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 .....................................