PhotoluminescenceResults 27
1.500
1.495
1.490
1.485
1.480 Weighted Mean Energy (eV)
1.475
1.470 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 0.01 0.1 1 Power (mW)
Figure 3.6: Peak position vs. power for the spectra plotted in gures 3.4 and 3.5 (blue squares correspond to the SAGA10 data and orange circles correspond to the SAGA11 data). Peak position was calculated as a weighted mean as described in the text.
Chapter3:PL 3.3PhotoluminescenceResults 28
3.4 Interpretation of Results and Relevant E ects
Table 3.1: Summary of peak assignments for dominant PL peaks.
Peak Position (eV) Assignment ≈1.49 Carbon defect band ≈1.485-1.51 DAP — peak increases in energy with increasing power ≈1.51 Band edge
The decreased band edge energy indicates a high level of doping in the nanowires [100, 101].
The bare GaAs nanowires have a PL spectrum matching that of p-doped GaAs, grown at
400 ◦C [102]. A sign of how much carbon is incorporated is that our spectra are completely
missing the free-exciton peak, which is clear when our spectra are compared with spectra
from high quality GaAs – this applies to both the bare GaAs nanowires and the core-shell
nanowires [79].
3.4.1 Bandgap Narrowing in Highly Doped Semiconductors
The nature of semiconductors is that a small impurity content leads to a signicant change in
their electrical properties through the addition of free carriers. At higher doping concentrations,
the band structure changes as is observed through a number of e ects. The Burstein-Moss shift
is an e ect observed in the absorption spectrum of highly doped semiconductors [103, 104].
The Burstein-Moss shift appears as a blue shift in the absorption spectrum of highly doped
semiconductors, while the bandgap of the semiconductor is in fact reduced by the high
concentration of dopants. While the Burstein-Moss shift is explained by the lling of states,
the reduction of the bandgap is instead related the introduction of states by the dopants.
Qualitatively, this can be argued from the standpoint that the bandgap of a semiconductor
arises from a description of the material as a perfect crystal. The introduction of impurities
Chapter3: PL 3.4InterpretationofResultsandRelevantEffects 29
creates disorder in the material, which will in e ect be a perturbation on the model of the
material as a perfect crystal. The change in the shape of the band structure of doped GaAs is
related to band tails, also known as Urbach tails for Franz Urbach who rst documented their
presence in semiconductors [92, 105–107].
Another description is that at low concentrations, acceptors (or donors) create isolated
states within the bandgap. At higher concentrations, the wavefunctions of the acceptor states
begin to overlap, creating a band of energies, that eventually will overlap with the band edges;
in addition the decreasing the band edge, these e ects modify the peak shape and broaden the
peaks [2, 107, 108].
3.4.2 Donor-Acceptor Pair Luminescence
Donor-acceptor pair transitions result from carriers created by optical excitation being
trapped at ionized donor (D+) and acceptor (A–) sites, producing D0 and A0 sites. When an
electron transitions from the neutral donor to the neutral acceptor, a photon is released; this
process can be written:
0 0 + − D + A −−→ }ω + D + A . (3.2)
The energy of }ω should clearly depend on the bandgap and the binding energies of the
carriers to the dopants, ED and EA. But more subtly, it is also dependent on the distance
between the donor and acceptor, because the Coulomb interaction between the ionized
dopants lowers the energy of the nal state of the system. Assuming a separation of R
2 between the donor and acceptor, the potential energy of the pair is −e /εr R, where e is the
charge of an electron and εr is the relative dielectric constant. The photon in equation (3.2)
Chapter3: PL 3.4InterpretationofResultsandRelevantEffects 30 has energy e2 }ω = Eg − ED − EA + . (3.3) εr R
What is not apparent from the above, is that R can only take on discrete values because the
donors and acceptors sit on particular lattice sites. At low enough temperatures (<2 K), the
DAP spectrum, in many semiconductors, can be resolved to lines corresponding to di erent
separations [2, 109].
Under low intensity excitation, there will be some average separation between donors
and acceptors participating in DAP luminescence. As the excitation intensity increases,
more donors and acceptors will participate, thus lowering the average separation between
participating pairs because the volume of the sample is unchanged; with the decreased
average separation, the DAP peak will increase in energy, until the intensity is high enough
that the sample reaches saturation [2, 110].
3.4.3 The Role of Hydrogen
We have been able to explain the decreased band edge energy in bare GaAs and core-shell
nanowires as resulting for carbon acting as a p-type dopant in the nanowires. But it isn’t
su cient to explain the di erences between the types of nanowire: the band edge of the
GaAs in the core-shell nanowires appears to be lower than the band edge of the bare GaAs
nanowires and the overall shapes of the spectra are very di erent. Both e ects can be
explained in relation to the behavior of hydrogen in these nanowires.
Hydrogen is the second of the two elemental impurities that must be contended with in
MOCVD growth of GaAs as a consequence of the precursor chemistry. Pyrolysis of the
precursors creates elemental hydrogen during the growth, which can then incorporate into the
Chapter3: PL 3.4InterpretationofResultsandRelevantEffects 31
GaAs, either on an interstitial site, or as a complex with an adsorbed carbon atom [111, 112].
In either case, in carbon doped GaAs, the hydrogen has the same net e ect of compensating
the p-doping, by either contributing an electron when it’s on an interstitial site or by forming
a neutral C−H complex that can be detected by infrared spectroscopy [113–116].
Heating GaAs above 530 ◦C quickly recovers much of the hole population compensated
by hydrogen [117, 118]. When annealed under an inert atmosphere at 600 ◦C, the hole
concentration can approach the carbon concentration within a few minutes in GaAs lms
over one micron thick [119, 120]. The high temperatures reactivate the carbon, by breaking
the C−H bonds and causing the hydrogen to di use out [117, 118]. But above 600 ◦C, carbon
related defects begin to form in GaAs, lowering the carrier mobility [117, 118, 121].
Our core-shell nanowires, were heated to 650 ◦C for the growth of the shells. The growth
of the shells also sees the formation of atomic hydrogen through the breakdown of precursors, which can potentially di use into the nanowires, but the rate of di usion into the material is
much smaller than the rate at which it di uses out [119, 120, 122].
3.5 Conclusions from PL
By comparing the peak positions in the bare GaAs wires to results from the literature, we can
tentatively attribute the strongest peak to carbon-bound exciton emission [79, 91, 123]. And
also just by comparison, the luminescence from the core-shell nanowires appears dominated
by donor-acceptor-pair (DAP) emission [2, 79]. The peak at 1.44 eV lines up with emission
from a heterojunction that forms at the interface between zinc blende and wurtzite GaAs [89].
As we will show below, these tentative assignments based strictly on comparison with
published results provide a good starting point for us to interpret our results.
Chapter3:PL 3.5ConclusionsfromPL 32
In order to explain our results, there are a number of factors we could focus on, most
related to defects. Control of defects in nanowires has been the topic of many recent papers
on nanowires, which have examined many factors in the growth of nanowires, including
growth temperature [124], precursor ow rate [79, 88, 125], seed particle [57, 126], and
substrates [127, 128]. In addition, we can look further, to the extensive literature on the
growth of GaAs lms for more insight on the formation of defects in GaAs. Point defects and
planar defects are common in III-V nanowires; in MOCVD grown nanowires, they can be
largely controlled via the growth parameters alone. Point defects are in the form of vacancies, which are never desirable, and atomic impurities, which can be a positive feature when the
goal is to dope the nanowires. Carbon and hydrogen are present during the nanowire growth:
the precursor chemistry has hydrogen and carbon in addition to the desired growth elements,
and H2 is used as a carrier gas during the growth. However, whether they are incorporated
into the nanowires depends on the growth conditions.
