Investigation of exciton dynamics and electronic band structure of InP and GaAs nanowires
A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics of the College of Arts and Sciences 2012 by Saranga Dilruk Perera
B.Sc. University of Ruhuna, Sri Lanka
M.S. University of Cincinnati, OH, USA Committee Chair: Leigh M. Smith, Ph.D. ABSTRACT
In this study we used Photoluminescence (PL), Time-resolved photoluminescence (TRPL) and Photoluminescence excitation (PLE) spectroscopy to investigate optical and electronic properties of individual
Zincblend GaAs/AlGaAs core-shell and Wurtzite InP nanowires (NWs) at low temperatures (10K).
GaAs/AlGaAs core-shell NWs were prepared by using Au catalyst- assisted metal organic chemical vapor deposition (MOCVD) method and a titanium-Sapphire laser was used to excite the nanowire sample. PL emission from single NWs exhibit an exciton peak at ~1.515eV. PL and TRPL spectroscopies exhibit high quantum efficiency and exciton lifetimes of
~1ns, which is equivalent to high quality two-dimensional heterostructures.
State filling and many-body interaction effects were observed by increasing the carrier densities using pulsed laser excitation.
Further, polarized TRPL spectroscopy was used to study exciton dynamics in these nanowires at 10K. The polarization of the emitted PL was monitored at the exciton emission peak (1.515~eV) as a function of time after excitation by a polarized pulse. With no quantum confinement effects, in thermal equilibrium the density of excitons dipoles parallel and perpendicular to the NW should be equal. This investigation revealed at low excitation intensities the excitons are created out of thermal equilibrium, but relax within several hundred picoseconds (~200 ps). At higher excitation
II powers, the exciton dipoles relax much more rapidly within a time less than our temporal system response of 80ps. This suggests that exciton dipole relaxation is very sensitive to carrier-carrier scattering.
PLE spectroscopy was used to investigate the electronic band structure of wurtzite InP NWs at 10K with nominal diameters of 50 and
100nm, along with PL and TRPL. The NWs were prepared by Au catalyst- assisted MOCVD growth with 420 ºC growth temperature and a precursor flow rate (V/III ratio) of 700.
PLE spectra show three main peaks for band-to-band transitions between the A, B and C hole bands to conduction band at energies of 1.504,
1.534 and 1.665eV in the 100nm diameter NW sample. From our PLE data we determined the energy splitting between A and B hole-bands as 30 meV and the energy splitting between A and C hole-bands as 161 meV. These measurements allow one to extract a crystal field splitting of 52 meV and spin-orbit interaction energy of 139 meV for these WZ InP nanowires.
Polarized PLE measurements probe the optical selection rules for these band-to-band transitions, which are expected not to be isotropic as for zincblende InP. PLE measurements were extended to probe transitions between the A, B and C valence bands to the higher-level conduction band using pulsed super continuum fiber excitation. The transitions from A, B and C hole-bands to first conduction band were clearly identified in this experiment and we interpret the resonances seen at 1.737, 1.780 and 1.906 eV as the transitions from the A, B and C hole-bands to second conduction
III band respectively. From these measurements we estimated that the second conduction band is 236 ± 6 meV away from the usual WZ band edge.
IV
V ACKNOWLEDGMENTS
I would like to express my gratitude to Professor Leigh M. Smith for be there as my research advisor and mentor during my graduate studies. The main driving forces behind my accomplishments are his ideas, advices and encouragements.
I also like to express my gratitude to Professors Howard E. Jackson and Jan Yarrison-Rice for helping me throughout my research studies and career search by providing ideas and guidance when needed.
I would like to thank Dr. Lyubov Titova, Dr. Thang Ba Hoang, Ashutosh
Mishra and Dr. Aaron Wade for helping me out during various stages of my research. They contributed a lot to my success and spent their valuable time with me in the lab while providing the necessary support and ideas.
My sincerely thanks to my colleagues: Dr. M. Fickenscher, K.
Pemasiri, M. Montazeri, P. Kumar, Y. Wang, S. Teng, B. Bekele who shared their valuable time with me and helping me out during my research study.
My special thanks go to John Markus who was a valuable person when it comes to technical assistant. I am thankful to Bob Schrott, Mark Sabatelli, and Mark Ankenbauer for their help in the machine shop.
I am grateful to the Department of Physics and the graduate school of
University of Cincinnati for giving me the opportunity to pursue my
VI graduate studies. My special thanks go to the Department head, the faculty and the staff for helping me out through my graduate studies and sharing their knowledge with me.
My special thanks go to our collaborators in Australian National
University: Professor C. Jagadish, Dr. H. J. Joyce, Dr. S. Paiman and all the group members for their collaboration with us by providing their samples and knowledge.
I am also grateful to the University of Ruhuna Sri Lanka for the support during my graduate studies.
Finally I am grateful to my Wife, Parents, Brother, all the family members and friends for their sacrifices, encouragements and support.
Because of them, I was able to manage my studies successfully here at
University of Cincinnati.
VII TABLE OF CONTENTS
ABSTRACT ...... II
ACKNOWLEDGMENTS ...... VI
LIST OF FIGURES AND TABLES ...... XII
LIST OF SYMBOLS ...... XVIII
Chapter 1...... 1
1 INTRODUCTION ...... 1
1.1 Importance of Investigation ...... 1
1.2 Semiconducting materials ...... 3
1.3 Band theory ...... 6
1.4 Band structure of ZB GaAs semiconductor ...... 10
1.5 Band structure of WZ InP semiconductor ...... 15
1.6 Excitons ...... 19
1.7 Photoluminescence ...... 23
1.8 Reduced dimensionality of semiconducting nanowires ...... 24
Chapter 2...... 27
2 NANOWIRE GROWTH ...... 27
2.1 Introduction ...... 27
2.2 Growth technique ...... 28
VIII 2.3 Growth parameters and defects ...... 32
2.4 Crystal structure ...... 36
Chapter 3...... 38
3 EXPERIMENTAL TECHNIQUES ...... 38
3.1 Sample preparation ...... 38
3.2 Experiment setup ...... 40
3.2.1 Laser ...... 41
3.2.2 Polarizing Optics ...... 42
3.2.3 Cryostat...... 44
3.2.4 Spectrometer ...... 45
3.2.5 Detectors...... 48
3.3 Photoluminescence spectroscopy ...... 52
3.4 Photoluminescence excitation spectroscopy ...... 52
3.5 Time resolved photoluminescence ...... 55
Chapter 4...... 58
4 GaAs/AlGaAs NW Characterization ...... 58
4.1 Introduction ...... 58
4.2 Growth and Morphology ...... 59
4.3 Photoluminescence measurements ...... 63
4.4 Time resolved photoluminescence ...... 65
IX 4.5 Result and discussion ...... 69
4.6 Summary ...... 72
Chapter 5...... 74
5 Polarization dynamics in twin free GaAs/AlGaAs NWs...... 74
5.1 Introduction ...... 74
5.2 Polarized time-resolved photoluminescence measurements ...... 75
5.3 Model for 2-level system ...... 80
5.4 Results and discussion ...... 84
5.5 Summary ...... 87
Chapter 6...... 89
6 Wurtzite InP nanowire band-structure ...... 89
6.1 Introduction ...... 89
6.2 Growth and Morphology ...... 91
6.3 Photoluminescence measurements ...... 93
6.4 Time-resolved photoluminescence ...... 95
6.5 PLE measurements ...... 98
6.6 Extended PLE measurements ...... 106
6.7 Result and discussion ...... 109
6.8 Summary ...... 110
APPENDICES ...... 113
X Mathematica program to solve the rate equations: ...... 113
REFERENCES ...... 118
XI LIST OF FIGURES AND TABLES
Figure 1: The graph of some commonly used binary semiconductors with their energy band gap versus the lattice constant [17] ...... 5
Figure 2: Energy levels of a single atom...... 6
Figure 3: Energy band structure of Solid: (a) Insulator ...... 8
Figure 4: Band diagram of a direct-(a) and indirect-(b) band gap semiconductor ...... 9
Figure 5: Energy band structure of ZB GaAs[20] ...... 11
Figure 6: ZB GaAs band structure at k=0 ...... 12
Figure 7: Predicted WZ InP band structure by De et al.[22] ...... 16
Figure 8: WZ InP band structure at zone center ...... 17
Figure 9: Wannier exciton with much larger exciton Bohr radius than unit cell ...... 19
Figure 10: Exciton energy levels with respect to two particle wave vector .. 22
Figure 11: Optical excitation, thermalization and emission process of a direct gap semiconductor ...... 23
Figure 12: schematic representation of nanowire growth (a) Au particle dispersion and heating up the substrate (b) Au/Ga alloy formation and growth initiation (c) NW formation and further growth from Au-NW interface...... 29
XII Figure 13: Axial heterostructure NW grown by switching the precursor gas flows...... 30
Figure 14: GaAs/AlGaAs core-shell radial heterostructure Nw...... 31
Figure 15: Schematic illustration of core-multi-shell NW ...... 32
Figure 16: SEM images of GaAs NWs (a) grown at 450 C (b) grown at 390 C (c) two-temperature growth procedure at 390 C (d) two temperature growth procedure at 350 C.[34] ...... 34
Figure 17: Growth temperature and V/III ratio dependence of InP NWs grown using Au-assisted MOCVD method. Scale bars are 2μm long[35]...... 35
Figure 18: NWs dispersed on a patterned Si substrate. The lithographically- defined pattern provides a reference to find a particular wire on the sample
...... 38
Figure 19: Schematic illustration of Photoluminescence setup ...... 40
Figure 20: Polarizing optics: How half wave plate rotate linear polarize light with respect to its optical axis...... 43
Figure 21: How quarter wave plate produces circularly polarized light from linearly polarized light incident at an angle of 45 degrees on its optical axis.
...... 44
Figure 22: Continuous flow liquid helium optical cryostat ...... 44
Figure 23: Spex spectrometer...... 46
Figure 24: Newport spectrometer ...... 47
Figure 25: Schematic diagram of a regular PMT[46] ...... 49
XIII Figure 26: Schematic structure of an MCP and principle of multiplication[46]
...... 50
Figure 27: Schematic illustration of Photoluminescence excitation experiment setup ...... 53
Figure 28: Schematic representation of Time-Resolved experiment setup .. 56
Figure 29: Bare GaAs NWs grown by H.J. Joyce et al...... 60
Figure 30: GaAs/AlGaAs core-shell NW usual single temperature growth .... 61
Figure 31: GaAs core grown using two temperature growth[63] ...... 62
Figure 32: CW PL spectra from GaAs/AlGaAs NW(wire 2) as a function of power. P ~30 µW...... 63 0
Figure 33: comparison of lifetimes between old and new growth of
GaAs/AlGaAs core-shell NWs...... 65
Figure 34: Time decays accumulated at the peak emission energy(1.51eV) from different single NW of GaAs/AlGaAs core-shell NW grown using the two-temperature growth technique at low excitation powers ...... 66
Figure 35 : Time-resolved spectral map for a GaAs/AlGaAs core-shell NW
(wire 4) which exhibit a recombination lifetime of ~1 ns...... 67
Figure 36 : Time resolved PL spectra extracted from time-resolved spectral map at 50,300,600 and 1000 ps after laser pulse ...... 69
Figure 37: Degree of linear polarization of PL emission as a function of excitation energy for wire1(circles) and wire2(square).[68] ...... 74
Figure 38: Polarized time resolved spectra obtain for GaAs/AlGaAs core- shell NW(wire-5). Four configurations were obtained by exciting the NW by
XIV using a linearly polarized laser parallel/perpendicular to NW and obtaining the linearly polarized emission parallel/perpendicular to the NW. Excitation laser power is around ~0.5mW and is measured before the microscope objective...... 77
Figure 39: Emission polarization when excitation source polarized parallel
(Pǁ) and perpendicular (P ) to NW as a function of time after laser pulse. ... 79
Figure 40 : Schematic diagram of the exciton states and its possible transitions when exciting the NW with a laser polarized parallel to the NW 82
Figure 41: Polarization variation with Time after laser pulse. Blue and Red dotted curves represent the experimental emission polarization as a function of time after laser pulse when excited parallel/perpendicular to the
NW. Light blue/pink lines are the same emission polarization predicted by the model for same conditions...... 85
Figure 42: Emission Polarization as a function of time after laser pulse for
NW-5 with higher excitation power (~9mW-measured before the microscope objective). Red/Black color-excitation laser polarized parallel/perpendicular to NW...... 86
Figure 43: (a)-Band diagram of ZB InP semiconductor. Low temperature band gap is around 1.424eV as indicated. Heavy hole and light hole bands are degenerated. (b) Band diagram of WZ InP with low temperature band gap is
1.504eV. The valence band degeneracy is completely removed because of spin-orbit interaction and crystal field effect...... 91
XV Figure 44: (a) FESEM micrograph of 100nm diameter WZ InP NWs (45 degrees tilted substrate). (b) TEM micrograph of a single 100nm diameter WZ InP NW showing excellent crystallinity. Gold seed can be seen at the tip...... 92
Figure 45: Low temperature (10K) CW Power dependent photoluminescence measurements done on typical 100nm WZ InP NW...... 94
Figure 46 : Time-resolved spectral map of single WZ InP 100nm diameter
NW. Time decays are obtained by using 200 fs pulsed excitation wavelength tuned to 780nm...... 96
Figure 47: Time-resolved photoluminescence extracted from TRPL map at early and late time for 100nm WZ InP NW. At early time(240 ps) PL shows emission from WZ band edge. At later time it decays into long lived defect lines...... 97
Figure 48: Typical PL spectrum acquired by the newport spectrometer(blue curve). WZ and ZB band edges are marked for reference. Red arrow shows the filter cut off edge. 1.494eV low pass filter block the emission from
1.494eV and above including the band edge...... 98
Figure 49: Red color line-PLE spectrum from single 100nm diameter WZ InP
NW showing three exciton resonances as A, B and C. Gray color line-Filtered
PL spectrum showing the defect emission for laser excitation tune to the energy marked as B...... 100
Figure 50: Polarized PLE measurements for 100nm single WZ InP NW.
Excitation laser was polarized parallel/perpendicular to NW growth axis while circularly polarized emission from the NW was collected ...... 103
XVI Figure 51: Polarized PLE measurements for 50nm single WZ InP NW.
Excitation laser was polarized parallel/perpendicular to NW growth axis while circularly polarized emission from the NW was collected...... 105
Figure 52: PLE spectra obtain by exciting the 100nm WZ InP NW with light polarized parallel to the NW (red curve) and exciting with light polarized perpendicular to the NW (Blue curve). Transitions from second conduction band to valence band are clearly visible and energy positions are marked on the PLE spectrum...... 106
Table 1: Important physical parameters for GaAs bulk semiconductor are obtained from “survey of semiconductor physics” by Karl W. Böer [21] ...... 14
Table 2: Some important band parameters calculated by A. De and Craig E.
