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CATALYST-FREE GALLIUM NITRIDE NANOWIRE
NUCLEATION

presented by

Kaylee McElroy

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5/08 K:IProlecc&Pres/CIRC/DateDue.indd

CATALYST-FREE GALLIUM NITRIDE NANOWIRE NUCLEATION
By
Kaylee McElroy

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Electrical Engineering

2009

ABSTRACT
CATALYST-FREE GALLIUM NITRIDE NAN OWIRE NUCLEATION
By
Kaylee McElroy

Extensive research on nanowire devices and applications has unleashed exciting pos-
sibilities in a quest for smaller, faster electronic equipment, more sensitive detectors,
and new devices that take advantage of the quantum mechanical world. One of the
roadblocks to these new technologies is a clear understanding of how nanowires are
formed and how to control their growth. N anowire growths can be grouped in two
broad categories: catalytic growths and catalyst-free growths. Catalyst-free nanowire
growths are useful in applications where catalyst particles are not desirable.

This thesis deals exclusively with gallium nitride catalyst-free nanowire nucleation
and growth mechanisms. GaN nanowires are of particular interest because of GaN’s
unique optical and electronic properties. This thesis contributes fundamental under—
standing of the formation mechanisms of catalyst-free GaN nanowire growth through
investigations of the matrix from which the nanowires grow and through novel use
of the nanowires themselves as a diagnostic of their own growth mechanism. This
work shows that nanowire orientation changes as a function of growth temperature
and investigates this orientation change in terms of availability of nucleation sites and

constituent adatom materials.

TABLE OF CONTENTS

List of Tables .................................

List of Figures ................................

Introduction ...............................
1.1 The Band Structure of Semiconductors .................
1.2 Present and Future Applications of Gallium Nitride ..........
1.2.1 Photonic Applications ......................
1.2.2 Electronic Applications ......................
1.3 Crystal Structures of GaN ........................

Nanowire Growth and Nucleation ..................
2.1 Catalytic Growth .............................
2.2 Non-catalytic Growth ...........................
2.3 Crystal Growth Mechanisms .......................
2.4 Nanowire Growth used in this Study ..................

Characterization Methods .......................
3.1 Transmission Electron Microscopy (TEM) ...............

3.2 Scanning Electron Microscopy (SEM) ..................
3.3 X—Ray Diffraction (XRD) ........................

Results ..................................
4.1 Matrix Growth and Evolution ......................
4.1.1 SEM of Matrix Cross Sections ..................
4.1.2 SEM of the Top Surface of the Matrix .............
4.1.3 SEM of the Bottom Surface of the Matrix ...........
4.1.4 XRD of the Matrix ........................
4.1.5 TEM of the Matrix ........................

4.2 (1120) Nanowire Nucleation and Growth ................
4.2.1 SEM of (1120) Nanowires ....................
4.2.2 TEM N anowire Cross Sections: Nanowires as a Nucleation
Mechanism Diagnostic ......................

4.2.3 Asymmetric Cross Sections ....................

4.3 [0001] Nanowire and Rod Nucleation and Growth ...........
4.3.1 SEM of [0001] Nanowires and Rods ...............
4.3.2 TEM Nanowire Cross Sections: Nanowires as a Nucleation
Mechanism Diagnostic ......................

iii

(COOKINNl-l

18
18
19
20
24

34

46
49
49'
51
55
58
58

61

5 Models of Crystal Formation ..................... 63

5.1 Supersaturation .............................. 63
5.1.1 Dislocation Driven Growth .................... 65
5.1.2 2D Growth ............................ 65
5.1.3 Dendrites ............................. 65

5.2 Crystallography of the Matrix: Twinning ................ 65

5.3 Nanowire and Rod Growth ........................ 68

5.3.1 Discussion of the [0001] Growth Direction Nucleation Mechanism 68
5.3.2 Discussion of the (1120) Growth Direction Nucleation Mechanism 72

6 Conclusions ................................ 74

A Appendix: Structure Factor Calculations for Zinc-Blende and Wurtzite

GaN .................................... 76
Al Zinc-blende Structure Factor ....................... 77
A2 Wurtzite Structure Factor ........................ 80
Bibliography ................................. 85

iv

LIST OF TABLES

A.1 Results of the zinc—blende structure factor calculations. ........ 79

A2 Results of the wurtzite structure factor calculations ........... 84

‘7

1.1

1.2

1.3

1.4

1.5

1.6

LIST OF FIGURES

Free atom electron energy levels for Ga and N are. shown on either
side. Molecular orbitals of GaN are displayed in between. (This image
is from Dudesek et al. [1].) .......................

Calculated pseudopotential band structures for wurtzite (top) and zinc-
blende (bottom) GaN. Symmetry points of the Brillouin zone for the
appropriate crystal lattice are marked along the x-axis. (This image is
from Kolnik et al. [2].) ..........................

Density of States of zero, one, two, and three dimensions. (This figure
is subject to the GNU Free Documentation License Version 1.2- or any
later version published by the Free Software Foundation.) .......

Theoretical calculation of the conductivity along the axis 0; and per-
pendicular to the axis 0;; for a cylindrical wurtzite GaN wire with a
radius of 2.5 nm. The 1D density of states influences the conductivity
of the nanowire. (This figure is from Maslov and Ning [3].) ......

a) the fcc crystal structure. b) the zinc blende structure has a different

1 1 1
species of atom located at (1513. 113,15). In both a) and b) the lines

mark the boundaries of the conventional unit cell. (Images produced
using the VESTA software package [4]) .................

a) the hcp crystal structure. b) the wurtzite structure has one Type II
atom directly above each Type 1 atom of the hcp structure. In both a)
and b) the lines indicate nearest neighbors. Lines are drawn between
nearest neighbors, and the number of lines touching each atom in the

crystal structure is the coordination number of the crystal structure.
(Images produced using the VESTA software package [4]) .......

vi

10

11

1.7

1.8

1.9

2.1

2.2

3.1

3.2

3.3

3.4

4.1

4.2

a) the hcp unit cell. b) the wurtzite unit cell. In both a) and b)
the lines mark the boundaries of the conventional unit cell. (Images
produced Using the VESTA software package [4]) ...........

Layer 1: The (0001) and (111) planes are identical. Layer 2: Atoms
stack in the cavities between the atoms of the first layer. Layer 3: The
third layer of hcp stacks directly above the first layer. The third layer
of fcc stacks in the cavities that are not directly above the first layer.

Miller-Bravais notation in the hexagonal system. a) The lattice vectors
are 511, £12, 613, and ('3. b), c), and d): Directions perpendicular to the
c, a, and m faces, respectively. (Image produced using the VESTA
software package [4]) ...........................

Step ledge growth .............................
Screw dislocation step ledge growth ...................

A diagram of the electron beam of a TEM going through the sample
and a series of electro—magnetic lenses. .................

A diagram of the electron beam of a SEM going through a series of
electro—magnetic lenses and interacting with the sample. Secondary
electrons escape the surface of the sample and get detected. .....

The sample (illustrated as a star) is held in a goniometer. The sample
diffracts the x-rays, and the intensity of the x-rays is measured by the
detector ...................................

The geometry of a 26 scan .........................

(a), (b), and (c) are SEM images of the side view of the matrix growth
at 850°C, 950°C, and 1000°C, respectively. The approximate thick-
nesses of the samples, indicated by the arrows, are (a) 87pm, (b) 53pm.
and (c) 339nm. ..............................

Side view of matrix growth at 850°C . (a) Comparison of the side view
and top view of the uppermost matrix formation type. (b) Layered
growth at 850°C. Lines and labels on the left side of the picture mark
the boundaries between the different matrix layers. (c), (d), and (e)
Close-up images of layers 3, 2, and 1, respectively ............

vii

12

14

15

22

23

27

29

32

32

34

35

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

Side view of matrix growth at 950°C. (a) Comparison of the side view
and top view of the uppermost matrix formation type. (b) Layered
growth showing three different matrix formation types. (c), (d), and
(e) Close—up images of layers 3, 2, and 1, respectively ..........

(a) Side view of the 1000°C growth. (b) Close-up of the top portion
of the cross section. Inset shows hexagonal pits. (c) Middle portion of
the sample. (d) Holes near the bottom of the sample. .........

SEM images of typical GaN matrix and nanowire growth. (a) SEM
images of typical 850°C growth showing several nanowires growing
from the matrix (b) SEM images of typical 950°C growth. (c) Matrix
growth at 1000°C. Type 1 matrix consists of large GaN crystallites,
Type 2 matrix consists of medium-sized platelets with sizes on the
order of 1 pm, and Type 3 matrix consists of small platelets on the
order of 0.1 pm. .............................

(a) Matrix morphology of the top and bottom surfaces of the 850°C
growth are similar. (b) Close-up of the boxed area in (a). Arrows point
to nanowires on the top surface. No nanowires were observed from the
bottom surface. ..............................

(a) A wide angle view of the bottom surface of the 1000°C growth. The
area in the solid square is shown in (b) and contains nanowire growth
near the base of the rod. The area in the dotted square is shown in (c)
and contains nanowire growth. .....................

(a) and (c) Two different areas on the bottom surface of the 1000°C
growth. (b) The top surface of the 1000°C growth is comparable to
(a). (d) The cross section of the matrix is comparable to (c) ......

(a) Region of unique matrix formation on the bottom of the 1000°C
growth. (b) Close-up of (a). .......................

Relative intensities of each peak for powder diffraction of wurtzite [5]
and zinc-blende [6] GaN. The 26 scan of the 850°C sample is included
for comparison. ..............................

20 scans for each growth temperature. The control sample was the
steel puck and silver epoxy used in the sample preparation .......

viii

37

39

40

42

43

45

45

47

48

4.12

4.13

4.14

4.15

4.16

4.17

4.18

TEM of the matrix platelets. (a) A platelet grown at 850°C with
smooth sides. (b) A platelet grown at 850°C with nanoscale ledges.
(c)‘A platelet grown at 1000°C which has decomposed at the corners.
(d) Close-up of the area indicated in (c). (Figure adapted from pictures
published in Nanotechnology [7].) ....................

SEM images of nanowire nucleation sites and tips. (a) and (b) 850°C
growth of two different nanowires. (a) Nucleation site. (b) NW tip. (c)
Nucleation site of a 950°C nanowire. (d) Nucleation site of a 1000°C
nanowire grown from the Type 2 matrix. (e) and (f) Two different
nanowires from the Type 3 matrix of the 1000°C growth. (e) Nucle-
ation site. (f) NW' tip. ..........................

(a) Cross section of a nanowire grown at 850°C. Dotted lines indicate
incoherent interfaces between crystal domains and solid lines indicate
a coherent interface. F FTs for each domain is given on the left. (b)
Close up of crystal domain 2. (Figure adapted from pictures published
in Nanotechnology [7].) ..........................

(a) Cross section of a nanowire grown at 950°C. The Au and Pt coat-
ings protect the nanowire during the FIB process. (b) Outlines of the
apparent crystallographic regions. FFTs of each region are given on
the right. Region 1 was the only zinc-blende region; all other regions
are various orientations of wurtzite GaN. Arrows on the FFTs point in
the (111) direction for region 1 and in the (0001) direction for the oth-
ers. (c) HRTEM of the interfaces between the zinc—blende and wurtzite
regions. The solid line indicates a coherent interface the dash-dot lines
indicate boundaries with stacking faults, and the curved dash-dot line
indicates the boundary between domains 2 and 3c where equivalent
planes nearly line up. (TEM images courtesy of B. W. Jacobs.)

Side facets of the 950°C TEM cross section. The solid lines indicate co-
herent interfaces. dotted lines indicate incoherent interfaces, and dash—
dot lines indicate equivalent planes that nearly line up. (TEM image
courtesy of B. W. Jacobs.) ........................

Non-symmetric nanowires were observed at each growth temperature.
The nanowire shown for the 1000°C growth originated from the Type
2 matrix area, which is the matrix type most similar to the matrix
observed at 850°C and 950°C .......................

(a) Rod base from step-ledge c-face. (b) Rod base from 1011 planes. .

ix

50

52

54

57

59

4.19

4.20

5.1

5.2

5.3

5.4

5.5

5.6

5.7

A.1

A2

(a) Rod end displaying spiral growth. (b) Rod imaged end on with a
hole off the center of the rod. (c) View of a rod from the side showing
the pointed end structure. ........................

(a) Cross section of a cluster of rods grown at 1000°C. (b) Close-up
of the bottom rod in (a). Insets show that the rod is oriented along
the [0001] zone axis and that the light contrast area near the center of
the rod appears to be electron transparent. (0) SEM of the cluster of
rods. The dotted line indicates where the cross section was made near
the base of the rods. (Figure adapted from pictures published in N ano
Letters [8]) .................................

Growth rate as a function of supersaturation. (Image from Wilcox [9]).

(a) Layered growth of the matrix at 1000°C. (b) Matrix from (a) tilted
for a side view. (c) Layered growth at 1000°C making pyramid planes.
((1) Layers observed in the 850°C matrix cross section. ........

(a) Rods from parallel growth at 1000°C. Near the base of the rods is
some dendritic growth. (b) Close up of the dendritic growth.

(a) Interpenetrant cubes twinned about a triad axis [10]. (b) Growth
at 950°C. .................................

(a) A twinned octahedron [10]. (b) The twin plane of (a) [10]. (c)
Growth at 1000°C. The arrow is parallel with the twin plane. (Image
courtesy of B. W. Jacobs.) .......................

(a) Elbow twin of a tetragonal crystal [10]. (b) and (c) Repeated elbow
twinning [10]. ((1) Growth at 1000°C ...................

(a) top and middle: Parallel growth of octahedra [10]. bottom: Parallel
growth of hexagonal prisms [11]. (b) Rod growth at 1000°C. (Image
courtesy of B. W. Jacobs.) (c) Growth at 1000°C ....... . .....

Illustration of the position of each atom in the basis of the zinc-blende
structure. (Image produced using the VESTA software package [4].) .

