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

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165 along direction k; and the dots represent unique permutations of the states. The contribution of three photon processes to x~]L(w = 2wo) depends of several factors. First, resonant enhancement of X~~k(w = 2wo) occurs when w :::::: Wng (two photon resonance) or Wo :::::: Wn'g (one photon resonance). Second. contributions to '(~~k('''': = 2wo) are constrained by the matrix: elements in the numerator of equation (6.36). In other words, the matrLx elements determine whether a process is allowed and influence the magnitude of allowed processes. Third, the occupancy of the states requires that the first virtual transition in the three photon process originates from an occupied state and connects to an unoccupied state. These constraints limit the type of process responsible for a two photon resonance with energy 2.80 eV in X~]k(w = 2wo). Because GaN is a direct band gap semiconductor \vith a band gap energy of 3.4 eV, the two photon resonance cannot result from virtual transitions between valence and conduction band states only. In addition. the requirement that the process begin with a virtual transition between an occupied and an unoccupied state precludes any process that occurs only in the valence or conduction bands. Thus, it is unlikely that the 2.80 eV feature results purely from the band structure of GaN. On the other hand, it is well known that Ga~ contains a variety of defect states [63]. Thus, the spectral feature could result from a three photon process that involves both a defect state and the GaN bands. For example. a bulk defect state (or defect band) with energy 2.80 eV above the valence band (a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
166 midgap state) could playa role in this resonance. 'vVe present a simple analysis of the X~~x spectrum that can somewhat constrain the properties of the defect state within the simple model. vVe decompose the susceptibility into resonant and nonresonant terms [4] as where the symbols have the same meaning as in equation (6.36) and el
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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
Page 133 and 134: 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: 164 approximation. The agreement be
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
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 (
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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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William Angerer - Department of Physics and Astronomy - University ...

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