Pryor[22] ...... 18
XVII LIST OF SYMBOLS
- Radiative exciton lifetimes perpendicular to the NW
ǁ - Radiative exciton lifetimes parallel to the NW
- Exciton spin scattering time s
- Hole mass
- Electron mass a – exciton Bohr radius B
APD – Avalanche Photo Diode
CB – Conduction Band
CCD – Charge Coupled Device
CW – Continuous Wave
E -exciton binding energy b
E – Band gap g fcc – Face centered cubic
FESEM -field emission scanning electron micrograph
G - The pumping rate with laser polarized perpendicular to the NW
Gǁ - The pumping rates with laser polarized parallel to the NW
XVIII ℏ- reduced plank constant hh – Heavy hole
J – Total angular momentum
L – Orbital angular momentum lh – Light hole
MOCVD – Metal Organic Chemical Vapor Deposition n - Electron hole plasma density n - Exciton density where their dipoles align perpendicular to the NW
N.A. – Numerical Aperture nǁ - exciton densities where their dipoles align parallel to the NW
NW - Nanowire
PL - Photoluminescence
PLE – Photoluminescence Excitation
PMT – Photo Multiplier Tube
S – Spin angular momentum
TEM -transmission electron micrograph
Ti:S – Titanium Sapphire
XIX TRPL – Time Resolved Photoluminescence
VB – Valence Band
VLS – Vapor Liquid Solid
WZ – Wurtzite
ZB – Zincblende
Δ - band gap renormalization BGR
Δ - crystal field splitting CR
Δ - spin-orbit coupling SO
ε -background dielectric constant
흍 -exciton wave function
XX Chapter 1
1 INTRODUCTION
1.1 Importance of Investigation
Semiconductor nanowires (NWs) are quasi-one-dimensional structures formed with cylindrical or hexagonal cross sections and diameters in the range of 5~300 nm and lengths up to several micrometers. Depending on the size of the diameter compared to exciton Bohr diameter there may be some quantum confinement in the radial direction but generally we don’t expect any confinement in axial direction because of the large length scale.
But there are some methods that can create quantum confinement effects in the axial direction of a NW and some of them are explained in detail in chapter 2. Exploration of optical and electronic properties semiconductor nanowires has gained a lot of interest in the research community because of the extensive potential applications such as single nanowire lasers, photo detectors, bio sensors, single electron devices etc. [1][2][3][4][5]. However, uncontrollable growths of surface or volume defects within the nanowires dramatically decrease their luminescence and quantum efficiency as a result of the large surface to volume ratio[6]. This is a particularly difficult problem for III-V nanowires such as Gallium Arsenide (GaAs) which are highly sensitive to nonradiative surface recombination due to surface states[7]. Using optical spectroscopy to probe the nanowires, we intend to
1 help the growers to develop new methods to optimize the electronic structure of nanowires and at the same time probe the unique physics, which is possible in these novel one-dimensional structures. In coordination with the crystal growers in Australia, in this thesis we describe the significant improvements, which have been recently made in GaAs/AlGaAs core-shell nanowires, which were grown using a newly developed two- temperature growth method.
Indium Phosphide (InP) nanowires are of special interest because of their high quantum efficiency and uniquely low sensitivity to surface defects
[8][9] enabling them to be used in applications including single nanowire lasers, photo detectors, bio sensors, photovoltaic applications and single electron devices[1][2][3][4][10]. While bulk InP is nearly always in the cubic
Zincblende (ZB) phase, in nanowires both ZB and hexagonal Wurtzite phases can appear. So far, very little work has been done in probing the electronic band structure in wurtzite InP NWs[11][12][13][14]. The experimental work done in this thesis will help in understanding the WZ band structure and fundamental band parameters including crystal field and spin-orbit energies. How these parameters change with the NW diameter and how optical selection rules work for small nanowires are both of significant interest and likely will lead to new physics. In this thesis-project, the electronic structure of WZ InP NWs was investigated by using experiment techniques such as photoluminescence (PL), time-resolved photoluminescence (TRPL) and photoluminescence excitation (PLE).
2 This thesis consists of six chapters. The first chapter gives a brief introduction about the semiconducting materials, their band structure, the dynamical processes, which happen after photoexcitation, and how these processes may change from bulk semiconductor to nanowires. Chapter 2 explains the NW growth procedures and chapter 3 dedicated to our experimental techniques for investigating single semiconducting NWs. 4th and 5th chapters devoted to characterize the optoelectronic properties of
GaAs/AlGaAs core-shell NWs. The Final chapter 6 is dedicated to characterization of the electronic band structure of WZ InP NWs.
1.2 Semiconducting materials
All solid material can be categorized into three sub groups such as conductors, insulators and semiconductors according to their ability to conduct electrical current through them. Conductors have a large conductivity (104~107Ω-1m-1) compared to insulators (10-18~10-8Ω-1m-1).
Semiconductors have conductivity between of those conductors and insulators. The number of outer shell electrons contributes to the conductivity. These most outer shell electrons are called valence electrons and in a conducting material one would observe smallest number of valence electrons. Since these electrons are loosely bound to the atoms in the material, an applied electric or magnetic field can easily remove them from their orbit and used to conduct current. In insulators valence electrons are tightly bound to the atoms and they hardly contribute to conductance of
3 current. On the other hand semiconducting materials, which have 3 to 6 valence electrons, may conduct some current under suitable conditions.
This phenomenon can be explained through consideration of the energy band structures of each material and will be discussed briefly in the next section. The elements in group III, IV and V in the periodic table are good candidates for semiconductors. Semiconductors like Si and Ge are called elemental semiconductors because the material is made from a single element. Also materials formed by blending group II & VI, group III & V and some metals with oxygen together are used as efficient semiconductors and they are called binary compound semiconductors. Similarly there are ternary and quaternary semiconductors prepared from combining three and four different elements from suitable groups respectively. The properties of semiconductors can be dramatically affected by the introduction of defects. The properties of the semiconductor can be divided between intrinsic and extrinsic behavior. An intrinsic semiconductor means pure semiconducting material. Extrinsic semiconductors are made by adding some impurity to the pure semiconductors on purposely to change its characteristics favorable to the situation. In reality it’s hard to find intrinsic semiconductors as they are nearly always incorporated with minute amount of foreign materials that act as donors, acceptors and deep level centers[15],
[16]. Figure 1 shows some examples for binary compound semiconductors(group II - VI, III – V). Note that there are more semiconductors not shown in this figure [17]. The graph in Figure 1 shows
4 the band gap energy of the semiconductor versus its lattice constant and also the information whether it’s a direct or indirect band gap semiconductor. The left hand Y- axis shows the band gap energy in terms of its corresponding wavelength.
Lattice constant Å
Figure 1: The graph of some commonly used binary semiconductors with their energy band gap versus the lattice constant [17]
5 1.3 Band theory
3s 2p
2s
Energy levels Energy 1s
Figure 2: Energy levels of a single atom
Every solid material regardless of being a conductor, semiconductor or an insulator has properties, which are defined by the underlying band structure. Atoms inside the solid material arrange in a way that they form a crystal structure, which is formed by a repeated block of atoms called unit cell. There are approximately on the order of 1022 atoms in a one cubic centimeter of volume. Consider a single atom that has some number of electrons orbiting the nucleus. Figure 2 shows the energy levels of a single atom. The electrons in this atom occupy discrete energy levels. According to the Pauli Exclusion Principle only two electrons can occupy in a single
6 energy level having opposite spin. When a solid forms, a large number of single atoms are packed together in a very small volume. Each atom feels the potential energy from all the other neighboring atoms around it and atoms may have overlapped energy levels because they are identical.
Therefore the energy levels of the crystal are split into very closely spaced energy levels. Instead of discrete energy levels such as 1s or 2s, several continuous bands of energy appear which are associated with electrons from the atomic. In addition, forbidden gaps of energy between these energy bands appear where no electron can reside. Most inner shell electrons are strongly attracted to the nucleus while most outer shell electrons are screened from the nucleus because of those inner shell electrons. Therefore outer shell electrons are frequently not confined to the nucleus potential. They can move through the crystal while forming bonds with other atoms in the crystal lattice. When the crystal is in its ground state, the highest completely filled band with these valence electrons is called the valence band (VB), while higher lying energy bands that are either partially filled or contain no electrons (disregarding any possible thermal excitation from the valence band) is called the conduction band (CB)[18].
As shown in Figure 3 , if the CB is completely empty it may be an insulator or a semiconductor. If the CB is partially filled (see hash marks) it is a conductor. With an applied electric field, the partially filled electrons can be scattered into higher empty states within the same CB very easily. The
7 difference between the insulator and the semiconductor depend on the gap between the maximum energy of the VB and the minimum energy of the CB.
Insulator Conductor
CB Semiconductor CB
CB
VB VB VB
(b) (c) (a)
Figure 3: Energy band structure of Solid: (a) Insulator
(b) Conductor (c) Semiconductor
This gap is called the Band Gap and it’s traditionally denoted by the symbol
E . A material is usually considered to be a semiconductor rather than an g insulator if the band gap is in the order of visible photon energy (1 to 3 eV) or less. Since semiconducting materials exhibit moderate band-gaps, it is possible to promote a valence band electron to the conduction band through thermal, optical or other suitable excitation process [19].
8
E(k) E(k)
E E g g
k k 0 0
(a) (b)
Figure 4: Band diagram of a direct-(a) and indirect-(b) band gap semiconductor
Semiconductors can also be divided between direct gap and indirect gap materials. Figure 4 shows two different band diagrams for deferent semiconducting materials. A band diagram is a plot of electron energy versus wave vector in a crystalline material. As shown in Figure 4-a if the minimum energy of the conduction band and the maximum energy of the valence band lie within the same K value it is called direct band gap
9 semiconductor. In this case an excited electron in the conduction band can fall in to valence band or one can excite a valence band electron to the conduction band without changing its momentum. Such transitions are known as direct transitions. This is because the momentum of the associated photon is very small compared to the crystal momentum of the electron in the conduction band and the valence band. Therefore in direct band gap material vertical transitions are the allowed ones. On the other hand in an indirect gap semiconductor maximum energy of the valence band and the minimum energy of the conduction band don’t occur at the same K value making it is impossible to promote an electron from conduction band minimum to valence band maximum or vice versa without changing its momentum. These types of transitions are called indirect transitions and can only be accomplished with the absorption or emission of phonon (lattice vibration) to conserve the momentum. Because such a transition is involves three objects the efficiency can be very small.
Because a direct transition only involves the initial and final electron states, optical processes can occur with very high efficiency.
1.4 Band structure of ZB GaAs semiconductor
GaAs is a direct band gap semiconducting material. Bulk GaAs crystallizes in the cubic Zincblende (ZB) structure. This ZB structure is very similar to the cubic crystal structure in diamond. ZB structure is formed by the mergence two face centered cubic (fcc) lattice together. But it doesn’t have the
10 inversion symmetry of the diamond cubic structure. In GaAs ZB structure the atoms that two fcc lattices are occupied by Ga and As atoms respectively. Figure 5 shows the energy band structure of ZB GaAs semiconductor and it is calculated by using an empirical nonlocal pseudo- potential scheme by J. Chelikowsky and M. Cohen[20].
Figure 5: Energy band structure of ZB GaAs[20]
11 The center of the 1st Brillouin zone is the point where most of the optical transitions take place because of zero wave vector(k=0) of the photon. The most important area of the band structure is highlighted in Figure 5 for further discussion and shown in Figure 6.
E
6 Γ
CB
E ~1.424eV g
k
hh 8 Γ lh
VB 7 Γ SO
Figure 6: ZB GaAs band structure at k=0
The outer shell electrons contribute to form a covalent bond between Ga(3) and As(5). When these s and p atomic energy level mixed to form bonds it tends to split the atomic energy levels into two main levels as antibonding
12 and bonding because of s and p hybridization. All the bonding levels filled with electrons form the valence band and all the empty antibonding levels form the conduction band in the GaAs semiconductor. Electrons in the conduction band have s-type wave function with total angular momentum(J= L+S) equal to 1/2 and m =±1/2. This is because for s-type j orbitals, angular momentum(L) equal to 0 and spin(S) of the electron is 1/2.
The valence bands are formed from the three atomic p orbitals. Coupling of
Spin and orbital angular momentum causes the lifting of degeneracy by shifting down one of the valence band as shown in the Figure 6. For p-type orbitals in the valence band, angular momentum(L) is equal to 1 and spin(S) is equal to 1/2. Therefore the possible total angular momentum(J) values are 3/2 and 1/2. For J=3/2 the spin angular momentum(m ) are -3/2, -1/2, j
1/2 and 3/2. Upper two bands in the valence band correspond to J=3/2 are called heavy hole(J=3/2, m =-3/2, 3/2) and light hole(J=3/2, m =-1/2, 1/2) j j respectively. The other band further down is called the split off band(SO) correspond to J=1/2 and m =-1/2, 1/2. In a radiative recombination j processes the conservation of energy and crystal momentum is satisfied by emitting a photon. For conservation of momentum the total angular momentum should be equal to the value of the spin of a photon. Since photon carries a spin of ±1, the possible recombinations between conduction band and heavy/light hole band in the valence band are
|3/2,1/2˃, |-3/2,-1/2˃, |1/2,-1/2˃ , |-1/2,1/2˃ considering their spin angular momentum. There are other four different states with total spin
13 equal to 0 and ±2 called dark states, which are not optically active and hence not directly observable in optical spectroscopy.
Table 1: Important physical parameters for GaAs bulk semiconductor are obtained from “survey of semiconductor physics” by Karl W. Böer [21]
Property Value/description
Crystal structure Zincblende
Lattice constant 5.6533 Å
Dielectric constant 12.9(static), 10.9(optical)
Band gap 1.424eV(at 300K), 1.519eV(at 0K)
Spin-orbit splitting 340meV
0.067m Effective mass of electrons (at Γ) 0
Effective mass of holes (at Γ) heavy hole-0.5m , light hole-0.082 0
14 m 0
LO phonon energy (at Γ) 36.2meV
TO phonon energy(at Γ,X,L) 33.3, 31.0, 32.7meV
LA phonon energy(at X) 27.8meV
TA phonon energy(at X,L) 9.8, 7.9meV
Debye temperature 345K
Thermal conductivity 0.46 W/cm ºC
Intrinsic carrier density at 300K 2.1 x 106 cm-3
Temperature coefficient -0.39meV/deg
Pressure coefficient 12µeV/bar
1.5 Band structure of WZ InP semiconductor
In the Bulk, the InP semiconductor crystalizes in the ZB cubic structure as seen in GaAs. Therefore, the ZB InP band structure is very similar to the ZB
15 GaAs band structure describe section 1.4. Recent advances in growing nanowires made it possible to grow InP also in the hexagonal WZ crystal structure. The WZ InP semiconductor is a direct band gap material and since pure material occurs only in the nanowire form, very limited information is available about the band structure. WZ structure is formed by two interpenetrating hexagonal close packed crystal structures with In and P atoms. When viewed along its [111] direction each structure looks like consecutively stacked hexagonal layers. Each layer consists of identical atoms of either In or P.
