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DEVELOPMENT OF GROUP III/NITRIDE CORE/SHELL HETEROSTRUCTURES BY ATOMIC LAYER DEPOSITION ON NANORODS

By

JOSEPH C. REVELLI

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2013

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© 2013 Joseph C. Revelli

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To my parents, Joseph F. Revelli Jr. and Dorothy M. Lutz Revelli

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ACKNOWLEDGMENTS

First and foremost, I would like to thank my parents, Dorothy M. Lutz Revelli and

Dr. Joseph F. Revelli Jr. for teaching me how to work hard and be successful from a

young age. My father always has been, and will continue to be, my academic advisor in

all things scientific. I would also like to thank Dr. Tim Anderson for giving me the

opportunity to work in his labs and for giving me the freedom to follow my own academic

curiosities. I would like to thank my committee members; Dr. Jason Weaver, Dr. Lew

Johns, Dr. Mark Davidson and Dr. Nicholas Rudawski, each of whom I have interacted

with in very influential ways. Additionally I would like to thank Dr. Ranga Narayanan for

being a good mentor. I would also like to thank Dr. Al Raisanen at Rochester Institute

of Technology for teaching me about ellipsometry. Additionally, I would like to thank my

brother Tom Revelli for being an awesome guy.

I would also like to thank my lab mates and class mates, especially the ones who

were in the trenches with me: Dr. Vaibhav Chaudhary, David Wood, Christopher

O’Donohue, Christopher Muzzillo, Dr. Patrick McKinney, Dr. Ranga Krishnan, Dr. Joo

Young Lee, Michael Hague, Barrett Hicks, Seo Young Kim, Stephanie Yakaun Yao,

Chien-Tsung Chen, Tae Hee Kim, Dr. Oh Hyun Kim, Dr. Trey Batson and Dr. Dojun

Kim.

Finally I would like to thank all the people in the Gainesville community who

supported me during this amazing phase of my life: Mary-Anne Primack, Eduardo

Arenas, Keith Weeks, Jon Josephson, Q Crawford, Meg Taylor, Chris Pearce, Josh

Hintermister, Corwin Klein, Wester Joseph, Jon Jackson, Pat Kennedy, Chet Honeycut,

and the many, many more amazing people who make Gainesville special.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 7

LIST OF FIGURES .......................................................................................................... 8

ABSTRACT ................................................................................................................... 10

CHAPTER

1 INTRODUCTION ..................................................................................................... 12

1.1 Overview of Lighting ........................................................................................ 12 1.2 Conventional GaN LED .................................................................................... 12

1.3 Novel Nanostructured GaN LED ...................................................................... 14 1.4 Prior Work: Nanorods Used in this Study ......................................................... 15 1.5 Thesis Overview .............................................................................................. 16

2 LITERATURE REVIEW .......................................................................................... 21

2.1 Brief History of GaN ......................................................................................... 21

2.2 Atomic Layer Deposition of GaN, InyGa1-yN and AlxInyGa1-x-yN....................... 23

2.3 Doping GaN ..................................................................................................... 24

2.3.1 n-type ..................................................................................................... 24 2.3.2 p-type ..................................................................................................... 25 2.3.3 p-type Delta Doping ................................................................................ 26

2.4 State-of-the-Art Lighting Technology ............................................................... 27

3 ATOMIC LAYER DEPOSITION OF GALLIUM NITRIDE ......................................... 31

3.1 Preliminary Remarks ........................................................................................ 31 3.2 Experimental Setup and Procedure .................................................................. 32 3.3 Experimental Results ....................................................................................... 35

3.4 Sample Characterization .................................................................................. 31

3.4.1 Thickness Measurements ....................................................................... 36 3.4.2 Film Surface Morphology over the ALD Process Window ...................... 37 3.4.3 Structural Composition of ALD Films ...................................................... 40

4 ATOMIC LAYER DEPOSITION OF GaN ON InN NANORODS .............................. 53

4.1 Preliminary Remarks ........................................................................................ 53 4.2 Experimental Setup and Procedure ................................................................. 55 4.3 Experimental Results ....................................................................................... 56 4.4 Discussion of Experimental Results ................................................................. 59

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5 CORE/SHELL NANOROD HETEROSTRUCTURE STRAIN MODELS .................. 73

5.1 Hooke’s Law .................................................................................................... 73 5.2 Analytical Model 1: Extension of Matthew’s Model to a Cylindrical System ..... 76

5.2.1 Basic Model ............................................................................................ 76 5.2.2 Minimization of Strain Energy without Dislocations ................................ 78 5.2.3 Introduction of Dislocations into the Model ............................................. 79

5.3 Analytical Model 2: Pressure Vessel Theory Applied to Core/Shell Nanorods ............................................................................................................. 81

6 CONCLUSION ........................................................................................................ 97

APPENDIX LITERATURE REVIEW OF SELECTIVE AREA GROWTH OF GALLIUM NITRIDE ................................................................................................. 99

A.1 Preliminary Remarks ....................................................................................... 99 A.2 Substrates, Stripe-Pattern Directions, and GaN Stripe Morphologies ............. 99

A.2.1 GaN/Sapphire Patterned Substrates ...................................................... 99

A.2.2 Sapphire Patterned Substrates ............................................................ 100

A.2.3 Changing Stripe Morphology with Carrier Gas ..................................... 100

A.2.4 Growth Rates ....................................................................................... 101 A.2.5 Patterned Silicon or Patterned GaN/Silicon Substrates ....................... 102 A.2.6 GaN Growth Conditions ....................................................................... 103

A.3 Mask Materials .............................................................................................. 104 A.4 Devices .......................................................................................................... 104

A.4.1 Quantum Confined Stark Effect and Variation of InGaN Growth Rates in III-V SAG Devices ................................................................................... 104

A.4.2 Dopant incorporation ............................................................................ 106

LIST OF REFERENCES ............................................................................................. 110

BIOGRAPHICAL SKETCH .......................................................................................... 122

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LIST OF TABLES

Table page 4-1 Values of elasticity tensor elements for InN and GaN in units of GPa. .................. 88

A-1 Selected Area Growth conditions for GaN reported in the literature. .................. 109

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LIST OF FIGURES

Figure page 1-1 Schematic diagram of p-AlxGa1-xN / i-InyGa1-yN / n- AlxGa1-xN double

heterostructure LED. ............................................................................................ 17

1-2 Proposed nanostructured LED on silicon showing core/shell p-GaN/i-InyGa1-

yN/n-GaN/GaN-heterojunctions. ........................................................................... 18

1-3 GaN nanowires grown by MOCVD in this laboratory. ............................................ 19

1-4 Well-oriented, uncatalyzed InN nanorods grown by HVPE in this laboratory ......... 20

2-1 Examples of complex epitaxial nanowire structures grown by glō™ ...................... 29

2-2 Schematic diagram of core/shell GaN/ InyGa1-yN nanorods grown by Lieber, et. Al.......................................................................................................................... 30

3-1 Schematic of GaN ALD reactor. ............................................................................ 42

3-2 Photograph of clean reactor chamber with nitrogen plasma inside ........................ 43

3-3 Photograph of home-made bubbler system. .......................................................... 44

3-4 ALD Process Window for GaN grown on Si(100) with GaCl3 and NH3 at 600 °C. ........................................................................................................................ 45

3-5 ALD Process temperature window for GaN/Si(100) grown with 8 sec GaCl3 pulse and 10 sec NH3 pulse. ................................................................................ 46

3-6 Sample XRR spectrum of run 239 GaN/Sapphire. ................................................. 47

3-7 Experimental ellipsometric data (dashed lines) and model data (solid lines). ......... 48

3-8 SPM image of surface height information for ALD GaN/sapphire with a 4 sec GaCl3 exposure time ........................................................................................... 49

3-9 ALD GaN/Si(100) surface roughness vs. GaCl3 exposure time. ............................. 50

3-10 SPM images of ALD GaN/Si(100). ....................................................................... 51

3-11 GIXD Spectra of ALD GaN on both sapphire(0001) and Si(100) substrates. ....... 52

4-1 TEM images of GaN coated and bare InN nanorods and SAED pattern of bare single crystal InN nanorod ................................................................................... 62

4-2 Comparison of HVPE and ALD coated nanorods. .................................................. 63

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4-3 EDS scan from JEOL 2010F HR-TEM .................................................................. 64

4-4 Growth map of ALD GaN on InN nanorods grown for durations of 40, 80, and 120 cycles at temperatures of 565 and 595 °C. ................................................... 65

4-5 HR-TEM and SAED for 120 cycle ALD GaN grown on InN nanorod at 565, 580, and 595 °C ........................................................................................................... 66

4-6 SAED patterns of InN nanorod core/ALD GaN shell heterostructures for: 40, 80, and 120 cycles of ALD growth at 565 and 595 °C. .............................................. 67

4-7 TEM images of 5, 10, 15, and 20 cycle ALD GaN on InN nanorods grown at 595 °C. ................................................................................................................. 68

4-8 Shell thickness as a function of number of ALD cycles for ALD GaN grown on InN nanorods at 595°C ........................................................................................ 69

4-9 Nanorod orientation during TEM imaging ............................................................... 70

4-10 HR-TEM image of ALD GaN/InN nanorod interface for 120 cycle ALD at 595°C ................................................................................................................... 71

4-11 Examples of InN nanorod decomposition at high temperatures ........................... 72

5-1 Schematic of coaxial nanowire heterostructure approximated as a cylinder .......... 89

5-2 Comparison of zero normal stress boundary condition for planar and nanostructured cases. .......................................................................................... 90

5-3 Numerically computed equilibrium lattice parameters for an InN/GaN core/shell system with core radius of 25 nm, and a length of 1000 nm ............................... 91

5-4 Plots of core radius as a function of the critical shell thickness for AlxGa1-xN

shells on GaN nanorod cores calculated by Matthew’s model for cylinders ......... 92

5-5 Plots of core radius as a function of the critical shell thickness for GaxIn1-xN

shells on InN nanorod cores calculated by Matthew’s model for cylinders. ......... 93

5-6 Plots of core radius as a function of the critical shell thickness for AlxGa1-xN

shells on GaN nanorod cores calculated by the Pressure Vessel Model ............. 94

5-7 Plots of core radius as a function of the critical shell thickness for GaxIn1-xN

shells on InN nanorod cores calculated by the Pressure Vessel Model ............... 95

5-8 Comparison of Pressure Vessel Model and Matthew’s Model for Cylinders for GaxIn1-xN/InN system at three different alloy compositions, x .............................. 96

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

DEVELOPMENT OF GROUP III/NITRIDE CORE/SHELL HETEROSTRUCTURES BY

ATOMIC LAYER DEPOSITION ON NANORODS

By

Joseph Christopher Revelli

December 2013

Chair: Timothy J. Anderson Major: Chemical Engineering

A nanostructured LED design has been proposed in which a p-GaN/i-InyGa1-

yN/n-GaN double heterostructure is deposited on p-GaN nanorods that are grown on a

Si substrate. The design advantages include: 1) a ten-fold increase in active area for

photo-generative recombination resulting in an increase in brightness, 2) increase in

photon extraction efficiency, and 3) growth on Si wafers that eliminates the need for

topside contacts and possible integration with other Si-based technologies.

The feasibility of using atomic layer deposition (ALD) was studied both

experimentally and theoretically as a means of fabricating the proposed nano-structure

LED. The ALD process window for growing thin films of GaN on Si substrates from

GaCl3 and NH3 was determined. Optimum ALD growth was obtained with a GaCl3

exposure time of 2-8 sec followed by a 30 sec nitrogen purge, a 10 sec NH3 pulse, and

another 30 sec nitrogen purge. One cycle resulted in 2.56 Å of growth over the entire

ALD process window and ALD films obtained with these conditions were found to be

extremely uniform in thickness with many samples having roughness as low as 0.3 to

0.5 nm. These ALD conditions were then applied to growth of GaN on InN nanorods.

Randomly-oriented polycrystalline structures were observed for samples grown in the

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temperature range 565 to 580°C. For growth at a temperature of 595°C the GaN shells

were more crystalline but at a cost of decomposition of the underlying InN nanorod. For

growth at any temperature in the range 565 to 595°C the InN and GaN domains tended

to delaminate and show two separate sets of diffraction spots as shell thickness

increased. Analytical models were developed to predict the mechanical stability of

core/shell heterostructures fabricated from materials with dissimilar lattice constants.

The models predict that there is no thickness of pure InN core and pure GaN shell that

yields stable, defect-free shells. However, with alloyed shells, the model predicts a

range of thicknesses of cores and shells over which the structures are stable.

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CHAPTER 1 INTRODUCTION

1.1 Overview of Lighting

Artificial lighting accounted for 14% of total energy use and 19% of electricity use

in the United States in 2009. Lighting was also responsible for ~6% of total carbon

emissions in the same year [3]. The incandescent light bulb with an efficacy of 16 lm/W

is woefully inefficient. Radiation is produced as a black-body and only a small amount

falls in the visible range, the rest is released as heat waste. Recently compact

fluorescent bulbs and high intensity discharge lamps have become competitive with

incandescent lighting reaching efficacies of 71 lm/W and 96 lm/W, respectively [12, 20].

However, both of these technologies suffer from inherent limitations on efficiency. Solid

state lighting is the direct conversion of electricity to light by light-emitting semiconductor

diodes (LED’s). Consequently there is no theoretical limit on the efficiency of solid-state

lighting: efficacies approaching 400 lm/W may someday be achieved.

Solid-state lighting is currently competitive with incandescent lighting. The U. S.

Department of Energy has developed a Solid State Lighting Program that aims to make

LED technology competitive with fluorescent technology and to attain external

efficiencies of 35-50% by 2015 [20]. LEDs exist which are capable of light production in

the entire visible range and well into the UV and IR ranges. Multiple methods of

rendering white light exist, but every method relies, at least in part, on a blue or UV

LED. GaN, with an energy bandgap of 3.4 eV, is an ideal material for this.