Illustration of the coordinate system used in these calculations and the
position of each atom in the basis of the wurtzite structure. (11 is in

the 5: direction and 51.3 is in the 2 direction. (Image produced using the
VESTA software package [4].) ......................

61

62

64

66

70

71

78

81

Chapter 1

Introduction

Gallium nitride (GaN) nanowires have been under extensive investigation in recent
years due to their unique optical and electrical properties. GaN nanomaterials are
currently extensively researched due to interest in their potential for applications such
as blue nanowire lasers [12] and high electron mobility transistors (HEMTS) [13].
For device applications, control of crystalline quality and orientation is essential.
The nanowire nucleation and growth mechanisms are not well understood, and it
is critical to understand these mechanisms in order to develop controlled nanowire

growth processes.

The nanowires used in this study were grown using a catalyst-free growth method.
Catalyst free nanowire growths have no metal impurities in the nanowires and can be
used in applications where device fabrication steps are incompatible with the presence
of a metal catalyst [14, 15]. Investigations using multiple analysis techniques have
been performed by our group and have contributed new understanding of nanowire
structures. First, we have demonstrated that the nanowire growth orientation is
influenced by growth temperature in catalyst free growth. Original work presented in
this thesis will discuss the dynamic evolution of the growth matrix that controls the

availability of nucleation sites and how the matrix effects nanowire orientation. This

thesis further explores the nucleation mechanisms that result in the observed nanowire
orientations and discusses the availability of constituent adatom materials. Second,
we have demonstrated that GaN nanowires from the growths studied have internal
crystal structures that continue along the entire length of the nanowire. Within this
thesis the internal nanowire structure is used as a diagnostic for the nanowire growth
mechanism. Understanding how and why internal nanowire structures form is critical
for successful nanowire device engineering.

The remainder of chapter one deals with the basic physics and crystallography
necessary to understand GaN devices. Chapter two discusses factors that are known
to affect catalytic and non-catalytic nanowire growths. Additionally, an outline of
crystal growth theories is provided. Chapter three covers the various instruments
used to characterize the samples and explains how they operate and what informa-
tion relevant to the present investigations can be obtained from using them. The main
experimental results are presented in chapter four. Models for growth mechanisms
based on the experimental results are (presented in chapter five. The final chapter
summarizes the main achievements of this thesis and discusses future research direc-

tions.

1.1 The Band Structure of Semiconductors

Each electron of a single atom is only allowed to have certain energies, or in other
words, the energy of the electrons is quantized. When two atoms bond together, their
energy levels split into bonding and anti-bonding molecular orbitals. The molecular
orbital structure for GaN is shown in Figure 1.1. The molecule can exist as long as
more bonding orbitals are filled with electrons when compared with filled anti-bonding

orbitals.

As more and more atoms are added to the molecule, the energy levels continue to

2

Gallium nitride

Ga N

Energy (eV)

-10

-15

-20

 

-25

Figure 1.1: Ffee atom electron energy levels for Ga and N are shown on either side.
Molecular orbitals of GaN are displayed in between. (This image is from Dudesek et
al. [1].)

split as the electron orbitals interact. Adding a large number of atoms, resulting in a
three dimensional solid, causes the energy levels to be so close together that energy

can be thought of as having bands of continuous values, instead of discreet values.

However, even if there are an infinite number of atoms in a solid, there may still
be electron energy levels that are not allowed. This gives rise to the band structure
of the solid. The groups of energies that are allowed are known as energy bands, and
the groups of energies that are not allowed are known as band gaps. The highest
energy band that has electrons in it at UK is known as the valence band, and the next
highest energy band is known as the conduction band. Electrons in the valence band
are in bonds and are therefore not free to move about the solid like electrons in the
conduction band are. The band structure of a solid has an enormous impact on the

electrical properties of the solid. If the highest energy electrons are at the very top

3

of an energy band and there is a large band gap above the band, the material is an
insulator because the electrons are unlikely to acquire enough energy to go to the next
energy level. Because an insulator has no electrons in the conduction band, the solid
will not conduct electricity very well. If the valence band and the conduction band
overlap, the material is a metal because electrons can easily gain enough energy to
get to the next level and move throughout the solid. A third case occurs when there
is a relatively small band gap above the valence band; these materials are known as
semiconductors. Electrons in a semiconductor can gain sufficient energy to get to the
conduction band by absorbing the energy of either a photon or a phonon (a phonon
is a quantized lattice vibration due to thermal energy). There is no set band gap
width that determines whether a material is an insulator or a semiconductor so the

distinction is usually made in the way the material is used.

The band structure of a solid also depends on the structure of the crystal. The

energy E of an electron is dependent on the wave vector ii: since

 

E = {’2
2m*
13 = his (1.1)

where 15 is the momentum and m* is the effective mass of the electron. Thus E is
dependent on the individual electron’s momentum as it travels through the crystal
lattice. The band structures of zinc-blende and wurtzite GaN as a function of the

wave vector is plotted in Figure 1.2.

The energy density of states g(E), which is the number of allowed states at each
energy level in an energy band, is dependent on the dimensionality of the crystal. For
a three dimensional crystal, g3D(E) or B, so the number of allowed states smoothly
increases at higher energy levels (see Figure 1.3). When momentum is restricted in

one dimension (i.e. the crystal is shaped like a two dimensional flat plane only a

4

 

1V2Vurtzite

 

 

 

 

 

 

 

 

 

 

 

W

8 — c
i“: 4 Z t’\7
53 E i
is 0 :Bn§7jk X;
-4 R4W/\ _‘
'8A L M r A H K r
Wave Vectork
ginc-Blende
8 E. :
A l /
a A
V 4 ’
56 I
LE 0 \

 

 

 

 

 

 

 

 

'-1
><
2
r:
"1
7:

Wave Vector I:

Figure 1.2: Calculated pseudopotential band structures for wurtzite (top) and zinc-
blende (bottom) GaN. Symmetry points of the Brillouin zone for the appropriate
crystal lattice are marked along the x-axis. (This image is from Kolnik et al. [2].)

 

 

 

Density of States
as
8

 

 

 

‘ ~ I Quantum Well (20)
l --- QuantumWireUD)
[ - - — QuantumDot(OD)

"l

 

l
I l

l
l l

l
E . ,
5 R; 5 ------ Bulk (30)
l l
I l

l

l

l

 

 

0 10 20 30 4O 50 60 7O 80 90 100 110 120

Energy (meV)

Figure 1.3: Density of States of zero, one. two, and three dimensions. (This figure
is subject to the GNU Free Documentation License Version 1.2 or any later version
published by the Free Software Foundation.)

few nanometers thick) the energy states in the corresponding direction are quantized.
The energy states in this thin crystal plane may be approximated by a 1D quantum
well. In this case, 92D(E) cc 0,, where 0,; is a constant corresponding to the nth

energy level of the quantum well. Cn increases with higher energy. When a crystal is
fit
x/E

is a constant corresponding to the nth energy level of the quantum wells. This means

restricted in two dimensions so that it is shaped like a wire, g1D(E ) oc where Dn
that there are relatively large numbers of available energy states near the energy levels
of the quantum wells. The conductivity (which is related to the density of states) of
a theoretical wurtzite GaN nanowire is shown in Figure 1.4. If all three dimensions
are restricted, a quantum dot is formed. The quantum dot acts much like an atom
because only specific energy levels are allowed for the electrons; all other energy levels

are forbidden.

 

 

 

 

 

 

 

 

 

 

 

 

A o
m 2
3 15~ csx ------ .
E
5
10 -
X
D
E
to 5-
DN
0
3700

 

Energy (meV)

Figure 1.4: Theoretical calculation of the conductivity along the axis 02 and perpen-
dicular to the axis 09; for a cylindrical wurtzite GaN wire with a radius of 2.5 nm.
The 1D density of states influences the conductivity of the nanowire. (This figure is
from Maslov and N ing [3].)

1.2 Present and Future Applications of Gallium
Nitride

1.2.1 Photonic Applications

There is no set band gap width that determines whether a material is an insulator
or a semiconductor; the distinction is usually made in the way the material is used.
Gallium nitride is what is known as a wide band gap semiconductor because it has
a larger band gap than most traditional semiconductors. This wide band gap is one
reason why GaN is a good material to produce blue-violet light. In bulk material,
wurtzite GaN has a bandgap of 3.39 eV, resulting in an emitted wavelength of approx-
imately 366 nm (A = 1:14;) [16]. Likewise, the bandgap of bulk zinc-blende GaN is 3.2
eV, resulting in an emitted wavelength of approximately 387 nm. Gallium nitride is

also a direct band gap semiconductor. The electron energy levels are different for the

7

various orientations within the crystal structure. When the minimum energy level of
the conduction band occurs at the same crystal orientation as the maximum energy
level of the valence band (as in Figure 1.2), the material is known as a direct band
gap semiconductor. In a direct band gap material, if an electron in the conduction
band loses energy and goes to the valence band, the lost energy is emitted in the
form of a photon with energy approximately equal to that of the band gap. Until the
1990’s, blue LEDs were made out of SiC, which is an indirect bandgap material, and
therefore the devices had very low efficiencies. In 1993 Shuji Nakamura created the
first high-brightness blue LEDs using an InGaN/AlGaN double heterostructure [17].
This breakthrough has been critical to the development of full color LED displays and
white LEDs. Since then efficiencies of GaN based LEDs have increased even more as
device design and fabrication techniques are refined [18]. Additionally, the availabil-
ity of GaN substrates with low dislocation densities has added to the efficiency and
lifetime of blue LEDs and laser diodes [19].

Current research is introducing the use of 1D GaN nanowires for photonic appli-
cations. UV lasers have been created from GaN quantum wires [12, 20]. Additionally,
GaN nanowires have been used to create ultra violet LEDs by positioning an n-type

GaN nanowire so that it crosses a p—type Si nanowire [21].

1.2.2 Electronic Applications

A high electron mobility transistor (HEMT) uses two materials with different bandgaps
to create a quantum well to trap the electrons in a high quality crystal. HEMTS are
capable of handling large amounts of current because the quantum well region does
not have any dopants in it (dopants can scatter or trap the electrons and impede
the electron mobility). AlGaN/GaN HEMTs have been fabricated [22, 23], and have
potential to be used for high power, high frequency applications because GaN is able

to withstand high voltages [24, 23, 13] and has higher efficiencies than the current

8

standard silicon technology [13]. The lowest energy in the conduction band of AlGaN
is higher than the lowest energy in the conduction band of GaN, thus electrons will
get trapped in the GaN layer. Controlling the polarity of the GaN is important for
HEMTS [25].

GaN nanowire field effect transistors (nanoFETs) made from individual GaN
nanowires have been fabricated [26, 27]. GaN nanoFETs have been electrically tested
to Show that the electron mobility of the devices can be between 150-650 cm2/V-s
which is comparable to or better than 100—300 cm2/V-s for thin film GaN [26]. A
nanoFET fabricated using a multiphase nanowire showed high current density con-

sistent with results reported from single phase nanowire systems [27].

1.3 Crystal Structures of GaN

For maximum performance of photonic and electronic applications, the crystal struc—
ture of GaN nanowires should be defect free. Therefore, it is important to understand
the crystalline nature of GaN. GaN can form in either the zinc-blende or the wurtzite
crystal structures. The zinc—blende structure is closely related to the face centered
cubic (fcc) structure, and the wurtzite structure is closely related to the hexagonal
close pack (hcp) structure. In turn, fcc and hcp are very similar structures. This
section will explain the details of the zinc-blende and wurtzite structures and how
they are related. It will also cover the basics of hexagonal crystal notation, which is
often left out of introductory solid state textbooks.

The conventional unit cell of an fee structure has a Type I atom at each corner of
the cube and in the center of each face of the cube (see. Figure 1.5a). The zinc-blende
structure is formed by adding a Type II atom g(f, 3;, f5) away from each Type I atom
where a is the length of a side of the cube, as shown in Figure 1.5b.

An hcp structure has Type I atoms at each corner of a hexagonal prism, in the

9

 

Figure 1.5: a) the fcc crystal structure. b) the zinc blende structure has a differ-
ent species of atom located at (155,117,122). In both a) and b) the lines mark the
boundaries of the conventional unit cell. (Images produced using the VESTA software

package [4])
center of each hexagonal face, and three atoms which are half-way in between the
hexagonal faces and nestled in the cavities formed by the atoms in the hexagonal
faces (see Figure 1.6a). The wurtzite structure is formed by adding a Type II atom
directly above each Type I atom in the c direction, as shown in Figure 1.6b. While
it can be easier to picture these crystal structures with a full hexagonal base, the
conventional unit cell consists of g of the hexagon base, as shown in Figure 1.7.
The fcc and hcp structures are closely related. In order to see this, it is necessary
to realize that the (111) plane of the fee structure is equivalent to the (0001) plane of
the hop structure. If we start with the (111)/(0001) plane and start adding the next
layer of atoms, the atoms will position themselves in the wells in between the base
layer of atoms for both fcc and hop, as shown in Figure 1.8. With the third layer of
atoms, however, the structures differ. In the hop structure, the third layer of atoms

forms directly above the first layer. The third layer of atoms in the fee structure stack

10

a) b)

Figure 1.6: a) the hop crystal structure. b) the wurtzite structure has one Type II
atom directly above each Type I atom of the hop structure. In both a) and b) the
lines indicate nearest neighbors. Lines are drawn between nearest neighbors, and the
number of lines touching each atom in the crystal structure is the coordination number
of the crystal structure. (Images produced using the VESTA software package [4])

11

 

 

 

 

 

 

o

o 9

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.7: a) the hcp unit cell. 1)) the wurtzite unit cell. In both a) and b) the

lines mark the boundaries of the conventional unit cell. (Images produced using the
VESTA software package [4])

12

in the cavities that are not directly above the first layer. This difference gives rise to

the notation that hcp has ABAB stacking and fee has ABCABC stacking.