Figure 7: Predicted WZ InP band structure by De et al.[22]
16
Because of the combination of hexagonal crystal field potential arising from the nearest neighbor atoms and spin orbit coupling, the valence band of WZ crystal structure is split in to three separate hole bands called A,B and C – hole bands at the Γ point. The A, B and C hole bands have Γ9, Γ7 and Γ7 symmetry respectively.
Predicted 8 E Γ Second CB
7 Γ CB
Eg~1.504eV
k
9 A Γ 7 Γ B VB 7 Γ C
Figure 8: WZ InP band structure at zone center
17 Figure 7 is the predicted band structure for WZ InP semiconductor calculated by A. De and Craig E. Pryor [22]. Figure 8 shows the band structure near the zone center as highlighted by the blue dashed box in
Figure 7. According to A. De and Craig E. Pryor, there is another higher-level conduction band just 238meV above the usual conduction band which has the Γ8 symmetry.
Table 2: Some important band parameters calculated by A. De and Craig E. Pryor[22]
Zone center E(eV) mǁ m states
Γ8 1.712 1.094 0.132
Γ7 1.474 0.105 0.088
Γ9 0.000 1.273 0.158
Γ7 −0.063 0.839 0.169
Γ7 −0.348 0.097 1.205
Γ9 −0.849 1.894 0.23
18 Table 2 displays some important band parameters for Zone center states, their energies and effective masses for the WZ phase of InP, calculated by A.
De and Craig E. Pryor [22]. A large collection of band parameters for III/V compound semiconductors and their alloys can be found in the applied physics review article by I. Vurgaftman et al.,[23].
1.6 Excitons
electron
Exciton
hole Bohr radius
Figure 9: Wannier exciton with much larger exciton Bohr radius than unit cell
19 In this thesis we mainly consider absorption of a photon to promote a valence band electron to the conduction band leaving a positively charged vacancy (hole) in the valence band. This electron-hole pair can be bound into a hydrogenic-like state by the Coulomb interaction and is called an exciton, which can transport energy by moving through the semiconductor.
There are two types of excitons called Wannier and Frenkel excitons. In a
Wannier exciton, the exciton Bohr radius is much larger than the lattice unit cell. But in a Frenkel exciton, the exciton Bohr radius is comparable or smaller than the unit cell. In all of the semiconductors we are dealing with, only Wannier excitons are relevant.
Figure 9 shows a schematic picture of a Wannier exciton with electron shown by the blue colored dot, hole by the black colored dot and lattice unit cells by yellow colored dots. The distance between the hole and the electron is called exciton Bohr radius and it is represented by an arrow in Figure 9.
As explain by N. Peyghambarian, S. Koch and A. Mysyrowicz[24] and P. Yu and M. Cardona[25] the Schrodinger equation for the exciton given by
ℏ ℏ { } | |
Where is coulomb potential energy, -energy with respect | | to band gap energy, -background dielectric constant, -electron mass, - hole mass and -exciton wave function. By changing the equation (1) into
20 center of mass(R) and relative(r) coordinates we can derive an equation for the relative motion of the electron-hole pair as
ℏ { }
Equation (2) is called the Wannier equation and is electron-hole reduced
ℏ mass. Energy eigenvalue is given by ℏ
ℏ ℏ Where is exciton Bohr radius and represent the exciton
binding energy (E ). b
By using the above formula we can calculate the exciton Bohr radius and binding energy for bulk GaAs semiconductor as =11.3nm ; binding energy = 5.95 meV by using the appropriate values for reduced mass, plank constant, dielectric constant and electron’s charge [26][27].
In equation (3) n is an integer between 1 and ∞ which represents the order of the exciton state. Total energy of the exciton is given by
ℏ ℏ
Where M is the total mass of the electron-hole pair and K is the center of mass wave vector.
21
E ex
n=∞
n=2
n=1 E b E g
K
Figure 10: Exciton energy levels with respect to two particle wave vector
Figure 10 shows the exciton energy levels with respect to electron-hole pair center of mass wave vector. As n goes from 1 to higher order levels it is possible to see a continuous band of exciton levels that merge in to conduction band. There are numerous ways to excite a semiconductor using different kinds of excitation sources. As a result different type of transition may occur. Photoluminescence is a very important process dealing with optical excitation and emission and will be discuss in next section.
22 1.7 Photoluminescence
CB
electron 2
Excitation Emission 1 3 E g hν1 hν2
hole E
VB k
Figure 11: Optical excitation, thermalization and emission process of a direct gap semiconductor
Figure 11 shows a possible optical excitation and emission process of a direct band gap semiconductor. The whole process shown here consists of three main steps such as 1-excitation, 2-thermalization and 3- recombination. Excitation source (optical photons) with frequency equal to
has used as the excitation source. If the energy of the incoming photons ν1 is greater than the band gap it can excite a valence band electron to the
23 conduction band leaving a positively charge hole in the valence band. At this time the excited electron can recombine with the hole without relaxing into the band extrimas radiatively or nonradiatively (not shown in the
Figure 11.) In the thermalization process the excited carriers relaxed into their corresponding band edges by emitting phonon(lattice vibrations).
Finally the electron at the conduction band minimum possibly will form an exciton with the hole at the valence band maximum. Because of the binding energy the total energy of the exciton is smaller than the band gap energy.
Step 3 shows the recombination process of the electron-hole pair. If it forms an exciton and recombines through a radiative process, there will be a band of exciton emission below the band gap energy. We call this optical excitation and resulting radiative emission process as photoluminescence.
Similarly we can get luminescence in the recombination process by using different excitation sources. If we use electric current it is called electroluminescence and from electron beam we get cathodoluminescence.
The advantages and the way of measuring the photoluminescence will be discussed in the section 3.3.
1.8 Reduced dimensionality of semiconducting nanowires
So far we have discussed some important properties of bulk semiconductors. The main physical difference between a bulk semiconductor and a semiconducting nanowire is the dimensionality. We can think of nanowires as one dimensional structure depending on their
24 diameters. In a previous section we described the exciton as an electron- hole pair that moves through the semiconductor with a unique exciton Bohr radius. In a bulk semiconductor it can move in all three X, Y and Z direction.
If the diameter of the nanowire is less than the exciton Bohr radius the exciton only allow to move freely in the length of the nanowire and it is confined in the radial direction. This could change the energy band structure of the nanowire and as a result we may observe the quantum confinement effects in the emission or excitation spectrum. If the exciton
Bohr radius is less than the nanowire diameter these confinement effect may not be prominent. But because of the geometrical shape of the nanowire there may be some modification to the energy landscape. This geometry introduces a high surface to volume ratio compared to the bulk semiconductor. Therefore these nanowires are very sensitive to surface states, defects and structural inhomogeneities. Also the large dielectric contrast of the NW compared to surrounding vacuum introduces new physics when we measure the polarization index compared to bulk semiconductors. As an example the bulk GaAs semiconductor is unpolarized to any polarized excitation source in any crystal direction. But in GaAs NWs there is significant difference in the polarization index along the growth axis of the NW compared to its radial direction. This is mainly because of the dielectric contrast and the small diameter of the NW and some detailed discussion can be found in chapter 5. Because of the new growth techniques it is possible to grow nanowires by combining different
25 semiconducting materials in many ways and as result one could alter the band structures compared to bulk material and engineered it in the way of favorable to an application. Therefore optical and electronic properties of nanowires may reflect a clear difference compared to bulk semiconducting material and investigation of these properties will be a profitable one. Some of the growing techniques used to grow the samples used in this thesis have explained in detail in next chapter.
26 Chapter 2
2 NANOWIRE GROWTH
2.1 Introduction
There are two main methods for fabricating nanowires and nanostructures.
These are top-down and bottom-up methods. In the top-down method one starts with a bulk semiconducting material and remove material until the desired structure form using lithography and etching processes. In this method there are limitations to the smallest length scale which can be achieved because of defects which arise through the etching process. On the other hand bottom up method can be used to grow a nanostructure with minimum defects and smaller length scale compared to top-down approach.
The growth starts from the molecular level and then develops into more complex desired structure by using chemical synthesis methods. Most importantly it has the ability to control the growth and the materials and the concentration of alloys. There are some growth techniques developed under bottom-up approach such as template assisted nanowire growth, catalyst assisted free-standing growth and catalyst free free-standing nanowire growth. All the nanowires used in this experiment were grown by
Prof. C. Jagdish’s research group at the Australian national university by using gold-catalyst assisted Vapor-Liquid-Solid (VLS) method inside a horizontal flow metal-organic chemical vapor deposition (MOCVD) reactor
27 operating at low pressure. This method will be discussed in detail in the next section.
2.2 Growth technique
In 1964 Wagner and Ellis performed a unique experiment that grew silicon
“whiskers” on a semiconductor surface. This was the first observation of the
Vapor-Liquid-Solid (VLS) method of growing one dimensional heterostructures. They dispersed small gold particles on a Silicon (Si) surface and heated it up approximately to 950°C. When a mixture of
Hydrogen gas and Silicon-chloride (SiCl ) vapor (precursors) was introduced 4 into the system Si atoms were absorbed into the gold particles and then condensed out as solid Si at the semiconductor and gold particle interface.
Thus whiskers were grown perpendicular to the growth surface [28]. Since then this method has been used to grow nanowires using desired combinations of (group III-V and II-VI elements in periodic table) semiconductors [29],[30],[31]. The MOCVD method described below is very similar to the VLS method used by Wagner and Ellis. In this method first one chooses a suitable growth substrate. As an example if one wants to grow
GaAs nanowires, a GaAs (111)B substrate is the most preferable one because the nanowires grow along the (111) direction and so they will be aligned perpendicularly to the substrate. After dispersing the gold catalyst, the growth substrate is heated to 600 ºC to remove any surface contaminants
(Figure 12-a). Then the temperature is reduced to the growth temperature
28 around 450 ºC for GaAs. When the group III(TMGa) and V(AsH ) precursors 3 are introduced into the MOCVD reactor using Hydrogen as carrier gas, gold and Ga starts to form a eutectic alloy as shown in Figure 12-b.
Figure 12: schematic representation of nanowire growth (a) Au particle dispersion and heating up the substrate (b) Au/Ga alloy formation and growth initiation (c) NW formation and further growth from Au-NW interface.
29 When the gold nanoparticle becomes super-saturated with GaAs, the GaAs crystalizes underneath the Au particle and pushes the Au particle upward as the NW grows epitaxially (Figure 12-c). This axial growth mainly arises from the precursors impinging on the Au particle. The diffusion of atoms on the growth surface and on the sidewall of the NW towards the Au particle give rise to radial as well as axial growth of the Nw. This radial growth results in tapered NWs and it’s a major disadvantage in this growth method.
Figure 13: Axial heterostructure NW grown by switching the precursor gas flows.
Figure 13 illustrates a schematic diagram of an axial heterostructure nanowire grown using MOCVD method. It is done by switching the precursor gas flows to the desired material. In this example the growth initiated with
GaAs and after some time it is TMIn gas flow is switch on and then switch off allowing GaAs growth again. By repeating this process axial heterostructure NW supperlattice can be grown [32].
30 Figure 14 illustrates the growth of GaAs/AlGaAs core-shell nanowire. The
NW core is grown as explain in Figure 12. After the core growth the temperature is elevated to 600º C to grow an AlGaAs shell around it. At the shell growth time TMAl precursor is switch on with the TMGa to grow
AlGaAs shell[33].
Figure 14: GaAs/AlGaAs core-shell radial heterostructure Nw.
Figure 15 shows a schematic diagram of a GaAs/AlGaAs core-multishell NW.
In this case GaAs core has grown in usual way followed by an AlGaAs shell.
Then a very thin GaAs shell has grown on top of the AlGaAs shell. This is done by reducing shell growth time and shutting off the TMAl precursor flow. After that a thick AlGaAs shell has grown to form the quantum well
31 structure. Finally a thin GaAs capping layer has added to prevent the oxidation of AlGaAs shell.
Figure 15: Schematic illustration of core-multi-shell NW
2.3 Growth parameters and defects
There are three main parameters which can change the NW diameter, morphology and crystal structure such as Au-particle size, growth temperature and V/III ratio. The diameter of the NW mainly depends on the
Au-particle size but as the NW grows vertically the diameter changes. Figure
16 [34] shows an example of temperature dependence of the GaAs NW growth. The set of NWs consider here were grown on a GaAs (111)B substrate using the Au assisted MOCVD method. When the growth
32 temperature increases from 390 ºC to 450 ºC the wires grow in vertical direction without any kinks and irregular shapes (Figure 16-a, b). But they are significantly tapered and contain twin defects as described in Hannah J.
Joyce et al [34]. Figure 16-(c), (d) made a significant advance by showing that the NWs grown using a two-temperature growth procedure can significantly reduce both the tapering and twin defects. In this method the growth initiated at high temperature (450 ºC) for about 1 minute for the nucleation step and then reduce to lower temperature for the prolong growth. Most importantly without the nucleation step NWs won’t grow with such uniformity at such low temperatures.
33 1 μm
(a) (b)
(c) (d)
Figure 16: SEM images of GaAs NWs (a) grown at 450 C (b) grown at 390 C (c) two-temperature growth procedure at 390 C (d) two temperature growth procedure at 350 C.[34]
34 Figure 17: Growth temperature and V/III ratio dependence of InP NWs grown using Au-assisted MOCVD method. Scale bars are 2μm long[35].
35 Figure 17 [35] also illustrates how the growth temperature and the V/III ratio affects the nanowire growth. According to S. Paiman et. al. [35] all the
NWs shown in Figure 17 were grown on InP (111)B substrate using Au-article assisted MOCVD method. Growth temperature has varied from 400ºC to
510ºC. PH flow rate has changed from 5.34×10-4 mol.min-1 to 8.53×10-3 3 mol.min-1 while keeping the TMIn flow rate constant at 1.21×10-5 mol.min-1.