1.2 Conventional GaN LED

The advancement of GaN technology has been plagued by the lack of an

inexpensive substrate with similar lattice parameters. High concentrations of threading

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defects arise due to strain from the non-lattice-matched substrate. These create non-

radiative recombination centers which dramatically lower the efficiency of the LED

devices. Doping of GaN is also difficult, especially p-type doping, due to a high native

n-type carrier concentration resulting from nitrogen vacancies and unintentional oxygen

incorporation in films. Figure 1-1 depicts a typical planar GaN LED. An insulating

sapphire substrate is first covered with a low-temperature GaN buffer layer on which

higher quality conductive n-type GaN can be deposited. A p-i-n junction is formed by an

undoped (intrinsic) layer of InyGa1-yN sandwiched between two layers of larger

bandgap AlxGa1-xN doped to be p-type and n-type, respectively. The top conductor is

formed by p-type GaN, usually doped with Mg. The InyGa1-yN active layer has a smaller

bandgap and a larger index of refraction than the GaN cladding layers. Consequently

this double heterostructure confines electrons and holes as well as photons produced

by recombination to the active layer. Photons are guided to the edges of the device

where they are emitted. This design suffers from several drawbacks. First, since

sapphire is an insulator, a large portion of the top of the device must be used for making

contacts. This reduces the surface area of emission and hence decreases the

brightness of the device. Also, this design has poor photon extraction efficiencies due

to the fact that photons emitted in the center of the device must travel long distances to

be emitted. Furthermore, the inability to grow large crystalline domains of GaN on

sapphire leads to poor material quality leading to decreased device efficiency, and limits

growth to two-inch wafers limiting production efficiency. Finally, the lack of suitable

cleavage planes in sapphire makes device-processing very inefficient.

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1.3 Novel Nanostructured GaN LED

A nanostructured GaN LED has been proposed which addresses many of these

issues. These devices consist of n-type nanorod structures which are coated by a

double heterostructure to form a core/shell configuration. The active layer is a vertical

cylinder and emission occurs at the edge of the cylinder as shown in Figure 1-2. Note

that this structure differs from that of the Vertical Cavity Surface Emitting Laser (VCSEL)

in which light is emitted orthogonally to the plane of the active layer.

A possible fabrication sequence for the proposed structure is as follows. A GaN

buffer layer is first grown on conductive silicon wafer. An insulating layer could be put

down in one of two ways: 1) GaN nanorods could be grown directly on the GaN buffer

layer followed by sputtering an insulating layer to cover the area between the bases and

the tops of the nanorods. 2) The insulating layer could be sputtered first and selectively

etched away. The nanorods would then be grown in the selected etch areas. Next an

n-GaN layer is deposited on the sidewalls and tops of the nanorods by atomic layer

deposition (ALD). ALD has the advantage of being able to coat high aspect ratio

features uniformly due to the fact that single monolayers are deposited in each cycle. A

three dimensional CVD growth mode would completely cover the tops of the nanorods

and leave the bases bare so it is not useful in growth of the quantum well but may be

useful in forming top contacts [128]. The InyGa1-yN active layer is also deposited on the

sides of the nanorods by ALD as is the p-GaN layer. This completes the double

heterostructure. Ni/Au contacts are then deposited to cover the sides and tops of the

nanorods. The area between the nanorods could be filled with metal or some insulator

such as spin-on glass to give the nanorods mechanical support. Finally the top of the

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device is chemically-mechanically polished to reveal the active layers of the core/shell

nanorods. Since the silicon substrate is conductive, a backside n-contact can be used.

The nanorods are almost perfect single crystals and can be grown to cover

arbitrarily large areas. Since the area of the bases of the nanorods are so small, on the

order of 1 µm2, there is not enough strain built up to cause significant dislocations.

Additionally, the dislocations do not propagate directly in the [0002] direction, so they

quickly terminate at the sides of the nanorods leaving the majority of each nanorod

completely dislocation-free. The core/shell nanorod design also offers a ten-fold

increase in surface area over the conventional device. The geometry will also allow for

an increased photon extraction efficiency and the orthogonalization of carrier injection

currents and recombination currents may lead to increases in efficiency as well [107].

1.4 Prior Work: Nanorods Used in this Study

Although the proposed nanostructure device uses GaN nanorods as a basis, InN

nanorods were chosen for the basis of this work. While catalyst-free hydride vapor

phase epitaxy (HVPE)-grown GaN nanorods have been demonstrated by other groups

[59], attempts to grow this substrate in this laboratory have not yet been successful.

Preliminary investigations of GaN and InyGa1-yN nanorods grown by metal-organic

chemical vapor deposition (MOCVD) resulted in “spaghetti-like” nanowires as depicted

in Figure 1-3. On the other hand this research group has produced single crystal,

[0002]-oriented InN nanorods (see Figure 1-4). InN and GaN nanorods have the same

wurtzite crystal structure and have comparable lattice constants and thermal expansion

coefficients. These nanorods are grown in a hot-wall HVPE reactor and require no

catalyst. The density of nanorod growth and the size and aspect ratio of the nanorods

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can be controlled through reaction conditions. The uniform, vertical orientation of these

nanorods makes them ideal for device applications. Consequently it was felt that InN

nanorods would be suitable for development of an ALD core/shell nanostructure

fabrication process.

1.5 Thesis Overview

This thesis is organized as follows. Chapter 2 reviews the literature associated

with the fabrication of large area devices based on III-N materials on sapphire and

silicon substrates. Chapter 3 describes the experimental apparatus used in this thesis

to grow thin films of GaN by ALD on sapphire and silicon substrates using GaCl3 and

ammonia as precursor materials. Chapter 3 also presents the results obtained from

experiments including sample characterization and the ALD process window for GaN

growth on sapphire and silicon substrates. Chapter 4 extends Matthew's model for the

equilibrium values of the c and a lattice parameters for strained planar structures to the

cylindrical geometry of core/shell structures. In addition, the model is extended to

derive a relationship between the core radius and the shell thickness that insures that

line dislocations cannot form. Pressure Vessel Theory is used to provide an alternate

derivation of this relationship. Chapter 5 discusses experimental results for the growth

of GaN shells on InN nanorods and Chapter 6 presents a literature survey on SAG and

its application to fabrication of devices based on III-N materials. SAG is believed to be

an attractive alternative to ALD on nanorods. The thesis concludes with Chapter 7.

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Figure 1-1. Schematic diagram of p-AlxGa1-xN / i-InyGa1-yN / n- AlxGa1-xN double heterostructure LED.

Sapphire Substrate

LT - GaN

n -

contact

n - GaN

n – AlxGa1-xN i – InyGa1-yN

p – AlxGa1-xN p - GaN

p - contact

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Figure 1-2. Proposed nanostructured LED on silicon showing core/shell p-GaN/i-InyGa1-

yN/n-GaN/GaN-heterojunctions.

GaN (under

nanorods)

Insulator (between

bases of nanorods)

GaN Nanorod Core n-GaN

InyGa1-yN

p-GaN Top

contact

Core/Shell

Nanorods

Silicon Substrate

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Figure 1-3. GaN nanowires grown by MOCVD in this laboratory.

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Figure 1-4. Well-oriented, uncatalyzed InN nanorods grown by HVPE in this laboratory [reprinted by permission from Chaudhary, Vaibhav. 2012. Growth of InN and GaN on Silicon Using Metal Organic Vapor Phase Epitaxy (Page 81, Figure 2-12a). University of Florida].

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CHAPTER 2 LITERATURE REVIEW

2.1 Brief History of GaN

The first mention of Gallium Nitride in the literature was in 1928 when it was

noted that “Gallic nitride is an exceedingly stable compound” [48]. Indeed, the chemical

stability of GaN at high temperatures along with its large band gap have made GaN a

desirable material for high temperature transistors and blue light emitters. Gallium

Nitride formed by running ammonia through liquid gallium at high temperatures was first

characterized by Juza and Hahn in 1938 [49], at which point its theta 2-theta x-ray

diffraction spectrum was measured. The photoluminescence (PL) of GaN was first

measured by Grimmeriss and Koelmans in 1959 [34]. GaN film was first deposited by

CVD on a sapphire substrate in 1969 by Maruska and Tietjen [79].

Over the next two decades little attention was paid to GaN due to the fact that it

proved very difficult to grow a high quality crystal. Lack of a substrate with comparable

lattice parameters and thermal expansion coefficient led to difficulties in growing large

crystalline domains of GaN. Furthermore, the high vapor pressure of N2 at growth

temperatures caused the formation of high concentrations of nitrogen vacancies. It is

believed that these nitrogen vacancies are the main cause of the high concentrations of

native n-type carriers in GaN films. Improvements in the structural quality, surface

morphology, and electrical and optical properties of GaN were reported in the late

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1980’s through the use of a low-temperature (LT)-AlN buffer layer on a sapphire

substrate [6, 130].

Due to the difficulty of p-type doping, the original GaN based light emitters were

not conventional p-n junction devices. Instead, they were metal-insulator-n-type (MIN)

structures in which heavily compensated insulating GaN was grown on uncompensated

n-type GaN [100, 101]. P-type GaN was achieved in 1989 through the use of Low

Energy Electron Beam Irradiation (LEEBI) [5]. LEEBI was necessary to partially

eliminate neutral Mg-H species which prevent Mg from acting as an acceptor [32]. It

was later discovered by Nakamura that a thermal annealing process under N2 activates

the Mg [87]. The first UV-LED was created by Amano in 1989 by utilizing a

homojunction of native, n-type GaN and p-type GaN activated by LEEBI [5].

GaN-based Field Effect Transistors (FET) [54] and Heterojunction Bipolar

Transistors (HBT) [99] were fabricated in the 1990’s, but threading dislocation densities

were still 109 to 1010 cm-2, about 106 times higher than typical semiconductors. The

long-term reliability of these devices was questioned. In 1994 lateral epitaxial

overgrowth on a patterned SiO2 or Si3N4 mask was adopted [53]. Because threading

dislocations tend to form parallel to the growth axis, vertical blocking of these

dislocations led to threading dislocation densities as low as 104-105 cm-2. Nakamura’s

two-flow reactor design yielded improved crystal quality by injecting inert gas or H2

vertically onto the substrate hence thinning the region of boundary layer flow and

improving film uniformity [89].

Following these improvements, GaN and InGaN based LEDs and laser diodes

(LD) improved in intensity and lifetime, due in part to the work of Nakamura at Nichia

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Corporation. Perhaps the most famous GaN based device is the Blu-Ray LD used in

Blu-Ray discs and HD DVDs. Lack of a suitable substrate and difficulties growing large

(i.e., greater than 2”) diameter freestanding GaN wafers continues to be a problem for

the GaN industry. Additionally, the poor thermal conductivity of the sapphire substrate

has created problems for high temperature devices. Growth of GaN on silicon would

overcome many of these issues. The incorporation of 12” silicon wafer technology

would also improve device throughput and lower fabrication costs.

2.2 Atomic Layer Deposition of GaN, InyGa1-yN and AlxInyGa1-x-yN

Atomic Layer Deposition (ALD) has been reported in several works, most notably

those coming from the Bedair group at N. C. State in the 1990’s. Boutros et al. report

the growth of high quality InyGa1-yN with a value of y as high as 0.27 by ALD with a

unique, rotating disk susceptor [11, 82]. In this reactor the substrate rotated between a

stream of Ga/In precursors and a stream of NH3 separated by purge streams of N2. The

flow rates and rotation speed could be controlled to optimize conditions. InyGa1-yN films

were growth with trimethyl-gallium (TMG), Ethyl dimethyl Indium (EDMI) and NH3 at

temperatures from 600 to 700 °C. Pseudo-ternary AlxInyGa1-x-yN alloys have also been

grown by ALD [82, 131]. Zhang et al. used ALD to grow superlattices of AlxInyGa1-x-yN

in which each atomic layer of a lattice consists of a single component. For example, for

a (3,2,1)150 alloy, 3 pulses of trimethyl-aluminum (TMA) alternating with NH3 would be

followed by 2 pulses of trimethyl-indium (TMI) alternating with NH3 and then one pulse

of TMG followed by NH3. This entire routine would be repeated 150 times as indicated

by the subscript 150. All mentions of InyGa1-yN and AlxInyGa1-x-yN alloying by atomic

layer deposition in the literature used metal organics with methyl and ethyl groups as

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ligands. There is only one study that used trihalides as a Ga source to grow III/N alloys

by ALD.

Kim grew ALD films of GaN on a Si (100) substrate [66] with GaCl3 as the Ga

source and NH3 as the N source in a temperature range of 375 to 750 °C. The ALD

process window for this reaction was examined to find the self-limiting region. It was

found that the growth rate of GaN was constant after about the first 15 ALD cycles,

consistent with self-limiting growth. The first 15 cycles showed a slower growth rate due

to the difficulty of nucleation on the Si (100) surface. Additionally, exposure times of the

metal-organic source were varied. It was hypothesized that longer exposure times

would correspond to a more CVD-like film. It was found that GaN films deposited by

ALD showed both the (0002) and the (1011) orientations while films deposited by CVD

showed only the (0002) orientations. All films grown were polycrystalline. The amount

of Cl contamination and chemical bonding state of the films was also measured and it

was determined that as long as the GaCl3 exposure time is below the self-saturation

limit, the amount of Cl contamination is around 1%.

2.3 Doping GaN

2.3.1 n-type

As mentioned previously, GaN grows natively n-type probably due to nitrogen

vacancies which act as donor sites and dominate the point defect chemistry. Another

possible contributing factor could be the unintended incorporation of oxygen in the film.

Indeed, it has been shown that oxygen acts as a donor in GaN films. Oxygen implanted

in MOCVD-grown GaN films have carrier concentrations as high as 1017 cm-3 and

mobilities of 100 cm2V-1s-1. [17, 24, 115, 132] A more common approach to n-doped

GaN is to use silicon sources such as SiH4 or Si2H6 [31, 69, 88, 111]. SiH4 was found to

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produce films with carrier concentrations up to 2 x 1019cm-3. The activation energy of n-

GaN doped with SiH4 was found to be 12-17 meV and the ratio of free electrons to

incorporated Si atoms was 0.5±0.1. Si2H6 was used as an alternative n-type dopant

due to its increased reactivity. Carrier concentrations were increased up to 4 x 1019 cm-

3 while mobilities decreased from 450 to 100 cm2V-1s-1 with increasing flow of this

dopant.