From the literature, we expect that wurtzite is most likely in nanowires grown at the
lowest V:III precursor ratios [56, 88, 89, 129]. Even though most of the literature discussing
MOCVD grown nanowires is based on experiments using AsH3 as a precursor instead of TBA
and ideal conditions depend on the growth system making comparisons between systems
inexact, we can use the estimate that TBA is ve times more e cient in delivering arsenic to
the reaction to have a rough comparison of the growth parameters with what has been
published [25, 88]. Based on the vefold estimate, the V:III precursor ratio of 5:1 with TBA would be approximately equivalent to a 25:1 ratio with AsH3, which is still much lower than
the ratios used by others to achieve defect free GaAs nanowires; for example, Joyce et al. use
ratios of 46:1 to 93:1 to produce nanowires free of planar defects [78].
Chapter3:PL 3.5ConclusionsfromPL 33
Other than precursor ratio, two parameters that a ect the quality of the nanowires are
temperature and growth rate. The temperature of the core growth was 400 ◦C, which is
higher than the temperature found by others to minimize planar defects in zinc blende
nanowires, 375 ◦C [124]. Our core-shell nanowires are approximately 8 µm long: the cores were grown for 60 minutes, therefore, we estimate the growth rate as ≈ 130 nm/min.A
comparison of our spectra to those for GaAs nanowires grown at similar growth rates reveals
a great deal of similarity [79].
Based on the above, the story seems to be that the bare-GaAs nanowires have a signicant
amount of carbon in them, but are compensated by hydrogen. The core-shell nanowires
have much less hydrogen as a result of the high temperatures used for shell growth.
So, we interpret the spectra from the bare GaAs nanowires as being dominated by the
free-electron—neutral-acceptor peak (e, A0)[130]; and the spectra from the core-shell
nanowires as being dominated by donor-acceptor-pair (DAP) luminescence.
Chapter3:PL 3.5ConclusionsfromPL 34
Chapter 4: Resonance Raman of GaAs/AlGaAs Nanowires
4.1 Raman and Resonance Raman Spectroscopy
Figure 4.1: Feynman diagram for the Raman process. Based on Fig. 7.28 in Yu and Cardona [2].
The Raman e ect is named after C. V. Raman, who won the Nobel Prize in Physics in 1930
for the discovery in 1928. Raman described the e ect as an optical analog for Compton
scattering. In the rst order Raman process, three events occur: a photon is absorbed creating
an excited state in the material, the excited state interacts with an elementary excitation, and
a photon is emitted as the excited state relaxes. Though it is not a very strong e ect, the
Raman e ect is an extremely powerful analytical tool, providing a way to measure many
types of non-optical excitations in a material [131, 132].
The power of Raman spectroscopy is that it is a means to measure the energies of
elementary excitations in a material, which do not themselves participate directly in radiative
transitions. Most commonly, Raman spectroscopy is used to measure the energy of phonons
(quantized vibrations) in a material. Not all phonons will Raman scatter and which do scatter
depends on the experimental geometry. The dependence on experimental geometry is a result
of the symmetry of the process that leads to selection rules, however these rules are often
relaxed under resonant conditions. 35
Figure 4.1 shows a Feynman diagram for the rst order Raman e ect. A Feynman diagram
is a graph, the edges of which are called propagators and represent (quasi–)particles that
interact with each other at the vertices, with each vertex contributing a Hamiltonian to a
product of perturbed Hamiltonians [2, 133, 134]. Figure 4.1 shows a photon (dashed line on
the left), being absorbed to form an electron-hole pair (double line), which emits a phonon
(wavy line), and nally emits a photon (dashed line on the right) [2]. This corresponds to the
equation:
2 X 0 0 hi | HeR | n ihn | He-ion | nihn | HeR | ii P ≈ × δ [}ωi − }ω0 − }ωs] , (4.1) [ ω − (E − E )][ ω − ω − (E 0 − E )] n,n0 } i n i } i } 0 n i
0 where n and n are intermediate states with energies En and En0 respectively, HeR and He-ion
are the Hamiltonians for the interaction of an electron with electromagnetic radiation and
of an electron with a phonon respectively, }ωi and }ωs correspond to the energy of the
incoming and scattered photons respectively, }ω0 is the energy of the elementary excitation
(e.g. phonon), and the delta function ensures that the sum is over combinations of states that
conserve energy [2].
Resonance Raman spectroscopy (RRS) is an experimental technique that utilizes Raman
spectroscopy by modifying the Raman cross-section by tuning the excitation energy to
resonance with energy transitions in the material. Resonance Raman spectroscopy can be
used to measure the Raman spectrum of a sample as a function of the excitation energy; or
RRS can be used to enhance the cross-section so that weak Raman peaks can be observed
experimentally, such as electronic transitions between states in a quantum well or plasmon
excitations [135–137]. Raman scattering is an inherently low e ciency process compared
Chapter4: ResonanceRaman 4.1RamanSpectroscopy 36 with luminescence, which is something that Raman himself pointed out as evidence that it was a scattering process, stating “That the e ect is a true scattering and not a uorescence is
indicated in the rst place by its feebleness in comparison with the ordinary scattering, and
secondly by its polarisation, which is in many cases quite strong and comparable with the
polarisation of the ordinary scattering” [138]. The expression for the Raman process involves
the product of three Hamiltonians, each of which are small; but it is possible to minimize the
denominator in equation (4.1) by tuning the excitation wavelength (}ωi) to be close to
a transition in the material, that is, exciting the sample resonantly. This is the basis of
resonance Raman spectroscopy (RRS).
Near a discrete energy level, Ea, the Raman scattering probability is approximately
2 h0 | HeR(ωs) |aiha | He-ion |aiha | HeR(ωs) | 0i P ≈ + C , (4.2) (Ea − }ωi − iΓa)(Ea − }ωs − iΓa)
where the term iΓa is a damping constant included to account for the nite lifetime of the
intermediate state. The lifetime (τ ) is related to Γa by Γa = }/τ . The non-resonant contribution
to the scattering is accounted for in the constant (C), and the summation and delta functions
have been removed by summing over the intermediate state [2].
In the denominator of equation (4.2), there are two terms in the denominator, leading to
two resonant conditions. When the incoming light is in resonance with Ea it is an incoming
resonance; when the scattered light is in resonance with Ea, it is an outgoing resonance.
These two conditions are illustrated in gure 4.2. The equation for the cross-section suggests
that the incoming and outgoing resonances should be of similar magnitude, as is the case in
some high quality samples [139–142]. Deviations from symmetric resonances are the result of
Chapter4: ResonanceRaman 4.1RamanSpectroscopy 37 a variety of factors, mostly related to material defects and Raman processes mediated by exciton states [2, 143]. For example, Kusch et al. observed a very symmetric resonance in
GaAs nanowires grown using MBE [142].
En }ω0 Ea Ea }ω0 En
}ωi }ωs }ωi }ωs
Incoming Outgoing resonance resonance
Figure 4.2: A schematic of the transitions involved in incoming and outgoing resonances for a Stokes process.
E CB
Eg
0 HH ∆SO LH
SO k0
Figure 4.3: A schematic of the band structure of GaAs, showing the direct band gap between the conduction band and the light and heavy hole bands (Eg) and the split-o band gap (∆SO).
Our motivation for using resonance Raman spectroscopy was based on our hypothesis that growth conditions a ected the bandstructure of the nanowires. Based on the assumption that
Chapter4: ResonanceRaman 4.1RamanSpectroscopy 38 we were looking for changes in the band structure, this was an appropriate choice of method,
particularly there was a hope that we were working with a quantum well structure [137].
