William Angerer - Department of Physics and Astronomy - University ...

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xi Band Structure and Electronic Properties of GaN 113 5.2.1 Band Gap Physics 115 5.2.2 Electronic Properties 118 5.3 Defects in GaN . . . . . . . 119 5.4 Application of Group Theory to Optical Process 120 5.4.1 Second-Order Nonlinear Optical Processes at k = 0 123 5.5 ~IOCVD Growth of GaN . . . . . . . . . . . . . . . . . . . 134 6 Nonlinear Optical Spectroscopy of GaN 137 6.1 ~onlinear Optical Spectroscopy as a Probe of Condensed ~Iatter Systems 138 6.2 ~onlinear Rotational Symmetry of GaN .......... . 139 6.3 Theory of Nonlinear Optical Spectroscopy from GaN/Al 2 0 3 146 6.4 Second-Harmonic Generation Spectra from GaN/Ah03 158 6.5 Possible Origin of the 2.80 e V Resonance 164 6.6 Effect of Interface Strain . . . . . . . . . 170 7 SHG Microscopy 174 7.1 Historical Context of Second-Harmonic Generation Microscopy 176 7.2 Nonlinear Microscope. 177 7.2.1 Optical Setup 179 7.2.2 Detection .. 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Xll 7.3 7.2.3 Registering and Positioning Samples 7.2.4 Detection Limits and Noise ..... Calculated SHG Signal from Carbon Nanoropes 191 197 200 8 Conclusion 206 A Justification of First Order Expansion of the Phase 209 B Theory of Nonlinear Response Functions 212 C Justification of Zeroth Order Expansion of the Coefficients in the Ultrafast Nonlinear Pulse Calculation 215 D Derivation of Optical Transmission through a Thin Film Equations217 0.1 Derivation of equation (4.15) . 0.2 Derivation of equation (4.21) . 0.3 Derivation of equation (4.33) . 211 219 219 0.4 Derivation of equation (0.23) for complex indices of refraction 220 E Effect of Sapphire Miscut on Nonlinear Optical Measurements 222 F Code for Fitting Index of Refraction to Transmission Data 227 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Page 1 and 2: SHG SPECTROSCOPY OF GALLIUM NITRIDE
Page 3 and 4: COPYRIGHT vVilliam E. Angerer 1998
Page 5 and 6: ACKNOWLEDGEMENTS I am most grateful
Page 7 and 8: vi and support over the last three
Page 9 and 10: viii and we report on photoluminesc
Page 11: x 2.5 ~ovel Technique and Apparatus
Page 15 and 16: xiv
Page 17 and 18: xvi 2.10 Device for measuring ultra
Page 19 and 20: xviii 6.5 Polarization and propagat
Page 21 and 22: 2 scopies as a probe of these featu
Page 23 and 24: 4 tionallinear microscopy is unable
Page 25 and 26: 6 interference by group velocity mi
Page 27 and 28: Chapter 2 Introduction to Nonlinear
Page 29 and 30: 10 the electric fields as In this t
Page 31 and 32: 12 SHG is a virtual process, Le. th
Page 33 and 34: 14 2.3 (2) Xijk and Symmetry In gen
Page 35 and 36: 16 X (2) zxx = ,\.zyy v(2) (2) = v(
Page 37 and 38: 18 X~}k(W = 2wo) of our GaN samples
Page 39 and 40: 20 nonlinear element of quartz, X~~
Page 41 and 42: 22 the transmitted wave, E:t'°, Th
Page 43 and 44: 24 150 I I "1 I :) ~ >- -. iii c v
Page 45 and 46: 26 Quartz fundamental Figure 2.5: I
Page 47 and 48: 28 The bound wave, which propagates
Page 49 and 50: 30 1/e 2 its ma.'{imum value. This
Page 51 and 52: 32 Here, x~;!Aw = 2wo) is a constan
Page 53 and 54: 34 simplifications (2.39) and (2.40
Page 55 and 56: 36 nonlinear waves. This model assu
Page 57 and 58: 38 Fourier transform to E /2 (r, w)
Page 59 and 60: 40 3 mm and with the parameters dis
Page 61 and 62: 42 I " i iii iii iii iii iii iii ii
Page 63 and 64:
44 parameter value Bl 2.35728 B2 -0
Page 65 and 66:
46 is measured as a function of tra
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48 send pulse into device \11 input
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50 2.6 Conclusion In this brief sec
Page 71 and 72:
52 LOCK-IN AMPLIAER LOCK-IN AMPLIAE
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54 After polarization, the beam was
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56 PO HR !l o IV team BP Figure 3.3
Page 77 and 78:
58 .. ........... • / ~ '" ~ r --
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60 The production of ultrafast, hig
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62 800 ~ 0 0 J 0 0 0 0 J ~ 0 600~ 0
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64 measurements. Typically, I incre
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66 described below. Note that laser
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68 sentiallya nonlinear optical int
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70 780 800 820 840 860 880 900 920
Page 91 and 92:
72 Unlike the linear spectroscopic
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74 fore, the ratio of these two qua
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76 of :UN is deposited on the Ah03
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78 computer HeNe Las polarizer chop
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80 ~------".... GaN A12a3 index flu
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82 + d I , GaN A12a3 Figure 4.3: Co
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84 4.2 Measurement of Indices of Re
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86 fields at the lh interface to th
Page 107 and 108:
88 traveling wave, i.e. (-1.7) wher
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90 Note that the additional subscri