Another thing to note is that GaN, like many other crystals, has both a covalent
and an ionic character in its bonding. The ionic character of the bond can be quan-
titatively defined by the Phillips ionicity, fi, of the crystal. f,- is zero for a perfectly
covalent bond, and one for a perfectly ionic bond, so it can be thought of as the
percent of ionicity of the bond [28]. For zinc-blende, fz- = 0.519, and for wurtzite
fi = 0.500 [29, 30]. The ionic nature of the bond causes planes that have uneven
numbers of gallium and nitrogen atoms to be polar. For example the (0001) wurtzite

plane is polar because it contains atoms of only one species.

Crystal planes and directions are conveniently described using the Miller indices
(hkl). Because crystals are three dimensional materials, only three vectors are re-
quired to describe the crystal planes. Cubic structures, such as zinc-blende, are
easily described using the vectors i, ii, and 2. Hexagonal crystals, on the other hand,
are typically described using four vectors, three pointing out of every other corner of
a flat hexagon ([11, {12, and a3) and one perpendicular to the plane of the hexagon (c)
(see Figure 1.9a). Four digit Miller-Bravais indices (hkil) use all four directions, and
the i index corresponds to the 513 direction. However, the (2.3 direction is redundant
because

63 = —<a1 + a2) (12)

Or equivalently,

d1 +dg+é3=0 (1.3)

For hexagonal systems, three digit Miller indices (hkl) are derived from the {11, (“12,
and 6 directions, respectively. To switch (hkil) to Miller notation, simply remove the i
index (i.e. (10I0) = (100)). To switch (bid) to Miller-Bravais notation, get the i term

by adding the h and k terms and multiplying that sum by -1 (i.e. (111) = (1121) since

13

Hex Close Pack Face Centered Cubic
Layer 1 A

 

Figure 1.8: Layer 1: The (0001) and (111) planes are identical. Layer 2: Atoms stack
in the cavities between the atoms of the first layer. Layer 3: The third layer of hcp
stacks directly above the first layer. The third layer of fee stacks in the cavities that
are not directly above the first layer.

14

’a3' [2110) ——
at

b)

l0001l

[1010]

Figure 1.9: Miller-Bravais notation in the hexagonal system. a) The lattice vectors
are til, {12, £13, and c. b), c), and d): Directions perpendicular to the c, a, and m
faces, respectively. (Image produced using the VESTA software package [4])

—(1 + 1) = —2). The advantage of the four digit notation for hexagonal symmetries

is that it makes equivalent planes easier to see. For example,

{1120} = (1120) , (i110) , (1210)

= (110) , (Q10) . (120) (1-4)

In the three digit notation, it is not obvious that (110) is related to (210) and (120),
but including the fourth digit shows the symmetry of the related directions. However,
the three digit notation is used in all computations (because i is redundant), and all

other crystal structures use the same three digit notation.

The Miller index for a direction is given by the smallest integers whose ratio
u : v : w is equivalent to the ratio of lengths along the 51,13, and 6 directions of the

vector Ii pointing in the given direction. Only for cubic systems is the direction [hktl]

15

perpendicular to the (MCI) plane. Generally, the direction perpendicular to the (hkl)
is [wow], and [uuw] # [hkl].

In hexagonal systems, vector directions can be expressed as three or four digit
indices. For three digit indices, R = 11511 +v&2+wc, and [uvw] is the three digit Miller
index for the direction. For four digit direction indices, R = U (11 + V52 + T53 + W (3

where T = —(U+V). The four digit Miller-Bravais index for the direction is [UVTl/V].

Given a random direction, the direction vector may be expressed as
R1 = U511 + V512 + T513 + we (1.5)

01‘

A

R2 = 11.5.1 + ”0&2 + wé‘ (1.6)

where R1 and R2 point in the same direction but may not have the same magnitude.

In other words, E1 = nRg. Since (1.3 = 411 — (12,

A

R1 = U611 + V512 - T511 - Til-2 + l/Vé

 

 

= (U — T)(i.1 + (V — T)a2 + we (1.7)
so
U — T
u =
n
V — T
v =
n
”I,
u! = — (1.8)
'n,

This system of equations can be solved for U, V, T, and W' in terms of u, v, and u) in
order to switch from the three digit notation to the four digit notation. n is chosen

to get the lowest valued integers which point in the direction of B. As an example,

16

consider the direction [2110] which points out one of the corners of the hexagon in

the c-plane and gives R1 a magnitude of 3. Converting to the three digit notation,

_2—1

 

’U =

 

(1.9)

-3 .
gives [Tl—00]. n is chosen to be 3 for this example so that R2 has the smallest

magnitude in the desired direction. Thus [2110] = [100]. Once again, the three digit

notation is used in computations and computer software because all other crystal

structures use the same notation.

The interplanar spacing for hexagonal crystals is given by [31]

1_4h2+hk+k2+12

d2 3 a.2 c2

 

The angles between planes for hexagonal crystals is given by [31]

1 30.2
hlhg + [Cle + -(h.1k2 + h-2k1)+ _21112
2 4c

 

cosrz') =

 

2 2
h2+1~2+h k +—3a 12 h2+k2+h 1- +—3“ 12
'1 '1 11 4621 2 2 '2‘2 4022

and angles between directions for hexagonal crystals is given by [32]

2
1 ~ 0
11.1112 + plug — 5(u1ug + 11121.2) + $101102

 

cosp =

 

 

c2 .2
\ (21% + if? — ulrl + (T220? “(£3 + ug- — 212112 + 32-11%

17

(1.10)

(1.11)

(1.12)

Chapter 2

Nanowire Growth and Nucleation

The exact growth mechanisms of nanowires are still being debated. Nanowires can
be formed by two general growth methods: catalytic and non-catalytic. While cat-
alytic growths have been studied extensively in recent years, non-catalytic growths
may be able to provide a greater variety of nanostructures for specific applications
if the growth can be controlled. Additionally, non-catalytic growths have no metal
impurities in the nanowires and can be used in applications where device fabrication
steps are incompatible with the presence of a metal catalyst [14, 15]. This chapter
reviews literature for both catalytic and non-catalytic nanowire growth. Additionally,

relevant crystal formation theories are discussed.

2.1 Catalytic Growth

A typical catalytic nanowire growth uses a substrate coated with nanoscale metal
beads (often Au or Ni) to act as a catalyst for the nanowires. The vapor liquid solid
(VLS) growth mechanism can be described by three stages: alloying, nucleation, and
axial growth [33]. When the substrate is heated and gases containing the necessary

elements for the nanowires flow over the substrate, some of the gases get incorporated

18

into the metal beads. The catalyst particle attracts the reactants within a certain
distance and thus acts as a sink in the chemical potential [34]. The incorporation
of other elements into the metal catalyst is known as alloying. This incorporation
can cause the beads to melt [33]. Once the catalyst is super-saturated with atoms
absorbed from the vapor, atoms precipitate from the alloy, causing the nucleation of
the wire. A nanowire is formed as atoms continue to precipitate, causing extension
along the nanowire axis. Research indicates that the diameter of the nanowires is
proportional to the size of the metal beads [35]. Additionally, patterning the metal
catalyst can pattern the location of the as-grown nanowires [35]. If nanowires are
grown on a substrate that matches their lattice, the growth can be epitaxial [35].
Nanowires often have preferred growth directions, although this can be influenced by
the choice of substrate and the growth conditions such as annealing the catalyst before
growth [34, 35]. GaN nanowires grown by VLS methods have resulted in nanowires
that grow in the (0001) [36], (1120) [36, 37], (2130) [37], and (1010) [38] directions.
Coaxial wires can be grown by first growing a nanowire and then changing the growth
conditions to allow for lateral growth [34].

Not all growths that use metal catalysts fit the VLS model for growth. A study
by Dick et al. has shown that gold particles used in growing InAs may only serve as
a low energy interface for the reactants [39]. Group V elements do not accumulate
in the metal beads, but the group III elements do [39, 40, 41]. GaN nanowires only
lengthen when in a N rich environment; if the environment switches to be Ga rich,

the wires will thicken [40].

2.2 Non-catalytic Growth

Non-catalytic growth is sometimes called vapor solid (VS) growth and the nanowire

nucleation mechanisms differ from that of a catalytic growth. Less is known about

19

VS nanowire growth than VLS and other catalytic nanowire growths. Although little
is known about the exact mechanisms of formation for the VS system, several param- ,
eters are known to change the nanowire and/ or matrix crystal formation. VS growth
mechanisms allow different structures to form because the system is not constrained
by the catalyst. For example, using catalyst methods GaN preferentially grows in
the (1010) direction [42]. GaN can grow in different directions using VS methods.
Peng et al. grew nanowires in the (1011) direction or the (0002) direction, depend-
ing on the growth temperature [42]. Other factors that are known to influence the
growth include: gas flow rate [43], temperature [44], and gas phase supersaturation
[44, 45]. Thus, VS nanowire growth is sensitive to gas phase kinetics during the
growth. Growth rates of nanowires have been calculated theoretically, and non-linear
growth rates have been observed [46]. Additionally, the morphology of the crystals
obtained from a VS growth is inherently dependent on the properties of the crystalline
structure that is grown. The 0001 and 0111 planes of wurtzite structures are polar
due to the fact that only one species of atom is on the surface. This polarization

affects the growth of GaN and other wurtzite crystals [43, 47, 48].

2.3 Crystal Growth Mechanisms

The surface of a solid inherently has a higher energy than the interior of a solid.
This is because the atoms on the surface are not as satisfied with their bonds as the
atoms in the bulk of the material. One way the surface energy can be lowered is to
have low index facets on the crystal formations. Other ways a solid can lower the
surface energy is through relaxation or surface reconstruction. Relaxation is where
the layer of atoms at the surface have a shorter bond-length than normal with the
layer of atoms underneath of them. In some solids, relaxation occurs by the top layer

shifting laterally relative to the expected position, so that the atoms are in the wells

20

between the lower layer of atoms. Surface reconstruction refers to the surface having
an entirely different crystalline structure than that of the bulk material, whereas for

surface relaxation the structure is the same, just shifted a little.

In order for crystal growth to occur, more atoms must attach to the crystal surface
than are removed. For this non-equilibrium condition to occur, the liquid or vapor
from which new atoms are added to the surface must be supersaturated. The level of

supersaturation will effect crystal growth.

Consider a single atom landing on an atomically flat surface. Such an atom is
called an adatom. This single atom will be weakly bound to the place where it lands.
Depending on the thermal conditions, the atom may jump back off of the surface or it
may diffuse across the surface, jumping into nearby lattice positions [49]. The greater
the number of bonds formed with an adatom, the lower the surface energy. So if
there is another adatom in a lattice position adjacent to the first adatom, both atoms
will be less likely to jump off the surface than if they were each a single adatom. If
adatoms continue to cluster around the original adatom, at some point the cluster
will be large enough that it is statistically unlikely for the entire cluster to “dissolve”
back to the original state [50]. The formation of such a cluster on the surface is
referred to as 2D nucleation, since adatoms can continue to increase the size of the
cluster and the crystal. Higher supersaturations will increase the number of clusters

that form and speed the growth of the crystal.

Step ledge growth can now be considered for the cluster of adatoms. If there is a
ledge of atoms on the surface, an adatom. may diffuse to the ledge because it will have
more neighboring atoms to bond to and thus will be more likely to stay on the surface
(see Figure 2.1). Particularly in vapor solid growths, surface diffusion is important
for the step ledge growth to occur [50]. If there is a kink in the ledge, the adatom will
have even more neighbors to bond to, and additionally, the adatom will not increase

the surface energy[49, 50]. Once the ledge grows to the edge of the crystal, however,

21

 

Figure 2.1: a) Adatom on a smooth crystal plane. This atom is weakly bound and
may jump 0E the surface or diffuse across the surface. b) L is an atom attached to
a ledge. J is an atom attached to a jog, or a kink, in the ledge (This figure is from
Porter and Easterling [49]).

there are no readily accessible locations for more atoms to be added. The continued
growth of the crystal depends on a sufficient number of atoms adsorbed onto the new

surface to form another ledge.

What if the supersaturation is not sufficient to cause a cluster of atoms to form?
Dislocations, particularly screw dislocations, in the existing crystal can be a step-
ledge site for new atoms to adhere to [51]. A screw dislocation creates a ledge that
will spiral upwards as more and more atoms are added to the ledge (see Figure 2.2).
If the Burgers vector of the dislocation is large, the central part of the screw will
be considerably strained. If the Burger’s vector is very large, atoms will not occupy
the center portion of the screw dislocation in order to relieve the strain, even though
this means accommodating the additional surface energy [52]. Additionally, the step

ledges have a tendency to bunch together as the ledges spiral around [50]. Step

22

 

Figure 2.2: The screw dislocation causes the ledge to spiral around the crystal. (This
figure is from Porter and Easterling [49])

bunching can create steps several atomic layers thick.

Another concept related to crystal growth is surface roughening. Burton, Cabrera,
and Frank had some concept of surface roughening. They knew that at low temper—
atures step ledges would have lower kink densities than at higher temperatures [51].
This has since been observed as both geometrical and round shaped spirals around
screw dislocations [9]. Round spirals have rough steps with a high kink density. This
allows the step to advance in all crystallographic directions. Geometrical spirals have
smooth-edged steps and a symmetry that follows the symmetry of the face. For ex-
ample, (0001) SiC spirals can be either triangular or hexagonal as both shapes follow
the symmetry of the (0001) face [9]. Surface roughening is found in three dimensions
as well [53]. When cubes of NaCl are at equilibrium with the surrounding vapor
above the roughening temperature, the corners and edges of the cube round off [54].
Jackson added to the discussion of surface toughening with the introduction of the
a factor. The Jackson a factor assigns an approximate value for the relative surface

roughness of various materials [55].

Another method of crystal growth is described by chemical vapor transport (CV T).
CVT is where a gas picks up an atom in a high energy state on the surface of a solid

and deposits it in a location on the solid where it will have a lower energy. ZnO and

23

InN nanowires have been reported to grow by a self catalyzed vapor transport process

[56, 57].