2.3.2 p-type

Growth of p-GaN has proven difficult due to its natural n-type behavior and also

due to compensation of Mg by an undesired Mg-H complex. p-type carrier

concentrations as high as 2 x 1016 cm-3 with mobilities of 8 cm2V-1s-1 and resistivity

around 35 Ω-cm have been attained by LEEBI [5]. Nakamura and Götz showed that the

Mg can also be activated by rapid thermal annealing (RTA) [33, 87] in the temperature

range of 600 to 775°C. This process increases p-type carrier concentrations to 2.3 x

1018 cm-3 with mobilities of 10 cm2V-1s-1 and resistivities of 2 Ω-cm.

It was demonstrated that hydrogen plasma exposure reduces the free hole

concentrations in p-type GaN films [12], which led to a computational study by

Neugebauer et al. [92] showing that H does not bind to Mg directly but prefers the anti-

bonding orbital of one of the neighboring N atoms. Thus the Mg-H complex contains a

modified Mg-H bond with a dissociation barrier of about 1.5 eV [92]. LEEBI or RTA

breaks this bond and allows the Mg dopant to act as an acceptor. It should be noted

that p-type GaN films grown by Molecular Beam Epitaxy (MBE) do not require activation

by LEEBI or RTA as H is not present in the growth process [85].

26

While other group II elements have been investigated as possible p-type

dopants, none have been as successful as Mg. Bergman investigated the behavior of

Zn and Cd as p-type dopants but found that they formed deeper level acceptors than

Mg and were therefore less efficient at creating free holes [10]. Neugebauer and Van

de Walle reported a first-principle total energy calculation for various dopants (Li, Na, K,

Be, Zn, and Ca) [91] and found that only Be is expected to be an alternative to Mg,

although it may have other issues such as solubility limitations and compensation by Be

interstitial donors.

Kim investigated the growth of p-type GaN doped with bis-cyclopentadienyl

magnesium. In this work a sapphire substrate with a thin GaN buffer layer was used.

GaN films were grown by nitridating the substrate surface under NH3 for 30 min at 750

°C. LT-GaN was then grown for 5 min at 550°C. The growth temperature was then

raised to 700°C and a 450 nm thick polycrystalline Mg-doped GaN film was grown. The

film was then treated by thermal annealing to activate the Mg acceptor. The carrier

concentrations, mobilities, resistivities, and optical properties of the films were examined

and it was confirmed that the p-type film was achieved with a p-type carrier

concentration of 3.2x1017 cm-3 [64].

2.3.3 p-type Delta Doping

As mentioned previously, Mg is prevented from acting as an acceptor by H

complex compensation. Although LEEBI or thermal annealing can activate this Mg, the

activation energy increases as a function of Al in AlxGa1-xN. One method that has

shown promise for improving crystal quality and hole concentrations in GaN films is

delta doping. In this method the dopant is only introduced as a single atomic layer in

27

the otherwise undoped film. Nakarmi et al. [90] have reported a two-fold increase in

lateral conductivity and a five-fold increase in vertical conductivity in delta doped GaN

and AlxGa1-xN films as compared to uniformly doped GaN:Mg. The Mg atoms do not

diffuse far into the bulk GaN but the holes are shared throughout the bulk. Additionally,

Nakarmi reports an order of magnitude decrease in etch pit density (related to threading

dislocation density) in GaN:δ-Mg and AlxGa1-xN:δ-Mg over uniformly doped films. It is

proposed that the Mg substitutes for 0.01% to 10% of the Ga in the topmost layer of the

film and helps block threading dislocation propagation. Complex-type compensating

defects are also reduced. These films are grown with TMGa, TMAl, NH3, and bis-

cyclopentadienyl magnesium (Cp2Mg) with H2 as a carrier under MOCVD-like conditions

at 1050ºC. The NH3 flows the whole time, even when Ga (and Al) are shut off and Mg

is turned on for the delta doped region.

Bayram et al. [8] optimized delta doping by growing repeated layers of MOCVD

GaN grown with TMGa and NH3 followed by a period of surface nitridation under NH3

and a delta doped Mg layer grown with Cp2Mg and NH3. The number of times this cycle

was repeated was varied as were Mg exposure time, thickness of GaN interlayers, and

nitridation time. It is hypothesized that overlapping of the coulombic potentials of the

Mg doped regions decreases the activation energy of the Mg-H complexes. Hole

concentrations of 1018 were achieved under optimized conditions. Kim et al. [63] have

also shown increased efficiency of AlxInyGa1-x-yN lasers through the use of delta doping.

2.4 State-of-the-Art Lighting Technology

The Swedish company glö AB has developed arsine and phosphine based III-V

nanostructured LEDs commercially [30]. These LEDs are catalyzed by gold

28

nanoclusters and contain multiple axial heterostructures per nanorod, as opposed to the

radial (horizontal cylinder) heterostructures proposed in this work. These nanorods are

also grown on silicon and are capable of covering 6 inch wafers or larger without

degradation of material quality. Examples of nanostructures grown by glö AB are

shown in Figures 2-1 a-f.

Lieber et al. have demonstrated core/shell GaN/ InyGa1-yN nanorods similar to

the ones proposed in this work which are shown in Figure 2-2. Their growth method

consisted of using HVPE with a nickel nanocluster catalyst on r-plane sapphire. Growth

proceeded by a vapor-liquid-solid (VLS) mechanism and produced extremely high

quality materials but had the usual drawbacks of catalyzed nanorod growth such as

catalyst contamination and increased dislocation density due to strain at droplet-

semiconductor interface [21, 105-107].

29

Figure 2-1. Examples of complex epitaxial nanowire structures grown by glō™. A) GaP nanotrees. B) axial InAs/InP double barrier heterostructure. C) InAs nanowires grown by CBE. Details of Figure 1-3 C) are shown: D) from the side, E) from the top, and F) Contacting scheme [reprinted from glō™ (2012) http://www.glo.se/ technology.html].

30

Figure 2-2. Schematic diagram of core/shell GaN/ InyGa1-yN nanorods grown by Lieber, et. Al. A) cross-section of n-GaN/i- InyGa1-yN /p-GaN double heterostructure. B) n-GaN/p-GaN homojunction as produced by VLS mechanism and corresponding energy level diagrams [reprinted from Dong, Yajie. Nanoletters 9 (2009) Coaxial Group II-Nitride Nanowire Photovoltaics (Page 2184, Figure 1)].

31

CHAPTER 3 ATOMIC LAYER DEPOSITION OF GALLIUM NITRIDE

3.1 Preliminary Remarks

Atomic layer deposition (ALD) has garnered much attention for its ability to

uniformly coat high-aspect-ratio features such as nanorods and trenches [62, 65]. ALD

is a subset of chemical vapor deposition (CVD) in which the reactants are sequentially

introduced to the reactor and separated by an inert purge flow. Each reactant species

chemically bonds to the surface of the growing crystal to a self-limiting extent. Ideally, a

single atomic layer of a reactant remains chem-adsorbed to the surface after the purge

step while other phys-adsorbed molecules of the reactant desorb and are swept away

during the purging step. In this work GaN films were grown by ALD with a 4 step cycle

consisting of a 2-8 sec GaCl3/N2 pulse, a 30 sec nitrogen purge, a 10 sec NH3 pulse,

and another 30 sec nitrogen purge.

Methods described in early publications for identifying the ALD process window

for GaN film growth often incorporated in situ monitoring techniques. For example, film

thickness or total mass has been measured with a quartz crystal microbalance [70] and

film surface state has been determined through UV-VIS reflectivity [55] or surface

phonon absorption measured with a xenon lamp and Si diode detector [127]. Success

in finding the ALD process window using ex-situ methods, such as measuring thickness

by cross sectional SEM or XRR [66], has also been reported. These measurements are

used to determine the growth rate per cycle, and to identify a window of exposure times

32

where the growth rate per cycle remains constant. Exposure times leading to self-

limiting steady-state surface coverage define the ALD process window.

Early reports of ALD GaN in the literature were focused on achieving exactly one

monolayer (ML) of film per growth cycle [55, 70, 127]. This definition often resulted in

gallium precursor exposure times of 40 sec or longer with no self-limiting behavior.

These gallium precursor exposure times were sometimes an order of magnitude longer

than the corresponding purge times. Khan [55] even went as far as to say that the ALD

process window yielded only 0.75 ML of coverage based on the self-limiting surface

coverage, but then went back and changed the reactor pressure until he was able to

force 1 ML of growth per cycle, most likely leading to incomplete purging and CVD-like

growth. The current consensus in the literature is that the GaN ALD growth rate can be

less than 1 ML per cycle, presumably a result of blocking of potential adsorption sites by

adsorbed reactant. Most commonly growth rates of ~0.75 ML/cycle are observed,

although values as low as 0.29 ML/cycle have been reported [66, 95].

3.2 Experimental Setup and Procedure

Gallium nitride films were grown in a home-made CVD/ALD reactor. Figures 3-1

and 3-2 show a schematic of the reactor setup and a photograph of the reactor tube

filled with nitrogen plasma, respectively. Gallium trichloride (Alfa Aesar 99.999%) and

anhydrous ammonia (Airgas South 99.99%) were used as reactants and N2 (Airgas

South 99.999%) was used as a carrier and purge gas. Solid GaCl3 was loaded into a

custom bubbler, shown in Figure 3-3, in a glove box with O2 and H2O concentrations

less than 1 ppm. The bubbler was heated to 80°C in an oil bath before and during the

run to melt the GaCl3 (Tm = 78°C) at which temperature the vapor pressure of the GaCl3

33

is 13 Torr. Melting the precursor was necessary to ensure uniform GaCl3 flux over most

of the lifetime of the bubbler charge. The total pressure in the bubbler was maintained

at 375 Torr by a downstream throttling valve leading to a GaCl3 mole fraction in the feed

stream of 0.035. N2 carrier gas bubbled through the liquid GaCl3 at 10 sccm controlled

by a mass flow controller (MFC) calibrated for N2. The NH3 flow rate was set to 499

sccm in a second gas line with another N2 MFC. It was necessary to apply a conversion

factor of 0.71 to this controller due to the difference in gas density between N2 and NH3

so the NH3 flow rate was 354 sccm based on the corrected N2 readout. N2 purge gas

flowed at a rate of 499 sccm in a third gas line. All three gas lines led to 3-way (one-in,

two-out) pneumatically actuated valves, which could either send the gas to the reactor

or to bypass lines that led directly to scrubbers and exhaust. The pneumatic valves

were controlled by a LabVIEW program such that each pulse time and the total number

of pulses could be set by a computer program.

Sapphire, Si(100), and Si(111) were use as substrates in this work. Prior to

introduction into the reactor, all substrates (except for nanorods) were cleaned by a

TCE/acetone/methanol routine and Si substrates were also subjected to a buffered

oxide etch to remove thermal oxides. Cleaned substrates were placed on a quartz

sample holder and set on a mechanical loading arm in a load lock chamber, which was

then sequentially purged and refilled with N2 four times. The sample holder was then

loaded into the reactor by the loading arm and placed directly on a graphite susceptor

with an embedded thermocouple. The susceptor was heated by a Lepel T-7.5-3-KC-

SW, 230 Volt, 42 Amp RF generator and the temperature was monitored by the

thermocouple and manually adjusted.

34

Runs of 150 cycles were conducted at susceptor temperature of 600ºC with

varying pulse times. Nitrogen purge times were set at 30 sec, which is considerably

longer than the residence time of 8 sec that was estimated based on the reactor volume

and N2 flow rate. Purge times by definition must be at least as long as reactor

residence times, but are often longer, for example to account for dead zones or finite

desorption rates. Growth rates were investigated while NH3 exposure times were varied

from 5 to 30 sec and GaCl3 exposure times were varied from 0.5 to 40 sec.

After completion of the reaction, the RF generator power was slowly lowered to

cool the reactor at a rate of about 2 °C per min with NH3 flowing over the substrates

until the temperature fell below 500°C. The bubbler was removed from the oil bath and

allowed to cool with nitrogen flowing while source gasses were routed to the bypass

lines until the GaCl3 solidified. The bubbler outlet was then closed and the bubbler

pressure was raised to ~5 psig where it remained between runs. Over-pressurizing the

bubbler, in addition to minimizing oxygen diffusion into the bubbler, caused a spike on

the pressure gauge when the bubbler outlet was reopened for the next run, which

served as an indicator that the bubbler outlet was clog-free and leak-minimized. This

helped to reduce further clogging or entrainment of liquid GaCl3 upon opening the

bubbler inlet. The samples were removed from the reactor once the temperature

reached 100°C. N2 continued to flow through the reactor for several hours to remove

residual GaCl3 and HCl. Once samples were removed from the reactor, a program was

run to switch the pneumatically actuated valves open and closed every few sec to

loosen up any condensed GaCl3 and extend the lifetime of the valves. Heat tapes were

35

set at 5% power at all times whether the reactor was in use or not, and N2 flow of 20

sccm was passed through all gas lines when the reactor was not in use.

3.3 Experimental Results

GaN films were grown on Si (100) and Si(111) for 150 cycles of pulsed

deposition at 600 °C and ~14 Torr with NH3 exposure times of 10 sec and N2 purges of

30 sec showed a plateau in growth rate per cycle over the range 2 to 8 sec of GaCl3

exposure as shown in Figure 3-4. GaCl3 exposure times greater than 8 sec showed

increasing growth rates per cycle and considerable thickness variations from non-

uniform temperature and mass transfer, and thus not showing self-limiting adsorption

characteristic of ALD. NH3 pulses of greater than 15 sec also showed CVD-like growth

accompanied by much higher growth rates. The films produced within the ALD process

window showed expected uniformity across each substrate. The error bars of the

thickness measurements within the ALD process window in Figure 3-4 are limited to

±0.5 nm, which is the resolution of the instrument, while the error bars for films grown

with longer exposure times were mainly due to variations in thickness between samples.

This is evidence of good thickness uniformity within the ALD process window.

