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

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121 ref. sample defect energy method [88] undoped VCa vb + 1.0 eV photocapacitance and optical current deep level transient spectroscopy [80] p-type I(Ga) or I(N) vb +1.8 eV deep level transient spectroscopy ? vb + .45 eV spectroscopy and photoemission ? vb + .30 eV capacitance spectroscopy ? vb + .21 eV [53] n-type ~:v cb + .8 eV very high pressure optical absorption. transmission, luminescence and Raman scattering [89J undoped ? vb + .72 eV photothermal deflection ? vb + .22 eV spectroscopy and constant photothermal current method [90] undoped ? cb-.042 eV photoluminescence and and doped ? cb - 1.0 eV optically detected ? vb + .19 eV magnetic resonance p-doped ? vb + .5 eV Table 5.3: Defects in GaN Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
122 equation (5.2), is represented using matrix elements of the form (mlrili) as (5.2) + (1Ir,ln)(nlrilm)(mlrkll) [(W-Wmn )+hmn J[(Wo-rWnl) -hnl J + (1Ir,ln){n1r,lm)(m1rkll).. [(W+Wnm )-l1'nm J[(Wo-Wml )+17ml! + (1Ir,ln)(nlrk Im)(mlr.ll) ) [(w+wmil-hmd[(wo+wnil+I"Ynd • In equation (5.2), Ii), 1m), and In) are the quantum mechanical states of the system: pf?) is the unperturbed density of the state Ii); -eri is the dipole moment operator along the direction i; hW nm is the energy difference between states In), and 1m): and ~/nm is a dephasing term. Determination of nonzero matrix elements is greatly simplified through group theory. Group theory assigns symmetries to states based on the underlying symmetry of the crystal. The power of group theory to determine band symmetries becomes clear when we examine the relationship between the Hamiltonian, H, the symmetry operations of the crystaL P(Xd, and the eigenstates of the Hamiltonian. wnJo Note the index n corresponds to the an eigenstate of energy En and j labels the I-fold degenerate states. In general, P(Xd are all of the symmetry operations of the crystal including translations and point operations of the crystaL vVe will state without proof the following theorem. If H is invariant under the group G of P(Xd then the eigenfunctions belonging to the same energy level, l/JnJ' form a basis of the representation of G. 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
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: 120 high intrinsic electron concent
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 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
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, 172 .----. ::l U'J Q) ttl 0 '-.,;
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Chapter 7 SHG Microscopy The majori
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176 7.1 Historical Context of Secon
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178 comPJter - - - - - - - - - ~ ,-
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180 second-harmonic light towards t
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182 ~ 20 _____ ~ ____ J -----f- ---
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184 wave at normal incidence is (7.
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186 polarization is negligible for
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chopper AGate B Gate Signal Figure
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190 E 4000 1 c: 0 3000 ~ rJl -' 0 c
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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
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198 mean square deviation, of the p
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200 7.3 Calculated SHG Signal from
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202 parameter symbol value laser re
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204 parameter symbol value surface
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Chapter 8 Conclusion In this brief
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208 properties of carbon nanotubes.
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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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