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

More documents

Recommendations

Info

I 141 400 I ~ ::J < ..... ~ >-- en c Q) ..... c (.!) :r: (/) I 200 ~ ~ f I X10 I I I I L .J I l I J I ~ I ! ! l : 01 a 200 ¢ Figure 6.2: Rotational symmetry of SHG from GaN/Ah03 [0001]. The angle of incidence is 15°. ¢ is the angle between the miscut direction and the plane of incidence. o (0) is the data from the p-in/p-out (s-in/p-out) polarized second-harmonic field. The solid (dashed) line is a fit to the p-in/p-out (s-in/p-out) data with the miscut angle as a free parameter. The fitted miscut angle, a, is 0.79° (0.82°) for the p-in/pout (s-in/p-out) polarizations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
142 Fig. 6.2 displays the azimuthal dependence of SHG for GaN in the p-in/p-out and s-in/p-out polarizations at an angle of incidence of 15°. The p-in/p-out and s in/p-out polarized SHG data exhibit a one-fold symmetric modulation. These data are inconsistent with misaligned polarizers, which would result in non-zero isotropic signals for both polarizations. On the other hand, a simple sample miscut model was applied successfully to interpret the data. A miscut between the normal to the surface and the z-a.xis of the crystal results in a precession of the z-a.xis about the surface normal during the azimuthal scan. This precession induces an azimuthally dependent coupling of the fundamental fields to generate the anisotropic second-harmonic signal. Assuming the angle between the surface normal and the z-a.xis of the crystal is o. X~~k,lab is related to x~2J~ystal by equation (6.1) but with equation (6.2) replaced by cos 1> sin 0 coso 0 -sino Rmiscut = - sin ¢> cos 0 0 0 1 (6.3) 0 0 1 sin 0 0 cosa 2\iote, equation (6.3) assumes the [0001] a.xis is miscut in the xz plane. Since the x- and y-a.xes of GaN are equivalent, this assumption simply produces a phase shift between the experimental and calculated data. Table 6.2 displays the calculated azimuthal dependence of SHG from GaN [0001] with a small miscut angle, o. Note that higher order terms in the miscut, i.e. terms with miscut dependences of sin 2 0 and sin 3 o, are not displayed. The best fits to the p-in/p-out and s-in/p-out data yield a sample miscut angle, 0, of 0.80° ± 0.05°. The data were fitted with a function that 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 and 12:
x 2.5 ~ovel Technique and Apparatus
Page 13 and 14:
Xll 7.3 7.2.3 Registering and Posit
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
Page 67 and 68:
48 send pulse into device \11 input
Page 69 and 70:
50 2.6 Conclusion In this brief sec
Page 71 and 72:
52 LOCK-IN AMPLIAER LOCK-IN AMPLIAE
Page 73 and 74:
54 After polarization, the beam was
Page 75 and 76:
56 PO HR !l o IV team BP Figure 3.3
Page 77 and 78:
58 .. ........... • / ~ '" ~ r --
Page 79 and 80:
60 The production of ultrafast, hig
Page 81 and 82:
62 800 ~ 0 0 J 0 0 0 0 J ~ 0 600~ 0
Page 83 and 84:
64 measurements. Typically, I incre
Page 85 and 86:
66 described below. Note that laser
Page 87 and 88:
68 sentiallya nonlinear optical int
Page 89 and 90:
70 780 800 820 840 860 880 900 920
Page 91 and 92:
72 Unlike the linear spectroscopic
Page 93 and 94:
74 fore, the ratio of these two qua
Page 95 and 96:
76 of :UN is deposited on the Ah03
Page 97 and 98:
78 computer HeNe Las polarizer chop
Page 99 and 100:
80 ~------".... GaN A12a3 index flu
Page 101 and 102:
82 + d I , GaN A12a3 Figure 4.3: Co
Page 103 and 104:
84 4.2 Measurement of Indices of Re
Page 105 and 106:
86 fields at the lh interface to th
Page 107 and 108:
88 traveling wave, i.e. (-1.7) wher
Page 109 and 110: 90 Note that the additional subscri
Page 111 and 112: 92 £b, are defined only at the int
Page 113 and 114: 94 Equations (4.30) and (4.32) are
Page 115 and 116: 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
Page 123 and 124: 104 a photoluminescence measurement
Page 125 and 126: 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
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: 140 y lab X)lSlaJ / 2m Figure 6.1:
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 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
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,
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?