The plateau in growth rate per cycle was achieved at a thickness of 2.5 +/- 0.5Å

per cycle, which is consistent with half of the c lattice parameter of GaN, 5.18Å. Since

there are exactly two atomic layers of GaN in the c-direction of one unit cell (see Figure

4-9 for reference), this thickness equates to exactly one atomic layer per growth cycle.

Previous studies have often found less than one monolayer of coverage per ALD cycle

[66, 95].

36

The fact that the ALD growth window is achieved at the very low exposure time

of 2 sec is attributed to the difficulty of seeding the initial layer of GaN on Si. A relatively

high GaN flux was required to seed this first layer which subsequently led to

overexposure and the need for long purge times once the film had seeded and GaN on

GaN growth occurred. The total GaCl3 vapor pressure in the feed was 13 Torr at a flow

rate of 10 sccm. The flux of atoms impinging on a surface is proportional to the

pressure and exposure time A flux of 1 Langmuir (L) corresponds to flux that occurs

at10-6 Torr of pressure over one sec. One L yields about one monolayer of coverage

with unity sticking coefficient. By this measure of exposure, 108 L was dosed onto the

surface for each ALD cycle. While delicate high-vacuum measurements would be

necessary to accurately determine the sticking coefficient of Ga, it is likely that the

sticking coefficient is very low for Ga on Si, possibly on the order to 1/108, but is

probably much higher for GaN on GaN growth.

Figure 3-5 shows the process temperature window for ALD GaN grown on

Si(100) and Si(111) in this reactor [65]. Growth rates increase with temperature below

500 ºC but remain at 1 ML per cycle for temperatures ranging from 500ºC up to 750ºC

for GaCl3 exposure times of 7 sec and NH3 exposure times of 10 sec.

3.4 Sample Characterization

3.4.1 Thickness Measurements

Several methods were investigated to determine film thickness. Since the films

were so thin (<50nm), methods such as cross-sectional SEM provided inconclusive and

unreliable measurements. X-Ray Reflectometry (XRR) was successful in measuring

very thin films, down to 8 nm as shown in Figure 3-6. However, XRR requires an

37

extensive alignment procedure which makes the technique time-consuming and

therefore unsuitable for high-throughput characterization.

Ellipsometry is an ideal technique for measuring film thicknesses with a

resolution of ±0.5 nm. A J. A. Woolam white light ellipsometer was used to measure

film thickness with considerable speed and accuracy. The ellipsometer scanned the

sample with 88 different wavelengths of polarized light and measured amplitude ratio

and phase difference (more commonly translated to s-plane and p-plane polarization) of

the reflected beam. A model was then constructed of a stack of materials with known

refractive index. The thickness of selected layers was then iterated to obtain the best fit

to the experimental data. Complex indices of refraction were also be optimized by the

software after the thicknesses were determined. The end result yields a thickness

measurement in good agreement with XRR data and also in agreement with the visible

color of the film (thickness of film = 2*index of refraction*wavelength of observed color

of film). Figure 3-7 shows an example of experimental ellipsometric spectral data along

with data obtained for the model with the best fit for Run 285. The thickness of this

sample was determined to be 995Å. The main source of error in these measurements

was that the refractive indices of the thin films were not known and were assumed to be

the bulk literature values for chemically pure GaN.

3.4.2 Film Surface Morphology over the ALD Process Window

This study began with the hypothesis that the growth-mode of GaN grown on a

sapphire substrate should be 2-D for ALD and 3-D for HVPE or MOCVD. It was

assumed that the surface morphology of 2-D GaN films (grown by ALD) should show

less roughness than 3-D GaN films (grown by CVD). This suggests that surface

morphology measurements might be used to find the ALD process window.

38

Atomic force microscopy (AFM) was used to assess the surface morphology of

ALD and “near-ALD” GaN films produced in this study. Although the use of AFM as a

primary means of identifying the ALD process window has not been reported in the

literature, it has been used to characterize other changes in ALD growth mode. Aarik

and Rammula have studied the surface morphology of HfO2, Ru, and TiO2 grown by

ALD [1, 72, 108, 113]. For all three of these material systems ALD growth rates are

NOT constant with number of cycles. In other words, at some critical thickness, the

growth rate per cycle changes. This phenomenon has been attributed to the change

from amorphous to crystalline phases or, alternatively, a change from one crystalline

phase to another at some film thickness. Aarik [1] states:

ALD-type layer-by-layer growth proceeds with a constant thickness increment per deposition cycle, if the adsorption capability of the thin film surface does not change in the deposition process. In a real process, however, deviations from this requirement may appear. In case of non-epitaxial growth of polycrystalline films, for instance, the surface roughness usually increases with the film thickness. In addition, the relative amounts of crystalline phases as well as the preferential orientations of crystallites may depend on the film thickness. Therefore, the adsorption capacity of the film surface and the growth rate do not have to stay constant in the ALD process even if the adsorption of precursors is completely self-limited.

Furthermore, Paivasaari has reported that surface roughness of CeO2 films

increases when the temperature is raised above the ALD process window [96]. Kukli

[72], Li [76], Rammula [108], Aarik [1], and Paivasaari [96] all report amorphous films

with RMS roughness similar to the underlying substrate.

A Dimension 3100 Scanning Probe Microscope (SPM) was used to investigate

the surface roughness of GaN films grown with varying GaCl3 exposure times. ALD

GaN films grown on sapphire were rougher than the underlying sapphire substrate due

to the large grain size of the largely epitaxial films. Figure 3-8 shows an SPM image of

39

the rough surface of an ALD GaN/sapphire film. Films grown on silicon, however, were

polycrystalline with very small grain sizes. Many films from the ALD process window

grown on silicon (100) were extremely smooth, with RMS roughness around 0.5 nm (in

comparison with the RMS roughness of silicon of 0.2 nm). Figure 3-9 shows the

surface roughness of ALD GaN/Si(100) films for different GaCl3 exposure times. Each

data point represents an average over several different films or different areas on the

same film. It is clear from Figure 3-9 that GaN surface roughness increases for very

long GaCl3 exposure times. However, the boundary between the ALD process window

and the slightly overexposed region is not very distinct. In fact, Figure 3-12 shows

several examples of SPM images from different GaN/Si(100) films where the growth

mode changes on a single film. Figures 3-10a and 3-10c show 2D and 3D growth

modes, respectively, for different regions of the same film and Figure 3-10b shows a

region where there is a transition from one growth mode to the other. This film was

grown with a GaCl3 exposure time of 8 sec, inside of the ALD process window.

Similarly, Figures 3-10d and 3-10e show a 2D growth mode and a transition from 2D to

3D growth mode for a film outside of the ALD process window with a 16 sec GaCl3

exposure time. Figure 3-10e shows 3D growth mode for a highly overexposed (24 sec

GaCl3 exposure time) film. It is clear that films grow in 2D and 3D modes both inside

the ALD process window and just outside of it. Therefore based on these results one

must conclude that AFM alone will not be able to define the ALD process window. On

the other hand, it is still possible that a higher quality ALD growth tool could produce

films that grow in a 2D growth mode inside of the ALD process window and a 3D growth

mode outside of the process window. This is worth investigating in future work.

40

3.4.3 Structural Composition of ALD Films

Grazing Incident X-Ray Diffraction (GIXD) was performed on ALD GaN samples

since these samples were too thin to measure with bulk x-ray techniques. The

penetration depth of x-rays in common semiconductors is ~5 µ. Since ALD films were

as thin as 4 nm, bulk techniques such as powder x-ray diffraction (XRD) would not have

been sensitive enough to measure the structural properties of the GaN. X-rays at a low

incidence angle to the film travel a longer distance in the film material and consequently

are much more sensitive to the structural properties of the film. If the incidence angle is

chosen correctly, an evanescent wave can be formed on the surface of the film by the x-

rays and 4x increase in x-ray counts can be achieved.

Figure 3-11 compares GIXD diffraction patterns of ALD GaN on both

sapphire(0001) and Si(100) substrates. All low index peaks are present in both spectra.

This indicates that both films contain GaN and exhibit some degree of polycrystallinity.

No unidentified XRD peaks were observed. Two peaks stand out from the others: the

(0002) peak on the Si substrate and the (1013) peak on the sapphire substrate. These

peaks are enlarged for very different reasons. For GaN/Si(100), grains are very small

and randomly oriented on the silicon substrate. Because (1) they elongate in the (0002)

direction, and (2) the (0002) direction has a large structure factor, an intensified (0002)

peak is observed. On the other hand, for GaN grown on sapphire there tends to be

large epitaxial domains (although polycrystalline domains are clearly present as well as

demonstrated by all the low-index peaks being visible). These epitaxial grains are

generally not detected by the directional probing of the GIXD scan because when the d-

spacing of a particular plane is being probed by GIXD, chances are the detector is not

41

at the appropriate angle to receive the signal. However, since the crystal is growing in

the <0002> direction, the (1013) plane meets the (0002) plane at 32°, and the d-

spacing of the (1013) plane just happens to be measured at a 2θ value of 64° (θ=32°),

the peak is very visible by GIXD. Hence there is an epitaxial nature to the ALD GaN

grown on sapphire.

42

Figure 3-1. Schematic of GaN ALD reactor.

Thermocouple

Oil bath N2

cylinder

P

P

P

N2

cylinder

NH3

cylinder

MFC 20

SCCM

MFC 500

SCCM

MFC 50

SCCM

MFC 500

SCCM

GaCl3/N2

NH3

Load-Lock

Chamber

Mechanical

Loading Arm

Pneumatically actuated 3-

way valves

N2 purge

Concentric

inlet tubes

Reactor body / RF Coils /

Graphite Susceptor

Solid

Scrubber HCl

Scrubber

To building

exhaust

Gate valve

GaCl3 bubbler P

Bypass Lines

43

Figure 3-2. Photograph of clean reactor chamber with nitrogen plasma inside. Photo courtesy of author.

44

Figure 3-3. Photograph of home-made bubbler system. Photo courtesy of author.

45

Figure 3-4. ALD Process Window for GaN grown on Si(100) with GaCl3 and NH3 at 600 °C.

1 ML

46

Figure 3-5. ALD Process temperature window for GaN/Si(100) grown with 8 sec GaCl3 pulse and 10 sec NH3 pulse [reprinted by permission from Kim, Oh Hyun. 2009. ALD of GaN and TaN (Page 73, Figure 4-2). University of Florida].

47

Figure 3-6. Sample XRR spectrum of run 239 GaN/Sapphire. 2θm-2θm+1 = .13° = .002269 radians. Thickness = 679 Å.

48

Experimental Data

Wavelength (nm)

200 300 400 500 600 700 800

in d

egre

es

in

degre

es

0

10

20

30

40

0

30

60

90

120

150

180

Model Fit Exp -E 75°Model Fit Exp -E 75°

Figure 3-7. Experimental ellipsometric data (dashed lines) and model data (solid lines) with both GaN film thickness and GaN complex index of refraction fit to minimize difference between model and experimental data for run 285 ALD GaN on Si(100), thickness t=997Å.

49

400nm

Figure 3-8. SPM image of surface height information for ALD GaN/sapphire with a 4

sec GaCl3 exposure time. RMS Roughness = 11.7369 nm. RMS Roughness of Sapphire substrate =0.3 nm. A) Top view. B) 3-D view.

A) B)

50

Figure 3-9. ALD GaN/Si(100) surface roughness vs. GaCl3 exposure time.

51

Figure 3-10. SPM images of ALD GaN/Si(100). A) 8 sec exposure time with 2D growth

mode. B) 8 sec exposure time with changing growth mode. C) 8 sec exposure time with 3D growth mode. D) 16 sec exposure time 2D with growth mode. E) 16 sec exposure time with changing growth mode. F) 24 sec exposure time with 3D growth mode.

GaCl3 pulse = 24s Rq=3.6673

GaCl3 pulse = 8s Rq=0.5105

GaCl3 pulse = 16s Rq=4.1969

GaCl3 pulse = 16s Rq=0.3793

GaCl3 pulse = 8s Rq=0.8637

GaCl3 pulse = 8s Rq=2.3901

A) B) C)

D) E) F)

52

Figure 3-11. GIXD Spectra of ALD GaN on both sapphire(0001) and Si(100) substrates.

53

CHAPTER 4 ATOMIC LAYER DEPOSITION OF GaN ON InN NANORODS

4.1 Preliminary Remarks

Group III-nitride materials are important for optical electronic devices since their

bandgap energy can be varied over the entire visible spectrum. Modern white LEDs

typically utilize a stack of III-N materials grown upon a sapphire substrate to form a p-i-n

junction and waveguide structure. This conventional device structure suffers from high

cost and low brightness. The high cost is due, in large part, inefficient use of the

available emission area. Since sapphire is an insulator, both the p- and n-type contacts

must be made to the top of the device, hence a significant portion of the device

structure is often etched to expose the underlying n-type material. Also, sapphire has

no convenient cleavage planes, so large portions of the wafer are wasted in dicing.

Furthermore the significant lattice mismatch between GaN and sapphire produces wafer

bowing to limit the maximum wafer size is to 2”. The nanostructured III-N device

described in this thesis avoids these problems: (1) the nanorods can be grown on Si,

allowing for backside contacts and efficient device processing. (2) The nanostructured

device has a tenfold increase in area for recombination allowing for increased

brightness. (3) The nanostructured device allows better photon extraction allowing for

increased efficiency. N-type InxGa1-xN nanorods are grown by a catalyst-free MO-HVPE

method on a LT-GaN buffer/Si substrate. The proposed p-i-n structure would then be

fabricated by depositing an InyGa1-yN active region and a Mg-doped InxGa1-xN p-type

region (y>x) on the six equivalent {1100} side faces of the hexagonal nanorods. Since

precise thickness control and uniform coverage of the high-aspect-ratio nanorods is

54

required, atomic layer deposition (ALD) is the proposed method to grow the device

structure.

