Determination of Electrostatic Potential and Charge Distribution of
Semiconductor Nanostructures using Off-axis Electron Holography
by
Luying Li
A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree
Doctor of Philosophy
Approved April 2011 by the Graduate Supervisory Committee:
Martha R. McCartney, Co-Chair
David J. Smith, Co-Chair Michael J. Treacy
John Shumway Jeff Drucker
ARIZONA STATE UNIVERSITY
May 2011
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ABSTRACT
The research of this dissertation involved quantitative characterization of
electrostatic potential and charge distribution of semiconductor nanostructures
using off-axis electron holography, as well as other electron microscopy
techniques. The investigated nanostructures included Ge quantum dots, Ge/Si
core/shell nanowires, and polytype heterostructures in ZnSe nanobelts. Hole
densities were calculated for the first two systems, and the spontaneous
polarization for wurtzite ZnSe was determined.
Epitaxial Ge quantum dots (QDs) embedded in boron-doped silicon were
studied. Reconstructed phase images showed extra phase shifts near the base of
the QDs, which was attributed to hole accumulation in these regions. The
resulting charge density was (0.03 0.003) holes/nm3, which corresponded to
about 30 holes localized to a pyramidal, 25-nm-wide Ge QD. This value was in
reasonable agreement with the average number of holes confined to each Ge dot
determined using a capacitance-voltage measurement.
Hole accumulation in Ge/Si core/shell nanowires was observed and
quantified using off-axis electron holography and other electron microscopy
techniques. High-angle annular-dark-field scanning transmission electron
microscopy images and electron holograms were obtained from specific
nanowires. The intensities of the former were utilized to calculate the projected
thicknesses for both the Ge core and the Si shell. The excess phase shifts
measured by electron holography across the nanowires indicated the presence of
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holes inside the Ge cores. The hole density in the core regions was calculated to
be (0.4 0.2) /nm3 based on a simplified coaxial cylindrical model.
Homogeneous zincblende/wurtzite heterostructure junctions in ZnSe
nanobelts were studied. The observed electrostatic fields and charge accumulation
were attributed to spontaneous polarization present in the wurtzite regions since
the contributions from piezoelectric polarization were shown to be insignificant
based on geometric phase analysis. The spontaneous polarization for the wurtzite
ZnSe was calculated to be psp = -(0.0029 0.00013) C/m2, whereas a first
principles calculation gave psp = -0.0063 C/m2. The atomic arrangements and
polarity continuity at the zincblende/wurtzite interface were determined through
aberration-corrected high-angle annular-dark-field imaging, which revealed no
polarity reversal across the interface.
Overall, the successful outcomes of these studies confirmed the capability
of off-axis electron holography to provide quantitative electrostatic information
for nanostructured materials.
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ACKNOWLEDGMENTS
First of all, I would like to express my deepest gratitude to my advisors
Professor Martha R. McCartney and Regents Professor David J. Smith for their
esteemed support and guidance that made all the exciting achievements possible.
As an expert in the area of electron holography, Professor McCartney is so
experienced in experimental details as well as creative in generating new ideas,
discussing with her is really a spiritual enjoyment. Professor Smith is really
enthusiastic to work with, and his meticulous attitude and patience in front of
students deeply impresses me. Study in their group will be a great memory for me.
I would like to thank Professors Michael Treacy, John Shumway, and Jeff
Drucker for serving on my dissertation committee. I am grateful for the use of
facilities in the John M. Cowley Center for High Resolution Electron Microscopy,
and I thank for Karl Weiss and Dr. Zhenquan Liu for their technical support and
assistance throughout my research.
I would like to express my appreciation to Professor Jeff Drucker, Dr.
Sutharsan Ketharanathan, Dr. Eric Dailey, and Dr. Prashanth Madras of Arizona
State University, and Professor Jianbo Wang and Dr. Lei Jin of Wuhan University
for their collaboration and for providing the samples used for investigation in this
dissertation. Financial support from US Department of Energy (Grant No. DE-
FG02-04ER46168) is also gratefully acknowledged.
Particular thanks to our research group members for their help during my
stay. I thank Dr. Lin Zhou, Lu Ouyang, Wenfeng Zhao, Michael Johnson, Allison
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Boley, Sahar Hihath, Jae Jin Kim, Dinghao Tang, and Zhaofeng Gan for their
friendship and kindness.
Finally, I am very grateful to my family for their love and encouragement
in sunny and rainy days.
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TABLE OF CONTENTS
Page
LIST OF FIGURES .................................................................................................... ix
CHAPTER
1. INTRODUCTION .......................................................................................... 1
1.1 Backgound ................................................................................................ 1
1.2 Tailoring of Charge Distribution in Semiconductors .............................. 6
1.2.1. p-n junctions ......................................................................................... 6
1.2.2. Band-alignment-induced charge distribution ...................................... 9
1.2.3. Polarization-induced charge distribution ........................................... 11
1.3. Growth of Semiconductor Nanostructures ........................................... 15
1.3.1. Epitaxial growth ................................................................................. 15
1.3.2. Thermal evaporation .......................................................................... 20
1.4. Outline of Dissertation .......................................................................... 20
References ..................................................................................................... 23
2. EXPERIMENTAL DETAILS ..................................................................... 27
2.1. Off-axis Electron Holography ............................................................... 27
2.1.1. Background ........................................................................................ 27
2.1.2. Experimental setup ............................................................................. 28
2.1.3. Reconstruction of electron holograms ............................................... 30
2.1.4. Mean inner potential .......................................................................... 36
2.2. Scanning Transmission Electron Microscopy ...................................... 38
2.2.1. Energy-dispersive X-ray spectroscopy .............................................. 39
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CHAPTER Page
2.2.2 High-angle annular-dark field imaging .............................................. 40
2.3. Sample Preparation ............................................................................... 42
References ..................................................................................................... 45
3. STUDY OF HOLE ACCUMULATION IN INDIVIDUAL GERMANIUM
QUANTUM DOTS IN P-TYPE SILICON ................................................ 47
3.1. Introduction ........................................................................................... 47
3.1.1. Hut, pyramid and dome structures ..................................................... 47
3.1.2. Composition and shape transition for capped Ge quantum
dots ...................................................................................................... 50
3.1.3. Electron charging behavior of Ge quantum dots ............................... 51
3.2. Experimental Details ............................................................................. 53
3.3. Results and Discussion .......................................................................... 55
3.3.1. Charge distribution in n-type and p-type Ge quantum dots .............. 55
3.3.2. Electron holography study of n-type Ge quantum dots .................... 57
3.3.3. Electron holography study of p-type Ge quantum dots .................... 58
3.3.4. Comparison of hole density with C-V measurement ........................ 65
3.4. Conclusions ........................................................................................... 66
References ..................................................................................................... 68
4. OBSERVATION OF HOLE ACCUMULATION IN Ge/Si CORE/SHELL
NANOWIRES .............................................................................................. 70
4.1 Introduction .....................................