This will keep V/III ratio changing from 44 up to 700. According to this discussion low growth temperature and high V/III ratio will produce straight
InP nanowires with less tapering. Also low V/III ratio and high growth temperatures will produce similar results.
2.4 Crystal structure
In bulk semiconducting materials there are a large number of atoms or molecules packed into precise crystalline structure with a periodic arrangement. Most group III-V semiconducting bulk material crystalizes in the Zincblende (ZB) phase in nature. Nanowires preferentially crystalize in either the ZB or Wurtzite (WZ) phases for the same III-V semiconducting material depending on the growth conditions[35][36][37]. Therefore nanowires give the opportunity to investigate different crystal phases that does not occur in nature. Several methods have been applied to grow ZB and
WZ nanowires. According to Hadas Shtrikman et. al. [36] GaAs and InAs nanowires grow in WZ phase in small diameters (~10nm). P. Caroff et al. [37]
36 have observed when they change the diameter from 24nm to 110nm in InAs nanowire crystal phase changed from WZ to pure ZB. For intermediate diameters they have seen a mixture of WZ and ZB phases. They also reported by changing the growth temperature they can control the crystal phase. According to Rienk E. Algra et al.[38] the addition of Zn as a dopant can control the crystal structure in InP to crystalize in ZB structure instead of WZ structure, the commonly found one. According to Hannah J. Joyce et al.[39] they can control the crystal phase of InAs nanowires by changing the growth temperature and V/III ratio. In this case at low growth temperature (400ºC) and high V/III ratio (46) will promote pure ZB nanowire growth. High growth temperature (500ºC) and low V/III ratio (2.9) will result pure WZ phase in nanowires. This method is very important because they don’t have a diameter limitation or the addition of impurity to the system to grow desired crystal phase. Similar methods have been used by S. Paiman et al. [35] in the growth of InP nanowires. In this case higher growth temperature and higher V/III ratio promote WZ InP nanowire growth and lower growth temperature and V/III ratio will result in ZB InP nanowire growth. A detailed explanation about ZB and WZ crystal structures growth in
NWs can be found in H.J. Joyce et al.[40 ], K.A. Dick et al[41] and Y. Xia et al[42].
37 Chapter 3
3 EXPERIMENTAL TECHNIQUES
3.1 Sample preparation
Nws
Figure 18: NWs dispersed on a patterned Si substrate. The lithographically-defined pattern provides a reference to find a particular wire on the sample
Figure 18 shows a magnified optical image of NWs dispersed onto a patterned Silicon (Si) substrate. The pattern on the Si substrate helps us to find the position of a particular NW each time we perform an experiment.
Before dispersing NWs the Si substrate is carefully cleaned to eliminate any contamination. The substrate is rinsed in acetone at room temperature for
38 two minutes and then with methanol at room temperature for 2 minutes followed by another rinse with isopropyl alcohol. The Si substrate is cleaned by rinsing in room temperature distilled water for two minutes and then dried using nitrogen gas. There are two common methods for dispersing NWs onto the substrate. The first is done mechanically by gently sliding a piece of growth substrate (nanowires down) on top of the Si substrate. This process disperses many NWs which frequently form clusters on the silicon substrate. The high-density clusters can be very useful for preliminary investigations. The second dispersion process is done by sonicating a small piece of growth substrate inside a glass vial with some methanol solution. A small pipet is used to transfer a small drop of solution onto the Si substrate. A nitrogen gun can be used to dry the sample. This method results in a much lower density of nanowires and can be very useful to obtain isolated single NWs.
Silver-paste is used to mount the sample to a copper sample holder.
The sample holder with the sample is then mounted to the cold finger of a low temperature optical cryostat. A schematic illustration of our photoluminescence setup is shown in the next section in detail.
39 3.2 Experiment setup
Spectrometer
Polarizing optics P-Linear polarizer B-Babinet-Soleil compensator
L-Lens Detector L
P B
P B
Beam Ti:S laser splitter
76 MHz L
Pin hole Sample 50X Microscope objective XYZ translational Cryostat stage
Figure 19: Schematic illustration of Photoluminescence setup
Figure 19 shows a schematic illustration of the photoluminescence setup. A tunable Titanium: Sapphire laser was used as the excitation source for the experiments described in this thesis. As shown in the Figure 19 the polarization of the incoming laser beam was controlled by using a matching set of Glann-Thomson linear polarizers and Babinet soleil compensators for
40 both the incident laser and also the collected photoluminescence. By using a beam splitter and a convergent lens the collimated beam was directed towards the NW sample. The laser was focused onto the NW sample using a
50X/0.5-Numerical-Aperture(N.A.) long working distance microscope objective. As shown in Figure 19 the NW sample was mounted on the cold- finger of the low temperature optical cryostat. By using the back scattering geometry the emitted PL is collected by the same microscope objective and directed through the similar polarizing optics described before. Polarizing optics used to manipulate the polarization of the emitted PL and the Glann-
Thompson linear polarizer was used to analyze the emission polarization.
Finally the PL signal was focused onto the entrance slit of the spectrometer using a converging lens. PL was dispersed by the spectrometer and a charge coupled device(CCD) camera was used to detect the PL signal.
3.2.1 Laser
A Titanium:Sapphire (Ti:S) laser (model :Mira 900) has been use throughout the experiments described in this thesis as the excitation source. The 5W, 532 nm CW output of solid state Coherent Verdi laser was used to pump the Ti:S laser. The Ti:S crystal in the laser cavity can emit coherent radiation for any wavelength between 680-1100nm. Broadband laser mirrors and a bi-refringent filter are used to tune over this entire range of wavelengths. The Ti:Sapphire laser can be efficiently tuned between 710 and 1000nm in wavelength in both continuous (cw) and pulsed
41 modes. In the pulsed mode the laser produces 200fs(pulse width) laser pulses with a repetition rate of 76MHz (Eg. time duration between two consecutive pulses is about 13.2ns). The laser rod is cooled using a water cooling system at 19 C where the gain is maximum, and a minimum of 0.08 gal/min flow rated should be maintained. For efficient mode-locked operation at specific wavelengths the laser cavity should be purged by dry nitrogen gas so as to eliminate water absorption lines. More detailed explanations about mode-locked lasers can be found in the book ‘Ultrafast spectroscopy of semiconductors and semiconductor nanostructures’ by
Jagdeep Shah[43]. Further technical detail and working principles can be found in the operator’s manual for the Ti:S laser[44].
3.2.2 Polarizing Optics
Polarizing optics play an important role in the optical measurements. Two sets of Glan-Thompson linear polarizers and Babinet soleil compensators have been employed in the experiments described in this thesis. The Glan-
Thompson linear polarizer allows linearly polarized light to pass through which has a definite direction and orientation with respect to the optical axis. The Babinet soleil compensator is a special kind of wave retarding plate constructed of two wedged-shaped quartz plates. It produces a uniform retardance over its surface without any beam deviation.
42 The Babinet-Soleil compensator can be set to any arbitrary phase delay, but here it is usually set to act as either a half wave plate or as a quarter wave plate. A half wave plate introduces a π phase change between two orthogonal electric field components and as shown in Figure 20 it will rotate the linearly polarized light incident with an angle θ to its optical axis by
Optical axis
θ θ θ
Linearly polarized Half wave plate Linearly polarized
Figure 20: Polarizing optics: How half wave plate rotate linear polarize light with respect to its optical axis.
twice as much. Figure 21 illustrates how we can use a quarter wave plate to change linearly polarized light in to circularly polarized light. For this we need to set linearly polarized light incident on the quarter wave plate at an angle of 45˚ to its optical axis. Depending on whether it is ±45˚to the optical axis the quarter wave plate produce right or left circularly polarized light. More information can be found by referring the book ‘Optics’ by
Eugene Hecht[45].
43
Optical axis
45˚ 45˚
R-circularly Linearly polarized Quarter wave plate Polarized
Figure 21: How quarter wave plate produces circularly polarized light from linearly polarized light incident at an angle of 45 degrees on its optical axis.
3.2.3 Cryostat
Radiation Vacuum valve Sample holder shield Cold finger
Glass Helium
window in
Helium out Vacuum jacket Temperature Heater coil sensors
Figure 22: Continuous flow liquid helium optical cryostat
44 Figure 22 shows a schematic diagram of the optical cryostat used in the experiments. It was originally manufactured by the Janis Company and has undergone several modifications for the needs of experiments. During the experiments it is maintained under high vacuum (~106 torr) to help to keep the sample at low temperature and to eliminate heat loss from convection. A radiation shield also significantly reduces heat transfer from radiation. The cryostat is cooled by using a continuous flow of liquid helium and temperature can be maintained in between 6 to 300K by using a temperature controller. The heater coil is used to increase and maintain the desired temperature. There are two temperature sensors to measure the temperature near the sample holder and near the heater coil. The sample is mounted on the sample holder and this holder is attached to the cold finger which transfers the heat energy from the cold finger to the liquid helium flow.
3.2.4 Spectrometer
Figure 23 and Figure 24 show the schematic diagrams of the spectrometers used in the experiments described in this thesis. The Spex-1m spectrometer was used in the characterization of GaAs/AlGaAs core-shell nanowires. It uses the Zerny-Turner optical configuration and the focal lengths of the two concave mirrors are 1m. The grating used in this spectrometer is interchangeable and for a slit width of 25µm the maximum theoretical resolution is 2nm for a 1200 g/mm grating.
45
APD Concave
Movable mirror mirrors
CCD
Grating
Figure 23: Spex spectrometer
The exit port of this spectrometer was changed from its original configuration to accommodate APD(avalanche photo diode) detector used in time-resolved measurements. For the photoluminescence measurements of
GaAs/AlGaAs core-shell nanowires the 2nd order light from a grating with
600 grove/mm was used. This grating is blazed to increase the diffraction efficiency at 1600nm in first.
46
CCD camera
Interchangeable gratings
PMT
Entrance slit
Figure 24: Newport spectrometer
The Newport(MS260i) spectrometer uses the asymmetric in plane Czerny-
Turner optical geometry. There are two gratings(1200 and 300 groves/mm) mounted on a rotating stage, which is very convenient when it is comes to switch between gratings. The 300 groves/mm grating was used to investigate a PL spectrum over a wide range of wavelengths while the 1200 groves/mm grating was used to investigate a narrow spectral range but at significantly higher resolution. This spectrometer has been used to investigate a wide variety of nanowires including GaAs/AlGaAs core-shell
NWs as well as WZ InP. A PMT detector was mounted by the side of the
47 spectrometer as shown in Figure 24 for used in the time-resolved measurements.
3.2.5 Detectors
CCD
A Silicon CCD (charge coupled device) camera was attached to each of the spectrometers used in our experiments to detect the light coming from the sample. The CCD consists of an array(2000 X 800) of pixels(small capacitors) which can detect the photons dispersed by the grating used in the spectrometer. When a photon reaches a particular pixel it can generate a charge using photoelectric effect and transfer these charges to an interface connected to the CCD. Therefore the interface will record a 2D map of charges corresponding to the positions of pixels in the array where hit by the dispersed photons. The intensity of a particular position is proportional to the number of photons that have reached a particular pixel of interest.
The vertical position on the CCD corresponds to the position the light was focused onto the entrance slit while the horizontal position corresponds to the wavelength of the photon. Ultimately one can map these positions to the corresponding positions on the nanowire sample these photons originated from as well as the energy of the photon which is emitted as a result of a particular decay process. If the spectrum of emission as a plot of
Intensity versus energy is required one can integrate the intensity by adding the charges in all vertical pixels as a function of energy.
48 MCP-PMT and APD
We used a MCP-PMT( micro channel plate photomultiplier tube) and APD
(avalanche photo diode) when we want to study the exciton dynamics as a
Figure 25: Schematic diagram of a regular PMT[46] function of time. Before discuss the working principle of the MCP-PMT it is useful to understand the theory behind the regular PMT. As shown in Figure
25, [46] the PMT consist of three main parts such as photocathode, electron multipliers(Dynodes) and anode. When the disperse photons impinge on photocathode it generate electrons by the photoelectric effect and they are emitted in to the vacuum. These photoelectrons are accelerated and focused onto the first electron multiplier as shown in the
Figure 25. They emit secondary electrons by using the photoelectric effect and theses process keep repeating at each photomultiplier sections. Finally all the secondary electrons emitted from final electron multiplier section
49 are collected by the anode and directed towards the discriminator in the time-resolved set up after external amplification. The MCP-PMT has the same working principle but it uses a Micro Channel Plate(MCP) instead of
Dynodes.
Figure 26: Schematic structure of an MCP and principle of multiplication[46]
Figure 26 displays a schematic structure of an MCP and its multiplication principle. As shown in Figure 26-a the MCP consist of large number of glass capillaries bundle together to form the disk. These glass capillaries(channels) have a diameter ranging from 6 to 20 microns and their inner walls are coated with metal to emit secondary electrons. Each glass channel act as an independent electron multiplier. Figure 26-b illustrates how each channel produce secondary electrons. As shown in the
50 Figure 26-b the electric field created across the MCP disk accelerates the secondary electron towards output end. Large number of secondary electrons (105~106) will result in a fast response time(~50ps) in the operation of the MCP-PMT. The MCP-PMT we used (model: Hamamatsu
R2809U-11) which operates at a high voltage (2900V) must be cooled down to -45ºC by using liquid nitrogen reduces the dark count rate (~100 counts per second). Depending on the emission energy we are interested in we choose PMT(400-860nm) or APD(>800nm) to be employed as the detector.
APD is a very sensitive photo diode that operates at high gain by applying a reverse bias to the diode. When photon impinges on the photodiode it creates electron-hole pairs if the light energy is higher than the band gap.
Under the applied reverse bias voltage to the PN junction diode, the electrons drift towards to the N side and holes drift towards to the P side after the electron-hole pair creation by incident photons. When the applied electric filed is increased these carriers will collide with crystal lattice and generate new electron-hole pairs. This chain reaction will repeat again and it is called avalanche multiplication. A thermo electric cooler is used to reduce the dark count rate therefore no need to cool by liquid nitrogen as with the PMT. Compared to PMT, APD is very small in size and therefore very easy to mount in a location. Because of the small size it’s very hard to align the APD with incoming photons. Compared to MCP-PMT, APD has higher quantum efficiency and can detect the emission toward the far infrared region because of the Si photo diode.