ALD has commonly been used to coat high-aspect ratio features such as

trenches and nanorods. Nanorod core/shell structures have been produced by ALD

with amorphous shells made of TiO2 [2, 36, 73, 75, 93, 124], ZnO [13, 37, 45-47, 50,

52, 60, 61, 97, 103, 104, 124], ZnMeTe [29], Al2O3 [43, 124], SnO2 [44, 47, 58], SnO2

[44, 47, 58], HfO2 [84], and NiO [74]. A few groups have even demonstrated single

crystal coatings on nanorods (NR) by ALD including ZnO/Si-NR [50], MgO2/SnO-NR

[58], and TiO2/SnO2-NR [75]. Li et al. have reported that amorphous coatings of TiO2

on square SnO2 nanorods show uniform conformal coverage, but single crystal coatings

form octagonal coatings of TiO2 on the square SnO2 nanorods [75]. These studies

demonstrate that fabrication of epitaxial core/shell structures by ALD is possible,

although sometimes the coatings formed by crystalline shells are less conformal that

their amorphous counterparts.

No reports have been found in the literature of growth of III-N on NRs or of ALD

of any material on III-N nanorods. Core/shell III-N nanostructures have, however, been

fabricated where the shell material has been coated by methods other than by ALD.

GaN nanorod p-n homojunctions have been fabricated by HVPE overgrowth of GaN:Mg

shells on GaN nanorods [71, 114], and by changing reaction temperature and precursor

flows mid-reaction during nanorod growth catalyzed by nickel nanoclusters [80].

Additionally, Cui et al. [19] reported MBE growth of InGaN shells on InN nanorods.

These structures showed superior crystal quality as only a single set of diffraction spots

was observed by selected area electron diffraction (SAED). Also, Wierner et al. [128]

55

were able to grow multi-quantum well (MQW) InGaN photovoltaic (PV) devices by

MOCVD overgrowth that included a canopy layer connecting the p-type top region of

the nanorods allowing for standard device contacting schemes. Finally, MOCVD growth

of heterostructures by a VLS mechanism with reactant and growth temperature changes

mid-reaction has produced a nanorod LED with an AlGaN cladding layer and an InGaN

active region [106], a nanorod LED with a MQW InGaN [28, 106], a MQW laser [107],

and a MQW nanorod PV device [21].

III-N core/shell heterostrutures have been fabricated with epitaxial junctions by

MOCVD, and III-N heterostructure devices have been demonstrated. Other material

systems have shown that epitaxial nanorod shells can be deposited by ALD. This work

focuses on the fabrication of epitaxial GaN/InN core shell structures by ALD of GaN on

InN nanorods.

4.2 Experimental Setup and Procedure

Single-crystalline, hexagonal, InN nanorods were grown by HVPE as descried

elsewhere [14], and loaded into a separate, custom, RF-heated reactor for GaN growth.

The ALD process described in Section 3.1 was employed. One ALD process cycle

consisted of an 8 sec pulse of GaCl3/nitrogen with a GaCl3 mole fraction of 0.1 at 10

sccm, a 30 sec nitrogen pulse at 499 sccm, a 10 sec NH3 pulse at 499 sccm, and

another 30 sec nitrogen pulse at 499 sccm. During a pulse of any particular gas, the

other gasses were pneumatically switched to the bypass line. ALD reactions were

carried out on the nanorod substrates for durations of 40, 80, and 120 cycles at

temperatures of 565, 580 and 595 °C. These InN/GaN core/shell heterostructures were

56

compared to HVPE GaN/InN nanorod shell/core structures grown previously at 600°C

for 10 min [14].

4.3 Experimental Results

Nanorod heterostructures were characterized by both regular and high resolution

(HR) transmission electron microscopy (TEM), selected-area electron diffraction

(SAED), and energy dispersive X-ray microanalysis (EDS) to determine the core and

shell composition and crystallographic orientation. Figure 4-1 compares (a) a 10 min

HVPE GaN shell on an InN nanorod, (b) a 120 cycle ALD GaN shell on an InN nanorod,

and (c), an as-grown InN nanorod with no shell deposition. Figure 4-1d shows a SAED

pattern for the as-grown InN nanorod in Figure 4-1c. The pattern represents the

reciprocal lattice of the <1010> direction of InN. The reciprocal lattice directions, d-

spacing, and indexed planes are shown. It is clear from Figure 4-1 that the ALD

approach results in a smoother conformal coating than CVD. Figure 4-2 shows the tips

of the HVPE and ALD coated nanorods from Figure 4-1. Again it is clear that ALD

produces a smoother shell. On first inspection, it appears that the faceted (1011) tips of

the nanorod grew at a faster rate than the (1010) sidewalls. However, upon closer

inspection, an interface between the original InN nanorod and a GaN shell of uniform

thickness can be seen surrounding the entire tip. The appearance of a thicker shell on

the (1011) facets is attributed to a combination of electron transparency of the InN in

thinner regions and the decomposition of the InN nanorod at GaN growth temperatures,

which will be discussed in-depth in Section 4.4. Figure 4-3 shows an EDS mapping of a

single core/shell nanorod heterostructure lying on its side looking down in the <1010>

direction. It shows a Ga rich shell surrounding an In rich core. The composition map

shown in Figure 4-3 along with SAED data offer compelling evidence of GaN shells

57

grown on InN nanorods. It should be noted that this is not a cross-sectional mapping of

the nanorod, so the Ga signal is from the shell wrapping around the nanorod and not

from Ga diffusing into the InN core.

Figure 4-4 shows a set of TEM images that illustrate variations with the number

of ALD cycles and growth temperature on the ALD GaN coating of InN nanorods.

Core/shell heterostructures produced by 40, 80, and 120 cycles of ALD coverage are

grown at 565 and 595 °C. At 565 °C the GaN shells begin as polycrystalline “fuzzy-

looking” shells and remain polycrystalline for any growth duration. At 595° C the ALD

GaN shells appear to seed in a fashion similar to the growth at 565 °C. This is

attributed to the significant lattice mismatch between GaN and InN. However, as growth

proceeds the shell becomes markedly smoother and more uniform in thickness. The

initial domains behave as a buffer region that allows for subsequent crystalline GaN

growth. Figure 4-5 shows HR-TEM images and accompanying SAED patterns of

heterostructures with shells grown for 120 cycles of ALD growth at three different

growth temperatures. At 565 °C no crystal structure can be seen in the HR-TEM image.

In fact, the shell is so randomly oriented that it obscures the view of the extremely

crystalline InN nanorod below it. The SAED pattern for the 120 cycle growth at 565°C

shows an inner set of sharp spots, corresponding to the reciprocal lattice of the <1010>

direction of the InN lattice. An outer ring is also observed, corresponding to a

polycrystalline GaN shell. Since the spacing in the SAED reciprocal lattice pattern is

inversely proportional to the lattice parameter, the larger InN a- and c-parameters (3.53

and 5.70 Å, respectively), form a set of spots with a slightly smaller spacing than the

rings attributed to the polycrystalline GaN (GaN a- and c- parameters are 3.18 and 5.18

58

Å, respectively). While the ring pattern is brighter near the spots of the InN, indicating

there is some preference for the GaN to align with the underlying InN, the evidence

overall points to a randomly aligned, polycrystalline GaN shell at 565 °C. At 580 °C the

HR-TEM image shows a shell that is considerably more crystalline and now the crystal

structure of the underlying InN nanorod can clearly be seen. The SAED pattern still

shows a set of spots from the InN core but the GaN shell is now more aligned than at

565 °C. The SAED contribution from the GaN shell shows an arc near the positions of

the InN spots, indicating preferential alignment with the InN core but still some

polycrystalline nature. At 595 °C, however, the SAED pattern shows a distinct set of

double dots indicating good crystal quality for both InN core and GaN shell, as well as

excellent crystallographic alignment between the two materials. If a pseudomorphic

relationship existed between the GaN and InN domains only one set of diffraction spots

would be visible. In this case the GaN and InN domains would have relatively few

defects at their interface and would cause stress on one another. The smaller GaN unit

cell would be under tensile stress while the larger InN unit cell would be under

compressive stress and a single lattice constant would be shared between the two

strained materials at the interface. The double spots indicate that while the crystalline

quality and alignment of the core and shell materials are excellent, no pseudomorphic

relationship exists. The two materials form separate crystalline domains.

Figure 4-6 shows the evolution of the SAED patterns with number of cycles at

both 565 and 595 °C. For 40 cycles of growth only the [1010] reciprocal lattice of the

InN core is visible at both temperatures. While it is possible that this could indicate a

pseudomorphic interface, it is also possible that there is just not enough GaN material to

59

cause significant diffraction. For 80 cycles of growth the ring pattern at 565 °C is still

difficult to see, but is beginning to emerge. For 80 cycles of growth at 595 °C still only

the InN SAED pattern is visible. For 120 cycles the full ring pattern is visible at 565 °C

and a double pattern at 595° C has evolved. This indicates a crystalline, well-aligned

shell for 120 cycles of growth at 595 °C and a polycrystalline shell for 120 cycles of

growth at 565 °C.

4.4 Discussion of Experimental Results

ALD GaN growth on the sidewalls of InN nanorods should not be expected to

proceed at the same rate as ALD GaN grown on a planar Si substrate. The growth rate

of half of a c-lattice parameter determined from Figure 3-4 does not apply because the

GaN is growing in the <1010> direction instead of the <0001> direction. As shown in

Figures 4-5 and 4-6 the GaN grown at 595 °C is crystallographically aligned with the InN

nanorod, meaning that one a-lattice parameter per cycle, or 3.18 Å, should be expected

(A GaN unit cell is depicted in Figure 4-9a for reference).

To determine the growth rate of ALD GaN on InN nanorods, growths of 5, 10, 15,

and 20 cycles were performed using the ALD process conditions described in Section 4-

2 at 595 °C. Figure 4-7 shows these heterostructures imaged with a JEOL 200CX TEM

as well as digitally enlarged sections of the images to determine shell thickness. Figure

4-8 shows a plot of shell thickness as a function of number of ALD growth cycles. The

slope is measure as 5.6 Å/cycle. This is considerably more than the 3.18 Å in the GaN

unit cell. Due to the geometry of the nanorod structure, as depicted in Figure 4-9b, the

thickness measurement is artificially enlarged due to the fact the the TEM is viewing the

thickness of the shell right at a <1120> point of the hexagonal nanorod instead of at a

60

flat (1010) face. A geometric correction for this yields a growth rate of 4.8 Å/cycle. This

is still larger than expected. This discrepency is attributed to the decomposition of InN

at GaN growth temperatures.

It is well known that the InN nanorod cores will begin to decompose at the growth

temperatures of the GaN shells [14]. Figure 4-10 shows the “wavy” nature of the

GaN/InN interface due to InN decomposition. This leads to an overestimate of the GaN

shell hickness. This phenomenon is also responsible for the decomosition of the tip of

the InN nanrod in Figure 4-2b. Due to the geometry of the tip the decomposition is

accelerated. Figure 4-11 shows several previously encountered examples of InN

decomposing at GaN growth temperatures from both this work and previous work [14].

Figure 4-11a and b show a GaN shell grown on an InN nanorod at 600 °C before and

after condensing the TEM beam on the structure. The InN on the interior had

decomposed completely during the GaN growth and, when charged by the electron

beam, was ejected from the broken end of the shell structure. Figure 4-11c shows an

SAED pattern from an 80 cycle ALD GaN growth at 620 °C. The pattern shows a set of

double rings, indicating both the GaN and the InN had no long range crystal structure.

The decompositionof the InN at GaN growth temperatures plays a large role in

the growth of the heterostructures. If lattice strain alone were not enough to cause a

poor interface between the GaN and the InN core, the fact the InN is thermally unstable

during GaN growth is certainly enough to prevent a [seudomorphic relationship between

the two materials. The perfect crystallographic alignment between the two materials

indicates that the GaN seeded epitaxially on the InN nanorod. It is even possible that

the diffraction patterns from the 40 and 80 cycle growths in Figure 4-6 show a

61

pseudomorphic relationship between the two materials and only after some critical shell

thickness dislocations will begin to form. Photoluminesence or Raman spectroscopy

could be used to measure strain in the materials to determine if the two domains are

applying stress to one another. Analytical models could also be used to determine

critical dimsions for coherently strained heterostructures as will be discussed in Chapter

5. Either way, the decomposition of InN nanorods at GaN growth temperatures is a

major concern for InN/GaN core/shell nanorod device fabrication.

62

Figure 4-1. TEM images of GaN coated and bare InN nanorods and SAED pattern of bare single crystal InN nanorod: a) TEM image of 10 min HVPE GaN on InN nanorod at 600°C, V/III=570 and Cl/III=2, b) TEM image of 120 cycle ALD GaN on InN nanorod at 595°, 1 cycle consists of 8 sec GaCl3 exposure, 30 sec purge, 10 sec NH3 exposure, 30 sec purge, c) SEM image of InN nanorods as-grown, with no coating, and d) SAED pattern showing (1010) reciprocal lattice of as-grown InN nanorod as in Figure 4-1c. [Fig 4-1d) reprinted by permission from Chaudhary, Vaibhav. 2012. Growth of Indium Nitride and Gallium Nitride on Silicon Using Metal Organic Hydride Vapor Phase Epitaxy (Page 86, Figure 2-17). University of Florida].

50 nm

b) a)

c) d)

63

Figure 4-2. Comparison of HVPE and ALD coated nanorods: a) TEM image of 10 min

HVPE GaN on InN nanorod at 600°C, V/III=570 Cl/III=2, and b) TEM image of 120 cycle ALD GaN on InN nanorod at 595°C, 1 cycle consists of 8 sec GaCl3 exposure, 30 sec purge, 10 sec NH3 exposure, 30 sec purge. ALD shell is clearly more uniform and conformal. Tip of InN nanorod in Figure 4-2b is either electron transparent due to its thickness or partially decomposed, but boundary between GaN and InN materials can clearly be distinguished.

a) b)

GaN

Electron-transparent /Decomposed InN

64

Figure 4-3. EDS scan from JEOL 2010F HR-TEM. Image shows single core/shell nanorod lying on its side looking through the <1010> direction. A Gallium rich shell coats an Indium rich core.