2.4 Nanowire Growth used in this Study

Gallium nitride nanowires were grown by our collaborators at Howard University.
They were formed by a direct reaction between elemental gallium and ammonia. (NH3)
[58, 59]. Metallic gallium was placed on a boron nitride boat, which was then po-
sitioned in a quartz liner within the furnace tube. The furnace was then evacuated
and 100 sccm of ammonia was flowed through the tube as the furnace was heated to
850°C, 950°C, or 1000°C. A matrix of GaN platelets forms on the quartz liner inside
the furnace tube. N anowires nucleate from active sites on the GaN platelets. The
evolution of the matrix as a function of furnace temperature and growth time is a

major contribution of this thesis and is discussed in Chapter 4.

24

Chapter 3

Characterization Methods

GaN nanowires and the matrix they grew from were characterized using a. variety
of methods. Each method gives different information about the GaN crystalline
formations and their growth process. This chapter describes each method used to
characterize the GaN crystals and explains what knowledge can be gained by using

each method.

3.1 Transmission Electron Microscopy (TEM)

Transmission Electron Microscopes (TEMS) use an electron beam to image a very
thin sample. The TEM takes advantage of the wave-like behavior of electrons to
obtain high resolution images. From the Rayleigh criterion (sin(6’) z 1.22%, where
6 is the angular resolution limit, A is the wavelength of light, and D is the diameter
of the circular aperture), we know that the resolution of a microscope is limited in

part by the wavelength used to form the image. Short wavelengths will give higher

resolution than long wavelengths in otherwise identical systems. The wavelength of

25

an electron can be calculated by

 

 

h.
A = -—
P
h 1
— (3.1)
v 2m0qV 2qV
1 + —
moc2
where h is Plank’s constant, p is momentum, mo is the mass of the electron, q is the
2 V
charge of the electron, and V is the electric potential. The 1/ 1 + q 2 term is
moc

a relativistic correction which is necessary due to the high speeds of electrons in a
TEM. The wavelength of an electron that has been accelerated by a 200kV potential (a
typical TEM operating parameter) is 2.5pm, which is about five orders of magnitude

smaller than the wavelength of visible light.

Within the column of a TEM, a beam of electrons is sent through the thin sample.
The atoms in the sample diffract the electrons. When the diffracted electrons from
one lattice plane have the same phase as the diffracted electrons from another lattice
plane, the Bragg condition (given in 3.2) is satisfied and the waves will constructively
interfere.

2dsin(6) = nA (3.2)
A diagram of a TEM is given in Figure 3.1.

Depending on how the electro—magnetic lenses are focused, either the diffraction
pattern or an interference pattern (the image of the sample) can be observed. High res-
olution TEM (HRTEM) can image samples at an atomic resolution. However, when
looking at an HRTEM image, you are not “seeing” the individual atoms. HRTEM
images are formed by allowing many diffracted beams as well as the transmitted beam
to contribute to the image. When the beams are combined they constructively and

destructively interfere, resulting in phase contrast. Phase contrast can be described

26

electron source

 

 

 

 

 

 

 

 

 

_ sample
c: :3 objecflve lens
4: fi- 3 intermediate lens
(:41: ‘ f :3 projector lens
.............. . screen/camera

 

Figure 3.1: A diagram of the electron beam of a TEM going through the sample and
a series of electro—magnetic lenses.

by [60]
T(u) = 2A(22) sin(x('&)) (3.3)

where 12 is a reciprocal lattice vector. A(u) is the aperture function and takes into
account that an aperture placed after the objective lens will limit the number of
beams used in forming the HRTEM image. x('&) is the phase-distortion function and
takes into account the fact that spherical aberration, astigmatism, and defocus affect

the phase of each beam.

The diffraction pattern of a specific area of the sample can be obtained by putting
an aperture around a selected area of the sample while in imaging mode, and then
switching the TEM to diffraction mode. This technique is known as selected area
electron diffraction (SAED). The resulting diffraction pattern can then be indexed
to obtain the crystal structure of that particular area of the sample by comparing
the relative distances and angles between the difiraction spots. The pattern can be

thought of as the crystallographic structure in reciprocal space. This technique works

27

best when a single crystal is in the selected area, so that all the diffraction spots are
from the same crystal orientation or phase.

Due to the spherical aberration of the objective lens, there is a limit to the size
of the area that can be selected with an aperture [60]. In cases where the area of
interest is too small to be imaged using SAED, a fast Fourier transform (FFT) can
be applied to an HRTEM image of the area of interest to get a pattern similar to the
SAED pattern. The Fourier transform switches between real space (:5) and reciprocal
space (i), so the mathematical processing of the interference pattern of an HRTEM
image results in the same pattern of spots that would be expected from an SAED of
the crystal structure.

In this study, a JEOL 2200FS TEM was used to image the nanowires. The TEM
is an important tool in the study of nanowire growth because it allows the crystalline
structure and growth direction of the nanowires to be determined by solving the
diffraction patterns and fast Fourier transforms (FF Ts) of HRTEM images. The high

resolution of the TEM allows the internal structure of the nanowires to be observed.

3.2 Scanning Electron Microscopy (SEM)

Scanning Electron Microscopes (SEMS) are similar to TEMs in that they also image
samples with an electron beam. SEMS typically operate at around 15kV which means
the wavelength of the electrons are approximately 9.7pm. Therefore SEMs have much
better resolution than light microscopes, but lower resolution than TEMs. The main
difference between a T EM and an SEM is that in a TEM the electrons go through
the sample and in an SEM the electrons only interact with the surface of the sample.
This means that sample preparation is generally much easier for SEM than for TEM
because SEM samples do not need to be thin and electron transparent.

To take an SEM image, the electron beam is rastered across a selected area of

28

electron source

condenser lens

 

scan generator seen coils
com uter monltor
p objective lens
detector & amplifier
sample

Figure 3.2: A diagram of the electron beam of a SEM going through a series of
electro—magnetic lenses and interacting with the sample. Secondary electrons escape
the surface of the sample and get detected.

the sample. The high energy electrons from the electron beam transfer some of their
energy to electrons of the samples atoms, causing the atoms to ionize. The electrons
resulting from the ionization (called secondary electrons) have a low energy, which
means they can only escape the sample if they are close to the surface of the sample.
Electrons that escape the sample are accelerated toward a detector. As the electron
beam is raster—scanned across an area of the sample. the number of electrons detected
is translated into an intensity for each pixel on a computer monitor. Because electrons
near sharp corners or edges can more easily escape the sample and get to the electron
detector, SEM images have a 3D appearance. The basic mechanics of SEM operation

is illustrated in Figure 3.2.

In this study a Hitachi S-4700 II Field Emission SEM was used to examine the
differences in morphology of samples grown under different conditions. It was also
used to characterize the size and shape of the nanowires as well as how the nanowires

are connected to the growth matrix.

29

3.3 X-Ray Diffraction (XRD)

X—ray diffraction (XRD) is useful for determining the crystal orientations found near
the surface of a sample. The sample is placed in a goniometer which can rotate the
sample about multiple axes to precise angular positions. A beam of x—rays is directed
to the surface of the sample and is diffracted according to Bragg’s law (Equation 3.2).
The intensity of the diffracted beam is then detected. This set-up is illustrated in
Figure 3.3. The angle of the sample and the detector are changed relative to the x-ray
source to determine which crystal planes diffract the strongest. For a plot of intensity
vs. 26, the detector and sample are rotated simultaneously so that the x-ray source
and the detector are at the same angle with respect to the detector (see Figure 3.4).
When Equation 3.2 is satisfied, there will be a peak in intensity. Each peak is related
to the distance between the diffracting planes. For cubic structures, the distance d

between planes is given by
a

d: '
\flfl+k2+fl

where a is the length of the unit cell and h, k, and l are the Miller indices. The

 

(an

 

distance between planes for hexagonal structures is given by [31]

 

1
gh2+hk+k2 12

3 a2 62

d:

 

(3.5)

 

where a and c are axes of the unit cell. Thus a peak of x-ray intensity at a specific
diffraction angle corresponds to the specific plane that is causing the diffraction. Not
all planes cause a peak in the intensity. The structure of the crystal determines which
planes cause peaks and which do not. This is characterized by the structure factor.
For a calculation of the structure factor of zinc-blende and wurtzite GaN, see the

appendix.

30

Pole figures relate the relative intensity of the detected x—rays to the crystal ori-
entation near the surface of . the sample. This is done by rotating through (i) and
incrementally changing X while keeping the 26 angle constant. If the observed peak
intensities do not change as a function of beam-sample orientation, the sample surface

does not have a preferred orientation.

31

 

Figure 3.3: The sample (illustrated as a star) is held in a goniometer. The sample
diffracts the x—rays, and the intensity of the x—rays is measured by the detector.

.......... /\/9 x'ray
source
’,26\

Figure 3.4: The geometry of a 20 scan.

32

Chapter 4

Results

The effect of temperature on GaN nucleation and nanowire growth was investigated
at furnace growth temperatures of 850°C, 950°C, and 1000°C. From previous studies
[61, 62] it is known that nanowires grown from 850°C and 950°C have both wurtzite
and zinc-blende crystalline domains along the entire length of the nanowire. The
growth direction is (11?0) for the wurtzite domains and (110) for the zinc-blende
domains. However, the majority of the nanowires and rods grown at 1000°C are pure

wurtzite with a (0001) growth direction.

4.1 Matrix Growth and Evolution

In order to understand why the growth orientation changes as a function of temper-
ature and how nanowires with multiple phases form, it is necessary to understand
what kind of environment the nanowires are growing in. Thus an in-depth study
of the growth matrix was carried out. The matrix, like the nanowires, forms from
the direct reaction of gallium with ammonia. A better understanding the formation
mechanisms of the matrix will also lead to a better understanding of the nanowire

growth.

33

 

l 100 pm

Figure 4.1: (a), (b), and (c) are SEM images of the side view of the matrix growth at
850°C, 950°C, and 1000°C, respectively. The approximate thicknesses of the samples,
indicated by the arrows, are (a) 87pm, (b) 53pm, and (c) 339nm.

4.1.1 SEM of Matrix Cross Sections

The matrix growth and evolution was investigated at the micron scale by imaging
cross sections of the matrix in the SEM. Matrix cross sections were prepared by natu-
ral fracture so that the sample could be viewed edge-on in the SEM. The thicknesses
of each sample is given in Figure 4.1, although it should be noted that the thickness
of each sample varied widely. All SEM images of the matrix cross sections are ori-
ented so that the top of the image corresponds to the “top” of the sample, except
Figure 4.1a, where the matrix is shown at an angle. In both the 850°C and 950°C
growths, distinct changes in the matrix morphology were observed between the top
and bottom surfaces of the matrix, however, such changes in morphology were not
observed in the 1000°C growth.

The matrix grown at 850°C is shown in detail in Figure 4.2b and exhibits distinct
layers of different platelet morphologies. The bottom-most layer (labeled Layer 1) of
the matrix consists of thin bent sheets of GaN, and therefore has a lighter contrast
than other regions of the cross section. The next layer (Layer 2) of the matrix has
small formations with rounded edges. The layer above that consists of relatively large
hexagonal plates and resembles matrix formations on the top surface of the 1000°C

growth (discussed later in this chapter). From the cross section, it appears that the

34

 

Figure 4.2: Side View of matrix growth at 850°C. (a) Comparison of the side View and
top View of the uppermost matrix formation type. (b) Layered growth at 850°C. Lines
and labels on the left side of the picture mark the boundaries between the different.
matrix layers. (c). (d). and (c) Close-up images of layers 3. 2. and 1, respectively.

large platelets prefer to be vertically oriented. Close—up images of Layers 3, 2. and l

of this matrix are shown in Figure 4.2c, d, and e.

The upper most layer of the 850°C matrix. which corresponds to the nanowire
growth surface, consists of small platelets with sharp corners. A close-up of the upper
most layer of the matrix is shown in Figure 4.2a, where the line on the left side of
the image marks the boundary between the top surface and the cross section of the
top matrix region. While some of the large platelets appear to penetrate the surface
(this can also be seen in an SEM of the top surface in Figure 4.5), the majority of
the surface consists of the smaller platelets. It is unclear exactly why small crystals
would form on top of the larger platelets. It is possible that the larger crystals were
etched or otherwise decomposed to form the top layer of small crystals. N 2 is known
to be a carrier in chemical vapor transport mechanisms and could be present in the

growth furnace from dissociated ammonia [63].

The cross section of the 950°C growth showed three different layers of matrix
growth (Figure 4.3b). The top layer (layer 3) appeared to be composed of small
crystallites with relatively sharp edges (Figure 4.3a and c), similar to the top layer of
the 850°C growth. Layer 2, pictured in Figure 4.3d, had distinct, rounded formations
that appear similar to the layer of 850°C growth shown in Figure 4.2d. The size and
shapes of the matrix in the bottom layer (Figure 4.3e) are comparable to those in

layer 2, but they are more densely packed.

It is interesting to note that the top surface of both the 850°C and 950°C are
similar, even though in the 850°C growth the top layer forms on large crystals, and
in the 950°C growth the top layer forms on small rounded crystals. The 950°C
growth appears to skip the large crystal growth altogether and jump directly into the
small crystal formations from which the nanowires nucleate. Alternatively, it may be
possible that the large crystals did form, but were etched more quickly than those of

the 850°C to create the small crystals.

36

top

side

 

Figure 4.3: Side View of matrix growth at 950°C. (3) Comparison of the side view
and top View of the uppermost matrix formation type. (b) Layered growth showing
three different matrix formation types. (c). (d), and (e) Close—up images of layers 3,
2, and 1. respectively.

37

The cross sectional view of the 1000°C sample did not show any evidence of
layered platelet morphologies. Relatively large crystal domains were present from the
top to the bottom of the sample (see Figure 4.4a). However, interesting formations
were observed. Figure 4.4d shows a number of holes formed in one portion of the
sample near the bottom of the matrix. Most of the cross section had structure that
was similar to that shown in Figure 4.4c, which was imaged near the middle of the
cross section. Hexagonal pits were observed near the top of the sample (see Figure
4.4b). The bottom of the hexagonal pits appear to be flat. These pits could have
come about by an etching process, since it seems unlikely that the matrix selectively

grew around the pits.