The band structure of GaAs has two direct transitions from the lowest point in the
conduction band, which is at Γ = 0. One is to the valence band and the other is to the split-o
band; the split-o band is the result of the coupling between electron spin and orbital angular
momentum via the spin-orbit interaction [2]. At 4 K the direct bandgap of GaAs has energy,
Eg = 1.517 eV; while the split-o band is of energy, Eg + ∆SO = 1.851 eV [94].
One of the strengths of RRS is that it can be applied to individual nanostructures, or even
used to map structure within a single nanowire [86]. There are some recent examples of RRS
being used to characterize GaAs nanowires published by Ketterer et al., where they used
RRS to measure the bandgap and split-o band energies for zinc-blend and wurtzite GaAs
nanowires [144, 145]. Our experimental conditions made it di cult to estimate the number of
nanowires in the laser spot with any accuracy, because we were most successful measuring
RRS from mats of nanowires that placed a large number of randomly oriented nanowires in
the laser spot. The optics were also non-ideal – because the microscope objective we used is a
plan view objective, the cryostat window cause a signicant amount of spherical aberration –
making accurate calculation of the spot size di cult. But based on our experience with the
system, the spot size of the laser was approximately 5 µm, so our lowest estimates are that
hundreds of nanowires were in the laser spot.
Generally Eg +∆SO is the preferred transition to use for RRS, though exciting at Eg
directly is a viable technique [137, 146]. The primary disadvantage of exciting near the
bandgap is that the luminescence from the direct bandgap will then overlap with the Raman
spectrum. This makes the detection of the Raman spectrum more di cult because of how
Chapter4: ResonanceRaman 4.1RamanSpectroscopy 39 weak a process Raman scattering is, particularly when it is non-resonant. The background
luminescence, imparts the requirements that the detector used have a large dynamic range
and that subsequent data analysis include the removal of the background luminescence.
4.2 Experimental Procedures
Sample preparation was identical to the preparation described in section 3.2.1, with the
nanowires dispersed on SiOx on Si substrates which were then mounted on the cold nger
of the cryostat. For each Raman spectrum making up the resonance Raman spectra, the
following procedure was used:
1. The CCD was placed in optical train, blocking the monochromator input.
2. Using the grating mounted to the rotation stage, the laser was realigned to the sample
by observing the laser with the CCD.
3. The laser’s power was measured using the Newport 883-SL sensor and recorded in
LabSpec.
4. The laser wavelength was recorded in LabSpec.
5. The CCD was removed from the optical train and then the measurement was started.
Prior to acquiring any spectra, there were several hours of warm-up and stabilization time
for the instrumentation, allowing the lasers time to warm-up, the cryostat time to reach a
stable temperature, and the mechanical parts of the system to settle.
The analysis procedure began with each individual Raman spectrum t using a Lorentzian with a linear baseline correction (f (x) = fLOR(x) + m · x); the linear baseline was added to
Chapter4: ResonanceRaman 4.2ExperimentalProcedures 40 account for the background uorescence that overlapped the Raman spectrum as a result of our choice to excite the samples at Eg rather than the split-o resonance (Eg +∆SO). The
Lorentzian was chose as the tting function because it is the solution to a damped oscillator equation. Fits were calculated initially in IgorPro, but then recalculated in Origin.
The form of the Lorentzian t was:
2A w fLOR(x) = y0 + 2 2 , (4.3) π 4(x − x0) + w
from which the parameters A, w, and x0 were taken as the peak area, line width, and peak position respectively. These were then plotted as a function of the excitation energy, with the error bars based on the standard error from the t parameters.
Figure 4.6 shows the output of the analysis procedure applied to the data taken using the
SAGA06 nanowires. The set of three plots shows the magnitude, width, and position of the
LO Raman peak plotted as a function of the excitation energy.
Chapter4: ResonanceRaman 4.2ExperimentalProcedures 41
Excitation Energy (eV) 1.625 1.6165 1.6081 1.5998 1.5916 1.5835 1.5754 1.5635 1.5556 1.5498 1.5479 1.545 1.5421 1.5402 1.5383 1.5345 1.5326 1.5307 1.5269 1.525 1.5231 1.5194 1.5176 1.5157 1.512 1.5083 1.5065 1.5047 1.501 1.4992 1.4974 1.4938 1.492 1.4902 1.4866 Intensity (Arbitrary Units)
1.46 1.48 1.50 1.52 1.54 1.56 1.58 Energy (eV)
Figure 4.4: Initial data replotted by transforming wavenumbers to absolute energy; wavenumber w measured using excitation wavelength λ, E = E(λ) − E(w).
Chapter4: ResonanceRaman 4.2ExperimentalProcedures 42 ) s t i n U
y r a r t i b r A (
y t i s n e t n I
2 8 0 2 8 5 2 9 0 2 9 5 3 0 0 3 0 5 3 1 0 R a m a n S h i f t ( c m - 1 )
Figure 4.5: An example of the RRS data being t in OriginPro.
Chapter4: ResonanceRaman 4.2ExperimentalProcedures 43
Laser Excitation Wavelength (nm) 820 800 780 760
1000 800 600 400 200
LO peak mag. (Arb. Units) 0 )
-1 2.0
1.5
1.0
0.5 LO peak width (cm 0.0 293.6 ) -1 293.4 293.2 293.0 292.8 292.6 292.4 LO peak position (cm
1.48 1.52 1.56 1.60 1.64 Laser Excitation Energy (eV)
Figure 4.6: RRS data from sample SAGA06, measured at 78 K.
Chapter4: ResonanceRaman 4.2ExperimentalProcedures 44
4.3 Results and Interpretation
4.3.1 Summary of Results
Following the previously described analysis, results in gures 4.6 to 4.9, showing the output
of the RRS for SAGA06, SAGA11, NW40, and the GaAs wafer.
3 14x10 12 10 8 6 4 2
LO Peak Mag. (Arb. Units) 0
4 ) -1 3
2
1 LO Peak Width (cm 0
296.0 ) -1 295.8 295.6 295.4 295.2 295.0 294.8 LO Peak Position (cm 294.6
1.48 1.50 1.52 1.54 1.56 Excitation Energy (eV)
Figure 4.7: SAGA11 RRS data
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 45
300 200 100 0 (Arb. Units) LO Peak Mag. -100
3.0 )
-1 2.0
(cm 1.0
LO Peak Width 0.0 293.4
) 293.2 -1 293.0 (cm 292.8 LO Peak Pos.
120 80 40
(Arb. Units) 0 TO Peak Mag.
0.6
) 0.4 -1 0.2 (cm 0.0 TO Peak Width
270.2 ) 270.1
-1 270.0 269.9 (cm 269.8
TO Peak Pos. 269.7
1.48 1.50 1.52 1.54 1.56 Excitation Energy (eV)
Figure 4.8: NW40 RRS data
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 46
120
80
40 (Arb. Units) LO Peak Mag.
0 293.7 293.6 293.5 ) -1 293.4 (cm 293.3 LO Peak Pos. 293.2
160
120
80 (Arb. Units) TO Peak Mag. 40
270.5 270.4 )
-1 270.3
(cm 270.2 TO Peak Pos. 270.1
1.48 1.50 1.52 1.54 1.56 Excitation Energy (eV)
Figure 4.9: GaAs Wafer RRS
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 47
4.3.2 Incoming vs. Outgoing Resonance ) s t i n U
. b r ) s A t ( i
y n t i U s
n y e r t a n I r t i b r 0 0 2 5 5 0 7 5 0 0 2 5 A . 5 . 5 . 5 . 5 . 6 . 6 (
1 1 1 1 1 1 y t
i E x c i t a t i o n E n e r g y ( e V ) s n e t n I
0 0 0 0 0 4 6 4 8 5 0 5 2 5 4 1 . 1 . 1 . 1 . 1 . O u t g o i n g E n e r g y ( e V )
Figure 4.10: The squares show the amplitude of the RRS signal from SAGA06 measured at 78 K, plotted as a function of outgoing energy, i.e. Eex − ELO. The solid line shows the PL signal measured under the same conditions.