In

Ga

Ga

65

Figure 4-4. Growth map of ALD GaN on InN nanorods grown for durations of 40, 80, and 120 cycles at temperatures of 565 and 595 °C. At 565 °C shells are always amorphous, but at 595 °C shells seed in crystalline domains which become increasingly smooth and conformal with increasing thickness.

40 Cycles 80 Cycles 120 Cycles

59

5 °

C

56

5 °

C

66

Figure 4-5. HR-TEM and SAED for 120 cycle ALD GaN grown on InN nanorod at 565, 580, and 595 °C. At 565 °C shells are amorphous and obscure crystalline alignment of InN nanorod. SAED pattern for this sample shows dot pattern from InN reciprocal lattice, but a ring pattern for the GaN SAED pattern, indicating amorphous growth. With increasing temperature HR-TEM shows more crystalline GaN and SAED patterns show ring evolving into a sec set of dots aligned with the InN reciprocal lattice

12

0 C

ycle

s, 59

5 °

C

12

0 C

ycle

s, 580 °

C

12

0 C

ycle

s, 56

5 °

C

67

Figure 4-6. SAED patterns of InN nanorod core/ALD GaN shell heterostructures for: 40, 80, and 120 cycles of ALD growth at 565 and 595 °C.

40 Cycles 80 Cycles 120 Cycles

59

5 °

C

56

5 °

C

68

Figure 4-7. TEM images of 5, 10, 15, and 20 cycle ALD GaN on InN nanorods grown at 595 °C, and digital zooms of portions of the TEM images to measure shell thickness (lower scale bar refers to zoomed images).

5 Cycle 10 Cycle 15 Cycle 20 Cycle

69

Figure 4-8. Shell thickness as a function of number of ALD cycles for ALD GaN grown on InN nanorods at 595°C as measured from Figure 4-7. Slope indicates growth rate per cycle on <1120> point of hexagon.

GaN Shell Thickness vs. Number of ALD Cycles

Slope=0.56 nm/cycle

70

Figure 4-9. Nanorod orientation during TEM imaging. a) GaN unit cell with lattice

parameters. b) Visualization of nanorod lying on its side, actual shell thickness = (thickness measured)*cos(30).

a=3.19Å

c=5.19Å

<1010>

<1120>

<0001>

a) b)

71

Figure 4-10. HR-TEM image of ALD GaN/InN nanorod interface for 120 cycle ALD at 595°C. Wavy nature of interface is due to decomposition of InN nanorod at GaN growth temperatures.

72

Figure 4-11. Examples of InN nanorod decomposition at high temperatures. a), b): GaN shell with partially decomposed InN/In(l) core before and after condensing TEM beam on the heterostructure. Beam caused charging and consequent ejection of In liquid from core region. c) SAED of 80 cycle ALD GaN shell/InN core grown at 620°C. Double ring pattern indicates that both GaN and InN are randomly oriented. . [Fig 4-11a) and b) reprinted by permission from Chaudhary, Vaibhav. 2012. Growth of Indium Nitride and Gallium Nitride on Silicon Using Metal Organic Hydride Vapor Phase Epitaxy (Page 166, Figure 4-11). University of Florida.

a) b)

c)

73

CHAPTER 5 CORE/SHELL NANOROD HETEROSTRUCTURE STRAIN MODELS

5.1 Hooke’s Law

Built-in stress and strain fields are inherent in semiconductor heterostructures.

At the bonding interface between two different materials of the same structure, the

material with the smaller lattice constant is under tensile stress (i.e. the equilibrium

lattice parameter is larger than the bulk value), while the material with the larger native

lattice constant is under compressive stress (i.e. the equilibrium lattice constant is

smaller than its bulk value). A finite amount of stress can be accommodated by

semiconductor heterostructures, but if the built-in stress exceeds a critical level,

extended defects will form to reduce the stress to below the critical value. Stress and

strain models of planar semiconductor heterostructures are fairly well developed.

Models such as the Matthews model have proven to accurately predict critical film

thicknesses in planar systems [81].

This work focuses on using InN nanorods as a platform for a heterostructured

device. Nanostructured devices have the advantage of being able to accommodate

stresses in all 3 directions as opposed to planar devices that can only relax in the

direction orthogonal to the hetero-interface (i.e. the growth direction). For this reason

nanostructures can exhibit dislocation-free materials systems that are not possible for

planar structures. Several methods have been developed to model stresses in

nanostructured systems [25, 77, 83, 109, 110, 122]. This work begins by extending the

work of Raychaudhuri [110] to predict the critical thickness of GaN shells grown on InN

74

nanorods. This is done by equating the energetic cost of forming a dislocation with the

energetic gains of relaxing a corresponding portion of the strain in the system [110].

The stress on a body is defined as the force per unit area on the surface of the

body [94]. Stresses can act either orthogonally to the surface (normal stresses) or

tangentially to the surface (shear stresses). Stresses can be uniform throughout the

body (homogeneous stress) or varying throughout the body (inhomogeneous stress).

Bodies at equilibrium are generally considered to be under homogeneous stress [94].

Stress is expressed in units of pressure; a force per unit area. The normal and shear

stresses acting on a body are combined to form a second-rank tensor known as the

stress tensor.

The measure of the deformation of a material resulting from applied stresses is

called the strain. The strain of a material is a dimensionless quantity and all the strains

taken in all directions combined also form a second-rank tensor. According to Hooke’s

law, the strain can be related to the stress applied on a material through a fourth-rank

tensor called the elasticity tensor:

3

1

3

1k l klijklij c (5-1)

where {i, j = 1,2,3}, σij are the stress tensor components, εkl are the strain tensor

components and cijkl are the elements of the elasticity tensor. Since the cijkl tensor

relates two second-rank tensors, it has 34=81 components. Due to the symmetry of both

the stress tensor (σij= σji) and strain tensor (εij = εji), only 36 independent components

remain to completely describe the elasticity tensor. Thus, the relationship between

stress and strain in matrix form is given by:

75

12

31

23

33

22

11

666564636261

565554535251

464544434241

363534333231

262524232221

161514131211

12

31

23

33

22

11

2

2

2

cccccc

cccccc

cccccc

cccccc

cccccc

cccccc

. (5-2)

This is known as the Voigt notation and is most commonly how Hooke’s Law is

expressed in material elasticity problems.

It should be noted that Hooke’s law approximates matter as a continuum rather

than as a discreet collection of atoms, and it assumes linear elasticity. Thus application

of Hooke’s law to the core and shell semiconductor materials implies that these

materials can be treated as a continuum and that the strain at any position in either

material can be expressed as a linear combination of the stresses on the material.

Further simplifications can be made based on the symmetry of the material. Since the

nanorods in this study grow in a hexagonal crystal structure, they can be assumed to be

transversely isotropic. This assumption yields the following simplified elasticity matrix:

12

31

23

33

22

11

1211

44

44

333231

232221

131211

12

31

23

33

22

11

2

2

2

2

100000

00000

00000

000

000

000

cc

c

c

ccc

ccc

ccc

. (5-3)

Furthermore, if a material shows rotational invariance about an axis for an angle

of 2π/n, where n≥5, then it can be shown to be invariant for all the angles about that

axis [123]. This implies that transversely isotropic materials like InN and GaN have

equivalent properties along any direction in the hexagonal basal plane. Thus, these

76

materials can be modeled as cylinders as opposed to hexagonal columns, which

considerably simplifies the analysis. This Hooke’s Law approach is common to most

stress and strain models. To further develop a specific model, boundary conditions and

continuity relations must be determined.

5.2 Analytical Model 1: Extension of Matthew’s Model to a Cylindrical System

5.2.1 Basic Model

The geometry of the nanorod system under consideration is shown in Figure 5-

1a. The system consists of an InN nanorod core with a wurtzite structure and the

<0001> direction along the axis of the nanorod. The nanorod is modeled as a smooth,

facetless cylinder for mathematical simplicity, although in reality the nanorods are

hexagonal. A GaN shell is grown around the InN core, which is also assumed

cylindrical. The core has radius R1, the total core/shell structure has radius R2 with shell

thickness h, and the concentric cylinder has length L. Cross-sectional and longitudinal

strain fields develop due respectively to mismatches in the a and c lattice parameters

between core and shell materials [110].

The objective of this simulation is to determine the critical dimensions at which it

is energetically favorable to insert a dislocation into either region of the semiconductor

heterostructure. In the case of planar structures, the thick substrate is often assumed to

be rigid and all of the strain is accommodated in the film. In the nanostructured case,

however, the volumes of both the core and shell regions are small so the strain energy

in each material can be similar and both regions can accommodate strain. This gives

rise to the concept of critical dimensions: combinations of core radius and shell

thickness that identify the stability limit, i.e. the point at which dislocations will form.

77

Before dislocations are considered, the total strain energy of the coherent, or

dislocation free, heterostructure and, particularly, the equilibrium lattice parameters

must be determined. Six boundary conditions or balance relations must be specified to

satisfy the six rows of Equation 5-3. For the conventional Matthew’s Model for planar

films it is assumed that the top surface is free to relax without constraint, described by

the boundary condition,

0normal . (5-4)

Similarly, for the nanorod structure the normal component of stress can be set to

zero since the radius is free to relax as shown in Figure 5-2. By the definition of strain

as normalized deformation per unit length, the tangential and longitudinal strains can be

related to the equilibrium lattice parameters and the bulk lattice constants of the InN

core and GaN shell:

)1(

)1()1(

a

aaf a

(5-5)

)2(

)2()2(

a

aaf a

(5-6)

)1(

)1()1(

c

ccf c

(5-7)

.)2(

)2()2(

c

ccf c

(5-8)

where a and c are the equilibrium hexagonal lattice parameters shared between both

materials in the system defined the same ways as in Figure 4-9a. The constants a(1)

and c(1) are bulk lattice parameters for the core material, and a(2) and c(2) are bulk lattice

constants for the shell material. Henceforth, the superscript (1) refers to the core

material and (2) refers to the shell material. These strain definitions can be used

78

directly as boundary conditions for the strain tensor tangential to the interface at any

point

(5-9)

. (5-10)

Furthermore, it is assumed that no shear strains arise from lattice mismatch, hence:

(5-11)

(5-12)

. (5-13)

From Equations (5-4) through (5-10):

11

1312

11c

fcfc ca . (5-14)

The six strain boundary conditions are now completely defined and the stresses can be

determined using Hooke’s Law.

5.2.2 Minimization of Strain Energy without Dislocations

Since the stress and strain are now defined at any point in the core and shell, the

strain energy density per unit volume, w, can be computed at any point by the equation

jiijji cw 2

1

2

1 . (5-15)

By assuming uniform energy density due to the structure being at equilibrium and

integrating the energy density over volume of each region, the total strain energy of the

heterostructure can be calculated:

2

1)1(

11

)1()1(

33

)1()1(

13

)1()1(

11

2)1()1(

13

)1()1(

12

2)1()1(

11)1(

2

2RL

c

fcfcfcfcfcfcU caccaa

(5-16)

79

2

1

2

2)2(

11

)2()2(

33

)2()2(

13

)2()2(

11

2)2()2(

13

)2()2(

12

2)2()2(

11)2(

2

2RRL

c

fcfcfcfcfcfcU caccaa

. (5-17)

Minimization of Utotal = U(1)+U(2) with respect to the lattice parameters a and c, yields the

equilibrium state. Since Utotal cannot be analytically minimized with respect to a and c

simultaneously, numerical minimization must be used. Values of the elasticity tensor

elements for each material are shown in Table 5-1.

Figures 5-3 (a) and (b) show a plots of the equilibrium values of a and c lattice

parameters, respectively, as functions of the shell thickness, h, with r = 25 nm and L =

1000 nm. It can be seen from this figure that the a and c lattice parameters vary

monotonically from the limit of the core material lattice constant for very thin shells to

the shell material lattice constants for thick shells.

5.2.3 Introduction of Dislocations into the Model

Introducing a dislocation into the system can relieve strain to allow the lattice to

partially relax towards its bulk lattice values. While this dislocation lowers the total

strain energy of the system, there is also an energetic penalty associated with the

formation of the dislocation itself. Two predominant types of stable dislocations are

possible for this nanorod heterostructure. A loop dislocation, shown in Figure 5-1b, is

the result of a stacking fault, a region in which a (0001) plane of either core or shell

atoms have been omitted. This type of dislocation will have a Burger’s vector in the

<0001> direction with a magnitude of the c-lattice parameter of either the core or shell

material, depending on which plane has been omitted. Alternatively, an edge

dislocation with a Burger’s vector in the <1120> direction with a magnitude of the a-

lattice parameter of the shell material is shown in Figure 5-1c. Loop dislocations serve

80

to relieve strain along the axis of the heterostructure while edge dislocations relieve

strain circumferentially. It has been shown that for the nanorod heterostructure in

question with a wurtzite crystal lattice, edge dislocations will always form at lower strain

energies than loop dislocations [110]. Since this analysis is only interested in the critical

limit for coherence, or the strain energy at which the very first dislocation will form, only

edge dislocations will be considered in the analysis.

The relaxation of strain due to dislocations is included in the model by modifying

the strain expressions:

linelinea bnaa

aa

a

aaf

)2()1(

)1(

)1(

)1()1( (5-18)

linelinea bnaa

aa

a

aaf

)2()1(

)2(

)2(

)2()2( (5-19)

where nline is the density of line dislocations and bline is the Burger’s vector of the line

dislocation, which can be taken to have a magnitude of the equilibrium lattice

parameter, a. Since only edge dislocations are considered, fc(1) and fc

(2) do not need to

be modified.

The energy penalty associated with a line dislocation is [22, 23]

line

line

lineline

b

hb

c

ccLRnU

4

log42

2

2

)2(

11

)2(

12

)2(

111

(5-20)

After substitution of the new expressions for fa(1) and fa

(2) into U(1) and U(2), Utotal

can be computed as Utotal=U(1)+U(2)+Uline. For any given value of L, r, and h, the

equilibrium lattice parameters for the dislocation-free heterostructure are given in

Section 5.2.2. Using the equilibrium values of a and c determined in Section 5.2.2 and

81

then setting , an expression is obtained for the conditions under which it

becomes energetically favorable for the very first dislocation to form (since the term is

evaluated at n=0). By repeated evaluation of at many values of L, r and h,

and substituting values for a and c calculated in Section 5.2.2, one can determine the

critical dimensions where ∂U/∂n becomes negative, i.e. where dislocation formation

becomes energetically favorable.