4.1.2 SEM of the Top Surface of the Matrix

Nucleation sites for nanowires are found on the top surface of the matrix for all three
growths. Nanowires were also observed on the bottom surface in the 1000°C growth,
and will be discussed later. SEM images of the top surface, for each of three matrix
samples grown at 850°C, 950°C, and 1000°C are shown in Figure 4.5. The matrix
morphology was observed to change as a function of growth temperature, and an
abrupt change occurs in the growth mechanism between 950°C and 1000°C.

The 850°C and 950°C matrix formations were similar and consisted of approxi-
mately 1pm sized platelets. Nanowires growing from this type of matrix had a cross-
sectional width of 50nm to 250nm. Note that a few larger crystals with lengths on the
order of 1011m emerge through the surface of the 850°C growth on the left hand side
of Figure 4.5a. These larger sized crystals were never observed at the 950°C growth,
and this observation is confirmed by the matrix cross sections. The nanowires appear
to grow from the edges of the platelets and have triangular cross sections.

At 1000°C three different types of matrix were observed. Type 1 had relatively

large 1-20pm crystallites of GaN. A few large rods with widths between 0.511111 and

38

 

Figure 4.4: (a) Side view of the 1000°C growth. (b) Close-up of the top portion of
the cross section. Inset shows hexagonal pits. (c) Middle portion of the sample. ((1)
Holes near the bottom of the sample.

39

 

Figure 4.5: SEM images of typical GaN matrix and nanowire growth. (a) SEM images
of typical 850°C growth showing several nanowires growing from the matrix (b) SEM
images of typical 950°C growth. (c) Matrix growth at 1000°C. Type 1 matrix consists
of large GaN crystallites, Type 2 matrix consists of medium—sized platelets with sizes
on the order of 1 pm, and Type 3 matrix consists of small platelets on the order of
0.1 pm.

40

30pm formed from the Type 1 matrix. These rods have a hexagonal cross section,
and no wires with diameters less than 100nm were observed growing from these parts
of the matrix. Because of the hexagonal cross section, these rods grow in the (0001)
direction, and this has been confirmed by TEM. Type 2 matrix had medium sized 0.1-
1pm platelets. The Type 2 matrix growth appeared to be comparable to the matrix for
850°C and 950°C and also had similar nanowire nucleation. Type 3 matrix consisted
of small platelets around 50—300mm wide and the platelets were typically clustered in
spherical mounds. NW growth was also observed from the Type 3 platelets. These
nanowires also had a triangular cross section, suggesting that the growth mechanism
may be the same as the nanowires that grew at 850°C and 950°C. Specific nucleation
sites for nanowires and rods will be discussed in Section 4.2.1. The remainder of this

section will continue to focus on the growth and morphology of the matrix.

4.1.3 SEM of the Bottom Surface of the Matrix

The bottom side of the matrix (the side that formed on the quartz tube in the growth
furnace) was also imaged using the SEM to study the evolution of the matrix. In
Figure 4.6, the top and bottom sides of two pieces of matrix from the 850°C growth
were placed side by side to be imaged. The morphology of the matrix on both surfaces
were similar, however, nanowires were only observed on the top surface of the matrix.

The bottom surface of the 1000°C growth is every bit as complex as the top
surface. A wide angle view of the bottom surface (Figure 4.7a) shows that multiple
matrix formations are present and that rod growth is possible. Near the base of
the rod, nanowires were also observed (Figure 4.7b). Nanowires were observed to
originate from areas of the matrix with smaller crystallites, as shown in Figure 4.7c.
Some of these nanowires had nodules on them, which may indicate the beginning of
dendritic growth.

One of the matrix regions on the bottom surface of the 1000°C growth looks like

41

 

Figure 4.6: (a) Matrix morphology of the top and bottom surfacrs of the 850°C
growth are similar. (b) Close-up of the boxed area in (a). Arrows point to nanowires
on the top surface. No nanowires were observed from the bottom surface.

42

 

Figure 4.7: (a) A wide angle view of the bottom surface of the 1000°C growth. The
area in the solid square is shown in (b) and contains nanowire growth near the base of
the rod. The area in the dotted square is shown in (c) and contains nanowire growth.

43

the top surface of the 1000°C growth. SEM images of these regions are shown for
comparison in Figure 4.8a and b. Hexagonal rods and medium and large crystallites
comparable to the Type 2 and Type 1 matrix described in Figure 4.5 were observed
on both the top and bottom surfaces. Nanowires were also observed to originate
from the medium platelets of both the top and bottom surfaces. A different region of
the bottom surface resembles matrix formations observed in the cross section of the
1000°C matrix. SEM images of these regions are shown for comparison in Figure 4.8c
and (1. Neither of these regions has a clearly defined platelet structure and a number
of holes are evident in both images. It may be possible that part of the bottom surface
broke off during sample preparation, revealing the matrix structure of the center of
the matrix instead of the true bottom surface.

Another region of the bottom surface had a unique structure not observed on any
other sample. This region is composed of 2-10 pm domains of platelets which are
all oriented in the same direction. SEM images of this matrix formation is shown in

Figure 4.9.

4.1.4 XRD of the Matrix

Nanowires grown at 850°C and 950°C contain zinc-blende crystalline domains. There-
fore, the growth surface of the matrix was carefully investigated to determine if it had
any significant portion of zinc-blende crystal structure to serve as a nucleation site.
XRD provides information about the crystal structure near the surface of the sam-
ple, since the x-rays only penetrate a few microns into the sample. Intensity peaks
occur for planes with allowed Bragg reflections, as determined by the structure factor
(see the Appendix for details of the structure factor calculation for zinc-blende and
wurtzite GaN). Most of the zinc-blende peaks occur very close to wurtzite peaks. The
exception is the (002) zinc-blende peak at 39.80, which makes it the main marker for

detecting the presence of zinc-blende.

44

bttm(b)

I . ‘

25 uni,”

bottom(d)3,

 

Figure 4.8: (a) and (c) Two different areas on the bottom surface of the 1000°C
growth. (1)) The top surface of the 1000°C- growth is comparable to (a). (d) The
cross section of the matrix is comparable to (c).

 

Figure 4.9: (a) Region of unique mater formation on the bottom of the 10000C
growth. (b) Close-up of (a).

Relative intensities of powder diffraction for wurtzite and zinc-blende GaN are
plotted in Figure 4.10 [5, 6]. The relative intensities of zinc-blende GaN had to be
obtained from recent literature instead of from the standard reference of the powder
diffraction files because zinc-blende GaN is an uncommon material. An ideal powder
diffraction sample has small crystal particles with completely random orientations.
A sample containing crystals with a preferred orientation will have different relative
peak intensities than a sample with random orientations [64]. Data from the 26 scan of
the sample grown at 850°C is also plotted in Figure 4.10. The relative peak intensities
from the 850°C sample are close to the relative intensities for powder diffraction from
wurtzite GaN, suggesting that the GaN platelets on the sample surface are randomly
oriented. A pole figure was taken of the 850°C sample, which also suggested that the
platelets were randomly oriented and the surface of the sample has no texture.

X-ray diffraction (XRD) of the growth surface of each of the three samples reveals
that the matrix is predominantly wurtzite. The 26 scans for each of the three samples
are compared in Figure 4.11. Silver epoxy was used to adhere the GaN samples to a
steel puck, so peaks from silver and iron are apparent in the 26 scans. A 26 scan of just
the epoxy and steel is also shown in Figure 4.11 for comparison. There was not enough
of the zinc-blende structure over the surface of the sample to form a significant peak
at 39.80. We therefore conclude that the growth surface is predominantly wurtzite.
This finding is important as it establishes that there is no evidence for a zinc-blende
nucleation site for the homoepitaxial growth of the zinc-blende domains within the

nanowires.

4.1.5 TEM of the Matrix

FF Ts of HRTEM images of growth matrix platelets further confirm that the platelets
are wurtzite. The platelets may have smooth sides and sharp corners (Figure 4.12a) or

nanoscale ledges on the sides (Figure 4.12l)—d). Smooth sides and nanoscale ledge sides

46

 

 

 

 

 

 

 

 

 

 

I wurtzite

_ A u A zinc blende
g u ——esoc
g I II
a " u .
a
g n
a ‘ - '
E - .
I
2 A A
g I I

so 40 so so 70 so

20(degroos)

Figure 4.10: Relative intensities of each peak for powder diffraction of wurtzite [5]
and zinc—blende [6] GaN . The 26 scan of the 850°C sample is included for comparison.

47

 

Intensity (arbitrary units)

 

 

 

 

. 950C
We:
850C
JMJJW i MM
control
so 40 so so 7h so
29 (degrees)

Figure 4.11: 26 scans for each growth temperature. The control sample was the steel
puck and silver epoxy used in the sample preparation.

48

may be present on the same platelet. The nanoscale ledges are 10—30 nm wide and,
judging from the electron transparency, on the order of tens of nanometers thick. The
nanoscale ledges are triangular with {1010} sides, and an apex pointing in a (1120)
direction. Some platelets had apparently decomposed in the [1120] direction. This
decomposition occurred both at the platelet level (Figure 4.12c), where the corners
are rounded instead of faceted, and at the nanoscale ledge level (Figure 4.12d), where
a {1120} plane could also be exposed. From the size of the platelet shown in Figure

4.12c, it is likely that the platelet came from the Type 2 matrix of the 1000°C growth.

4.2 (1120) Nanowire Nucleation and Growth

Orientation change, single phase vs. multiphase, and cross sectional width and shape
are the main points of differentiation between nanowires and rods. This section deals
with nanowires that grow in the (1120) direction and are typically multiphase with
a triangular cross section 30-250 nm in width. This type of nanowire growth is the
predominant form of nanowire growth at 850°C and 950°C. This type of nanowire

also grows at 1000°C from similar growth matrix surfaces.

4.2.1 SEM of (1120) Nanowires

N anowires from the 850°C and 950°C growths are oriented with the axis of the wire
in the [1120] (wurtzite) and [011] (zinc blende) directions, as demonstrated by TEM
(shown later). SEM images of these growths show that the nanowires originate from
the sides of the wurtzite platelets and the [1120] growth direction can often be inferred
from the images. Close-up images of nanowire base and tip morphologies are shown
for all three temperatures in Figure 4.13. Nanowires with triangular cross sections
were observed in the 850°C and 950°C growths, as well as the Type 3 matrix at

1000°C. This can be seen in Figure 4.13 (b) and (f). In Figure 4.13(a), the nanowire

49

850°C , 1000°C
‘ Decomposed platelet

[2110]

 

Figure 4.12: TEM of the matrix platelets. (a) A platelet grown at 850°C with smooth
sides. (b) A platelet grown at 850°C with nanoscale ledges. (c) A platelet grown at
1000°C which has decomposed at the corners. (d) Close-up of the area indicated in
(c). (Figure adapted from pictures published in Nanotechnology [7].)

50

(grown at 850°C) appears to originate from several layers of the matrix. Similar
nucleation sites were observed in the 950°C growth and in the Type 2 matrix 1000°C
growth. The nucleation sites shown in Figure 4.13(e) and (d) appear to come out
of the edges of the platelets. On both of these nanowires, a thin fin appears to be
attached near the base of the nanowire, indicating competitive growth in the (1010)
direction. In GaN thin films, the (1120) direction is the fastest growth direction, and
(1010) is the second fastest direction. In the ease of these nanowires, the growth rates
in the (1120) and the (1010) directions compete, and the (1120) growth eventually
dominates so much that a nanowire is formed instead of a platelet. Similar nucleation
sites were also observed in the 850°C growth.

Nanowires grown from the Type 3 matrix are shown in Figure 4.13(e) and (f) It
is not known for certain what growth direction these nanowires have, but the (1120)
direction is likely because of the triangular cross section. Additionally, a single phase
nanowire grown in the (1120) direction was observed in the TEM for the 1000°C
growth, so it is possible that the nanowires from the Type 3 matrix formations are

single phase.

4.2.2 TEM Nanowire Cross Sections: N anowires as a Nucle-

ation Mechanism Diagnostic

Cross sectional HRTEM of the nanowires was performed in order to obtain informa-
tion of the internal crystal structure of the nanowires. These samples were prepared
using a focused ion beam (FIB) to mill a thin slice from the center of the wire, and
the details of this procedure are described elsewhere [7, 8]. Nanowire cross sectioning

and HRTEM was performed by B. W'. Jacobs; however the analysis of the 950°C

cross section is a new contribution of this thesis.

A cross section of a nanowire grown at 850°C is Shown in Figure 4.14. Multiple

51

 

Figure 4.13: SEM images of nanowire nucleation sites and tips. (a) and (1)) 850°C
growth of two different nanowires. (a) Nucleation site. (b) NW tip. (c) Nucleation
site of a 950°C- nanowire. (d) Nucleation site of a 1000°C nanowire grown from the
Type 2 matrix. (e) and (f) Two different nanowires from the Type 3 matrix of the
1000°C growth. (0.) Nucleation site. (f) NW tip.

52

wurtzite and zinc-blende domains were observed in the nanowire, and the boundaries
between the domains are marked in Figure 4.14. FFTs from each domain are given on
the left side of the figure, and domains 1-4 were indexed as wurtzite with a (1120) zone
axis while domain 5 was indexed as zinc-blende with a (011) zone axis. The arrows
indicate the (0001) or (111) direction. The zinc-blende {111} plane is equivalent to
the wurtzite {0001} plane, so the two crystalline phases can form a coherent interface
along those planes. The arrows from domains 4 (wurtzite) and 5 (zinc-blende) are
parallel, and the two domains share a long coherent interface, indicated by a solid line
in Figure 4.14a. Domain 2 has additional crystal structure shown in Figure 4.14b.
While the interfaces between wurtzite domains were incoherent, zinc—blende regions
were able to fill in some of the gaps between the wurtzite domains with one or more

coherent interfaces.

Domains 1, 3, and 4 all have two facets on {0111} planes and one facet on the
(0001) plane. For all three regions the (0001) facet is found at an internal interface,

not on an external facet. The zinc-blende domain 5 faceted on the {111} planes.