51 3.3 Photoluminescence spectroscopy
Photoluminescence spectroscopy is an extensively used method for characterizing semiconducting material. It is a nondestructive technique which shows the energy distribution of the emitted light specific to the material. By analyzing this energy distribution one can probe directly the important material properties such as the band structure, defects, presence of impurities and the concentration of ions. But photoluminescence spectroscopy itself doesn’t provide any information about exciton dynamics, their eigenstates, and transport dynamics etc. To find that information we use different spectroscopic methods. The dynamical processes happening in the photoluminescence process has been discussed in section 1.4. An extensive review article can be found in literature about photoluminescence spectroscopy of crystalline semiconductors by G. D.
Gilliland[47]. In the next section we discuss how one can obtain the excited state energies which are coupled to the emitting states.
3.4 Photoluminescence excitation spectroscopy
In photoluminescence spectroscopy the sample is excited with a fixed wavelength. Depending on the energy of the excitation beam one could observe the band gap, free exciton emission, defect related emission and depending on the quality of the material or the intensity of excitation one could observe emission from higher energy states. Most often PL is emitted
52 predominantly from the lowest energy states: the ground states of the material. In particular, PL is not a good means for observing emission from
Ti:S laser Spectrometer
76 MHz
λ =800nm
Nonlinear Detector Optical Fiber L Polarizing optics P P-Linear polarizer Super-continuum B-Babinet-Soleil White Light B compensator Spectral filter L-Lens
Beam
splitter P B L
Pin hole Sample 50X Microscope objective XYZ translational Cryostat stage
Figure 27: Schematic illustration of Photoluminescence excitation experiment setup
53 the higher lying hole. In photoluminescence excitation spectroscopy the excitation laser energy is tuned over a large range while the intensity of the ground state emission is monitored. In the PL spectrum we concentrate on a particular emission state like free exciton emission, higher electronic state or a defect related emission state. When the excitation wavelength is scanned to higher energy, electrons and holes may be excited to higher lying states which then relax to the lower lying state which emit PL. Because the higher lying state absorbs the laser photons more efficiently, one would observe a large intensity enhancement in the PL signal of the lower lying state. Therefore the spectrum of integrated intensity versus excitation energy or wavelength will give some insight to the electronic states which were impossible to see with other spectroscopic methods. In this thesis research PLE spectroscopy was used to investigate the band structure of WZ
InP nanowires in great detail and will be explain further in Chapter 6. Figure
27 is a schematic diagram of the PLE setup used in this thesis project to do the extended PLE measurement in WZ InP NWs. It is very similar to our PL setup except the excitation source and the optical cryostat. To get a long excitation wavelength range we have used the 200 fs pulsed output of the
Ti-Sapphire laser to pump a super continuum nonlinear fiber to produce continuous white light. Two Brewster cut angle prisms and a spectral filter have been employed to select a narrow range of wavelength source to be used as the excitation source for the sample. The optical cryostat was made by the Janis research company and is a Model ST-500 continuous flow
54 optical cryostat for microscopy which uses an Attocube stage which is mounted to the cold finger and can position the single nanowire with nanometer accuracy. Because of its design architecture the cryostat is much more stable than the previous cryostat and so the mounted NW samples were able to stay in a fixed position for a long period of time.
3.5 Time resolved photoluminescence
The APD or MCP-PMT produce a current pulse for the each single photon it detects from the dispersed PL signal and therefore the number of pulses is directly proportional to the number of photons arrived to MCP-PMT or APD at that instant. This weak signal is then amplified by using a preamplifier before send it to a Constant Fractional Discriminator(CFD). The CFD converts the MCP-PMT current pulse to a standard NIM logic pulse while compensating the variances occur in the pulse height in the current pulse produced by PMT or APD. The output logic pulse from the CFD is sent to
Time-to-Amplitude Converter(TAC) act as a ‘stop’ signal to the photon counting system. The output of the fast photodiode reference is discriminated by a second CFD and the NIM logic pulse is used as the "start" signal to the TAC. The TAC converts the time interval between the start and stop signal to a voltage difference which is proportional to the time difference of creation of electron-hole pairs to annihilation of them. This generates a histogram of number of photons counted as a function of time after the laser pulse for selected emission energy.
55
TAC D Fast photo diode MCA S L PMT/APD
L 100
10
Intensity 1
0.1 -2 0 2 4 6 8 10 12 14 P Tim e (ns) B S-Spectrometer P B P-Linear polarizer Beam Ti:S laser B-Babinet-Soleil 76 MHz splitter compensator L L-Lens D-Discriminator Pin hole 50X Microscope Sample objective
XYZ Translational Cryostat stage
Figure 28: Schematic representation of Time-Resolved experiment setup
56
A detailed discussion can be found about Time-correlated photon counting in the review article “photoluminescence spectroscopy of crystalline semiconductors” by G. D. Gilliland[47].
57 Chapter 4
4 GaAs/AlGaAs NW Characterization
4.1 Introduction
Improvement of the quality of NWs is crucial to the development of sensitive nano-scale electronic and optoelectronic NW devices. NWs are very sensitive to surface and interface processes because of high surface to volume ratio. Also exciton recombination times are very sensitive to nonradiative surface recombination processes, NW interface and defects related to NW growth. Because photoexcited carriers are much less susceptible to surface defects, InP NWs have achieved a nearly intrinsic lifetimes equivalent to ~1ns and low surface recombination velocities[48],[49]. However, in GaAs, the electrons and holes are much more sensitive to surface states as compared with InP. GaAs has a much higher surface recombination velocity (~106 cm/s)[50],[51] compared to InP which is 1000 cm/s[52],[53]. The carrier lifetime in bare GaAs NWs was reported as 1ps in a time resolved experiment which used pump-probe terahertz spectroscopy [54]. The low temperature hole mobility in GaAs is an order of magnitude higher than that for InP. As a result, low temperature diffusion lengths for holes are three times higher in GaAs (~3 m)than for
InP(~1 µm). This increases the sensitivity of carriers generated within the
GaAs NW to defects since it samples a larger volume of the nanowire in a shorter time. Also the sensitivity of recombination lifetimes to the defects
58 like vacancies and arsenic-antisites has been reported [55],[56]. Hoang et al. showed by adding a AlGaAs shell around the GaAs NW core can enhance the quantum efficiency by a factor of 20 but the measured lifetime was still comparable to the system response (50ps) and so was not measurable[57],[58]. We believe that twin defects within the GaAs NW core and oxidation of the AlGaAs shell is responsible for the shorter lifetimes.
Twin defects arise from the rotation of the NW growth by 60º around the growth axis (the [111] direction). The density of twin defects is very high in
ZB material and reported in many semiconducting materials [59],[60].
Experiments done with GaAs/AlGaAs NWs by Hoang et al. showed shorter recombination lifetimes. These NWs had an AlGaAs shell around the GaAs core but the shell was exposed to air. The work done by Ryan et al. and
Orton et al. showed that in two dimensional heterostructures with oxidizing
AlGaAs part provide a way to incorporate oxygen into GaAs. Oxygen acts as a deep level center in GaAs and so can reduce the carrier lifetimes and quantum efficiency of the structure by an order of magnitude [61],[62].
4.2 Growth and Morphology
In coordination with the crystal growers in Australia, we describe here the significant improvements which have been made in GaAs/AlGaAs core-shell nanowires which were grown using a newly developed two-temperature growth method[63]. Previously, GaAs/AlGaAs core-shell nanowires were fabricated using Au catalyst assisted metal organic chemical vapor
59 deposition as follows. First the core was grown at a constant substrate temperature of 450ºC, and then the shell was grown along the outer surface of the nanowire at a higher temperature of 650ºC. The diameter of the wire depends mainly on the size of the catalyst Au particle and to a lesser extent the growth time[64]. Figure 29 shows the bare GaAs nanowire core and
Figure 30 shows the completed core-shell nanowire with prominent tapering. The higher band gap AlGaAs shell helps to confine the electron and holes to the interior of the nanowires which results in a significant increase in the quantum efficiency.
Figure 29: Bare GaAs NWs grown by H.J. Joyce et al.
60 However Titova et al. found that the recombination lifetime was still extremely small (less than the 80 ps)[65]. They concluded that extremely short lifetime was due to nonradiative recombination at twin defects in the nanowire core and/or mid-gap oxygen defects caused by oxidation of the
AlGaAs shell.
Figure 30: GaAs/AlGaAs core-shell NW usual single temperature growth
To improve the quantum efficiency and lifetime of the GaAs nanowires, the crystal growers developed a new technique which significantly enhances the structural quality of the nanowires[63]. Figure 31 shows the nanowires that
61 are grown using the new method in which the core is first nucleated from the gold nanoparticles(diameter~50nm) at 450ºC for 1minute with a V/III ratio of 45 and then grown at a lower temperature of 375ºC for 30 minutes.
This two-temperature growth technique has been shown to eliminate the formation of twin defects and significantly reduce the tapering of the GaAs
NW core. The confining 20nm thick shell is grown in the same way as before with 24% AlGaAs concentration, but a thin 5nm GaAs capping layer has added to prevent oxidation of the AlGaAs.
(b) (c) 100 nm
500 nm
Figure 31: GaAs core grown using two
temperature growth[63]
62 Figure 31-(a) shown here is a field emission micrograph(FESEM) of the two temperature grown GaAs/AlGaAs core-shell NWs with the GaAs capping layer. Figure 31-b,c show the transmission electron micrographs(TEM) of the
GaAs NW core without any shell growth. Figure 31-c displays a TEM image of the GaAs bare NW which shows that it is very uniform in diameter.
Moreover, no twin defects in the GaAs core are observed.
4.3 Photoluminescence measurements
1.0 9p 0 0.8 4.5p
0.6 0
0.4 2.5p0 1.5p Intensity(a.u.) 0.2 0 p0
0.0
1.50 1.52 1.54 Energy (ev)
Figure 32: CW PL spectra from GaAs/AlGaAs NW(wire 2) as a function of power. P ~30 µW. 0
63 As explained in section 3.1, the NWs were transferred to a patterned Si substrate and mounted inside the optical cryostat on the cold finger. PL measurements were carried out on the GaAs nanowires using the set up described in section 3.2. The sample was cooled down to 10 K and single
NWs were excited using Ti:S laser tuned to 1.59eV, operating in CW/Pulse mode. Detailed information can be found in section 3.2. By using a 50X
(NA=0.5) microscope objective the laser beam was focused to a spot of 1.5
µm, which was used to illuminate a single NW. The emitted PL was collected and focused onto the entrance slit of the Newport spectrometer for CW PL measurements and a Si CCD camera was used to acquire the CW spectra. For single photon counting measurements the emitted PL from sample was directed towards the 1 meter focal length SPEX spectrometer which is equipped with a silicon-APD for obtaining the time decays. For detailed information about the single photon counting system refer to section 3.5.
Figure 32 shows the CW PL spectrum for two-temperature grown
GaAs/AlGaAs core-shell NW (wire 1) as a function of laser power. Excitation laser (~1.59 eV) power was varied between 30 to 450 µW. At low excitation powers in PL spectrum, a peak was observed with 10meV full width at half maximum centered at 1.51 eV which is believed to be the free exciton emission line for GaAs at low temperature. The intensity of the PL was order of magnitude higher than the GaAs/AlGaAs core-shell NW sample used by
Hoang et al[57][58]. With higher excitation power one can clearly observe the asymmetric broadening of PL on both the high and low energy sides
64 while maintaining the peak intensity around 1.51 eV. This is a good indication of an upsurge of photoexcited carrier density without heating up the NW.
4.4 Time resolved photoluminescence
1
sample (2) 1.1 ns
0.1
sample (1) 80 ps
0.01 (counts) Intensity
0 1 2 3 4
Time (ns) Figure 33: comparison of lifetimes between old and new growth of GaAs/AlGaAs core-shell NWs
Figure 33 shows a comparison between the lifetimes of sample(1) and sample(2). Sample(1) is the GaAs/AlGaAs core-shell NWs without the GaAs capping layer used by Hoang et al. and it was grown with single growth temperature technique. Sample(2) is the GaAs/AlGaAs NWs grown using the
65 two-temperature growth technique along with an outer GaAs capping layer to prevent shell oxidation. The sample was excited using the Ti:S laser operated in pulsed mode with its wavelength tuned to 780nm(1.59eV). The exciton lifetime was significantly higher in the new growth suggesting their high quality.
1
Wire1 1.1ns
Wire3 0.40ns
0.1 Wire2
0.65ns NormalizedIntensity(counts)
0.01 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time (ns)
Figure 34: Time decays accumulated at the peak emission energy(1.51eV) from different single NW of GaAs/AlGaAs core-shell NW grown using the two-temperature growth technique at low excitation powers
66 Figure 34 shows time decays obtained from different NWs in a time resolved experiment using the same Ti:S laser in pulsed mode with excitation energy
1.59eV. All the decays were obtained by collecting the emission PL at the free exciton energy 1.51eV for the sample. Wire 1 exhibit a lifetime of 1.1 ns which is comparable to a lifetime from a very high quality 2D GaAs/AlGaAs wide double heterostructures [66]. Over half of the NWs we examined exhibited comparable lifetimes. On the other hand, approximately a third of the NWs showed shorter lifetimes of ~400 ps like wire 3. This suggests that there may be some rare twin defects or surface states at GaAs/AlGaAs interface which gave rise to nonradiative recombination centers.
0.0
0.5 100.0
1.0
10.00
1.5 2.000
Time Time (ns) 2.0
1.49 1.50 1.51 1.52 1.53 1.54 Energy (eV)
Figure 35 : Time-resolved spectral map for a GaAs/AlGaAs core-shell NW (wire 4) which exhibit a recombination lifetime of ~1 ns
67 Figure 35 shows a false-color image of the time-resolved spectral map for a
GaAs/AlGaAs two temperature grown NW (wire 4). It is constructed by acquiring time decays as a function of emission energy. Each single time decays is a plot of intensity versus time for the particular emission energy sampled (refer to Figure 34 for examples of single time decays). By arranging all the single time decays in the order of their emission energy one can construct the contour map as shown in Figure 35. The vertical axis shows the time after the laser pulse while the horizontal axis shows the emission energy. The false color bar represents the emission intensity in terms of counts and is on a logarithmic scale. The 200 fs pulse laser can create significantly higher density of electron-hole pairs (the average instantaneous photon flux is several orders of magnitude higher than for
CW excitation) that is possible with CW excitation. If we carefully examine
Figure 35, we can see the time evolution of the photoexcited carriers. Just after pulsed laser excitation a high density of carriers indicated by broad emission from both high and low energy side of the spectral map is observed. But at later times (~2 ns) a narrow emission line centered at 1.51 eV is seen, believed to be from the free exciton emission. This behavior is very similar to the emission from electron-hole plasma and a similar response has been reported by Titova et al.[49] for ZB InP NWs. It is possible to extract either time-decays as a function of emission energy, or spectral emission lineshapes as a function of time from these two dimensional arrays.