The RRS spectra from the core-shell nanowires show a peak from the outgoing resonance, with little if any contribution from the incoming resonance. The dominance of the outgoing
resonance is notable, but not altogether surprising. There are a number of published resonance
Raman studies of GaAs – including a study of GaAs nanowires – that observe both incoming
and outgoing resonances of the same order of magnitude. There has been debate in the
literature centered on the asymmetry between the two resonances; however, we conclude
that the purely outgoing resonance that we observe is consistent with the conclusion that the
nanowires contain a large number of point defects and strongly supports the conclusion that
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 48 the resonance is with an excitonic state [139–142, 147, 148].
An e ect closely related to the coupling of an outgoing resonance to an exciton state, is
the cascade e ect, which manifests as the appearance of multiple phonon peaks that can be
of comparable intensity to the luminescent background, when the excitation source is
tuned a multiple of ELO above certain transitions. The cascade e ect was rst observed
in CdS from which large numbers (n ≈ 10) of phonon peaks can be observed at room
temperature [149, 150]. This e ect also has been observed in GaAs nanowires; in both cases it
is due to the strong coupling between the bound exciton state and the LO phonon [2, 151].
In the cascade model, carriers are excited to a virtual state and then relax through a series
of allowed states, rather than through virtual states, making it competitive with luminescence,
because it avoids intermediary virtual states [2, 152, 153]. The cascade model has been used
to explain a number of exciton related spectral phenomena [143, 154]. It has been invoked in
arguing that at an outgoing resonance with an excitonic state, resonance Raman is equivalent
to hot-luminescence where photons are absorbed to a resonant state and then re-radiated;
though this stance is somewhat controversial, at outgoing resonances, resonant Raman
scattering is very similar to a luminescent process [155, 156]. The cascade model can also be
used, substituting elastic scattering by impurities rather than an LO phonon, to help explain
the strength of outgoing over incoming resonance in doped materials [2, 157].
This correlates with our PL results (gure 3.3), where we observed a phonon replica peak
resulting from coupling between the bound exciton state that dominated the spectrum and
LO phonons.
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 49
GaAs Wafer
Bare GaAs
Intensity (Arbitrary Units) Nanowires
Core-Shell Nanowires 310300290280270260250 Raman Shift (cm−1)
Figure 4.11: Selected spectra showing the lack of a TO peak in the core-shell nanowire data. This e ect was independent of the excitation power used, the spectra shown were selected only because they include the full region from 250 cm−1 to 310 cm−1 in a single contiguous scan, rather than being broken up into two separate scans as was often the case.
4.3.3 The Missing TO Mode
None of the core-shell nanowire resonance Raman data has a detectable TO phonon peak.
This is a somewhat surprising result; in non-resonant Raman of GaAs, the TO phonon is the
stronger mode. It does appear in the RRS spectra from the GaAs wafer and bare GaAs
nanowire samples, showing that it was not necessarily an instrumental artifact. And in
non-resonant Raman spectra (gure 5.9), only the TO mode is observed in the core-shell
nanowires.
The lack of a TO peak in the resonant spectra seems to be an extreme example of
the phenomena of the LO peak being enhanced in carbon doped GaAs. The LO mode is
preferentially enhanced over the TO mode because of the strong coupling between carbon
acceptors and excitons, through the Fröhlich mechanism [97, 99, 158].
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 50
(a)
(b)
Figure 4.12: LO and TO phonons
In polar materials, such as GaAs, longitudinal phonons couple with electric elds
more strongly than transverse phonons. This is because a longitudinal phonon involves
planes of atoms changing distance from each other (gure 4.12a), which induces a charge
transfer between the atoms giving rise to a macroscopic electric elds, while transverse
phonons involve planes of atoms moving within their planes, but because their distance
does not substantially change relative to each other (gure 4.12b), no net polarization is
induced [2, 158, 159].
More formally, the electric eld resulting from an LO phonon gives rise to an electric eld,
ELO = −FuLO, where: q − 2 −1 − −1 F = 4πN µωLO ε∞ ε0 . (4.4)
In equation (4.4), uLO is the atomic displacement due to the LO phonon, ε∞ and ε0 are the
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 51
high and low frequency limits for the dielectric constant, N is the number of atoms per unit volume, and µ is the reduced mass of the ions [2, 158]. The Fröhlich interaction is responsible
for a number of e ects near resonance that lead to otherwise forbidden scattering [153, 160].
4.3.4 Variation of the LO Peak Position
Another e ect we saw, but could not satisfactorily explain, was an apparent change in the
peak position of the LO phonon in the core-shell nanowires, but not the bare GaAs nanowires.
A possible explanation is that there is wurtzite present in the nanowires because wurtzite has
a slightly di erent resonant energy and due to strain may have a slightly di erent peak
position [144]. However, this would not explain why it was observed only in the core-shell
nanowires. Another possibility, is that it originates with the emission of acoustic phonons by
excitons near the outgoing resonance energy, which has been shown to give rise to a peak
splitting at a di erent resonance [99].
Because the resonance peak for the core-shell nanowires is at at a di erent energy than
anything else we measured, it is tempting to explain away the change in the LO peak position
as stemming from an experimental artifact. In order to check this possibility, the laser was
measured at a number of di erent energies, then the o set for each energy was calculated as P P a center of mass (i.e. ∆ = (y · x)/ y), with the results shown in gure 4.13. Thus we have
some certainty that it is a real e ect – although it is somewhat disconcerting that the e ect
seems to be independent of temperature, but it may also be that we are not sampling enough
energies to identify what is changing.
There are some weaknesses with the hypothesis that the change in LO peak position is a
result of wurtzite mixed in the nanowires. The LO phonon energies are not very di erent
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 52
Excitation Energy (eV) 1.5655 1.5615 1.5556 1.544 1.5402 1.5275 1.5269 1.525 0.25 1.5192 1.5157 1.5138 1.5078 1.5019 0.20 ) -1
0.15 Offset (cm 0.10 Intensity (Arbitrary Units) 0.05
0.00 -10 -5 0 5 10 1.50 1.52 1.54 1.56 -1 Raman Shift (cm ) Excitation Energy (eV) (a) (b)
Figure 4.13: (a) The laser line measured at a number of di erent excitation energies, measured through closed slits so as to avoid damaging the PMT. (b) The calculated o set for the laser at the di erent wavelengths.
between wurtzite GaAs and zinc-blende GaAs. However, there is some uncertainty as to what
ensemble e ects come into play because these measurements sampled a large number of
nanowires. The di erence in bandgap between the phases is less than 0.5 meV [145]. If there were wurtzite, there would be interface strain, which could in part account for the shift in
energy. Also, this e ect does not appear in the bare GaAs nanowires, which should contain at
least as much wurtzite as the core-shell nanowires. This e ect appears in all the core-shell
nanowires, independent of growth conditions. Therefore, this suggests that the cause may be
connected to the way that the core-shell nanowires di er from the bare nanowires. As was
discussed in the previous chapter, the core-shell nanowires contain approximately the same
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 53 amount of carbon, but because of the elevated temperatures used for the shell growth, they contain more active carbon. So, it makes sense to look at e ects associated with carbon doping in GaAs to identify whether any may account for the e ect we observe. However, the only similar e ect that we could nd, was scattering by longitudinal acoustic (LA) phonons enhanced by carbon doping documented by Huang and Ulbrich. This is an attractive explanation at rst sight, but it predicts a much larger shift than we observed: following their calculations predicts a 15 cm−1 shift [99].
