Positron trapping by negative vacancies trapping process can be described quantitatively by Delocalized state n trapping model KR Coulomb potential leads to Rydberg Rydberg states states from there:positrons may re- escape by thermal stimulation 人b Kt once in the deep state: positron is captured until Deep bound state n annihilation 2 detrapping is strongly Annihilation radiation temperature dependent m* ER binding energy of positron in Rydberg state I ER~10meV Py vacancy density Manninen,Nieminen,1981
ER~10meV
temperature dependence of positron trapping is rather complex K三 iRP,心RnT-I2 0.5 RPy+KRO m*kB 、3/2 Texp ER K oc T-0.5 2xh2 kgT 0.2 low temperature:~T-0.5 due to Ka T-1.2 diffusion limitation in Rydberg states 0.1 higher T:stronger temperature dependence due to thermal 10 20 50100 300 detrapping from Rydberg state Temperature T[K闪 Positron trapping rate Kin negatively charged gallium vacancies determined in semi-insulating gallium arsenide as a function of temperature T.The trapping rate is normalized to the value measured at 20 K.Different symbols stand for different samples
Po s i tro n trapp i n g ra t e κ i n n eg a ti v e ly c h a rg e d ga lli u m v a c a n c i e s de te rm i n e d i n s e m i - i n s u la t i n g g a lli u m a rs e n ide a s a fu n c t i o n of t e mp e ra t u r e T. Th e trapp i n g ra t e is n o rm a liz e d to th e v a l u e m e a s u r e d a t 2 0 °K. D iffe r e n t sy m b o ls s ta n d fo r diffe r e n t s a mp le s
Table 1.Compilation of positron trapping coefficients of vacancy-type defects experi- mentally determined in various semiconductors (Krause-Rehberg and Leipner 1997).Only such experiments where the independent reference method was applied to the same samples were taken into account. Material Defect Trapping coefficient r Reference method Authors [1015s- [10ecm2s-] [ Si:P VP)° 0.68 1.4 300 Hall effect 日 >1.3 >2.6 300 Resistivity 0 SiP (VP) 18 36 300 Hall effect >2 >4 300 Resistivity b Si v 0.8±0.40 1.5±0.8 300 EPR c 0.8 1.6 300 Hall effect Si V 2.6±1.3 5.2±2.6 300 EPR 10 20 300 Hall effect Si v 5.2±2.7 10.5±5.3 300 EPR 0 58 300 Hall effect a Si L社 ≤01 <0.2 300 Hall effect 日 GaP V 0.8±0.3 1.5±0.6 473 Hall effect d GaP 1.9±0.5 3.8±1.0 473 Hall effect d GaP V待 <0.1 <0.2 473 Hall effect GaAs:Te (VGsTess) 1.1±0.2 2.5±0.5 300 Hall effect e GaAs:Si VGaSica) 0.7±0.2 1.6±0.5 300 STM F GaAs Va (EL2杓 >3 >7 25 IR absorption g >30 >68 20 IR absorption h GaAlSb Vo DX 1±0.3 2.9±1 300 DLTS HgCdTe 花 2.1±0.3 7±1 300 Hall effect 0.1±0.025 0.3±0.1 800 Hall effect PbSe 0.1±0.01 0.3±003 300 Hall effect k CdTe VaC1生. 1.7±0.4 5.2±1.2 300. PL T temperature of the positron experiment;EPR-electron paramagnetic resonance,STM- scanning tunneling microscopy;IR-infrared;DLTS-deep level transient spectroscopy;PL- photoluminescence. Kawasuso et al.(1995c),bMakinen et al.(1992a),Mascher et al.(1989b),dKrause-Rehberg et al.(1993c),Krause-Rehberg et al.(1995b),Gebauer et al.(1997c),Krause et al.(1990b),FLe Berre et al.(1994),Krause-Rehberg et al.(1993b),Krause-Rehberg et al.(1995a),Polity et al. (1993),IKrause-Rehberg et al.(1998)
Defect ta [ps] Defect ta [ps] Defect d [ps V 146 Si V 256 Ge V 263 V2 206 V2 309 V2 316 AIP VAI 265 GaP VGa 264 lnP、 Vin 295 Vp 261 Vp Vp 275 VAIVP 319 VGaVp 316 VinVp 340 AlAs VAI 271 GaAs VGa 265 InAs Vin 299 VAs 274 VAs 268 VAs 285 VAIVAS 439 VGaVAs 321 VinVAs 347 AlSb VAI 298 GaSb VGa 287 InSb Vin 315 Vsb 319 Vsb 307 Vsb 322 VAIVsb 455 VGaVsb 350 VinVsb 369 CdTe Vcd 321 HgTe VHg 304 VTe 339 VTe 315 VcaVTe 384 VHgVTe 362 GaN VGa 273 VN - VGaVN 348 SiC Vsi 196 Vc 153 2V 214 d is the defect-related lifetime
Table 3.8.Positron bulk lifetimes (in ps)calculated according to the generalized gradient approximation (GGA)and compared with results from the local density approximation (LDA).The pseudo-potential calculations were carried out by Panda et al.(1997),and the linear muffin tin orbital in the atomic sphere approximation(LMTO-ASA)and the atomic superposition calculations by Barbiellini et al.(1995,1996). Pseudo-potential LMTO-ASA Atomic superposition 出PA GA h 出DA TGGA PUDA TGA p 100 86 96 一 105 87 Si 190 216 186 210 184 207 218 Ge 198 228 191 228 190 229 228 SiC 130 145 124 139 121 134 142 229 GaAs 197 232 190 231 190 232 InP 213 246 201 248 200 247 241 179 223 179 232 230 ZnS 292 228 290 228 310 280 CdTe 245 222 285 222 310 274 HgTe TuDA and rGA are the bulk lifetimes calculated for the local density approximation(LDA)and the generalized gradient approximation(GGA),respectively.rxP is the most reliable experimen- tal bulk lifetime