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92 £b, are defined only at the int
Page 113 and 114:
94 Equations (4.30) and (4.32) are
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96 the calculation of the transmitt
Page 117 and 118:
98 '- -0 OJ N 0.4 o E ~ o Z 0.2 o 2
Page 119 and 120:
100 2.0 "'"" "I 1.5 E ::t ~ --c 0 -
Page 121 and 122:
102 4.3 Photoluminescence of GaN To
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104 a photoluminescence measurement
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106 :J 0.01 0 ~ L ~ 0.008 r- :n :v
Page 127 and 128:
108 0.08 ~. j -i ,-... I I ""I :::l
Page 129 and 130:
Chapter 5 Properties of GaN In rece
Page 131 and 132:
112 5.1 Crystal Structure :\ crucia
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114 PJO'tI [{fall Figure 5.1: \Vurz
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116 e 4 r .1 It Figure 5.2: Calcula
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118 Parameter Symbol Value electron
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120 high intrinsic electron concent
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122 equation (5.2), is represented
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124 C6v E E £l. 2C3 2C 3 2C6 2C 6
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126 gap, the nonlinear susceptibili
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128 rrb 10.0 eV -------- 5 9.0 eV r
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130 In> 1m> 1m>
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132 Emission of a photon on the bra
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134 5.5 MOCVD Growth of GaN Our GaN
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136 # dopant thickness mobility car
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138 6.1 Nonlinear Optical Spectrosc
Page 159 and 160:
140 y lab X)lSlaJ / 2m Figure 6.1:
Page 161 and 162:
142 Fig. 6.2 displays the azimuthal
Page 163 and 164:
144 includes the effects of pulse p
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146 6.3 Theory of Nonlinear Optical
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148 L x i d 1 E( 00) air GaN sapphi
Page 169 and 170:
150 wavevector components. The free
Page 171 and 172:
152 z y x E( ro) air GaN Figure 6.5
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154 various free waves and summing
Page 175 and 176:
156 factors are: the nonlinearity o
Page 177 and 178:
158 where v /2 is the group velocit
Page 179 and 180:
160 i N -' '- 0 ::J a 0 o.sf fiftH!
Page 181 and 182:
162 4 ""' ::J en Q) - -' .D 2L ·oJ
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164 approximation. The agreement be
Page 185 and 186:
166 midgap state) could playa role
Page 187 and 188:
168 r: b S ~ r b I rs ~ r b I 0)1 r
Page 189 and 190:
170 in various bonding geometries w
Page 191 and 192:
, 172 .----. ::l U'J Q) ttl 0 '-.,;
Page 193 and 194:
Chapter 7 SHG Microscopy The majori
Page 195 and 196:
176 7.1 Historical Context of Secon
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178 comPJter - - - - - - - - - ~ ,-
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180 second-harmonic light towards t
Page 201 and 202:
182 ~ 20 _____ ~ ____ J -----f- ---
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184 wave at normal incidence is (7.
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186 polarization is negligible for
Page 207 and 208:
chopper AGate B Gate Signal Figure
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190 E 4000 1 c: 0 3000 ~ rJl -' 0 c
Page 211 and 212:
192 depend on two components: a hig
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194 nanorope ~ Figure 7.8: Carbon n
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196 of light reflected from the sam
Page 217 and 218:
198 mean square deviation, of the p
Page 219 and 220:
200 7.3 Calculated SHG Signal from
Page 221 and 222:
202 parameter symbol value laser re
Page 223 and 224:
204 parameter symbol value surface
Page 225 and 226:
Chapter 8 Conclusion In this brief
Page 227 and 228:
208 properties of carbon nanotubes.
Page 229 and 230:
210 that propagate through quartz a
Page 231 and 232:
Appendix B Theory of Nonlinear Resp
Page 233 and 234:
214 Fourier transforming equation (
Page 235 and 236:
216 and (CA) with f.b == t(.:.vo) a
Page 237 and 238:
218 The polarization, et, of the po
Page 239 and 240:
220 and (0.1.,1) respectively. Equa
Page 241 and 242:
Appendix E Effect of Sapphire Miscu
Page 243 and 244:
224 with cosO 0 - sin (} o 1 o (E.3
Page 245 and 246:
226 Let us compare the light transm
Page 247 and 248:
228 , .............................
Page 249 and 250:
230 it ( (fp·top..,(arr (ll, M r "
Page 251 and 252:
232 nal-2.00 tab'(:r[ihi]-:r[ila] )
Page 253 and 254:
234 1 - 2500.0; III - xU]; 1/ ti. t
Page 255 and 256:
Bibliography [1] R. K. Chang~ J. Du
Page 257 and 258:
238 [12] J. QL "V. Angerer, M. S. Y
Page 259 and 260:
240 Diamond, SiC and Wide Bandgap S
Page 261 and 262:
242 [40] M. M. Choy and R. L. Byer,
Page 263 and 264:
244 [55] \V. P. Lin, P. M. Lundquis
Page 265 and 266:
246 [70] J. vV. Yang, J. N. Kunzia,
Page 267 and 268:
248 [85] B. Monemar and O. Lagerste
Page 269 and 270:
250 [99] R. C. Miller, Optical Seco
Page 271 and 272:
252 [114] "V. de HeeL W. S. Bacsa,
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