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 54 Head Power Meter Mirrors CCD Camera Sample Coldfinger Objective Lens Cryostat Diagram of instrument. Lens Focusing Ti:SaLaser Grating on Figure 4.14: Rotation Stage Monochromator Laser + Has Been PMT Simplified Ar Optical Path
Chapter4: ResonanceRaman 4.3ResultsandInterpretation 55
Chapter 5: Single Nanowire Raman Spectroscopy
In order to better understand the resonance Raman spectra, we took additional Raman
measurements on a single nanowire, using a commercial Raman system – a Renishaw inVia
spectrometer, which we were kindly granted access to by Volker Presser and the W. M. Keck
Institute for Atto uidic Nanotube Based Probes. This provided us a way to better understand
the missing TO peak in the resonance Raman spectra and look for evidence of wurtzite
in the nanowires. The Renishaw inVia system we used is integrated with a microscope
making it easy see the sample being measured and is stable enough to enable single nanowire
measurements that take several several hours.
5.1 Experimental Rationale
Because wurtzite and zinc blende structures have di erent crystal symmetries, their Raman
tensors di er from each other. In bulk, GaAs only forms the zinc blende structure, but in
nanowires it can take on the wurtzite structure, which is the structure of a number of III-V
materials including GaN. Wurtzite GaAs (w-GaAs) consists of two types of bilayers stacked
(ABABAB...), while in the zinc blende phase it consists of three bilayers (ABCABC...) as is
illustrated in gure 5.1.
Because the wurtzite unit cell length is the [0001] direction is twice that of the zinc
blende unit cell in the [111] direction, the Brillouin zone has half the length in k-space, so the
phonon dispersion curves are in e ect “folded,” as is seen with the dispersion curves of 56
Figure 5.1: The di erence in stacking orders for (a) zinc-blend GaAs and (b) wurtzite GaAs leads to additional peaks in the Raman spectrum of wurtzite GaAs due to (c) the folding of the Brillouin zone. (Reprinted with permission from Zardo et al., Phys. Rev. B 80, 245324 (2009) Copyright 2009 American Physical Society)[129]. superlattice structures. This gives rise to new Raman peaks corresponding to the phonon modes at zone center, illustrated in gure 5.1c [129].
Chapter5: SingleNanowire... 5.1ExperimentalRationale 57
5.2 Procedure
Sample
Objective
λ/2 waveplate Analyzer
Dispersion, detection, etc Microscope
Figure 5.2: Diagram of experimental setup, the line with the arrows represents the path of the laser light, which includes segments in which incoming and scattered light overlap.
Nanowires were dispersed in isopropyl alcohol, drops of which were then placed on a
pyrex slide that was heated to evaporate o the solvent. The nanowires were then located
optically using the microscope integrated into the spectrometer; an example image is shown
in gure 5.9b.
Polarization was controlled using a λ/2-waveplate in the optical train positioned so that
both the light going to the microscope and the scattered light would pass through it, so it would return to the spectrometer in the same polarization regardless of the λ/2-waveplate
position to ensure that the experiment was not a ected by detector polarization sensitivity.
Chapter5:SingleNanowire... 5.2Procedure 58 ) ) s s t t
i 9 0 i n n U U
. . b b r 6 0 r A A ( (
y y t t i i
s 3 0 s n n e e t t n n I I
0
2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 R a m a n S h i f t ( c m - 1 ) R a m a n S h i f t ( c m - 1 )
Figure 5.3: Polarized Raman spectra from a single nanowire, grouped by the position of the polarization analyzer, with the angle of the λ/2-waveplate labeled, less a constant o set of 50°.
Scattered light passed through an analyzer so that either parallel or perpendicularly polarized scattered light was selectively collected.
The λ/2-waveplate was previously aligned to the mount so that the angle of the waveplate’s axis was known so that by rotating it θ/2, the polarization of the light rotated by θ. The scattered light was passed through a linear polarizer, which served as an analyzer by ltering one polarization at a time.
Chapter5:SingleNanowire... 5.2Procedure 59
5.3 Theoretical Considerations
The expected polarization dependence of the Raman scattering can be calculated from the
Raman tensor, R, according to the relation
2 Is ∝ eˆi · Re · eˆs , (5.1)
where Is is the intensity of the Raman scattered radiation and eˆi and eˆs are unit vectors in the
direction of the incident and scattered radiation, respectively – in the notation of Wu et al.
[161]. For the zinc-blende crystal structure, we can write Re for optical phonons with atomic
displacements in the h100i, h010i, and h001i crystallographic directions, corresponding to the vectors eˆ1, eˆ2, and eˆ3, as [2, 132, 161]:
0 0 0 0 0 d 0 d 0 Re(eˆ1) = 0 0 d , Re(eˆ2) = 0 0 0 , Re(eˆ3) = d 0 0 . (5.2) 0 d 0 d 0 0 0 0 0
In the backscattering conguration, conservation of momentum requires that the wavevector of the light and the scattering phonon be parallel. Assuming that the direction of
the scattering is in the eˆ1 direction, we require LO phonons to have q in the eˆ1 direction,
necessitating atomic displacements parallel to q, so the intensity of the Raman scattering
follows
2 LO Is ∝ eˆs · Re(eˆ1) · eˆi . (5.3)
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 60
xˆ1
0 φ xˆ1 211¯
[111] xˆ3
¯ 011 laser xˆ2 0 θ xˆ2
Figure 5.4: Schematic showing the scattering conguration and illustrating the vectors used in the calculation of the expected Raman scattering intensity.
While the atomic displacements for a TO phonon are orthogonal to q, so we have:
2 2 TO Re(eˆ2) Re(eˆ3) Is ∝ eˆs · √ · eˆi + eˆs · √ · eˆi . (5.4) 2 2
In our experimental setup, the nanowire was selected because its orientation was closely
aligned to the polarization of the laser without any rotation from the waveplate. In the
laboratory frame of reference, we consider the scattering to be along the xˆ1 direction. For
convenience, we can pick xˆ3 to be the direction corresponding to the polarization of the
unrotated laser light. We then choose xˆ2 so that it is orthogonal to both xˆ1 and xˆ3. The
scattering conguration is illustrated in gure 5.4.
