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

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167 [101]. Our model assumes a defect state lies in the GaN band gap with s-like or p like symmetry and that a three photon process originates at either the valence band ma.'
168 r: b S ~ r b I rs ~ r b I 0)1 rdefect I 0)1 0) 0) rdefect I A Figure 6.10: Three photon processes in Ga~ involving a midgap defect state. In Fig. A, the resonant transition is a transition between the defect state and the Ga).;" valence band. In Fig. 8, the resonant transition is a transition between the conduction band and the defect state. The virtual transitions are labeled by symmetry and by energy. e.g. liw 1 . The process is resonant for W = WI + W2. B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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SHG SPECTROSCOPY OF GALLIUM NITRIDE
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COPYRIGHT vVilliam E. Angerer 1998
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ACKNOWLEDGEMENTS I am most grateful
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vi and support over the last three
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viii and we report on photoluminesc
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x 2.5 ~ovel Technique and Apparatus
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Xll 7.3 7.2.3 Registering and Posit
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xiv
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xvi 2.10 Device for measuring ultra
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xviii 6.5 Polarization and propagat
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2 scopies as a probe of these featu
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4 tionallinear microscopy is unable
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6 interference by group velocity mi
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Chapter 2 Introduction to Nonlinear
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10 the electric fields as In this t
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12 SHG is a virtual process, Le. th
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14 2.3 (2) Xijk and Symmetry In gen
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16 X (2) zxx = ,\.zyy v(2) (2) = v(
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18 X~}k(W = 2wo) of our GaN samples
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20 nonlinear element of quartz, X~~
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22 the transmitted wave, E:t'°, Th
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24 150 I I "1 I :) ~ >- -. iii c v
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26 Quartz fundamental Figure 2.5: I
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28 The bound wave, which propagates
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30 1/e 2 its ma.'{imum value. This
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32 Here, x~;!Aw = 2wo) is a constan
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34 simplifications (2.39) and (2.40
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36 nonlinear waves. This model assu
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38 Fourier transform to E /2 (r, w)
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40 3 mm and with the parameters dis
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42 I " i iii iii iii iii iii iii ii
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44 parameter value Bl 2.35728 B2 -0
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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
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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
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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
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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
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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
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94 Equations (4.30) and (4.32) are
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96 the calculation of the transmitt
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98 '- -0 OJ N 0.4 o E ~ o Z 0.2 o 2
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100 2.0 "'"" "I 1.5 E ::t ~ --c 0 -
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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
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108 0.08 ~. j -i ,-... I I ""I :::l
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Chapter 5 Properties of GaN In rece
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112 5.1 Crystal Structure :\ crucia
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114 PJO'tI [{fall Figure 5.1: \Vurz
Page 135 and 136: 116 e 4 r .1 It Figure 5.2: Calcula
Page 137 and 138: 118 Parameter Symbol Value electron
Page 139 and 140: 120 high intrinsic electron concent
Page 141 and 142: 122 equation (5.2), is represented
Page 143 and 144: 124 C6v E E £l. 2C3 2C 3 2C6 2C 6
Page 145 and 146: 126 gap, the nonlinear susceptibili
Page 147 and 148: 128 rrb 10.0 eV -------- 5 9.0 eV r
Page 149 and 150: 130 In> 1m> 1m>
Page 151 and 152: 132 Emission of a photon on the bra
Page 153 and 154: 134 5.5 MOCVD Growth of GaN Our GaN
Page 155 and 156: 136 # dopant thickness mobility car
Page 157 and 158: 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
Page 165 and 166: 146 6.3 Theory of Nonlinear Optical
Page 167 and 168: 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
Page 173 and 174: 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
Page 183 and 184: 164 approximation. The agreement be
Page 185: 166 midgap state) could playa role
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
Page 197 and 198: 178 comPJter - - - - - - - - - ~ ,-
Page 199 and 200: 180 second-harmonic light towards t
Page 201 and 202: 182 ~ 20 _____ ~ ____ J -----f- ---
Page 203 and 204: 184 wave at normal incidence is (7.
Page 205 and 206: 186 polarization is negligible for
Page 207 and 208: chopper AGate B Gate Signal Figure
Page 209 and 210: 190 E 4000 1 c: 0 3000 ~ rJl -' 0 c
Page 211 and 212: 192 depend on two components: a hig
Page 213 and 214: 194 nanorope ~ Figure 7.8: Carbon n
Page 215 and 216: 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
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218 The polarization, et, of the po
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220 and (0.1.,1) respectively. Equa
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Appendix E Effect of Sapphire Miscu
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224 with cosO 0 - sin (} o 1 o (E.3
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226 Let us compare the light transm
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228 , .............................
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230 it ( (fp·top..,(arr (ll, M r "
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232 nal-2.00 tab'(:r[ihi]-:r[ila] )
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234 1 - 2500.0; III - xU]; 1/ ti. t
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Bibliography [1] R. K. Chang~ J. Du
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238 [12] J. QL "V. Angerer, M. S. Y
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240 Diamond, SiC and Wide Bandgap S
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242 [40] M. M. Choy and R. L. Byer,
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244 [55] \V. P. Lin, P. M. Lundquis
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246 [70] J. vV. Yang, J. N. Kunzia,
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248 [85] B. Monemar and O. Lagerste
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250 [99] R. C. Miller, Optical Seco
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252 [114] "V. de HeeL W. S. Bacsa,
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