68 4.5 Result and discussion
100 0.05 ns
Laser
10 0.3 ns
Intensity(a.u.) 1 ns 0.6 ns 18 -3 BGR 2.9 x 10 cm 1 e h EF + EF
1.50 1.55 1.60 Energy (eV)
Figure 36 : Time resolved PL spectra extracted from time-resolved spectral map at 50,300,600 and 1000 ps after laser pulse
Figure 36 displays time resolved PL spectra on a logarithmic intensity scale, extracted from time-resolved spectral map(refer to Figure 35) at 50, 300,
600, and 1000 ps after the laser pulse as indicated by horizontal arrows on the time-resolved PL map which show each time slice after the laser pulse.
Figure 36 shows a broad emission spectrum from a single NW at both the
69 high and low energy sides with a peak at 1.517 eV at early times which then rapidly narrows and red-shifts to 1.514 eV at later times. The high energy side of the PL emission drop back to background level by ~600 ps after the laser pulse, which is a good indication of rapid cooling of the ionized electrons and holes. Also we can see the emission at energies significantly below the expected free exciton emission line at early times which then relaxes back to background level at later times. In Figure 36 emission from low energy side in each PL spectrum was extrapolated using linear fit to estimate the bottom of the emission band. Bottom of the emission band for
50 ps time slice is at 1.479 eV making it 15 meV below the bottom of the free exciton line (left facing blue horizontal arrow in Figure 36) which is at
1.494 eV. The evolution of TRPL shown in Figure 36 provides a strong evidence of formation of electron-hole plasma. At early times with the high generation of electron-hole pairs, the excitons formed are completely ionized because of the coulomb screening. At later times once the average carrier density comparable to the Mott density, excitons begin to reappear.
The range of emission band from the low energy part to the high energy part at early is a measure of the sum of the electron and hole Fermi energies. The reason emission is observed well below the exciton emission energy is because of the band gap renormalization effect. The high carrier densities increase the exchange and correlation energies and as result band gap renormalization occurs. At later times because of the low carrier densities, the sum of the electron and hole Fermi energies are reduced and
70 as a result the emission form high and low energy tails move towards the free exciton emission. According to Vashishta and Kalia [67] the sum of the exchange and correlation energies are independent of the band structure considered. It depend only on the relative distance of the electron and hole pairs and exciton binding energy.
5
6
By using the equations 5 and 6 we can determine the electron hole plasma density(n). In these two equations Δ represent the band gap BGR renormalization, E is the exciton binding energy and a is exciton Bohr b x radius. r is a dimensionless quantity that varies between 0 and 1 and is the s ratio of the electron-hole particle separation divided by the Bohr radius. By measuring the energy difference between the bottom of the emission band between the time resolved PL at 50ps and 1000ps after laser pulse we can determine the band gap renormalization as 15 meV as a shift from the lower edge of the free exciton line. By using this information and appropriate values for binding energy and exciton Bohr radius for GaAs we determine the electron hole pair density as 2.9x1018 cm-3. The corresponding sum of electron and hole Fermi energies for this density is 120 meV which is indicated by the blue right facing horizontal arrow in Figure 36. At later
71 time the average carrier density decrease rapidly until it reach the Mott density (~3x1015 cm-3 at 10K) where we can observe the symmetric PL emission centered at 1.51 eV.
4.6 Summary
We have used time-resolved PL spectroscopy to study the exciton dynamics of GaAs/AlGaAs core-shell nanowires (NWs) at 10 K. NWs were prepared by
Au catalyst-assisted MOCVD and titanium-Sapphire laser (780nm) was used to excite the nanowire sample. PL emission from single NWs exhibits an excitonic peak at ~1.515eV. The exciton lifetime depends on the morphology and crystallographic defect density of the GaAs core, which are in turn dependent upon the growth conditions. Nanowires cores grown at higher temperatures (450 ºC) have exhibited short exciton lifetimes (<100 ps). We can reduce twin defects within the nanowire by using a new two temperature growth technique in which the core is nucleated at a higher temperature (450 ºC) for 1 minute and then grown at low temperature (375
ºC) for 30 minutes. In addition we put a 5nm GaAs cap around the AlGaAs shell which prevents the oxidation of the shell. These twin-free minimally tapered nanowires exhibit a high quantum efficiency along with an early- intrinsic exciton lifetime approaching 1.1 ns at 10 K. State filling and many- body interaction effects were observed by increasing the carrier densities using pulsed laser excitation. We found that 15 meV band gap
72 renormalization determines the electron hole pair density of 2.9x1018 cm-3.
The corresponding sum of electron and hole Fermi energies for this density is 120 meV.
73 Chapter 5
5 Polarization dynamics in twin free GaAs/AlGaAs NWs.
5.1 Introduction
The main objective of the investigation described in this section is to utilize the highly optimized two-temperature grown GaAs/AlGaAs NW samples to resolve the spin dynamics of excitons which are pumped into extremely non-equilibrium distributions. Specifically we are interested in attempting measure directly the spin dynamics of excitons in these nanowires. For example, previous work done by Hoang et al.[68] with the single temperature grown GaAs/AlGaAs core-shell sample with short exciton
Figure 37: Degree of linear polarization of PL emission as a function of excitation energy for wire1(circles) and wire2(square).[68]
74 lifetimes (<80ps) showed that it was possible to resonantly pump excitons into extremely non-equilibrium spin distributions where the exciton dipoles are aligned either along or perpendicular to the nanowire. As the laser is tuned closer to the exciton emission energy (0 meV in relative energy, refer to Figure 37), the distributions become more and more non-equilibrium.
Conversely, as the laser energy moves to higher energies, scattering between the excitons result in much more equilibrium dipole distributions
(refer to Figure 37)[68]. The major conclusion from this work was that the spin relaxation lifetime was approximately equal to the recombination lifetime or about 50 ps. With the longer recombination lifetime of excitons in the new optimized nanowires, we hope that it becomes possible to directly resolve the spin dynamics as the excitons come to equilibrium as a function of time after pulsed excitation.
5.2 Polarized time-resolved photoluminescence measurements
To investigate single NWs, the NWs were transferred to a patterned Si substrate and mounted inside the optical cryostat as described previously
(Refer to section 3.1). Polarized PL/TRPL measurements were carried out using the set up explained in section 3.2. Sample was cooled down to 10 K and single NWs were excited using either a pulsed or CW Ti:S laser tuned to one LO phonon energy above the exciton ground state for GaAs/AlGaAs core shell NWs (1.55eV/798nm). Detailed information can be found in section
3.2.1 for laser operation. By using a 50X (NA=0.5) microscope objective the
75 laser beam was focus to a spot of 1.5 µm, which was used to illuminate a single NW. The emitted PL was collected and focus into the entrance slit of the Newport spectrometer for CW PL measurements and a Si CCD camera was used as the detector. For single photon counting measurements the emitted PL form sample was directed towards the spex spectrometer which is equipped with a silicon-APD for obtaining the time decays. For detailed information about the single photon counting system refer to the section
3.5. Polarized time resolved spectra were obtained by exciting the NW using a linearly polarized laser with the polarization axis oriented either parallel or perpendicular to the NW long axis and analyzing the emitted PL by using a linear polarizer oriented either parallel or perpendicular to the NW axis.
Excitation/Emission 1000 (a) (a) ǁ / ǁ (b) ǁ /
(c) / ǁ (b) (d) / 100 (c)
(d) Intensity (counts) Intensity 10
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time (ns)
76
Figure 38: Polarized time resolved spectra obtain for GaAs/AlGaAs core-shell NW(wire-5). Four configurations were obtained by exciting the NW by using a linearly polarized laser parallel/perpendicular to NW and obtaining the linearly polarized emission parallel/perpendicular to the NW. Excitation laser power is around ~0.5mW and is measured before the microscope objective.
Figure 38 displays the linearly polarized time decays obtained for a two- temperature grown single GaAs/AlGaAs core-shell NW. The (a) and (b) decays were obtained by keeping the linearly polarized laser parallel to the
NW and collecting the linearly polarized emission either parallel and perpendicular to the NW respectively. The (c) and (d) decays were acquired by exciting the linearly polarized laser perpendicular to the NW and collecting the linearly polarized emission parallel or perpendicular to the
NW. The emission processes in (a),(b),(c) and (d) are dominated by radiative decay of excitons with average lifetimes equal to ~0.61 ns.
------7
------8
In equation (7), represent the linearly polarized emission intensity parallel(subscript) to the NW when linearly polarized excitation
77 parallel(superscript) to the NW. Similarly represent linearly polarized emission intensity perpendicular(subscript) to the NW when linearly polarized excitation parallel(superscript) to the NW. The only difference in the notation in equation (8) is the linearly polarized excitation source is perpendicular to the NW at this time. Using equations (7) and (8) we can calculate the emission polarization when the excitation polarization is
parallel to the NW (P||) or perpendicular to the NW (P ). In equation (7)
and correspond to (a) and (b) graphs in Figure 38. Similarly in equation
(8) and correspond to (c) and (d) graphs in Figure 38. Figure 39 represent the corresponding degree of linear polarization when laser is linearly polarized parallel and perpendicular to the NW as a function of time after laser pulse. According to Figure 39 when the excitation laser polarized parallel to the NW the degree of emission polarization decreases from 65% to 30% as the time evolve from 0.07 ns to 1 ns. But at this time duration when the excitation laser polarized perpendicular to the NW the degree of emission polarization increase from 20% to 30%. From previous results from our group and others we know the large dielectric mismatch between the NW and the surrounding vacuum both the excitation efficiency for polarized light and emission polarization are strongly oriented along the
NW(~92%) axis[69][70][71][72]. The resonant excitation experiment by Hoang et al. [68]
78
0.8
0.7
0.6
0.5 P||
0.4
0.3
Polarization Polarization 0.2 P 0.1
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time (ns)
Figure 39: Emission polarization when excitation source polarized parallel (Pǁ) and perpendicular (P ) to NW as a function of time after laser pulse.
described in the previous section showed that in a GaAs/AlGaAs core-shell
NW sample it was possible to create a none equilibrium exciton distribution when they excite the NW sample at low excitation energies closer to PL emission band. As the excitation laser energy increases, the measured
79 exciton dipole distribution comes closer to equilibrium. Furthermore, in their CW PLE experiment they describe when the excitation laser is polarized parallel to the NW, as they tune the laser from 135 meV above the free exciton resonance to 36 meV above the free exciton resonance the degree of emission polarization increased from ~76% to 94%. According to the analysis, these NWs had very short life time(<80 ps) and at very high excitation energies, because of the large carrier density, the exciton dipoles created parallel to the NW scatter more rapidly through optic phonon emission with shorter scattering time(~5 ps). Because of that, exciton- dipoles aligned parallel to the NW depolarized into the states with exciton dipoles aligned perpendicular to the NW creating an equilibrium dipole distribution. When the laser is tuned to low excitation energies because optic phonons can no longer be emitted, the scattering time becomes significantly longer (~50 ps) and comparable to the exciton life time. Very little depolarization of the excitons occur during their short lifetime and so non-equilibrium exciton dipole distribution are observed along the NW axis.
5.3 Model for 2-level system
The large dielectric mismatch (dielectric constant ~12) between the NW and the surrounding (vacuum) results in a large difference in the degree of emission polarization even for an equal distribution of exciton dipoles. This
80 behavior has shown in nanowires where there is no quantum confinement effect[73][74][70][72]. For nanowires where confinement effects becomes important, excitons with a dipole aligned parallel to the nanowire would have a lower energy than those aligned perpendicular to the NW and so the distribution would be predominantly along the NW axis at equilibrium. In our GaAs/AlGaAs core shell NWs the average diameter is around ~50nm and it is much high than the Bohr exciton diameter. Therefore we don’t expect any quantum confinement effects in the NW core. Therefore we can expect spherically symmetric wavefunctions for the exciton states with no preferred dipole orientation. Also we can express the exciton states wavefunctions in terms of their exciton dipole moment direction. For simplicity we can assume there are two types of exciton states such as exciton states with their dipole aligned parallel to the NW growth axis- | ⟩ and exciton states with their dipole aligned perpendicular to NW growth axis- | ⟩ . By neglecting the effect from the silicon substrate and assuming that the NW is a long perfect cylinder in a vacuum, we can treat a single exciton as a two level system such as when it is not excited it is in its ground state- | ⟩ and when it is excited parallel/perpendicular to the NW it is in its excited state | ⟩ | ⟩ respectively.
We can represent the exciton ground state, its excited state, possible transition between them and scatting between them schematically as shown in Figure 40.
81
Figure 40 : Schematic diagram of the exciton states and its possible transitions when exciting the NW with a laser polarized parallel to the NW
In Figure 40 it is considered that the NW is excited by a pulse laser source polarized parallel to the NW. therefore one can assume it creates exciton states with their dipole moment parallel to the NW. The measured exciton decay time is around ~610ps for this NW. Therefore we can assume the exciton decay is dominated by radiative recombination. Since we observed a non-equilibrium exciton distribution at early times and a much more uniform exciton distribution at later times, we can think that some of the
82 initially created excitons parallel to the NW were depolarized into the exciton states perpendicular to the NW via the exciton scattering mechanism. This suggests that the exciton spin scattering time is smaller than the exciton radiative lifetime. Similarly we can explain the decay process of exciton when it is excited by a laser source polarized perpendicular to the NW.
We can write the coupled rate equation for this situation by neglecting the nonradiative recombination rate compared to radiative recombination rate as follows.
𝑑
퐺 ------9 𝑑 휏 휏 휏
𝑑 퐺 ------10 𝑑 휏 휏 휏
In this coupled rate equations nǁ and n are exciton densities where their dipoles align parallel and perpendicular to the NW. Gǁ and G are the pumping rates with laser polarized parallel and perpendicular to the NW. ǁ,
and are radiative exciton lifetimes parallel to the NW, perpendicular to s the NW and exciton spin scattering time respectively.
83 5.4 Results and discussion
By solving the rate equation in steady state for parallel excitation with initial condition nǁ =90%, n =10% as well as nǁ =15%, n =85% for (t=0) (t=0) (t=0) (t=0) perpendicular excitation we can find the exciton densities nǁ and n as a function of time after laser pulse.
Also we can assume when t ∞, nǁ and n =n.
11 푃 ------
𝑑 I = ------12 ǁ 𝑑 휏
𝑑 I = ------13 𝑑 휏
By using equation 11, 12 and 13 one can find the ratio /ǁ as (1+P)/(1-P) when t ∞, P=30% . Also using equation 11, 12 and 13 with the
information /ǁ we can find the ratio and Polarization as a function of
time after laser pulse.