To translate between the laboratory coordinates (xˆm) and the crystal coordinates (eˆm), we
must make some assumptions about the crystallographic orientation of our nanowire, because we do not have TEM data from the same nanowire, which would allow us to unambiguously
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 61
determine its orientation. However, based on previous work by our collaborators, as well as
more general aspects of GaAs nanowire growth, we expect that the nanowire’s growth
direction is h111i and that the facets are of the 211¯ family [22, 23]. Thus, we will begin by calculating the Raman tensor for scattering from a 211¯ surface, using the orientation xˆ1 = 211¯ , xˆ2 = 011¯ , and xˆ3 = [111]. Later, we will account for the possibility that the
nanowire is not sitting ush on a face, so that it is rotated about the growth axis. From xˆm we can build the matrices
−2 1 −2 1 1 √ 0 √ √ √ √ 6 3 6 6 6 1 −1 1 T −1 1 Be = √ √ √ and Be = 0 √ √ . (5.5) 6 2 3 2 2 1 1 1 1 1 1 √ √ √ √ √ √ 6 2 3 3 3 3
Which allow us to calculate the Raman tensor in the xˆm basis by:
0 T 1 Re (xˆ1) = Be · √ −2Re(eˆ1) + Re(eˆ2) + Re(eˆ3) · Be (5.6a) 6 0 T 1 Re (xˆ2) = Be · √ − Re(eˆ2) + Re(eˆ3) · Be (5.6b) 2 0 T 1 Re (xˆ3) = Be · √ Re(eˆ1) + Re(eˆ2) + Re(eˆ3) · Be. (5.6c) 3
We describe the incident polarization by its angle θ with respect to xˆ1, thus:
0 eˆi = θ . (5.7) sin cosθ
The experimental design was intended to produce the same polarization for the incident
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 62 and scattered light, by having the light pass through the waveplate twice – once en route to the sample to rotate the polarization and then again as it was directed back to the spectrometer to counter-rotate the polarization, as depicted in gure 5.2 – so in the parallel conguration the scattered polarization is aligned with the incident polarization, i.e. eˆs = eˆi.
In the perpendicular conguration, the collected light is polarized perpendicularly to the incident polarization, thus:
0 0 k ⊥ eˆ = eˆi = θ and eˆ = θ . (5.8) s sin s cos cosθ − sinθ
0 Substituting Re (xˆm) for Re(eˆm) in equations (5.3) and (5.4), will enable us to calculate the expected scattering as a function of angle. We can calculate these by substituting equations (5.2) and (5.5) into equation (5.6):
√ √ √ − 6 0 − 3 0 6 0 0 1 √ 0 1 √ √ Re (xˆ1) = · 0 6 0 , Re (xˆ2) = · 6 0 − 3 , 3 3 √ √ − 3 0 0 0 − 3 0 √ (5.9) − 3 0 0 0 1 √ Re (xˆ3) = · 0 − 3 0 . 3 √ 0 0 2 3
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 63
Using equations (5.7) to (5.9) we nd for the parallel conguration:
√ k 6 2 eˆs · Re(xˆ1) · eˆi = sin θ , (5.10a) 3 √ k −2 3 eˆs · Re(xˆ2) · eˆi = √ cosθ sinθ , (5.10b) 3 √ √ − 3 2 3 eˆk · Re(xˆ ) · eˆ = sin2 θ + cos2 θ. (5.10c) s 3 i 3 3
And for the perpendicular conguration:
√ ⊥ 6 eˆs · Re(xˆ1) · eˆi = sinθ cosθ , (5.11a) 3√ ⊥ − 3 eˆs · Re(xˆ2) · eˆi = , (5.11b) √3 3 eˆ⊥ · Re(xˆ ) · eˆ = cosθ sinθ. (5.11c) s 3 i 3
If the scattering is not in fact from a 211¯ face, because the nanowire is rotated about the growth axis, we can account for that by rotating our basis appropriately to account for the
misalignment between the laboratory and crystallographic coordinate systems. First, it is
useful to generalize our notation a bit, so continuing in the notation used by Wu et al. [161], we describe the general transformation between the lab coordinate system xˆ1, xˆ2, xˆ3 and
0 0 0 the crystallographic coordinate system xˆ1, xˆ2, xˆ3 .
0 X X 0 xˆk = αkmeˆm, xˆk = βkmxˆm, (5.12) m m
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 64 where k,m = 1, 2, 3. From this we can dene matrices:
α α α 11 12 13 Be = α21 α22 α23 (5.13a) α31 α32 α33
β β β cos φ − sin φ 0 11 12 13 Te = β21 β22 β23 = sin φ cos φ 0 . (5.13b) β31 β32 β33 0 0 1
The matrix Te represents a rotation about the xˆ3 axis by an angle φ, which we take to be the angle between xˆ1 and 211¯ .
0 We can calculate the Raman tensor in an arbitrary direction xˆk by:
0 X Re(xˆk ) = αkmRe(eˆm). (5.14) m
0 And if we transform into the coordinate system xˆk , we have: n o
0 0 X −1 Re (xˆk ) = αkmBe · Re(eˆm) · Be . (5.15) m
Using this we can generate a set of plots of the intensity of the Raman peak given di erent values of φ. Due to symmetry, we need only examine the range 0◦ ≤ φ ≤ 30◦ for rotations
about the xˆ3 axis.
However, for reasons that are not clear, the instrument instead behaved as if the light only
passed through the waveplate once – as determined by measuring the response of a Si wafer with a known orientation [Livneh, private communication]. Thus, as we analyze the data,
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 65
TO:
LO:
φ = 0◦ φ = 10◦ φ = 20◦ φ = 30◦
Figure 5.5: Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = eˆi, where φ is the angle between the [211¯ ] and xˆ1.
k rather than assume that eˆs = eˆi for the parallel conguration, we will instead assume that the polarization of the scattered light is una ected by the rotation of the waveplate, i.e.
0 0 k ⊥ eˆ = xˆ3 = 0 and eˆ = xˆ2 = 1 . (5.16) s s 1 0
Repeating the calculations as before, we nd for the parallel conguration:
xˆ3 · Re(xˆ1) · eˆi = 0, (5.17a) √ 2 3 xˆ3 · Re(xˆ2) · eˆi = cosθ , (5.17b) 3√ − 3 xˆ · Re(xˆ ) · eˆ = sinθ. (5.17c) 3 3 i 3
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 66
TO:
LO:
φ = 0◦ φ = 10◦ φ = 20◦ φ = 30◦
Figure 5.6: Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration where eˆs is set orthogonal to eˆi, where φ is the angle between the [211¯ ] and xˆ1.
And for the perpendicular conguration:
√ 6 xˆ2 · Re(xˆ1) · eˆi = sinθ , (5.18a) 3√ − 3 xˆ2 · Re(xˆ2) · eˆi = cosθ , (5.18b) √3 − 3 xˆ · Re(xˆ ) · eˆ = sinθ. (5.18c) 2 3 i 3
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 67
TO:
LO:
φ = 0◦ φ = 10◦ φ = 20◦ φ = 30◦
Figure 5.7: Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = xˆ3, where φ is the angle between the [211¯ ] and xˆ1.
TO:
LO:
φ = 0◦ φ = 10◦ φ = 20◦ φ = 30◦
Figure 5.8: Plots of the predicted dependence of the Raman signal on the polarization angle of the incoming light for the conguration eˆs = xˆ2, where φ is the angle between the [211¯ ] and xˆ1.
Chapter5: SingleNanowire... 5.3TheoreticalConsiderations 68
5.4 Results and Discussion ) s t i n U
. b r A (
y t i s n e t n I
1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 R a m a n S h i f t ( c m - 1 )
(a) (b)
Figure 5.9: (a) Raman from a single SAGA06 nanowire. (b) Image of the nanowire from the microscope’s CCD.
Figure 5.9a shows a typical Raman spectrum of a single SAGA06 nanowire (shown in
gure 5.9b) measured using a 633 nm laser as the excitation source. The features at low wavenumber end of the spectrum (< 150 cm−1) are artifacts from the lter used to block the
back-re ected (i.e. elastically scattered) laser light from reaching the CCD. The feature from
≈ 190 cm−1 to ≈ 290 cm−1 (1.935 eV to 1.923 eV) appears to be a luminescent band. This
feature has nearly the same energy as the X -valley of the bandstructure of GaAs; though this
may be coincidental, it leads us to speculate that this luminescence is from the X-valley
because the excitation energy is nearly resonant with it (Eex = 1.959 eV and EX = 1.90 eV).