Simulations were carried out using Matthew’s formulation adapted for cylinders

for two different material systems: AlxGa1-xN shells on GaN nanorod cores and GaxIn1-

xN shells on InN cores. Figures 5-4 and 5 show combinations of critical core radius and

shell thickness for these two material pairs. In each figure, the plots are shown for

several values of x, the alloy composition of the shell. The lines in the figures indicate

the limits of coherency. Below and to the left of the limit, combinations of core and shell

dimensions result in coherent structures, while above and to the right of the limit are

regions where dislocation formation is energetically favorable. The “steps” in the

coherency limits are remnants of the steps in the numerical simulation, not a physical

phenomenon.

5.3 Analytical Model 2: Pressure Vessel Theory Applied to Core/Shell Nanorods

A second method to model critical dimensions in nanorod heterostructures is

derived from pressure vessel theory. This theory was originally derived to model stress

and strain within the walls of a cylindrical containing pressurized gas, but it has been

successfully applied to model core/shell nanorod systems. Liang et al. [77] originally

applied the model to a Si/Ge core/shell nanorod heterostructure with a cubic crystal

82

system. For simplicity it was assumed that Si and Ge had the same elastic constants.

Menendez et al. [83] extended the pressure vessel model by adding a scaling factor, γ,

such that the elasticity tensor of the second material was equal to the elasticity tensor of

the first material times γ. Both materials were cubic crystal structures. This work

extends the work of Liang et al. [77] to model a wurtzite crystal system. Both materials

are assumed to have the same transversely isotropic elasticity tensors in this derivation.

This is a valid assumption if the materials are alloys with similar compositions, as is the

case in many practical core/shell material systems. In addition to Young’s Modulus, E,

and the Poisson Ratio, υ, the quantities Ez and υz are introduced to capture the

anisotropy along the z-axis. The elasticity tensor is defined as:

E

G

G

EEE

EEE

EEE

C

z

z

z

zz

z

z

z

z

1200000

01

0000

001

000

0001

0001

0001

1 (5-21)

where Gz is the strain tensor for the θz and zr directions. This term does not need further

definition since it will vanish due to the zero shear strain boundary conditions. This

elasticity tensor used with standard pressure vessel model assumptions yields a

pressure vessel model for core/shell wurtzite nanorod heterostructures.

83

Pressure vessel theory dictates that for a cylindrical vessel at pressure P with

walls of a non-negligible thickness compared to the radius, the stresses in the r and θ

directions for the vessel walls and gas regions are:

Pr )1()1(

(5-22)

1

12

12

2)2(

RR

rRPr (5-23)

1

12

12

2)2(

RR

rRP (5-24)

where P is the pressure inside the vessel, R2 is the radius of the entire core/shell

structure, R1 is the radius of the core, and the superscripts (1) and (2) refer to the core

and shell regions. Shear stresses and shear strains are assumed to be zero. Through

Hooke’s Law, all stresses and strains can be expressed in terms of P, σoz and σiz.

These three parameters can be replaced with the physically meaningful quantities

Young’s Moduli (E and Ez), Poisson ratios (υ and υz), and a misfit parameter, εmisfit, which

is defined the same way as fa in Equation 5-5.

)1(

)1()2(

a

aamisfit

(5-25)

where a(1) and a(2) are the core and shell a lattice parameters. First the total

displacements, u, must be defined as a function of the mismatch parameter. Since the

strain is defined as the normalized deformation per unit length, for this axisymmetric

problem, the displacements are defined as:

(since ) (5-26)

and

84

(since 0

r

uu zz

). (5-27)

With the additional assumption that εmisfit is the same for both the a and c parameters,

which is a valid assumption for the InN/GaN system, these net displacement equations

can then be used in displacement balance equations to equate inside and outside strain

terms [77].

Radial mismatch: misfitRr

rRr

r Ruu 1)2()1(

11

(5-28)

Axial mismatch: misfitLz

zLz

z Luu

)2()1( (5-29)

Finally, a force balance in the z-direction can be used to equate z-stresses for the core

and shell regions:

. (5-30)

Combining Equations (5-22) through (5-30), all six normal stresses and six

normal strains (three outside and three inside) can be solved for in terms of radii R1 and

R2, and the quantities εmisfit, E, Ez, υ, and υz. The following expressions for the normal

stresses and normal strains are obtained:

12 22

2

22

2

2

1)2(

z

misfit

rrR

rRRE

(5-31)

12 22

2

22

2

2

1)2(

z

misfit

rR

rRRE

(5-32)

12

2

2

1)2(

z

misfitz

zR

RE

(5-33)

12

2

2

2

1

2

2)1(

z

misfit

rR

RRE

(5-34)

85

12

2

2

2

1

2

2)1(

z

misfit

R

RRE

(5-35)

12

2

2

1

2

2)1(

z

misfitz

zR

RRE

(5-36)

and

12

121

22

2

22

2

2

1)2(

z

zmisfit

rrR

rRR

(5-37)

12

121

22

2

22

2

2

1)2(

z

zmisfit

rR

rRR

(5-38)

2

2

2

1)2(

R

R misfit

z

. (5-39)

12

12

2

2

2

1

2

2)1(

z

zmisfit

rR

RR

(5-40)

12

12

2

2

2

1

2

2)1(

z

zmisfit

R

RR

(5-41)

2

2

2

1

2

2)1(

R

RRmisfit

z

(5-42)

With the normal stresses and strains completely defined, it is possible to

determine the strain energy that would be relieved from a variety of different types of

dislocations. For the same reasons discussed in Section 5.2.3, it is known that line

dislocations will determine the limit for coherency, so only line dislocations are

considered [77, 109, 110]. Line dislocations propagate from the core/shell interface to

the outside edge on the nanowire structure. In this model the strain energy relief is

86

determined by integrating σθ(2) across the thickness of the shell and multiplying this

integral by the magnitude Burger’s vector of the dislocation, bline:

12

2

2

2

1

2

21)2(1

2

z

linemisfitR

Rline

R

RRbREdrbW

(5-43)

The strain energy of formation of the dislocation per unit cylinder length is taken from

Dundurs and Sendeckyj [22, 23], and simplifies to:

32

1ln2

1116

2

21

2

2

21

2

RRRb

RRbEE

line

line

ndislocatio

. 5-44)

By setting ΔWθ=Edislocation, the critical thickness at which dislocation formation becomes

energetically favorable is determined.

Simulations were carried out using the pressure vessel model for the same two

material systems previously modeled by Matthew’s model for cylinders: AlxGa1-xN shells

on GaN nanorod cores and GaxIn1-xN shells on InN cores. Figures 5-6 and 7 show plots

of the limits of coherency for these two material systems. The lines in the figures

indicate limits for coherency. Below and to the left of the limit, combinations of core and

shell dimensions result in coherent structures, while above and to the right of the limit

are regions where dislocation formation is energetically favorable. The “steps” in the

limits are due to numerical steps of the simulation, not physical effects. In each figure,

the plots are shown for several values of x, the alloy composition of the system. Figures

5-8 (a), (b), and (c) compare results of the pressure vessel model and Matthew’s model

for cylinders. Three different alloy compositions of GaxIn1-xN shell on an InN nanorod

core are compared. Qualitatively Matthews’ model and the pressure vessel model

agree and at higher Ga compositions they also agree quantitatively. At low Ga mole

87

fractions, however, there is some disagreement between the models. This is attributed

to the fact that the pressure vessel model artificially assumes that the two materials

have the same transversely isotropic elasticity tensor, while in Matthew’s model for

cylinders the measured values for each elasticity tensor is used. This leads to more

strain in Matthew’s model, hence smaller critical dimensions.

88

Table 5-1. Values of elasticity tensor elements for InN and GaN in units of GPa.

InN GaN

C11 190 296

C33 182 267

C12 104 130

C13 121 158

C44 10 24

89

Figure 5-1. Schematic of coaxial nanowire heterostructure approximated as a cylinder a) dimensions applicable to model, b) geometry of loop dislocation c) geometry of line dislocation.

L

R1

h

<0001>

bloop

bline

a)

b)

c)

R2

(1)

(2)

90

Figure 5-2. Comparison of zero normal stress boundary condition for planar and

nanostructured cases.

σnormal

εplane εplane

σnormal

εtangential

-εlongitudina

l

91

Figure 5-3. Numerically computed equilibrium lattice parameters for an InN/GaN core/shell system with core radius of 25 nm, and a length of 1000 nm, a(1)=3.54 nm, a(2)=3.16 nm, c(1)=5.70 nm, and c(2)=5.19 nm. A) a parameter. B) c parameter.

A) B)

92

Figure 5-4. Plots of core radius as a function of the critical shell thickness for AlxGa1-xN

shells on GaN nanorod cores calculated by Matthew’s model for cylinders. Plots are shown for several values of x, the alloy composition of the pseudobinary system. The lines indicate the critical dimensions for each composition. Below and to the left of the lines are mechanically stable heterostructures. Above and to the right of the lines are unstable structures.

93

Figure 5-5. Plots of core radius as a function of the critical shell thickness for GaxIn1-xN

shells on InN nanorod cores calculated by Matthew’s model for cylinders. Plots are shown for several values of x, the alloy composition of the pseudobinary system. The lines indicate the critical dimensions for each composition. Below and to the left of the lines are mechanically stable heterostructures. Above and to the right of the lines are unstable structures.

94

Figure 5-6. Plots of core radius as a function of the critical shell thickness for AlxGa1-xN

shells on GaN nanorod cores calculated by the Pressure Vessel Model. Plots are shown for several values of x, the alloy composition of the pseudobinary system. The lines indicate the critical dimensions for each composition. Below and to the left of the lines are mechanically stable heterostructures. Above and to the right of the lines are unstable.

95

Figure 5-7. Plots of core radius as a function of the critical shell thickness for GaxIn1-xN

shells on InN nanorod cores calculated by the Pressure Vessel Model. Plots are shown for several values of x, the alloy composition of the pseudobinary system. The lines indicate the critical dimensions for each composition. Below and to the left of the lines are mechanically stable heterostructures. Above and to the right of the lines are unstable structures.

96

Figure 5-8. Comparison of Pressure Vessel Model and Matthew’s Model for Cylinders for GaxIn1-xN/InN system at three different alloy compositions, x. A) x=0.05. B) x=0.1. C) x=0.5.

A)

B)

C)

97

CHAPTER 6 CONCLUSION

It is evident that nanostructured III/V semiconductor materials are a critical part of

the next generation of LED and photovoltaic devices. Uncatalyzed nanorod growth

combined with ALD coatings to produce core/shell nanorod double heterostructures

offers a promising, inexpensive means to produce high quality optoelectronic materials.

This study has investigated the atomic layer deposition of GaN shells on InN nanorods

on the path to development of a nanostructured III-V LED grown on a silicon substrate.

The ALD process window for GaN growth with NH3 and GaCl3 was found to

produce 2.6 Å of growth per cycle for two to eight sec of GaCl3 exposure time per cycle.

These ALD process conditions were used to grow conformal GaN shells on the InN

nanorods at several different growth temperatures. It was found that growth at a

temperature of 595° C produced well-aligned, highly crystalline GaN coatings.

However, the coatings were not epitaxially connected to the underlying InN nanorods.

There are two basic reasons for the lack of epitaxial relationship: one reason is

the large lattice mismatch between GaN and InN and the other reason is that InN

decomposes at GaN growth temperatures. Using InxGa1-xN alloys with different

compositions in the core and shell domains is a possible alternative to growth of pure

GaN on InN. However, growth of the alloy would require either a hot-wall reactor or the

use of metal-organic precursors due to the inability for InCl to transport in the vapor

phase at temperatures below 500° C.

Analytical models were formulated to determine the core and shell alloy

compositions at which device quality materials could be fabricated. As seen in

experiment, pure GaN shells grown on pure InN cores showed no mechanically stable

98

heterostructures. For this reason it is doubtful that GaN shells ever formed epitaxially

on InN nanorods, however, this cannot be completely determined through SAED

patterns due to the small signal for thin GaN shells. Future work may involve

experimental strain mapping of core/shell heterostructures by Raman spectroscopy or

photoluminescence.

99

APPENDIX LITERATURE REVIEW OF SELECTIVE AREA GROWTH OF GALLIUM NITRIDE

A.1 Preliminary Remarks

Selected area growth (SAG) of gallium nitride is a useful technique in III/V

semiconductor engineering due to its ability to produce a number of different, smooth

crystalline facets with different polarities, and also for its use in the beginning stage of

epitaxial lateral overgrowth (ELO). ELO with hydride vapor phase epitaxy (HVPE) is a

particularly desirable method of growth because it takes advantage of the high growth

rate of HVPE and the superior crystal quality of ELO. SAG is also suited to HVPE due

to the ability to vary both V/III and Chlorine/III ratios to offer perfect intrinsic selectivity

[126]. SAG has even been proposed as a “one-step” method for LED fabrication in

which the numerous crystal faces created by SAG are used as the basis for creating p-i-

n junctions. Since each different crystal plane has a different polarity and different rates

of gallium and indium adsorption, many different recombination regions with varying

thicknesses, internal fields, and indium content can be fabricated in a single run.

A.2 Substrates, Stripe-Pattern Directions, and GaN Stripe Morphologies

A.2.1 GaN/Sapphire Patterned Substrates

Many studies of SAG GaN use sapphire or GaN/sapphire substrates due to the

fact that GaN-on-sapphire technology has already been commercialized. Typically,

SiO2 is used as a mask material and windows are opened along the <1120> or <1100>

direction. Under the growth conditions chosen for SAG, GaN will not seed on the mask

material but will readily grow on the exposed GaN or sapphire of the window region.

100

The resulting stripes of GaN show a distinct preference in crystallographic morphology

depending on the window stripe direction.

