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

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161 linear optical properties of GaN, we extracted X~;>x from the data. This parameter is displayed in Fig. 6.8. The magnitude of X~;>x is approximately 2.4x 10- 8 esu, which is consistent with Miragliotta's average value of 2.45 x 10- 8 esu measured at a single fundamental wavelength of 1064 nm [22]. This is lower than the other reported values for IX~~xl of9.25xlO- 8 esu [20] and 3.92xlO- 8 esu [23]. The data also exhibits a weak but distinct peak centered at a two photon energy of 2.80 e\". This feature is inconsistent with the expected spectral dependence based on Miller's rule [99]. For measurements in the p-in/p-out polarizations, SHG couples to X~?~: and :'(~2}x in addition to X~;>x. Therefore, we measured the SHG response of GaN at several angles of incidence to fit the two unknown susceptibility elements (see Fig. 6.9). vVe observed that our spectra were very weakly dependent on X~~~. The insensitivity of our spectra to X~~);: results from the fact that our nonlinear signal is proportional to Ie;:x~~~e:;e:; 12 ~ .004Ix~~~12. Therefore, we assume the theoretically predicted rela- . h· b (2) d (2)· (2) - -? (2) F· 6 8 h d tlOns lp etween Xx;:x an X;:zz' l.e. X;:;:z - -Xxzx . 19. . compares t e measure value of X~;>x to X~~)x averaged over all of our samples.. Although these elements are approximately equal, as predicted by the bound charge model [100], X~~x lacks a feature at a two photon energy of 2.80 eV. vVe compared our data with the calculated values of X~;>x and X~~x [25] in Fig. 6.8. Hughes and coworkers [25] calculated the second-order susceptibility elements with the full-potential linearized augmented plane-wave method within the local density Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
162 4 ""' ::J en Q) - -' .D 2L ·oJ n. Q) u en ::J IJl '- 0 Q) c c 0 z I dH .'. I ._ ••• - ••• - ~ I ~ I r --------- 01 2.6 2.8 3.0 3.2 Two Photon Energy ( eV) ./ 1 I I ~ I I Figure 6.8: :\Ieasured nonlinear susceptibility elements for GaN. 0 (D) denotes '(~~x (X~~x). Data represent the average values for all of the GaNjA1 2 0 3 samples. The solid line (dashed) is the calculated value of x~;'x (X~~x) from reference [25]. 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
Page 129 and 130: Chapter 5 Properties of GaN In rece
Page 131 and 132: 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: 160 i N -' '- 0 ::J a 0 o.sf fiftH!
Page 183 and 184: 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
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
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Appendix B Theory of Nonlinear Resp
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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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