Additional experiments would be necessary to clarify the origin of this feature, such as
observing the e ect of temperature on the luminescent band or a PLE experiment using a
laser that could be tuned in the 1.9 eV range.
A point of sharp contrast between the Raman taken out of resonance and the resonance
Chapter5: SingleNanowire... 5.4ResultsandDiscussion 69
2 6 8 c m - 1 ) s t i n U
y r a r t i b r
A (
y t i s n e t n I
1 5 0 2 0 0 2 5 0 3 0 0 R a m a n S h i f t ( c m - 1 )
Figure 5.10: Zoomed in plot of the single SAGA06 Raman data, showing an apparent luminescent background, and a clearly resolved TO phonon peak, but no sign of the LO phonon peak.
Raman spectra is the presence of a TO phonon peak and the absence of an LO phonon peak in the non-resonance data. Figure 5.10 shows the region between 150 cm−1 and 300 cm−1 of the data shown in gure 5.9a, which more clearly shows the position of the one Raman peak seen.
H Because we did not observe the LO mode or the E2 mode observed by Zardo et al. at approximately 256 cm−1 in nanowires with 30% wurtzite content, it seems unlikely that there is much, if any, wurtzite in the nanowires we measured [129].
The polarization dependence of the Raman intensity plotted in gure 5.11 appears to depend on the alignment of the polarization with the nanowire, because it clearly does not correspond to any of the patterns predicted in gures 5.5 to 5.8. This type of polarization sensitivity was rst observed in carbon nanotubes [162]. It is known that the response of nanowires to light is very dependent on polarization and their emission of light is strongly
Chapter5: SingleNanowire... 5.4ResultsandDiscussion 70
(a) (b)
Figure 5.11: Solid lines are cos4(θ ) ts to the data measured in the (a) parallel and (b) perpendicular congurations.
polarized when the diameter of the nanowire is much less than the wavelength of light in
question (λ d)[163, 164].
Given λ d, the electric eld is reduced inside the nanowire for light polarized
2ε0 perpendicular to the axis of the nanowire, such that E⊥ = δE0, where δ = [164, 165]. εGaAs + ε0 The ratio of parallel to perpendicularly polarized Raman intensities is calculated by, 2 Ik − I⊥ 1 − δ ρ = ; while the predicted value for ρ is given by, ρ = 2 [163, 164]. For GaAs Ik + I⊥ 1 + δ
at room temperature the dielectric constant for λ = 633 nm is εGaAs ≈ 14.8, leading to an
expected value for ρ of 0.97 [166].
4 The data in gure 5.11 are t to r (θ ) = r0 + A cos (θ − θ0), chosen based on the work of
Wu et al. [161]. Because each polarization measurement takes several hours, during which
time there is some drift in the sample position and the intensity of the Raman signal is very sensitive to the position of the sample, the overall shape of the polarization response
Chapter5: SingleNanowire... 5.4ResultsandDiscussion 71
measured is distorted. The lobes in gure 5.11 should be symmetric; the asymmetry is purely
an experimental artifact that limits the utility of the ts as a source for parameters to use in
the calculation of δ.
5.5 Conclusions
Through this experiment we did not nd any evidence of the presence of wurtzite in the
nanowires, which we would have potentially observed as additional peaks in the Raman
spectra, or as a di erent symmetry in the polarization response. This may be in part because
the only nanowires we were able to study in this manner were SAGA06, which were grown with a V:III precursor ratio of 20:1, the highest precursor ratio of the nanowires we studied
(table 2.1), and hence the least likely to contain wurtzite [88].
We were able to account for the missing TO peak discussed in section 4.3.3; because we
see it out of resonance, its absence was most likely an issue of instrument sensitivity. This
is in itself is not surprising; the resonance instrumentation was not sensitive enough to
measure the Raman spectra out of resonance from the nanowires. Nevertheless, it remains
striking how much the LO phonon was apparently favored in the resonance spectra from the
core-shell nanowires.
The polarization response of the nanowires showed that the Raman response of the cores
of the core-shell nanowires behaved as if they were still small in diameter compared to the
excitation wavelength, despite the presence of the shell giving them a total diameter on the
order of 100 nm.
Chapter5:SingleNanowire... 5.5Conclusions 72
Chapter 6: Conclusions, Open Questions, and Future Work
6.1 Conclusions
Using PL, resonance Raman, and single nanowire Raman spectroscopies, we have enriched
our understanding of the properties of the nanowires we studied. While we reject our initial
hypothesis that the interface between core and shell plays a signicant role in determining the
electronic properties of the nanowires, we have achieved a profoundly deeper understanding
of our samples. Instead of the interface being signicant, the concentration of impurities
resulting from the growth conditions plays the most signicant role, with the thermal history
playing a large role in di erentiating the properties of the bare GaAs nanowires from the
core-shell nanowires.
Our experimental accomplishments include:
• Low temperature PL with varied incident power, which allowed us to identify donor-
acceptor-pair luminescence as a major contribution to the PL spectra of the core-shell
nanowires. Our spectra were well enough resolved that we could more clearly identify
the origin of spectral features that had been part of spectra observed before from
similar nanowires.
• Resonance Raman spectra of the di erent types of nanowires that revealed di erences
in their resonant behavior. These experiments, along with the PL, were conducted on a
custom instrument built at Drexel. The combination of features – low temperatures,
tunable excitation, high resolution – our instrument was capable of is generally not 73
available commercially. Our resonance Raman experiments showed us that the LO
phonon was coupling especially strongly to the bound exciton state in the core-shell
nanowires.
• An experiment using polarized Raman spectroscopy on a single nanowire allowed us to
look for wurtzite based on scattering symmetry and polarization. This experiment also
helped resolve some questions regarding the TO phonon mode that were raised by the
resonance Raman experiment, showing that the lack of a TO phonon peak in the
resonance spectra of the core-shell nanowires was most likely an artifact of the low
sensitivity of the instrument.
6.2 Open Questions and Future Work
The overarching aim for this study was to support the rational design of nanowire structures
for device applications, by supplying growers with information about their product. In this
context, the relative value of possible future experiments is easier to assess.
The only additional experiments on the samples studied that seem advisable, would be
higher quality TEM microscopy in order to more accurately assess the quality of the nanowires
from the standpoint of crystalline defects. Correlating these results with spectroscopy would
greatly assist in the interpretation of the spectroscopic features.
The limits in quality for nanowires grown using tertiarybutylarsine remain unknown.
Most of the work to discover those limits depends on the growers, but we can assist by being
aware of the challenges they face.
Until the nanowire growth results in materials of controlled doping concentration, as we
characterize future samples, it is premature to worry about the more exotic phenomena that
Chapter6: Conclusions 6.2Open estionsandFutureWork 74
may occur at the interface between core and shell. In this sense too, while it is interesting that
the LO phonon energy appears to move, it would be more valuable to hold o from further
investigating it, until similar experiments could be repeated with better controlled nanowires.
That said, in order to better resolve the origin of the phenomena, it would be interesting to
conduct resonance Raman experiments on single nanowires in order to understand which
e ects were artifacts of the ensemble measurement.
Chapter6: Conclusions 6.2Open estionsandFutureWork 75
Appendix A: Finite Curvature-Mediated Ferroelectricity
Figure A.1: Polarization vs. distance from inner radius for the size nanowires used in the study, illustrating the e ect of strain in increasing the polarization of thin ferroelectric shells.
This appendix will highlight my contributions to two published papers: Nonnenmann et al. [OL8] and Johnson et al. [OL10] (see publications list, page 93). From the standpoint of the simulation the critical di erence between the two papers, was that Johnson et al.
[OL10] required agreement between more than one type of material and inclusion of the magneto-elastic parameters in the strain. Both papers are attached as a part of this appendix.