휏 푡 = ------14 휏
84
휏 [ ] 휏 푃 푡 15 = 휏 ------[ ] 휏
0.8
0.6 p ll
Polarization0.4
0.2
p
0.5 0.0 0.5 1.0 1.5
Time(ns)
Figure 41: Polarization variation with Time after laser pulse. Blue and Red dotted curves represent the experimental emission polarization as a function of time after laser pulse when excited parallel/perpendicular to the NW. Light blue/pink lines are the same emission polarization predicted by the model for same conditions.
Figure 41 represents experimental data (dotted curves) for the emission polarization as a function of time after laser pulse. Solid lines show the theoretical emission polarization as a function of time after laser pulse with
85 the same experimental conditions. Model curves best fit to the experimental data when the exciton spin scattering times equals to 200 ps with the initial condition nǁ =90% and n =10% for parallel excitation. For perpendicular (t=0) (t=0) excitation the initial conditions are nǁ =15% and n =85%. (t=0) (t=0)
0.8
0.6
Pǁ
0.4
0.2 Polarization P
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Time (ns)
Figure 42: Emission Polarization as a function of time after laser pulse for NW-5 with higher excitation power (~9mW-measured before the microscope objective). Red/Black color-excitation laser polarized parallel/perpendicular to NW.
Figure 42 displays the emission polarization as a function of time after laser pulse when excited by a polarized laser either parallel or perpendicular to
86 the NW(wire-5). At this time the excitation power was increased to 9mW and was measured before the 50X objective. If we compared this data with the data shown in Figure 39 we can see a remarkable change in the emission polarization with time after laser pulse. At this moment there is no difference between the two configurations of polarization. We believe the higher excitation power create more photoexcited carriers as a result at higher excitation powers, the exciton dipoles relax much more rapidly within a time, in less than our temporal system response of 80ps.
5.5 Summary
We use polarized time-resolved photoluminescence to study exciton dynamics in GaAs/AlGaAs core-shell nanowires (NWs) at 20 K. By pumping the nanowire with lasers polarized parallel and perpendicular to the nanowire, the polarization dynamics reflect the exciton dipole distributions within the nanowires. The NWs were prepared by Au catalyzed MOCVD and excited by a pulsed titanium-sapphire laser at 798 nm. The polarization of the emitted PL was monitored at the exciton emission peak (1.515 eV) as a function of time after excitation by a polarized pulse. The diameter of the nanowire is much larger than the exciton Bohr radius so that the exciton dipoles are degenerate regardless of orientation; thus in thermal equilibrium the density of excitons parallel and perpendicular dipoles should be equal. At low excitation intensities we find that the excitons are
87 created out of thermal equilibrium, but relax within several hundred picoseconds. At higher excitation powers, the exciton dipoles relax much more rapidly within a time, in less than our temporal system response of
80ps. This suggests that exciton dipole relaxation is very sensitive to carrier-carrier scattering.
88 Chapter 6
6 Wurtzite InP nanowire band- structure
6.1 Introduction
Exploration of optical and electronic properties of semiconductor nanowires has gained a lot of interest in the research community because of their extensive potential applications including nanowire lasers[75][76][77], nanowire sensors[78][79][80], nanowire photovoltaic[81][82][83], photo detectors[84][85][86], single electron transistors[87][88] etc. Indium
Phosphide (InP) nanowires are of special interest because of their high quantum efficiency and uniquely low sensitivity to surface defects[89][90].
InP NWs can be grown in two different crystal structures such as Zincblende
(ZB:cubic ) and Wurtzite (WZ:hexagonal). ZB structure is well investigated because the usual bulk InP semiconductor found nature is ZB. Pure WZ crystal structure only occurs in NWs. Thus the only way of investigating the electronic structure of WZ InP is to study the valence and conduction bands of these type of NWs. Before the work described here, very little work had been done in probing the electronic band structure in wurtzite InP NWs. In the literature one could find some experimental investigations done to measure the band gap difference between WZ and ZB InP[91][92][93], but there were no direct measurements of the higher lying band structure.
89 Mixed phase InP NW have shown a 45 meV band offset between WZ InP valence band and ZB InP valance band which is in good agreement with theoretical calculations[94][95][96]. Figure 43-(a,b) shows the schematic diagrams of ZB and WZ InP semiconductor. As shown in the Figure 43-a heavy and light hole bands of the ZB InP valence band are degenerated. The spin-orbit interaction shifts the third valence band (the split-off band) further down in energy, having smaller total angular momentum. On the other hand, because of the arrangement of atoms in the crystal structure of
WZ InP compared to ZB, the atoms feel an extra potential from neighboring atoms which produces the crystal field effect. As a result of the combination of spin-orbit coupling and the crystal field effect the degeneracy of the valence bands in WZ InP is completely removed. As shown in Figure 43-b, there are expected to be three separate hole bands traditionally named as A,
B and C hole. In this project, we try to measure the WZ band structure optically and so estimate the fundamental band parameters including the crystal field and spin-orbit energies. How these parameters change with the
NW diameter and how the optical selection rules work for small nanowires are both of significant interest and likely will lead to new physics. In this project we investigate the electronic structure of WZ InP NWs as a function of diameter using experiment techniques such as photoluminescence (PL), time-resolved photoluminescence (TRPL) and photoluminescence excitation
(PLE). Therefore, these works also provide important feedback to crystal growers in order to optimize the quality of NWs.
90
E 8 E Γ CB2
CB1 7 Γ 6 CB Γ
CB
E ~1.424eV g E ~1.504eV g
k k
hh 9 A 8 Γ Γ lh 7 Γ B VB VB 7
7 Γ C Γ SO
(a) (b)
Figure 43: (a)-Band diagram of ZB InP semiconductor. Low temperature band gap is around 1.424eV as indicated. Heavy hole and light hole bands are degenerated. (b) Band diagram of WZ InP with low
temperature band gap is 1.504eV. The valence band degeneracy is completely removed because of spin-orbit interaction and crystal field effect.
6.2 Growth and Morphology
The InP NWs in this project were grown by the research group of our collaborator, Professor C. Jagadish of Australian National University, on an
InP III(B) oriented substrate by using the VLS method inside a horizontal flow metal-
91
1 µm
(a)
(b)
100nm
Figure 44: (a) FESEM micrograph of 100nm diameter WZ InP NWs (45 degrees tilted substrate). (b) TEM micrograph of a single 100nm diameter WZ InP NW showing excellent crystallinity. Gold seed can be seen at the tip. organic chemical vapor deposition (MOCVD) reactor operating at low pressure. The NW growth process was accomplished using the process
92 explained in section 2.2 with growth temperature of 420 C and V/III ratio of
700. By using 20 to 100nm diameter gold particles as catalysts different sized NWs were grown at the same time under nearly identical conditions.
According to Paiman et al. such a high V/III ratio with above growth temperature provides the optimal conditions for formation of WZ InP
NWs[97][98]. Figure 44(a) is a field emission scanning electron micrograph
(FESEM) image of 100nm diameter WZ InP NWs on the growth substrate which tilted 45º to get the image. Figure 44(b) is a transmission electron micrograph (TEM) of a single 100nm diameter WZ InP NW removed from the growth substrate. The diameter of the NW is approximately determined by the diameter of the gold seed used to grow it, but the measured average diameter of these NWs is slightly larger at approximately 129nm and the length is around 6 microns. The NWs with catalyst diameter equal to 100nm shows excellent crystal quality with minimum structural defects and tapering.
6.3 Photoluminescence measurements
The InP WZ NW samples described in the previous section were removed from the growth substrate and mounted inside the optical cryostat that was cooled down to low temperatures (~10 Kelvin) using liquid helium. A wavelength tunable laser beam was collimated and focused onto single NWs by using a 50X (0.5 numerical aperture) long working distance microscope objective combined with beam splitters, lenses and mirrors. The emitted PL
93 was collimated and focused onto the entrance slit of a spectrometer. For a detailed description of experiment setup and methods refer to the section
3.2. A series of optical experiments utilizing the complementary optical techniques of photoluminescence, time-resolved photoluminescence, and photoluminescence excitation spectroscopy were carried out on these unique WZ InP nanowires.
1.0 7Po
0.8
0.6
5Po 0.4 3P PL PL Intensity o
0.2 2P ZBband edge o WZband edge
Po 0.0 1.40 1.42 1.44 1.46 1.48 1.50 1.52
Emission Energy (eV)
Figure 45: Low temperature (10K) CW Power dependent photoluminescence measurements done on typical 100nm WZ InP NW.
To make sure the InP NWs we studied were pure WZ, a CW power dependent
PL measurement was carried out for each single NW used. Figure 45 shows a power dependent PL measurement done for a single WZ InP NW. As explained by Pemasiri et al., if there is some significant amount of ZB
94 inclusions in a WZ InP NW (20% by volume) one could observe emission close to ZB band edge at low excitation powers. But with increasing excitation power this emission peak rapidly shift to high energy side by an amount of 70meV[99]. In Figure 45 one could observe the PL peak around
1.475 eV at low powers and it is 25 meV below the WZ band edge. It moved towards high energy side only by 10 meV when power was increased from
P (~40µW) to 7P . The emission we observed is not from WZ band edge 0 0 emission and since it didn’t shift rapidly with power we believe that there are no significant mixed phase inclusions. The emission we observed is well above the ZB band edge emission and it suggest that the PL we see is from an unknown defect emission that coupled with WZ band edge emission. To confirm the band edge emission we performed TRPL experiment using a tunable Ti:S laser with excitation energy tune to 780nm.
6.4 Time-resolved photoluminescence
Figure 46 shows the time resolved spectral map constructed by acquiring single time decays for a large range of emission energies from the NW after the laser pulse. We can extract data from this TRPL map and plot at Intensity versus Emission energy as a function of time after the laser pulse. This sort of spectra are called Time-resolved PL and display the most valuable information about how the PL evolves with time which regular CW time integrated PL does not. Figure 47 displays the TRPL extracted from TRPL map at early time(240ps) and later time(9.2ns) after pulsed laser excitation.
95 The band edge emission at 1.504 eV rapidly decays(200ps) into two long lived(2.5ns)defect lines at 1.475 and 1.460 eV.
12
10 5500
8 305.8
6
Time (ns) Time 4 17.00
2
0 1.46 1.48 1.50 1.52 1.54 1.56 Energy (ev)
Figure 46 : Time-resolved spectral map of single WZ InP 100nm diameter NW. Time decays are obtained by using 200 fs pulsed excitation wavelength tuned to 780nm.
96
5000 10K 15 4000 9.25ns 240ps
3000 10
2000 5 1000
Intensity(counts) 0 0
1.44 1.46 1.48 1.50 1.52 Energy (ev)
Figure 47: Time-resolved photoluminescence extracted from TRPL map at early and late time for 100nm WZ InP NW. At early time(240 ps) PL shows emission from WZ band edge. At later time it decays into long lived defect lines.
No emission from the ZB/WZ continuum which is above 1.54eV were observed which suggests that these NWs are nearly pure WZ. The lower energy PL lines are mostly likely point defects such as anti-sites, vacancies or interstitials caused by the very high V/III ratio(700) used to grow WZ InP
NWs. The time-resolved spectral map and time-resolved PL indicate that the band edge emission is strongly coupled to the two unknown defects explained above. While such defects are not optimal for devices, they do provide a good opportunity to implement a photoluminescence excitation
97 experiment using this defect line as a detector by observing its intensity as a function of laser excitation energy.
6.5 PLE measurements
1.0
0.8 Laser filter ~ 1.494eV
0.6
0.4
PLIntensity
0.2 ZB~1.418eV 0.0 WZ~1.504eV 1.30 1.35 1.40 1.45 1.50 1.55 1.60 Emission Energy (eV)
Figure 48: Typical PL spectrum acquired by the newport spectrometer(blue curve). WZ and ZB band edges are marked for reference. Red arrow shows the filter cut off edge. 1.494eV low pass filter block the emission from 1.494eV and above including the band edge.
The main objectives of this study are to observe the exciton energy positions and the optical selection rules using polarized laser excitation for
WZ InP NWs. This will determine the band structure including the positions of the A,B & C exciton energies and will provide a means for estimating the values for the spin-orbit coupling and the crystal field splitting. PLE was accomplished by collecting the PL spectrum(refer to Figure 48) while tuning
98 the laser excitation energy just below the band-edge to higher energies and plotting a graph by using integrated PL intensity versus excitation energy.
Any strong absorption into a particular valence band state should result in a strong enhancement in the intensity of the defect emission line and such valance band states can be readily identified by the corresponding PLE spectrum. We used a laser line filter to remove the laser light and so observe only the defect emission lines. In Figure 49 the red color curve shows the PLE spectrum at low temperature (10K) for 100nm diameter WZ
InP NW. The gray color curve is the filtered PL spectrum showing the defect emission from the NW. For that emission PL spectrum, the laser was tuned to an energy of 1.534eV. As we scanned the laser excitation energy just below the band gap to higher energy a weak resonance is observed at the expected WZ InP band edge at 1.504 eV and two additional strong resonances were observed at 1.534 and 1.665 eV. During the PLE measurements shown in Figure 49 the excitation laser was polarized parallel to the NW axis while the circular polarized emission was collected from the
NW to collect all the emission from the NW regardless of its polarization.
The two resonances corresponding to B and C exciton were seen for all the
WZ InP NWs diameters ranging from 20 to 100nm. The reproducible structures in PLE spectra were observed and it varied from nanowire to nanowire on the high energy side of resonance marked as B and on the low energy side of the resonance marked as C. The possible resonance positions
99 B and C were determine by the common resonance energies seen in all NWs.
We interpret the three resonances seen
1.2 C 10K A B 1.0 E = 30 mev Eexc=1.534eV BA E = 161 mev PLE 0.8 CA PL
0.6
0.4
0.2 Normalized Intensity Normalized 0.0
1.40 1.45 1.50 1.55 1.60 1.65 1.70 Excitation Energy (eV)
Figure 49: Red color line-PLE spectrum from single 100nm diameter WZ InP NW showing three exciton resonances as A, B and C. Gray color line-Filtered PL spectrum showing the defect emission for laser excitation tune to the energy marked as B.
in the PLE spectra as A, B and C excitons expected for wurtzite band structure. From these data we can provide preliminary valence hole-band to
100 conduction band energies for the excitons A, B and C as 1.504, 1.534 and
1.665eV. From our PLE data we determined the energy splitting between A and B hole-bands(E ) as 30 meV and the energy splitting between A and C BA hole-bands(E ) as 161 meV. Using the quasi-cubic approximation, we can CA estimate values for spin-orbit coupling and crystal field splitting[100].