An analysis of the 950°C cross section is given here. In Figure 4.15a the nanowire
is shown buried in gold and platinum to protect the wire from the ion beam. The cross
section has an asymmetric shape and has a number of contrast features on it. These
contrast features are related to the several crystallographic orientations within the
nanowire. The boundaries between the crystalline domains are highlighted in Figure
4.15b. None of the domains are triangular in shape, while three of the four wurtzite
domains from the 850°C cross section were'triangular. FFTs for each domain are
given on the right, and domains 2—4 were indexed as wurtzite with a (1120) zone axis
while domain 1 was indexed as zinc-blende with a (011) zone axis. The arrows on
the FF T 3 point toward the zinc-blende (111) or wurtzite (0001) directions. Three of
the five wurtzite domains have similar orientations and are labeled 3a, 3b, and 3c to

clarify their relation.

53

 

Figure 4.14: (a) Cross section of a nanowire grown at 850°C. Dotted lines indicate
incoherent interfaces between crystal domains and solid lines indicate a coherent
interface. FF Ts for each domain is given on the left. (b) Close up of crystal domain
2. (Figure adapted from pictures published in Nanotechnology [7].)

A close—up of the central region of the nanowire, which includes the parallelogram-
shaped zinc-blende region, is shown in Figure 4.15c. The zinc—blende domain is faceted
on the {111} planes. The triangular light. contrast region on the right hand side of
the zinc—blende region appears to be amorphous. On the left side of the zinc-blende
domain. a coherent interface is formed with the wurtzite (0001) plane of domain 2.
This is confirmed in the FF Ts of the two domains because the arrows pointing to
the (111) and (0001) directions are parallel. The interfaces between the zinc-blende
domain 1 and the wurtzite domains 3b and 30 (shown by the upper two dash—dot.
lines) are close to aligning. However, the orientations indicated in the FFTS are
not perfectly aligned. Because the coherent planes are not perfectly aligned, stacking
faults are expected and were observed. In the interface between domains 1 and 3c, the
stacking faults last for about 20mm and the lower boundary to the stacking faults is
indicated with the lowest dash~dot line. This region is neither zinc—blende or wurtzite,

as confirmed by F FT. Along the wurtzite (0001) and zinc—blende (111) directions. the

54

only difference between the crystal structure is that wurtzite has ABAB stacking and
zinc-blende has ABCABCstacking, so it is easy for planes of atoms to switch between
the stacking orders.

Some of the interfaces between the wurtzite domains are shared by equivalent
planes. The interface between between domain 2 and domain 3a are {0111} planes.
The interface between between domain 2 and domain 30 are {0113} planes. The in-
terface between between domain 3a and domain 3b are {0110} planes. The equivalent
planes in the interface between domains 2 and 3c and the interface between domains
3a and 3b are not aligned perfectly, causing thin regions of disorder at the interfaces.

The interfaces adjacent to domain 4 are not made up of equivalent planes. Zinc-
blende/wurtzite stacking faults extend along the entire length of the interface between
domains 3b and 4 and along about half of the interface between domains 3c and 4.
The Be / 4 interface has a {0111} plane on the Be side that meets with a {0001} plane
from the domain 4 side. If domain 4 were directly adjacent to domain 1, the {0001}
wurtzite plane would be against the {010} zinc-blende plane, which do not form a
coherent interface. Considering that the crystalline orientation of domain 4 is so
different from orientations of the adjacent domains, it is not surprising that the light
contrast area between domains 1 and 4 is amorphous.

Domain 3b of the 950°C growth is the only wurtzite domain that has an external
facet along the (0001) plane. All other wurtzite domains have external facets along

the {011x} pyramid planes (see Figure 4.16).

4.2.3 Asymmetric Cross Sections

W hile some nanowires appeared to have symmetric triangular cross-sections, others
did not. Nanowires with asymmetric cross sections were observed at all three growth
temperatures (see Figure 4.17). End on views of these nanowires suggest multiple

crystalline domains and the domains often have a triangular cross section. In SEM

55

 

Figure 4.15: (a) Cross section of a nanowire grown at 950°C. The Au and Pt coatings
protect the nanowire during the F IB process. (b) Outlines of the apparent crystallo-
graphic regions. F FTs of each region are given on the right. Region 1 was the only
zinc—blende region; all other regions are various orientations of wurtzite GaN . Arrows
on the FF Ts point in the (111) direction for region 1 and in the (0001) direction for the
others. (e) HRTEM of the interfaces between the zinc-blende and wurtzite regions.
The solid line. indicates a coherent interface the dash—dot lines indicate boundaries
with stacking faults, and the curved dash—dot line indicates the boundary between
domains 2 and 3c where equivalent planes nearly line up. (TEM images courtesy of
B. W. Jacobs.)

56

 

Figure 4.16: Side facets of the 950°C TEM cross section. The solid lines indicate
coherent interfaces. dotted lines indicate incoherent interfaces, and dash-dot lines
indicate equivalent planes that nearly line up. (TEM image courtesy of B. W. Jacobs.)

images of the 850°C and 950°C growths, nanowires that had non-symmetric cross
sections were generally shorter than other nanowires in the growth, suggesting that
the non-symmetric nanowires grew at a slower rate. The apparent domains are com-
parable in size to the domains observed in the TEM cross sections. Like the TEM
cross section of the nanowire grown at 950°C, these nanowires are likely to be shaped

this way in order to accommodate stacking faults between different crystal domains.

4.3 [0001] Nanowire and Rod Nucleation and Growth

This section deals with nanowires and rods that grow in the (0001) direction and are

typically single phase with a hexagonal cross section 0.1—30 11m in width.

4.3.1 SEM of [0001] Nanowires and Rods

Rods have a [0001] growth direction, hexagonal cross sections, and were observed only
in the Type 1 regions of the 1000°C growth. SEM images showing the connection of
the base of the rod to the matrix are shown in Figure 4.18 and confirm the [0001]
growth direction. Most, but not all, rods taper near the tip region, which has different
facets than the rest of the rod. SEM images of the tips of the rods are shown in Figure
4.19. The tip shown in Figure 4.19a appears to have a spiral. In Figure 4.19b the
rod has a hole off—set from the center of the rod. The hole was deep enough that any
feature at the bottom was not able to be observed because the electrons could not
escape the hole. In both Figure 4.19a and b the faceting of the tip are the (1121)
pyramid planes of the a face. Both the spiral shape of a tip and the presence of
a small deep hole in a rod are indicators of a screw dislocation growth mechanism.

Figure 4.190 shows a side view of a different rod tip.

58

 

Figure 4.17: Non-symmetric nanowires were observed at each growth temperature.
The nanowire shown for the 1000°C growth originated from the Type 2 matrix area.
which is the matrix type most similar to the matrix observed at 850°C and 950°C.

59

 

Figure 4.18: (a) Red base from step—ledge c—face. (b) Rod base from 1011 planes.

60

 

Figure 4.19: (a) Red end displaying spiral growth. (b) Rod imaged end on with a
hole off the center of the red. (C) View of a rod from the side showing the pointed
end structure.

4.3.2 TEM Nanowire Cross Sections: Nanowires as a Nucle-
ation Mechanism Diagnostic

A cross section of a cluster of rods and nanowires grown at 1000°C is shown in Figure
4.20a. Three of the four rods and one of the two nanowires had a light contrast area
near the center of the rod or nanowire [8] A close up of one of the rods and its
light contrast area is shown in Figure 4.20b. The light contrast area appears to be

completely electron transparent, indicative of a nanopipe in the center of this rod.

61

 

Figure 4.20: (a) Cross section of a cluster of rods grown at 1000°C. (b) Close-up of
the bottom rod in (a). Insets show that the rod is oriented along the [0001] zone
axis and that the light contrast area near the center of the rod appears to be electron
transparent. (c) SEM of the cluster of rods. The dotted line indicates where the cross
section was made near the base of the rods. (Figure adapted from pictures published
in Nano Letters [8])

62

Chapter 5

Models of Crystal Formation

Crystals grow due to supersaturation of the vapor surrounding the crystal. The level
of supersaturation is one parameter that can effect crystal morphology. Evidence of
local supersaturation effecting crystal growth is presented in the first section. Re-
laxation also plays a role in determining the final crystal morphology. Relaxation
is first discussed in the matrix growth in the context of growth twins. Relaxation
mechanisms are then discussed in the (0001) rod growth and finally in the (1120)

nanowire growths.

5. 1 Supersaturation

Crystal morphology is inherently tied to the conditions in which the crystals were
formed. Crystal growth requires a supersaturation of the constituent atoms in the
liquid or vapor surrounding the crystal, otherwise the crystal would lose atoms or
remain at equilibrium with its environment. However, crystal growth mechanisms
are a function of the level of supersaturation. This is illustrated in Figure 5.1. An
adatom is more likely to stay on the surface if it can bond to more than one atom in

the crystal lattice. At low supersaturations, the density of adatoms is low, so atoms

63

Stable growth /

 
  

  

 

 

 

(D
q—v
g l
, .1:
4: Dislocation . '3 E
E controlled I 3’
9. 2 3
' 1?.
(D - 2-D I:
l controlled 3
- i
O 0* one
Supersaturation

Figure 5.1: Growth rate as a function of supersaturation. (Image from Wilcox [9]).

will tend to stay on the surface only if they find a ledge or a kink in the surface. Ledges
and kinks are caused by dislocations in the crystal, and at low supersaturations crystal
growth is predominantly caused by dislocations. At higher supersaturations, adatoms
aggregate together until they form a cluster large enough that it is unlikely for the
atoms to remove themselves from the surface. This is known as 2D nucleation. At
very high supersaturations, adatoms can easily stick to the surface of the crystal,
even surfaces with higher surface energies, which causes branching. A structure with
repeated branching is known as a dendrite. There is evidence for all three of these

growth mechanisms in the 1000°C growth.

64

5.1.1 Dislocation Driven Growth

The nanopipes that were observed in the rods by both SEM and TEM cross section
(Figures 4.19b and 4.20) are compatible with a screw dislocation growth mechanism

and may represent dislocation driven growth.

5.1.2 2D Growth

Layered formations were commonly observed on the c faces of the Type 1 matrix
in the 1000°C growth (Figure 5.2a—c). These layers do not show evidence of spiral
patterns that would indicate a screw dislocation. The layers are tens of nanometers
thick, so each observed layer is composed of several layers of atoms. Similar layers

were observed in the cross section of the 850°C matrix (Figure 5.2d).

5.1.3 Dendrites

Dendritic growth was observed near the base of a group of rods (see Figure 5.3).
This group of rods is similar to the group of rods shown in Figure 4.20c used for the
TEM cross section and it is reasonable to assume that they too grew from a screw
dislocation growth mechanism. Because the dendritic growth was so close to the rod

growth, considerable variation of the local supersaturation is likely.

5.2 Crystallography of the Matrix: Twinning

The crystal formations on the surface of the matrix changed considerably from 850°C
to 1000°C. This section describes various crystal morphologies and how they relate
to the crystal structure.

In this growth process, the polycrystalline matrix exhibits several morphologies.

Some of the more exotic crystal morphologies provide evidence for twinning. Twins

65

 

Figure 5.2: (a) Layered growth of the matrix at 1000°C. (b) Matrix from (a) tilted
for a side View. (c) Layered growth at 1000°C making pyramid planes. ((1) Layers
observed in the 8500C matrix cross section.

 

Figure 5.3: (a) Rods from parallel growth at 1000°C. Near the base of the rods is
some dendritic growth. (b) Close up of the dendritic growth.

66

 

Figure 5.4: (a) Interpenetrant cubes twinned about a triad axis [10]. (b) Growth at
950°C.

can arise from the growth process, from a transformation as the system cools down
from growth, or as a result of stress after the crystal has formed [65]. Comparisons
between SEM images and various models of crystal twinning and morphology given in
Phillips [10] and Hahn [11] are illustrated in Figures 5.4, 5.5, 5.6, and 5.7. While none
of these features were common in these samples, each type of feature was observed in

at least two instances in the temperature series samples.

The first type of twinning is known as an interpenetrant twin. In these cases,
there is no well—defined plane of crystal orientations, but the two orientations seem to
grow through each other. In the temperature series, this type of twinning was only
observed in nanowires grown at 950°C where two wires intersected and seemed to

grow through each other (Figure 5.4).

The most frequently observed twinning was along the c direction in the matrix in
the 1000°C growth. Figure 5.53 shows a twinned octahedron. An octahedron has the
same symmetry as a cube, and the faces of an octahedron correspond to the {111}
face of a cube. Because a cubic {111} face is equivalent to the hexagonal {0001} face,

the twinned octahedron can represent twinning perpendicular to the c direction of

67

wurtzite. This is further exemplified in the hexagonal symmetry of the twin plane
shown in Figure 5.5b.

The next type of twinning is the elbow (or geniculate) twin. Figure 5.6a shows
a schematic of a tetragonal elbow twin and b) and c) show multiple elbow twins. A
similar type of morphology has been observed at 1000°C.

Parallel-growth, while not a form of crystal twinning, also involves adjacent crys-
tals with the same, or nearly the same, orientation of all edges. At 1000°C, two
different types of parallel-growth were observed. The first type is when the width of
the wire varies along the length of the wire, as shown in Figure 5.7b. The second
type is where multiple structures are connected at the base by a single structure, as
shown in Figure 5.7c.

Except for the interpenetrant twinning, which occurred in the 950°C growth,
twinning was generally observed in the Type 1 matrix growth at 1000°C. None of
these morphologies were observed in the 850°C growth. The surface of the Type
1 matrix has more distinct faceting, which may allow the twins to be recognized
more easily. It could be that the larger size of the crystalline platelets are formed
by growth processes similar to macroscopic crystals. Additionally, the larger crystal
size and distinct faceting may make each platelet less accommodating of strain at the

crystal interfaces, resulting in twinning to reduce strain.