Both of these papers discussed core-shell nanowires with a ferroelectric shell and a metallic core. Experimentally, it was shown that the ferroelectric properties of these 76
Figure A.2: Waterfall plot of the polarization across the thinnest shell, with color representing the temperature used in the calculation of the polarization.
nanowires were enhanced over what would be expected from thin lms of the same material.
My contribution to the work was to provide numerical models that helped explain the
experimental results as a consequence of the strain imposed on the shells by the high degree
of curvature imparted by their nite size. In general, surface e ects lead to a decrease in the
polarization of ferroelectric lms, an e ect that becomes more signicant the thinner they are.
The experimental results that these models supported, showed that very thin ferroelectric
lms could have their polarization enhanced when they were highly curved.
The models were implemented in Matlab. The main numerical task, solving a di erential
equation was achieved using code based on a non-linear nite di erence algorithm described
by Burden and Faires [167]. The high degree of curvature, imposes a stress eld on the
Appendix A: Finite Curvature-Mediated Ferroelectricity 77 system ! ! a2 b2 b2 a2 σ (r ) = 1 ∓ p − 1 ∓ p . (A.1) rr ,φφ b2 − a2 r 2 aρ b2 − a2 r 2 bρ
The ferroelectric polarization of a shell is calculated through the minimization of the
Gibbs free energy, written in terms of the Landau sti ness, renormalized to account for
the e ect of strain on the e ective material constants, Aˆ(r ) = A − 2Q11σrr (r ) − 2Q12σφφ (r ),
A = A0(T − TC ), the material constants A0, B, and C; and g to account for the energetic cost
of variation of Pr near surface and a depolarizing eld Ed . The Gibbs free energy is given by
b " ˆ # A 2 B 4 C 6 1 2 2 G = Pr (r ) + Pr (r ) + Pr (r ) + g(∇Pr ) − Ed (r )Pr (r ) rdr + Pr dS. (A.2) a 2 4 6 2 S
The Gibbs free energy is minimized through the use of the Euler-Lagrange equation
2 ˆ 3 5 g∇ Pr (r ) = APr (r ) + BPr (r ) + CPr (r ) − Ed (r ).
The algorithms for calculating the coercive eld and the e ect of the stress on the Curie
temperature (TC) for the ferroelectric shells were designed to be e cient by feeding the
previous answer in as the initial guess as a parameter (i.e. temperature or applied eld) was
changed. At some point, the only stable solution for the polarization is either the trivial
solution Pr = 0 (for T > TC) or only one sign for Pr will be a solution. Because we eventually
needed to deal with more than just one type of material, the original Matlab scripts were
turned into a more robust set of tools. And because the algorithms required thousands
of polarization proles be calculated, the code was carefully optimized in critical areas.
Figures A.1 and A.2 illustrate some of the results of these calculations.
Figure A.1 plots the results of the calculation of the polarization for thin ferroelectric
Appendix A: Finite Curvature-Mediated Ferroelectricity 78
shells in strained and unstrained states for shell thicknesses corresponding to the sizes that were investigated experimentally. The peak values of polarization curves for the strained
shells show an increase with decreasing shell thickness, because the thinner shells correspond
to smaller radius of curvature samples and strain increases as the inner radius shrinks. The
peak values for the unstrained shells have decreasing maxima as the shells get thinner,
because of the depolarizing eld at the surface.
Figure A.2 shows the polarization across a 7 nm shell as a function of temperature. At the
highest temperature plotted, the shell has become paraelectric and the polarization is zero.
In the printed version this appendix contains reprints of Nonnenmann et al. [OL8] and
Johnson et al. [OL10] (see publications list, page 93). Because the copyright to the articles
remains with the publishers, links are provided here rather than copies of the articles.
Nonnenmann et al. can be found at http://dx.doi.org/10.1021/nl903384p.
Johnson et al. can be found at http://dx.doi.org/10.1063/1.3657152.
Appendix A: Finite Curvature-Mediated Ferroelectricity
87
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Vita
Oren D. Lea er recieved a B.S. in Engineeering Physics from the University of California at
Berkeley.
Publications
[OL1] O. D. Lea er, S. Gupta, M. W. Barsoum, and J. E. Spanier. On Raman scattering from selected M2AC compounds. Journal of Materials Research, 22(10):2652, 2007. [OL2] M. K Drulis, H. Drulis, A. E. Hackemer, O. Lea er, J. Spanier, S. Amini, M. W. Barsoum, T. Guilbert, and T. El-Raghy. On the heat capacities of Ta2AlC, Ti2SC, and Cr2GeC. Journal of Applied Physics, 104(2):023526, 2008.
[OL3] B. Garipcan, J. Winters, J. S. Atchison, M. D. Cathell, J. D. Schi man, O. D. Lea er, S. S. Nonnenmann, C. L. Schauer, E. Pişkin, B. Nabet, and J. E. Spanier. Controllable formation of nanoscale patterns on TiO2 by conductive-AFM nanolithography. Langmuir, 24(16): 8944, 2008.
[OL4] T. H. Scabarozi, S. Amini, P. Finkel, O. D. Lea er, J. E. Spanier, M. W. Barsoum, M. Drulis, H. Drulis, W. M. Tambussi, J. D. Hettinger, and S. E. Lo and. Electrical, thermal, and elastic properties of the MAX-phase Ti2SC. Journal of Applied Physics, 104 (3):033502, 2008.
[OL5] V. R. Binetti, J. D. Schi man, O. D. Lea er, J. E. Spanier, and C. L. Schauer. The natural transparency and piezoelectric response of the Greta oto butter y wing. Integrative Biology, 1(4):324, 2009.
[OL6] B. Manoun, O. D. Lea er, S. Gupta, E. N. Ho man, S. K. Saxena, J. E. Spanier, and M. W. Barsoum. On the compression behavior of Ti2InC,(Ti0.5, Zr0.5)2InC, and M2SnC (M = Ti, Nb, Hf) to quasi-hydrostatic pressures up to 50 GPa. Solid State Communications, 149 (43-44):1978, 2009.
[OL7] T. H. Scabarozi, S. Amini, O. Lea er, A. Ganguly, S. Gupta, W. Tambussi, S. Clipper, J. E. Spanier, M. W. Barsoum, J. D. Hettinger, and S. E. Lo and. Thermal expansion of select Mn+1AXn (M = early transition metal, A = A group element, X = C or N) phases measured by high temperature x-ray di raction and dilatometry. Journal of Applied Physics, 105(1):013543, 2009. 101
[OL8] Stephen S. Nonnenmann, Oren D. Lea er, Eric M. Gallo, Michael T. Coster, and Jonathan E. Spanier. Finite curvature-mediated ferroelectricity. Nano Letters, 10(2):542, February 2010.
[OL9] Guannan Chen, Eric M. Gallo, Oren D. Lea er, Terrence McGuckin, Paola Prete, Nico Lovergine, and Jonathan E. Spanier. Tunable Hot-Electron transfer within a single Core-Shell nanowire. Physical Review Letters, 107(15):156802, October 2011.
[OL10] Stephanie H. Johnson, Peter Finkel, Oren D. Lea er, Stephen S. Nonnenmann, Konrad Bussmann, and Jonathan E. Spanier. Magneto-elastic tuning of ferroelectricity within a magnetoelectric nanowire. Applied Physics Letters, 99(18):182901, October 2011.
[OL11] Jonathan E. Spanier, Stephen S. Nonnenmann, and Oren David Lea er. Ferroelectric nanoshell devices, 2009. U.S. Patent Application: 2012/0098589.
Vita