Both pattern directions on GaN/sapphire substrates have produced trapezoidal

GaN stripes with different kinds of sidewalls. Stripes in the <1120> direction on a GaN

buffer tended to be bounded by the (0001) plane on top, and a combination of {1100}

vertical prism facets and {1101} pyramid facets at an angle of 62° (or in the case of an

H2-free environment the {1101} may be replaced by the {2203} at 51.4°). Stripes in the

<1100> direction are also bounded on top by the (0001) plane but the sides are

composed of nearly vertical {3362} planes at 72° and slanted {1122} planes at 58° [125].

GaN grows on sapphire with c-axes of the two materials parallel with a rotation of the

GaN 30° about the c-axis, so <1120> GaN || <1100> Sapphire and vice versa [126].

A.2.2 Sapphire Patterned Substrates

On <1100> patterned sapphire rectangular SAG GaN has been grown with a

(0001) top plane and {1120} side facets [16, 41, 125, 126]. However, SAG GaN grown

on <1120> patterned sapphire showed either polycrystalline growth with zig-zag

sidewalls [16, 125], or no growth at all [126] as opposed to the rectangular stipes grown

on <1120> patterned GaN/sapphire.

A.2.3 Changing Stripe Morphology with Carrier Gas

For either SAG stripe direction on a GaN/sapphire substrate, one extreme in

stripe morphology is triangular stripes with {1122} side facets (for <1100> stripes) or

{1101} pyramid facets (for <1120> stripes), and the other extreme is (nearly) rectangular

stripes with (0001) tops and either {3362} (for <1100> stripes) or {1100} (for <1120>

stripes). The word (nearly) indicating both the lack of vertical sidewalls in the 78° {3362}

101

sidewalls and also the fact that even the most “rectangular” stripes of GaN often have

very slightly faceted corners [16, 125]. In between these 2 extremes are the trapezoidal

strips of GaN with flat (0001) tops, vertical or nearly vertical sidewalls and also slanted

facets. By changing the carrier gas from pure N2 to pure H2, the two extremes of

triangular and rectangular stripes can be achieved. Intermediate H2/(N2+H2)

concentrations yeild trapezoidal stripes [125]. The growth mode in N2 ambient tends to

be 3D while the growth mode in H2 ambient is 2D [78].

A.2.4 Growth Rates

The slower the growth rate of a facet, the more that facet is developed in convex

growth. The dangling bond densities of the Ga-Polar (0001), the non-polar {1101}, the

N-polar {1100}, and the N-polar {1122} are 11.4, 12.1, 16.0, and 17.8 nm-2, respectively

[16]. The {1100} prism facets, the {1101} pyramid facets, (0001) facets have the lowest

surface energy and have only one dangling bond per unit cell. They are expected to

grow by a layer-by-layer growth mechanism, nucleation, or spiral growth mechanisms.

They limit the shape of the GaN surface morphologies [125]. In an H2 ambient GaN

tends to increase the surface areas of (0001) and {1100} facets while in an N2 ambient

{1101} facets are favored. Lower growth rate (lower V/III ratio), (0001) and {1100}

facets are favored over {1101} [78]. The N-polar {1100} and {1122} facets become

unstable under higher growth temperatures due to the high N2 desorption rate. The

{2203} facets, expected to grow by a step mechanism, appear only without H2 [125]. At

some H2 flow rate {1122} will appear.

Although there is a wide range of (0001) growth rates published for SAG GaN,

there in the most commonly reported rate is in the 32-33 µm/h range. The only real

102

consistency between various reports is that the <1120> GaN/sapphire substrate has a

higher vertical growth rate than that of the <1100> GaN/sapphire [16, 41, 125, 126].

This faster vertical (0001) growth rate is probably due to the increased supply of

reactants diffusing from the slow-growing {1101} region [41]. Parillaud et al. report that

growth is almost completely inhibited once a triangular stripe of {1101} facets is

completely formed [102] and Hiramatsu et al. report that vertical growth rates for the

<1100> and <1120> GaN/sapphire stripes are less than 10 µm/h and 2.7 µm/h (limited

by {1101}), respectively, once coalescence has occurred [41]. The lateral growth rates

for SAG GaN averaged about 26 µm/h and were found to be independent of growth

direction.

Tourret et al. found that the vertical growth rate of SAG GaN was not a function

of stripe width for samples grown on a GaN/sapphire substrate. However, for SAG on a

<1100> patterned sapphire substrate (as opposed to GaN grown on patterned

GaN/sapphire) the vertical growth rate increased and the lateral growth rate decreased

with increasing stripe width do to stress at the sapphire/GaN interface [126]. The

growth rate of any facet is slowed by increasing the percentage of H2 in the carrier gas.

Although both vertical and lateral growth rates are slowed by H2 addition, generally

when the ratio of H2 to total gas flow decreases, lateral growth is favored over vertical

growth relative to higher H2 flow rates [126]. Generally, the prism facets resulting from

the <1120> stripes are smoother than the pyramid facets on the <1100> stripes [16].

A.2.5 Patterned Silicon or Patterned GaN/Silicon Substrates

Parillaud et al. compare the use of an amorphous, LT-GaN/sapphire substrate

and a single crystal GaN/sapphire substrate and find, unsurprisingly, that amorphous

103

overgrown GaN grows on the amorphous buffer layer. They also find that lateral growth

rates are much higher than for the single crystal case, and find that on stripe-patterned

substrates amorphous rectangular or inverted trapezoidal (wider at top than base)

stripes grow [102].

Gu et al. deposited SAG GaN using GaN/Si(111) substrates patterned in the Si

<110> || GaN<1120> direction. This study showed the same faceting behavior as

GaN/sapphire substrates and showed that triangular, trapezoidal, or rectangular stripes

could be achieved just by increasing the HCl/Ga ratio by adding additional HCl to the

reaction [35]. Shin et al. used similar <110> patterned Si(111) substrates but with

AlGaN, GaN, or AlN buffer layers prior to patterning. Unsurprisingly, they found SAG

GaN regrown on GaN buffers to have a narrower ω-rocking curve FWHM and higher PL

intensities than GaN regrown on AlN or AlGaN buffers [121].

A.2.6 GaN Growth Conditions

Growth conditions, Cl/III and V/III ratios, in particular, are often unlisted or are

listed in a purposely confusing manner, in order to protect intellectual property. Some

growth conditions were found, however, and these are given in Table 6-1. All of these

Cl/III ratios were calculated assuming 100% conversion of HCl to GaCl at 800°C which

is a good assumption according to [7]. Also, the GaCl flow rate reported in [35] was

estimated by comparing GaN growth rates to other publications to back out GaCl flow

rate. Typically, no deposition on the dielectric mask was observed when a V/III < 12.5

was used [102].

104

A.3 Mask Materials

Some studies have used materials other than SiO2 as a mask material. The only

report of specifically HVPE GaN regrown over a mask material other than SiO2

encountered in this review was the work of Honda et al. [42]. The motivation to find

alternative mask materials is due to the appearance of 3 different domains of GaN

found in the overgrown region. In addition to the perfect domain with the c-axis

orthogonal to the c-axis of the substrate, regions with distinct 1° and 2° tilts were also

found. These regions were due to threading dislocations originating from the edges and

center of the SiO2 mask region, respectively, and appeared as distinct shoulder regions

in the XRC of the GaN (0004) peak. Interestingly, these tilted domains only appeared in

a scan orthogonal to the stripe direction of the mask: the parallel scan showed no such

tilting. The use of a tungsten mask eliminated these tilted domains for all scan

directions [42]. Several groups have reported on the use of Ti masks for MBE SAG

GaN [9, 68]. Growth temperatures over 900°C and nitridation of the Ti to form titanium

nitride before the MBE growth were reported. Nagae et al. compare the use of Ti and

SiO2 for SAG by RF-MBE [86]. They reported growth temperatures of 930°C and 940°C

respectively, for SiO2 and Ti. SAG by MBE has also been reported with Si3N4 [18, 38,

57] and W [119] masks while SAG by MOVPE has been reported for masks made of

carbonized photoresist [67] and high-dose N+ ion implantation in Si(111) [56].

A.4 Devices

A.4.1 Quantum Confined Stark Effect and Variation of InGaN Growth Rates in III-V SAG Devices

105

The wide variety of facets that can be produced by SAG is of particular interest

for optical device fabrication. For devices formed from conventional (0001) GaN, strong

piezoelectric fields in the quantum well region cause separation of the carrier wave

functions in the region, known as the quantum confined stark effect (QCSE), reducing

recombination rates and hence decreasing internal quantum efficiency. Device

fabrication on semi- and non-polar planes has been attempted to resolve this problem.

Scholz et al. formed triangular strips of GaN by MOVPE. The stripes were formed by

the {1122} and {1101} side facets for the <1100> and <1120> directions, respectively

[117]. GaN/InGaN multiple quantum wells (MQWs) were formed on the surface of these

facets with contact angles between the facet normal and the c-direction of 58 and 62°

respectively for the <1100> and <1120> directions. Solving Schrödinger’s equation with

these tilted potentials leads to a 2/3 reduction in internal fields over QWs on the c-plane

[117]. Fujiwara et al. used MOVPE SAG hexagonal pyramids made up of {1122} planes

as a substrate on which to grow GaN/InGaN MQWs. The width of the mask region

surrounding the openings where the pyramids were grown was varied to control the

amount of growth rate enhancement by diffusion from the mask area. Continuous

wavelength modulation from 446 to 500 nm was achieved [27].

A separate phenomenon to consider in SAG LED fabrication is the variation of

InGaN growth rates on different planes combined with the variation of dopant affinities

on different crystal planes. It has been observed that the growth rate of InN and InGaN

was much slower on c-planes as compared to {1122} and {1101} planes while the

growth rate of p-type GaN showed exactly the opposite behavior, growing thicker on c-

planes. This caused a very thin or non-existent QW at the apex of GaN triangular

106

pyramids, sometimes causing short circuiting of devices [117]. While growth rates were

similar for both {1122} and {1101} facets, <1120> stripes with {1101} facets showed a

significantly longer PL wavelength , indicating the incorporation of indium is more

efficient on {1101} facets [117]. In fact, the {1101} facets showed improved indium

incorporation even over (0001) plane meaning that for the exact same growth

conditions, a variety of quantum wells can be produced on different crystallographic

planes. Scholz has proposed using mask openings in a variety of directions to achieve

light emissions from the whole visible spectrum and hence creating single-step white

LEDs [117], while Fujiwara has proposed white LEDs by variation of mask widths [27].

A.4.2 Dopant incorporation

The incorporation of dopants on various growth facets will also have to be

controlled to produce optical devices by SAG. It was found that MOVPE with Cp2Mg as

a dopant caused Mg concentrations in the growth directions to vary such that the

concentrations on the {0001} facets > the concentrations on the {1122} facets > the

concentrations on the {1120} facets [4]. This difference was attributed to the difference

in dangling bond concentrations in the three facets which are 1.1x1015 nm-2, 1.4x1015

nm-2, and 1.8x1015 nm-2, respectively. This naturally selective Mg incorporation was

utilized to create current-confining structures by SAG in hexagonal micro-facet (HMF)

and Fabry-Perot lasers [4]. Mg-doping of (1101) GaN yields p-type materials, just as in

(0001) GaN:Mg. However, the (1101) GaN:Mg shows considerably less self-

compensation than its (0001) counterpart [116].

Semi-polar (1101), (1122), and non-polar (1120) GaN substrates were fabricated

by ELO on silicon [116]. On the {1101} growth front, Si acted as a p-type dopant at very

107

low levels of incorporation, but switched to an n-type dopant and showed a

monotonically increasing n-type behavior with increasing silane flow rate for higher

levels. Carbon doping was found to produce a shallow acceptor in (1101) GaN with

activation efficiency of 5-10%. However, no shallow acceptor levels for GaN:C have

been identified theoretically, so the p-type behavior may be attributed to some kind of

complex formation [116]. Similarly, (1122) GaN:C was prepared but it showed very

different CL characteristics than the (1101) GaN:C and is still under investigation [116].

SAG has also been used in optical devices to enhance light extraction efficiency.

Feng et al. used a triangular SAG pattern with all edges parallel to <1120> to produce

triangular micro-rings made up of only {1101} facets. This geometry has shown

superior light extraction characteristics. GaN/InGaN MQWs were grown on these

micro-rings but the indium incorporation showed some striations with a regular

periodicity which reflected the strain-striation/step edges in the underlying GaN micro

rings [26]. Shields et al. produced III-Nitride LEDs with enhanced light extraction by

growing SAG pyramids on the top p-layer. The pyramids acted as photonic crystals or

quasi-crystals defined by {1101} facets [120].

SAG has also been used to fabricate unique device geometries. Henry et al.

fabricated mass sensor arrays with VLS GaN nanowires (NWs) growing from SAG GaN

strips [40]. Ryu et al. used SAG to minimize wafer bowing prior to laser lift-off in LED

structures [112]. And of course SAG has been used for its ability to grow only in a

selected area, without trying to utilize novel growth facets or atomic incorporation

preferences. SAG has been used to grow selectively arrays of GaN/AlGaN HEMTs for

incorporation with silicon microelectronics [39]. It has also been used to deposit

108

selectively thin AlGaN layers in the channel region of AlGaN/GaN hybrid MOS-HFET in

order to increase drain current [51]. Finally, it has been used to deposit selectively

device contacts [98, 118].

109

Table A-1. Selected Area Growth conditions for GaN reported in the literature. Cl/III ratio 12-25 1.66-5 3 ~2*

V/III ratio 2-100 5-30 15 ~5-40*

Source [102] [16] [125] [35]

*estimated

110

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BIOGRAPHICAL SKETCH

Joseph C. Revelli was born in Rochester NY on January 1983. When he was 18

he attended Carnegie Mellon University in Pittsburgh, PA where he earned his B.S. in

chemical engineering with a minor in Physics. In 2007 Joseph came to Gainesville, FL

to pursue his Ph.D. in chemical engineering under the supervision of Dr. Tim Anderson

in the Electronic Materials Processing Group. Joseph graduated six years later in

December 2013 and took a job working for Intel Corporation in Portland, OR. During his

time in Gainesville Joseph blossomed as a musician and as a human being and plans

to continue pursuing musical endeavors aggressively in Portland.