5.3 Nanowire and Rod Growth

5.3.1 Discussion of the [0001] Growth Direction Nucleation

Mechanism

N anopipes have been observed both at the tip of a rod (Figure 4.19b) and near the

base of rods (Figure 4.20c). The nanopipes observed in these rods and nanowires

68

     

a) b)

      
    
  
 

 

,Vy’//~
W
A, . x4552
‘ fiZK//
/

 

Figure 5.5: (a) A twinned octahedron [10]. (b) The twin plane of (a) [10]. (c)
Growth at 1000°C. The arrow is parallel with the twin plane. (Image courtesy of B.
W. Jacobs.)

69

 

Figure 5.6: (a) Elbow twin of a tetragonal crystal [10}. (b) and (0) Repeated elbow
twinning [10]. ((1) Growth at 1000°C.

7O

 

 

 

Figure 5.7: (a) top and middle: Parallel growth of octahedra [10]. bottom: Parallel
growth of hexagonal prisms [11]. (b) Rod growth at 1000°C. (Image courtesy of B.
W. Jacobs.) (0) Growth at 1000°C.

71

indicate that a screw dislocation growth mechanism is likely. Although the screw
dislocation is what allows the rod to grow, it also introduces strain immediately
surrounding the dislocation. If the Burgers vector of a screw dislocation is large, a
hollow core will form in order to relieve strain from the dislocation. At this point, it
is more energetically favorable for the system to accommodate the surface energy of

the sides of the nanopipes than to have an enormous strain around the dislocation.

5.3.2 Discussion of the (11?0) Growth Direction Nucleation

Mechanism

The change in growth direction from (IIQO) to [0001] was caused by a change in the
matrix from which the nanowires and rods nucleate. At the lower temperatures and
in the Type 2 and 3 matrix regions of the 1000°C growth, nanowires nucleate from the
nanoscale ledges of the platelets, whereas in the Type 1 matrix, rods form from screw
dislocations. It is possible that exposed {11i0} planes of multiple nanoscale ledges
(see Figure 4.12) act as nucleation sites to the wurtzite domains of the nanowires.
Both the nanoscale ledges and the individual crystal domains observed in the TEM
cross sections of the nanowires are on the order of tens of nanometers wide. Any zinc—
blende component of the nanowires may form in order to relieve strain between the
multiple wurtzite domains. We have not found evidence of a zinc-blende nucleation
site in the matrix, so it is likely that the zinc-blende forms as a relaxation mechanism
to relieve strain between the multiple wurtzite domains of the nanowire. All the zinc—
blende regions found in the 850°C and 950°C cross sections had at least one coherent
interface with a wurtzite region. This suggests that the zinc—blende regions could
originate from one of the wurtzite regions, just by changing the stacking order from

ABAB to ABCABC in order to accommodate strain on the other sides.

This proposed growth mechanism is a new variation of templated nanowire growth.

72

W'urtzite domains provide a self-assembled template whereby a zinc—blende nanowire

forms in order to relieve strain between the wurtzite domains.

73

Chapter 6

Conclusions

Matrix growth surface morphology is dependent on the temperature, however, at all
three temperatures studied, the matrix platelets were found to be wurtzite by XRD.
In the 1000°C growth, multiple types of twinning was observed in the matrix with

the largest platelet formations.

One advantage of catalyst free nanowire growth is that the growth mechanism
is not limited by the catalyst. This study identifies three different nanowire growth
mechanisms that occurred in our samples of catalyst free GaN nanowire growth:
multidomain nanowire growth in the (011)/(1120) directions from nanoscale ledges
at the edge of wurtzite platelets, hexagonal rod growth in the (0001) direction from

screw dislocations, and dendritic nanowire growth due to a high local supersaturation.

Nanowires with multiple crystalline domains can have very complex structures.
These nanowires may have triangular cross sections or they may have asymmetric
cross sections with triangular components. The crystalline domains try to align to
other domains by matching equivalent planes, but this is not always possible. In order
to relieve internal strain, zinc-blende domains are formed by changing the stacking or-
der of the c-face planes. creating a zinc-blende nanowire within the wurtzite domains.

This represents a novel method of templated nanowire growth.

74

Hexagonal rods form from screw dislocations and are associated with regions that
may have had a low local supersaturation during growth. These rods sometimes
exhibit holes, which indicate that the Burger’s vector of the dislocation is very large.
Dendritic nanowires could be found originating from matrix close to the rods and
possibly formed due to high local supersaturation.

Future work on this nanowire growth could include using a nanomanipulator to
select a nanowire-platelet pair to prepare a sample for TEM. To date, a nanowire
connected to a growth matrix platelet has not been observed in the TEM. This would
give more information about the interface between the nanowire and the platelet, as
well as allow for observation of the platelet edges to test our hypothesis that nanowires
nucleate from nanoscale ledges of the platelets.

Another interesting experiment would be an attempt to synthesize rough platelet
edges to control nanowire growth locations and internal structure. Such experiments
would give further insight to multiphase nanowire formation and allow for closely con-
trolled experiments on electronic properties of these nanowires. Multiphase nanowires
will have unique electronic characteristics because crystal structure is inherently tied
to the electronic properties of a material.

The results from this thesis give further insight into the methods and mechanisms
of nanowire growth in a catalyst free environment. Fundamental understanding of
nanowire growth will aid future development of applications and devices utilizing

nanowires.

Appendix A

Appendix: Structure Factor
Calculations for Zinc-Blende and

Wurtzite GaN

The structure factor is given by

F = ije—zK-rj (A.l)
.7
where fj is the atomic form factor, K is the reciprocal lattice vector, and fj is the

position vector of the atom. The sum is over all atoms of the unit cell.

For GaN, the atomic form factor f 3' will be different for Ga and N and the values
can be looked up in the International Tables for Crystallography [66]. However,
because my main purpose in calculating the structure factor is to determine which
Bragg reflections are allowed (F 75 O) and which are not (F = 0), it will be assumed
that the Ga and N portions of the structure factor do not perfectly cancel each other

out. This is a reasonable assumption, as will be shown later on.

76

A.1 Zinc-blende Structure Factor

Consider the zinc-blende structure to be the simple cubic structure with a basis of 8

atoms. The position of each atom is given by

r, = 0
7“2 = $033M?)

r3 = g(aHfi)

r4 = gens)

r5 = g(a“:+y+:‘:)
t6 = ifa+m+§g
r7 = §f(e+2)+%g
r8 = §f(§+5)+%e

and can be visualized in Figure A1
The reciprocal lattice vector of a simple cube is

. 2.
K = germ-g +15)

(A.3)

Substituting equations A2 and A.3 into equation A1 and arbitrarily choosing Ga to

be in the 7‘1 position, the structure factor is

F = fade—firm) +e—i7r(h.+k)+e—i7r(h+l) +e—i7r(k+l)]+
fN[e—z'7r/2(h+k+l) +e—i7r/2(3h+3k+l)+

e-irr/2(3h+k+3[) + e—z’rr/2(h+3k+3l)]

77

(A4)

 

Figure A.1: Illustration of the position of each atom in the basis of the zinc-blende
structure. (Image produced using the VESTA software package [4].)

78

 

h k 1 Ga Atoms N Atoms Structure Factor
0 0 1 0 0 O

0 1 1 O 0 0

1 1 1 4 4-2' 4 fGa+4i f N
O 0 2 4 —4 4 fGa’4 f N
0 1 2 O 0 0

1 1 2 0 O 0

0 2 2 4 4 4 fGa +4 fN
0 O 3 0 0 0

1 2 2 0 0 0

0 1 3 0 0 O

1 1 3 4 -42' 4 fGa-4i. f N
2 2 2 4 -4 4 fGa'4 f N
0 2 3 0 0 O

1 2 3 O 0 0

0 O 4 4 4 4 fGa +4 f N
0 1 4 O 0 0

2 2 3 0 O 0

Table A.1: Results of the zinc-blende structure factor calculations.

Since 6—2.7? = —1 and (Tm/2 = —i, equation A.4 simplifies to

F : fGa[1+(_1)h+k+(_1)h-f-l+(_1)k+f]+

fN[(—'i-)h+k+’ + (_i)3h+3k+l +

The structure factor was calculated for all planes that could diffract with 26 S 90°. As
shown in Table A.1, all but six of the planes have a structure factor of zero, meaning
only six intensity peaks would be observed in the range 26 _<_ 90°. The intensity of
diffraction is proportional to IFI2, so complex structure factors are not a problem.
Because the masses of gallium and nitrogen are so different, the atomic scattering
factors fGa and f N are also quite different, as can be verified in the International
Tables for Crystallography [66]. Thus structure factors such as 4 fGa'4 fN will not. be

ZQI‘O.

79

A.2 Wurtzite Structure Factor

For wurtzite GaN, finding the reciprocal lattice vector and the position of the atoms
involves more geometry because the unit vectors are not perpendicular. Since wurtzite
is the hop structure with a two atom basis, and hop is the simple hexagonal struc-
ture with a two atom basis, the reciprocal lattice vector of the simple hexagonal
structure can be used. The unit vectors illustrated in Figure A.2 can be described

mathematically by

 

 

 

a1 2 at
. ai + ax/3 ,
a = — —
2 2 2 y
(33 = CE (A.6)
The reciprocal lattice vectors are therefore
A A, x ‘,
bl = 2n , a?“ a3,
a1 - ((12 X (13)
27r
= — x/Ezi: — ‘
N35 21)
~ 5L3 X EL]
()2 = 27?“ A A
a2 ° (03 X a1)
_ 471’ ,
ax/3y
. 51.1 X 51.2
b = 27: A A A
3 a3 ' (01 X 02)
2,
= is (A.7)
c
The reciprocal lattice vector K is therefore
I? = hf)1 + 1352 +1133
27r 471' 27:
= h— \/3:i‘.— * +k———" +1—2 A.8
a 3( .71) may c ( )

80

 

 

 

Figure A.2: Illustration of the coordinate system used in these calculations and the
position of each atom in the basis of the wurtzite structure. (”1.1 is in the 5: direction
and ('13 is in the 2 direction. (Image produced using the VESTA software package

[4].)

81

The atomic positions for an hcp crystal would be

51 = 0
(I. Cl C
7“- : -—5c+—*+—2 A.9

For wurtzite we need to add two more atoms to the basis. In order to express the :3
components correctly, it is necessary to recognize that there are two different distances
between the planes of gallium and nitrogen. One side of each plane is separated to
the next by the bond length between a gallium atom and a nitrogen atom. The other
side of each plane is separated by the height of the pyramid formed when one atom
is directly above a triangle formed by three atoms of the Opposite type. Because the
base triangle has sides of equal length. the pyramid is a regular triangular pyramid

which has the property that. [67]

e = h2 + 0'— (A.10)

where e is the length of the edge of the pyramid, h is the height of the pyramid, and
a. is the length of the side of the base of the pyramid (i.e. it is the lattice constant
a). However, Equation A.10 has two unknowns, e and h, but because 6 is equivalent
to the bond length between a gallium atom and a nitrogen atom, we can relate these

quantities to the lattice constant c:
c

Using Equations A.10 and All to solve for h and e in terms of the lattice constants

82

a and c results in

h. = 362—4a2
12c
3c2+4a2

From this it can be determined that the other two atoms are at the points

f __ c 3c2+4a2 ;
3 — ' 120 ~

2 2
a, 0 3c -4a
‘ = —“, —' ——f: A.13
7‘4 251‘ + 2\/§y + 12c ( )
Using Equations A.8. A.9, and A.13 in equation Al, the structure factor is
F = fGale—ik'nfl +e-ifif-f2]+fN[e—iK°f‘3 +e—iK-f4]
2 2
11+ k+l
= fGal1+ (-1)3 3 1+
2 2 2 2
36 4a 2 2 3c —4a.
2——'t2——l h+ k+—2——l
le(—1)( 6c ) + (_1)3 3 66 ] (A.14)

When $3 or 7:4 is dotted with A.8, the values for the lattice constants will not cancel

out, so it is necessary to know the numerical values for a. and c. For GaN, they are

[68]

a = 3.19><10-10

c = 5.18x10”10 (A.15)

Table A.2 displays the calculated structure factor for all planes that could diffract
with 26 S 90°. None of the planes results in a. structure factor of zero, so a diffraction

peak is expected to occur for each plane.

83

 

h k 1 Ga Atoms N Atoms Structure Factor

1 0 O 0.5+0.97§ O.03+0.32' (0.5+0.9i)fGa+(0.03+0.37j)fN
0 0 2 2.0 0.7+1.7i (2.0)fGa+(0.7+1.7i)fN

1 0 1 1.5-092’ -1.7-0.42' (1.5-0.9i)fGa+(-1.7—0.42'.)fN
1 0 2 0.5+O.9i. -0.9+1.327 (0.5+0.92')fGa+(-0.9+1.3i)fN
1 1 0 0.5—0.9i 1.3-1.02' (0.5-0.92‘)fGa+(1.3-1.0i)fN

1 0 3 1.5-0.92' -0.3-0.5i (1.5-0.9i)fGa+(-O.3-0.573)fN
2 0 0 0.5-0.9i. 1.3-1.01'. (O.5-O.9i)fGa+(1.3-1.0i)fN

1 1 2 0.5—0.92' 0.3+0.03i (0.5—0.9i)fGa+(0.3+0.03i)fN
2 0 1 1.5+0.9i —0.5-1.7i (1.5+0.9i)fGa+(-0.5-1.7z')fN
0 O 4 2.0 -O.3+0.7z’ (2.0)fGa+(-0.3+0.7i)fN

2 0 2 0.5—0.9i 0.3+0.03i (0.5—0.9i)fGa+(0.3+O.03i)fN
1 0 4 0.5+0.92i -2.0+O.3i (0.5+0.9i)fGa+(-2.0+0.3i)fN

Table A.2: Results of the wurtzite structure factor calculations.

84

BIBLIOGRAPHY

[1] P. Dudesek, L. Benco, C. Daul, and K. Schwarz, “d-to—s bonding in GaN,”
Journal of Physics: Condensed Matter 10, 7155-7162 (1998).