∆퐬퐨+∆퐜퐫 ∆퐬퐨+∆퐜퐫 퐄 = ∆ ∆ ------16 퐁퐀 퐬퐨 퐜퐫
∆퐬퐨+∆퐜퐫 ∆퐬퐨+∆퐜퐫 퐄 = + ∆ ∆ ------17 퐂퐀 퐬퐨 퐜퐫
Equations 16 and 17 represent the relation between the energy splitting between the A, B and C hole-bands and the spin-orbit coupling and crystal field splitting. From our measure measurements we calculated a crystal field energy, Δ =52 meV and a spin-orbit energy, Δ =139 meV. The CR SO calculated crystal field and spin-orbit energy values from our measurements are comparable to the theoretical predictions and other experimental values published in literature and these values also can be found in the following table.
101
Experimental values for WZ InP
E ~30meV E ~161meV BA CA
44 meV [1] 143 meV [1]
40 meV [2]
Theoretical values for WZ InP
Δ ~52meV Δ ~139meV cr SO
82 meV [3]
26 meV [4] 119 meV [4]
The spinorbit energy is comparable to the known bulk ZB InP
spin-orbit splitting of ~ 110 meV.
[1] GADRET et al., Phys. Rev. B 82, 125327 (2010)
[2] Gerben L. Tuin et al., Nano Res. 2011, 4(2): 159–163
[3] M. Murayama and T. Nakayama, Phys. Rev. B 49, 4710, 1994
[4] Lijun Zhang et al.,Nano Lett., 2010, 10 (10), pp 4055–4060
102
1.0 parallel perpendicular 0.8
0.6
0.4 Intensity
0.2
0.0 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 Energy(eV)
Figure 50: Polarized PLE measurements for 100nm single WZ InP NW. Excitation laser was polarized parallel/perpendicular to NW growth axis while circularly polarized emission from the NW was collected
Figure 50 shows the PLE spectrums of the single 100nm WZ InP NW when the excitation laser polarized parallel and perpendicular to the NW growth axis(c-axis). The emission from the NW was collected by using a circular polarizer to collect all emission from the NW. There are two possibilities that could affect the emission polarization of the PLE spectrum. They are dielectric mismatch between NW and surrounding vacuum(coupled with NW diameter and excitation energy) and optical selection rules. Because of the
103 large dielectric mismatch between the NW and the vacuum (ε=13), the electric field inside the NW is suppressed compared to the electric field outside the NW when it is excited using a source polarized perpendicular to the NW axis but the internal electric field is same as outside the NW when it is exited along the NW axis[101]. According to optical selection rules when the NW is excited by light polarize perpendicular to the NW growth axis(c- axis) all the transitions from A(Γ9), B(Γ7) and C(Γ7) hole-band to conduction band(Γ7) are dipole allowed. But when it is excited by light polarized parallel
NW c-axis the transition from A(Γ9) hole-band to conduction band(Γ7) is dipole forbidden while other two are allowed. The lowest lying transition at
1.504 eV is much weaker than other two when exciting parallel to the NW because of the forbidden selection rule. But because of the large dielectric mismatch, at that excitation energy the intensity of the A exciton peak is much weaker when excited by the laser polarized perpendicular to the NW compared to parallel excitation. Recent studies done with CdSe NWs showed that polarization anisotropy not only depend on the dielectric mismatch but also depend on the diameter of the NW and the excitation wavelength[102].
According to Giblin et al. excitation polarization decrease with increasing excitation energy for larger diameter NWs. Figure 51 shows the PLE spectrums of the single 50nm WZ InP NW when the excitation laser polarized parallel and perpendicular to the NW growth axis(c-axis). The
104 emission from the NW was collected by using a circular polarizer to collect all emission from the NW.
1.0
parallel perpendicular 0.8
0.6
0.4 Intensity
0.2
0.0 1.50 1.52 1.54 1.56 1.58 1.60 1.62 1.64 1.66 1.68 1.70 Energy(eV)
Figure 51: Polarized PLE measurements for 50nm single WZ InP NW. Excitation laser was polarized parallel/perpendicular to NW growth axis while circularly polarized emission from the NW was collected.
In this 50nm NW it is very clear that the transition from A(Γ9) hole-band to conduction band(Γ7) is forbidden when excite by a laser polarized parallel to the NW c-axis because of the selection rule. Also B(Γ7) and C(Γ7) hole-band to conduction band(Γ7) are dipole allowed. On the other hand when the NW is
105 excited by a laser polarized perpendicular to the NW c-axis all the transitions from A(Γ9), B(Γ7) and C(Γ7) hole-band to conduction band(Γ7) are dipole allowed. It is clear for this 50nm WZ InP NW, all the selection rules appear to be satisfied but because of the dielectric mismatch coupled with
NW diameter and excitation energy reduced the emission intensity when exciting the NW with a laser polarized perpendicular to the NW c-axis.
6.6 Extended PLE measurements
1.0
0.9
0.8
0.7 BCB2 ACB2
0.6 C CB2 C
0.5
C CB1 C BCB1
Intensity 0.4 InP WZ-100nm
0.3 ACB1
0.2 parallel 0.1 perpendicular
1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 excitation energy eV
Figure 52: PLE spectra obtain by exciting the 100nm WZ InP NW with light polarized parallel to the NW (red curve) and exciting with light polarized perpendicular to the NW (Blue curve). Transitions from second conduction band to valence band are clearly visible and energy positions are marked on the PLE spectrum.
106 Recently A. De and Craig E. Pryor [103] predict a second gamma point in (Γ8)
WZ InP just 238 meV above the first conduction band(Γ7). According to the group theory transitions from this second conduction band(Γ8) to the A hole- band(Γ9) have the same selection rules as from first conduction band(Γ7) to the A hole-band. Jesper Wallentin et al., experimentally partially resolved the upper conduction band in PL by using very heavily doped WZ InP nanowires where the second conduction band becomes populated because of band filling. They estimated that the second conduction band was 230 meV above the WZ conduction band edge at 1.49 eV[104]. In this project, we use mainly photoluminescence excitation measurements along with CW and time-resolved photoluminescence to identify this second conduction band and all the transition from this second conduction band to A, B and C hole- bands. For this measurement we used an optical cryostat made by the Janis research company and it’s a Model ST-500 continuous flow optical cryostat for microscopy which uses an Attocube stage. For the photoluminescence excitation spectroscopic measurements we used a supper continuum nonlinear fiber optic cable to produce white light as the excitation source.
Ti:Sapphire laser was used as the input source for the fiber optic cable with its wavelength tune to 800 nm and a matching set of Brewster cut prisms along with a spectral filter used to obtain monochromatic light to serve as the excitation source for the NWs. NWs were photoexcited by this filtered pulsed light from the white light which has a full width at half maximum
107 (FWHM) around 2nm. This excitation source was focused to a 1.5 micron spot using a long working distance 50X/0.5numerical aperture (NA) objective. The emitted photoluminescence was collected through the same objective and focused onto the entrance slit of a 250 mm focal length imaging spectrometer(Newport). The emitted PL was dispersed by a 1200 groves/mm grating and was detected by a back-illuminated silicone CCD camera. PLE spectrums shown in Figure 52 were obtained by using super continuum fiber as the excitation source. To construct the PLE spectrum of
WZ NWs, we integrate the filtered defect emission over all energies as the laser energy was tuned to higher energies. The Red and Blue curves were obtained by exciting the NW with light polarized parallel and perpendicular to the NW. Since we used pulsed excitation the energy width of the excitation light is little bit higher compared to the width of the CW laser and since this is a pulsed source the number of photoexcited carriers are order of magnitude higher than CW source. The transition from the first conduction band(CB1) to A-hole band usually we see at 1.504 eV in energy is very weak and we see this as an edge at 1.508 eV in parallel excitation. As the laser energy is scanned to higher energy (see Figure 52), some resonances were observed at 1.538, 1.573 and 1.670 eV below the second conduction band energy. Also some clear resonances were seen at 1.737,
1.780, 1.814 and 1.906 eV. In these measurements, the excitation light source was polarized parallel and perpendicular to the NW axis, while
108 circular polarized emission was collected from the NW to ensure collection of all emission from the nanowire, regardless of polarization.
6.7 Result and discussion
Because of the dielectric contrast between the vacuum and the NW (ε =
13)[105], an excitation laser polarized parallel to the NW has more intensity near band edge than perpendicular to the NW in the PLE plot. The emission polarization may change due to the selection rules and the complicated issues with the NW diameter, dielectric contrast couple with excitation energy as shown by some authors[105][102]. The resonances at 1.538 and
1.670 eV are identified as the B and C excitons and they were also well identified in our recent paper[106]. The resonance at 1.573 is 35 meV away from B exciton level and this could be due to some optical phonon interaction.
We interpret the resonances at 1.737, 1.780 and 1.906 eV are the transition from the second conduction band(CB2) to A, B and C hole-bands.
The weak resonance seen at 1.814 eV is 34 meV away from the resonance seen at 1.779 eV and we believe this also occurred due to an optical phonon transition. The energy difference between the WZ conduction band at 1.508 eV and the second conduction band edge at 1.737 eV is 229 meV.
We measure an energy splitting between the A and B hole bands of 30 meV, and an energy splitting between the A and C hole bands of 162 meV
109 and they are in good agreement with our previous data as 30 and 161 meV respectively. We can summarize the data as follows for comparison.
Second
Previous Data[106] New Data Conduction
band
CB1-A 1.504 eV CB1-A 1.508 eV CB2-A 1.737 eV
CB1-B 1.534 eV ΔBA=30meV CB1-B 1.538 eV ΔBA=30meV CB2-B 1.780 eV
CB1-C 1.665 eV ΔCA=161meV CB1-C 1.670 eV ΔCA=162meV CB2-C 1.906 eV
From these data we estimate the second conduction band is 236 ± 6 meV away from the WZ first conduction band edge.
6.8 Summary
We used photoluminescence excitation (PLE) spectroscopy to investigate the electronic band structure of wurtzite InP nanowires (NWs) at low temperature (10 K) with nominal diameters of 50 and 100nm, along with time-resolved photoluminescence (PL) and CW photoluminescence. The NWs were prepared by Au catalyst-assisted MOCVD growth with 420C growth temperature and V/III ratio of 700. PL from all NWs showed a dominant defect line around 835~840nm (1.484~1.475eV) and because of that the free
110 exciton line couldn’t be observed at the expected energy of 824nm
(1.504eV). Power dependent and time-resolved PL measurements confirmed that the observed PL does not come from type-II ZB/WZ InP transitions, but originates from possible phosphorous antisite defects resulting from the high V/III ratio. The TRPL measurement on the 100nm diameter NW showed short-lived band edge emission at 1.504 eV which rapidly relaxed to the defect emission within 50 ps. 50nm diameter NW showed PL emission at
1.504 eV at early time and rapidly relaxed in to the defect emission at
1.457eV at later time in the time resolve measurement.
PLE measurements were implemented by monitoring the defect line as a function of laser energy. A low-pass filter (830nm) was used to insure that only the defect emission line was detected by removing the laser line.
Polarization analysis of the PLE was made by polarizing the excitation laser parallel and perpendicular to the nanowire long axis(c-axis) and observing both polarization states for the emitted defect-related PL. CW PLE spectra showed three main peaks for band-to-band transitions between the A, B and
C hole bands to conduction band at energies of 1.504, 1.534 and 1.665eV in the 100nm diameter NW sample. Polarized PLE measurements probed the optical selection rules for these band-to-band transitions which were expected not to be isotropic as for Zinc blende InP. We have extracted a crystal field splitting of 52 meV and a spin-orbit interaction energy of 139 meV for these WZ InP nanowires. We have extended the PLE measurements to probe the transitions between A, B, and C hole-bands second conduction
111 band. We interpret the resonances seen at 1.737, 1.780 and 1.906 eV in extended PLE graph as the transition between A, B and C hole-bands to second conduction band. According to these results the estimated the second conduction band is 236 ± 6 meV away from the WZ first conduction band edge.
112 APPENDICES
Mathematica program to solve the rate equations: t1 and t2 are the data tables contains Polarized time resolved data for parallel and perpendicular excitation to the NW.
Emission polarization when excitation source polarized parallel(Blue) (Pǁ) and perpendicular(Red) (P ) to NW as a function of time after laser pulse. pl4 = ListPlot [t1, AxesOrigin{-0.5,0},AxesLabel{Time[ns],Polarization},
PlotStyle{RGBColor[0,0,1],PointSize[0.015]},PlotRange{{-0.5,2},{-0.1,0.8}}]
Polarization 0.8
0.6
0.4
0.2
0.0 Time ns 0.0 0.5 1.0 1.5 2.0
[ [ ]
[ ] [ ] ]
113
Polarization 0.8
0.6
0.4
0.2
0.0 Time ns 0.0 0.5 1.0 1.5 2.0
The function created to solve the rate equation is shown below when exciting parallel to the NW. nw and n1 are exciton densities where their dipoles align parallel and perpendicular to the NW. tr and tw1 are radiative exciton lifetimes parallel
/perpendicular to the NW and exciton spin scattering time respectively.
[ ] [ 푡
[푡] [푡] [푡] [푡] [푡] [푡] [푡] [푡]
[ ] [ ]
114 [ 푡 ]
[ ]⁄ [ ] ⁄ [ ]⁄ [ ] ]
Emission polarization when excitation source polarized parallel to NW as a
function of time after laser pulse by solving rate equations
[ [ ]
[ ]
[ ] [ ] ]
Polarization 0.8
0.6
0.4
0.2
Time ns 0.0 0.5 1.0 1.5 2.0 2.5 3.0
The function created to solve the rate equation is shown below when
exciting perpendicular to the NW
[ ] [ 푡
115 [푡] [푡] [푡] [푡] [푡] [푡] [푡] [푡]
[ ] [ ]
[ 푡 ]
[ ]⁄ [ ] ⁄ [ ]⁄ [ ] ]
Emission polarization when excitation source polarized perpendicular to
NW as a function of time after laser pulse by solving rate equations
[ [ ]
[ ]
[ ] [ ] ]
Polarization 0.8
0.6
0.4
0.2
Time ns 0.0 0.5 1.0 1.5 2.0 2.5 3.0
116
Polarization variation with Time after laser pulse: Blue and Red dotted curves represent the experimental emission polarization as a function of time after laser pulse when excited parallel/perpendicular to the NW. Light blue/pink lines are the same emission polarization predicted by the model for spin scattering times equals to 200 ps.
[
[ ] ]
Polarization 0.8
0.6
0.4
0.2
Time ns 0.5 0.0 0.5 1.0 1.5
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