[2] J. Kolnik. I. Oéuzman, K. Brennan, R. Wang, P. Ruden, and Y. Wang, “Elec-
tronic transport studies of bulk zincblende and wurtzite phases of GaN based
on an ensemble Monte Carlo calculation including a full zone band structure,”
Journal of Applied Physics 78, 1033 (1995).

[3] A. Maslov and C. Ning, “Band structure and optical absorption of GaN
nanowires grown along the c axis,” Physical Review B 72, 125319 (2005).

[4] K. Momma and F. Izumi, “VESTA: a three-dimensional visualization system
for electronic and structural analysis.” Journal of Applied Crystallography 41,
653—658 (2008).

[5] Powder Diffraction File 2-1078 Gallium Nitride (International Centre for Diffrac-
tion Data, Swarthmore, Pennsylvania, 1991).

[6] J. A. Jegier, S. McKernan, A. P. Purdy, and W. L. Gladfelter, “Ammonothermal
Conversion of Cyclotrigallazane to GaN: Synthesisi of Nanocrystalline and Cubic
GaN from [H2GaNH2]3,” Chemistry of Materials 12, 1003—1010 (2000).

[7] B. Jacobs, V. Ayres, M. Crimp, and K. McElroy, “Internal structure of mul-
tiphase zinc-blende wurtzite gallium nitride nanowires,” Nanotechnology 19,
405706 (2008).

[8] B. Jacobs, M. Crimp, K. McElroy, and V. Ayres, “Nanopipes in Gallium Nitride
Nanowires and Rods,” N ano Letters 8, 4353—4358 (2008).

[9] Preparation and Properties of Solid State Materials: Growth Mechanisms and
Silicon Nitride, W. R. Wilcox, ed., (Marcel Dekker, Inc., 1982), Vol. 7.

[10] F. Phillips, An Introduction to Crystallography (Longmans New York, 1963).

[11] T. Hahn and H. Klapper, “3.3. Twinning of crystals.” International Tables for
Crystallography D, 393-448 (2006).

85

[12] H. Choi, J. Johnson, R. He, S. Lee, F. Kim, P. Pauzauskie, J. Goldberger, R.
Saykally, and P. Yang, “Self-Organized GaN Quantum Wire UV Lasers,” Journal
of Physical Chemistry B 107, 8721—8725 (2003).

[13] U. Mishra, P. Parikh, and Y. Wu, “AlGaN/GaN HEMTs—An Overview of Device
Operation and Applications,” Proceedings of the IEEE 90, 1022—1031 (2002).

[14] C. Thelander et al., “Nanowire-based one—dimensional electronics,” Materials
Today 9, 28—35 (2006).

[15] M. HeiB, A. Gustafsson, S. Conwa-Boj, F. Peiré, J. Morante, G. Abstreiter, J.
Arbiol, L. Samuelson, and A. Fontcuberta i Mortal, “Catalyst-free nanowires
with axial InxGal-xAs/GaAs heterostructures,” Nanotechnology 20, 075603
(2009). '

[16] “Gallium Nitride: Band structure and carrier concentaration,”,
http:/ / www.ioffe.ru / SVA / N SM / Semicond / GaN / bandstr.html.

[17] S. Nakamura, T. Mukai, and M. Senoh, “Candela—class high-brightness In-
GaN/AIGaN double-heterostructure blue-light-emitting,” Applied Physics Let-
ters 64, 1687—1215 (1994).

[18] T. Fujii, Y. Gao, R. Shanna, E. Hu, 8. DenBaars, and S. Nakamura, “Increase
in the extraction efficiency of GaN-based light—emitting diodes via surface rough-
ening,” Applied physics letters 84, 855 (2004).

[19] K. Akita, T. Kyono, Y. Yoshizumi, H. Kitabayashi, and K. Katayama, “Improve-
ments of external quantum efficiency of InGaN-based blue light-emitting diodes
at high current density using GaN substrates,” Journal of Applied Physics 101,
033104 (2007).

[20] J. Johnson, H. Choi, K. Knutsen, R. Schaller, P. Yang, and R. Saykally, “Single
gallium nitride nanowire lasers,” Nature Materials 1, 106—110 (2002).

[21] Y. Huang, X. Duan, and C. Lieber, “Nanowires for Integrated Multicolor
Nanophotonics,” Small 1, 142—147 (2005).

[22] M. Khan, J. Kuznia, D. Olson, W. Schaff, J. Burm, and M. Shur, “Microwave
performance of a 0.25 pm gate AlGaN/GaN heterostructure field effect transis-
tor,” Applied Physics Letters 65, 1121 (1994).

[23] H. Xing et al., “Gallium nitride based transistors,” Journal of Physics: Con-
densed Matter 13, 7139—7158 (2001).

l24l S. Pear ton, F- R911, A- Zhang, and K. Lee, “Fabrication and performance of GaN
electronic devices,” Materials Science & Engineering R 30, 55—212 (2000).

86

[25] M. Murphy et al., “High—frequency AlGaN/GaN polarization-induced high elec-
tron mobility transistors grown by plasma-assisted molecular—beam epitaxy,” Ap—
plied Physics Letters 75, 3653 (1999).

[26] Y. Huang, X. Duan, Y. Cui, and C. Lieber, “Gallium Nitride Nanowire Nanode-
vices,” Nano Letters 1, 6 (2002).

[27] B. Jacobs, V. Ayres, R. Stallcup, A. Hartman, M. Tupta, A. Baczewski, M.
Crimp, J. Halpern, M. He, and H. Shaw, “Electron transport in zinc-blende
wurtzite biphasic gallium nitride nanowires and GaNFETs,” Nanotechnology
18, 475710—475710 (2007).

[28] J. Phillips, “The Chemical Bond and Solid-state Physics,” Physics Today 23,
23—30 (1970).

[29] M. Kanoun, S. Goumri-Said, A. Merad, G. Merad, J. Cibert, and H. Aourag,
“Zinc-blende AlN and GaN under pressure: structural, electronic, elastic and

piezoelectric properties,” Semiconductor Science and Technology 19, 1220—1231
(2004).

[30] H. Iwanaga, A. Kunishige, and S. Takeuchi, “Anisotropic thermal expansion in
wurtzite-type crystals,” Journal of Materials Science 35, 2451—2454 (2000).

[31] T. B. M. Charles S. Barrett, Structure of Metals: crystallographic methods, prin-
ciples, and data, 3rd ed. (McGraw—Hill Book Company, 1966), pp. 614—615.

[32] J. W. Edington, Practical Electron Microscopy in Materials Science (TechBooks,
1976), pp. 281—296.

[33] Y. Wu and P. Yang, “Direct Observation of Vapor-Liquid-Solid Nanowire
Growth,” Journal of the American Chemical Society 123, 3165—3166 (2001).

[34] W. Seifert et al., “Growth of one-dimensional nanostructures in MOVPE,” Jour-
nal of Crystal Growth 272, 211—220 (2004).

[35] Y. Wu, H. Yan, M. Huang, B. Messer, J. Song, and P. Yang, “Inorganic
Semiconductor N anowires: Rational Growth, Assembly, and Novel Properties,”
Chemistry—A European Journal 8, 1260—1268 (2002).

[36] C. Chen, C. Yeh, C. Chen, M. Yu, H. Liu, J. Wu, K. Chen, L. Chen, J. Peng, and
Y. Chen, “Catalytic growth and characterization of gallium nitride nanowires,”
Journal of the American Chemical Society 123, 2791—2798 (2001).

[37] T. Kuykendall et al., “Metalorganic chemical vapor deposition route to GaN
nanowires with triangular cross sections.” Nano Letters 3, 1063-1066 (2003).

[38] X. Duan and C. Lieber, “Laser-assisted catalytic growth of single crystal GaN
nanowires,” Journal of the American Chemical Society 122, 188—189 (2000).

87

[39] K. Dick, K. Deppert, T. Martensson, B. Mandl, L. Samuelson, and W. Seifert,
“Failure of the vapor-liquid—solid mechanism in Au-assisted MOVPE growth of
InAs nanowires,” Nano Letters 5, 761—764 (2005).

[40] L. Geelhaar, C. Cheze, W. Weber, R. Averbeck, H. Riechert, T. Kehagias, P.
Komninou, G. Dimitrakopulos, and T. Karakostas, “Axial and radial growth of
Ni-induced GaN nanowires,” Applied Physics Letters 91, 093113 (2007).

[41] L. Lari, R. Murray, T. Bullough, P. Chalker, M. Cass, C. Chéze, L. Geelhaar,
and H. Riechert, “N anoscale compositional analysis of N i-based seed crystallites
associated with GaN nanowire growth,” Physica E: Low-dimensional Systems
and Nanostructuras 40, 2475—2461 (2008).

[42] H. Peng, N. Wang, X. Zhou, Y. Zheng, C. Lee, and S. Lee, “Control of growth
orientation of GaN nanowires,” Chemical Physics Letters 359, 241—245 (2002).

[43] C. Nam, D. T ham, and J. Fischer, “Effect of the polar surface on GaN nanos—
tructure morphology and growth orientation,” Applied Physics Letters 85, 5676
(2004).

[44] Z. Dai, Z. Pan, and Z. Wang, “Novel Nanostructures of Functional Oxides Syn-
thesized by Thermal Evaporation,” Advanced Functional Materials 13, 9—24
(2003).

[45] A. Sekar, S. Kim, A. Umar, and Y. Hahn, “Catalyst-free synthesis of ZnO
nanowires on Si by oxidation of Zn powders,” Journal of Crystal Growth 277,
471—478 (2005).

[46] J. M. Blakely and K. A. Jackson, “Growth of Crystal Whiskers,” The Journal
of Chemical Physics 37, 428-430 (1962).

[47] X. Cai, A. Djuriéic’, M. Xie, G. Chin, and S. Gwo, “Growth mechanism of stacked-
cone and smooth-surface GaN nanowires,” Applied Physics Letters 87, 183103
(2005).

[48] D. Moore and Z. Wang, “Growth of anisotropic one-dimensional ZnS nanostruc-
tures,” Journal of Materials Chemistry 16, 3898—3905 (2006).

[49] D. A. Porter and K. E. Easterling, Phase Transformations in Metals and Alloys
(Chapman & Hall, 1993).

[50] Handbook of Crystal Growth, D. T. J. Hurle, ed., (Elsevier, 1993), Vol. 1, pp.
189, 410, 462, 481.

[51] W. K. Burton, N. Cabrera, and F. C. Frank, “The Growth of Crystals and the
Equilibrium Structure of their Surfaces,” Philosophical Transactions of the Royal
Society of London. Series A, Mathematical and Physical Sciences 243, 299—358
(1951).

88

[52] P. Bennema, “Spiral Growth and Surface Roughening: Developments Since Bur—
ton, Cabrera and Frank,” Journal of Crystal Growth 69, 182 (1984).

[53] Growth, dissolution, and pattern formation in geosystems, B. Jamtveit and P.
Meakin, eds., (Springer, 1999), p. 23.

[54] J. C. Heyraud and J. J. Metois, “Equilibrium Shape of an Ionic Crystal in Equi-
librium with its Vapour (NaCl),” Journal of Crystal Growth 84, 503—508 (1987).

[55] K. Jackson, “Constitutional supercooling surface roughening,” Journal of Crystal
Growth 264, 519—529 (2004).

[56] C. Geng, Y. Jiang, Y. Yao, X. Meng, J. Zapien, C. Lee, Y. Lifshitz, and S. Lee,
“Well-aligned ZnO nanowire arrays fabricated on silicon substrates,” Advanced
Functional Materials 14, 589—594 (2004).

[57] S. Vaddiraju, A. Mohite, A. Chin, M. Meyyappan, G. Sumanasekera, B.
Alphenaar, and M. Sunkara, “Mechanisms of 1D crystal growth in reactive vapor
transport: Indium Nitride nanowires,” Nano Letters 5, 1625 (2005).

[58] M. He, P. Zhou, S. Mohammad, G. Harris, J. Halpern, R. Jacobs, W. Sarney,
and L. Salamanca—Riba, “Growth of GaN nanowires by direct reaction of Ga
with N H3,” Journal of Crystal Growth 231, 357—365 (2001).

[59] A. ElAhl et al., “Systematic study of effects of growth conditions on the (nano-
, meso—, micro) size and (one-, two-, three-dimensional) shape of GaN single

crystals grown by a direct reaction of Ga with ammonia,” Journal of Applied
Physics 94, 7749 (2003).

[60] D. Williams and C. Carter, Transmission Electron Microscopy: A T ertbook for
Materials Science (Springer, 1996), pp. 186—187, 463.

[61] V. Ayres et al., “Investigations of heavy ion irradiation of gallium nitride
nanowires and nanocircuits,” Diamond & Related Materials 15, 1117—1121
(2006).

[62] B. Jacobs, V. Ayres, M. Petkov, J. Halpern, M. He, A. Baczewski, K. McElroy,
M. Crimp, J. Zhang, and H. Shaw, “Electronic and Structural Characteristics of
Zinc-Blende Wurtzite Biphasic Homostructure GaN Nanowires,” Nano Letters
7, 1435—1438 (2007).

[63] V. Ayres, M. Farhan, D. Spach, J. Bobbitt, J. Majeed, B. Wright, B. Wright, J.
Asmussen, M. Kanatzidis, and T. Bieler, “'Ifansitions in morphology observed in
nitrogen/methane—hydrogen depositions of polycrystalline diamond films,” J our-
nal of Applied Physics 89, 6062 (2001).

[64] Chapter 7: Basics of X—ray Diffraction, Scintag, Inc., Cupertino, CA, 1999.

89

[65] M. Buerger, “The genesis of twin crystals,” American Mineralogist 30, 469—482
(1945).

[66] International Tables for Crystallography, T. Hahn, ed., (Springer - Verlag, 2005),
Vol. C, pp. 553-564.

[67] “Wolfram MathVVorld: Triangular Pyramid,”,
http: //mathwor1d.wolfram.com/TriangularPyramid.html.

[68] “Gallium Nitride: Basic Parameters for Wurtzite crystal structure,”,
http://www.ioffe.rssi.ru/SVA/NSM/Semicond/GaN/basic.html.

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