The Simulation of Electret Effect in Zn 0.7 Cd 0.3 S Layers

Transcription

1 Nonlinear Analysis: Modelling and Conrol, 2005, Vol. 10, No. 1, The Simulaion of Elecre Effec in Zn 0.7 Cd 0.3 S Layers F. Kuliešius 1, S. Tamoši ūnas 2, A. Žindulis 1 1 Faculy of Physics, Vilnius Universiy Saulėekio av. 9, bldg. 3, LT Vilnius, Lihuania feliksas.kuliesius@ff.vu.l; aloyzas.zindulis@ff.vu.l 2 Insiue of Maerial Science and Applied Research Saulėekio av. 9, bldg. 3, LT Vilnius, Lihuania sasys.amosiunas@ff.vu.l Received: Acceped: Absrac. The regulariies of he dark discharge in ionic conac mode as well as of he hermoelecre effec have been invesigaed for Zn 0.7 Cd 0.3 S layers. The peculiariies of elecre charge formaion as well as he elecre volage dependences on poling elecric field, polarisaion ime and emperaure have been analysed in Zn 0.7 Cd 0.3 S layers during he presen work. The model of space charge accumulaion have been proposed. Keywords: hermoelecre, polarisaion, modelling. 1 Inroducion The elecre effec has been obained in he very broad variey of semiconducors as well as dielecrics. The effec can be observed while he space-charge or oriened permanen dipoles are frozen [1]. I has been shown ha phooconducive polycrysal solid soluions layers of Zn 0.7 Cd 0.3 S possesses well-defined spacecharge polarisaion [2], he origin of which remains unclear up o now. This polarisaion causes he long-ime memory, which can be used in he space-ime modulaors of ligh when consrucing he Zn 0.7 Cd 0.3 S layers in composiion wih liquid crysals. The goal of presen paper is o sudy he peculiariies of elecre volage dependencies on emperaure and layer hickness in Zn 0.7 Cd 0.3 S layers and o 77

2 F. Kuliešius, S. Tamoši ūnas, A. Žindulis simulae he dependencies of elecre volage decay, caused by depolarisaion, on emperaure. 2 Model background In he very large scale of semiconducor layers, in which he prevailing facors of he depolarisaion are he space charge exracion or/and neuralisaion of his charge by equilibrium conduciviy, he sponaneous discharge effecs can be explained by he Gorokhovasky model [1]. The case of blocking elecrodes proper for ion conac mode) as well as he experimenally observed concenraion of space charge in near-elecrode regions have been encounered in his model. When surface densiy of heerocharge σ and homocharge σ n has been inroduced, he emperaure dependence of charge redisribuion can be wrien as follows [1]: dσ n T)/dT) + λt/εβ)σ n T) = λt/εβ)σ T), 1) where σ = 1/2)en T)L, λt) = eµnt) equilibrium conduciviy, e elecron charge, µ mobiliy, n T) and nt) rapped and free charge carrier concenraion, L layer hickness, ε dielecric permiiviy, β heaing rae. According o his model, he depolarisaion curren densiy would be: jx) = dσ n /d = λ [ Ex) + E n x) ], 2) where Ex) and E n x) = σ n T)/ε are he heerocharge and he shielding homocharge elecric fields, respecively. I is obviously, ha charge carrier concenraion n and n in he TSD processes are deermined by he rapping and recombinaion mechanism. 3 Experimenal The Zn 0.7 Cd 0.3 S layers has been deposied by means of hermal evaporaion under he vacuum, Pa, a he condensaion emperaure T = 450 K ono he glass subsrae, which has been previously coaed by SnO 2 layer. The hickness of phooconducive layer L = µm) has been chosen by changing he deposiion ime, when he velociy of he flow has been held o be consan. 78

3 The Simulaion of Elecre Effec The samples of Zn 0.7 Cd 0.3 S have been invesigaed in he ion conac mode, i.e., SnO 2 layer has been grounded and he free surface of semiconducing layer has been charged in he air ambience by he corona discharge. The elecre volage has been ascerained by cooling he layer afer i parial free dark discharge, he subsequen discharging by force down o zero surface elecrical poenial, heaing he discharged layer and measuring simulaneously he revealed surface elecrical poenial of he same polariy, as he iniial charge was [3]. The rae of surface elecrical poenial change, due o he hermosimulaed depolarisaion, can be reaed o be sricly proporional o he elecrical curren of shorened elecre, when, during he depolarisaion, layer under invesigaion has been discharged recurrenively wih he aim o mainain zero volage beween SnO 2 conac and free surface of Zn 0.7 Cd 0.3 S layer. 4 Resuls and discussion I has been esablished, ha he elecre volage U e grows-up monoonically superlinearly wih he increasing emperaure and reaches sauraion a aproximally 320 K. The dependencies of he elecre volage on he polarisaion emperaure in Zn 0.7 Cd 0.3 S layer have been shown in Fig. 1. The sauraion bend poin shifs U, V T, K 2 1 Fig. 1. Dependences of elecre poenial of Zn 0.7 Cd 0.3 S layers on he poling emperaure a differen poling elecrical field: E = 17 1), E = 68 6) and E = 34 V/µm 2 5); poling duraion: p = 15 1, 4, 6), p = 2 2) and p = 60 min 5). Layer hickness L = 3.0µm. 79

4 F. Kuliešius, S. Tamoši ūnas, A. Žindulis o lower emperaures when poling ime is increased. Elecre volage U e shows linear dependency on he poling elecric field. I is necessary o noe, ha he raio of elecre volage o polarisaion one in he case of posiive surface elecrical charge is larger by 20 30% neiher in he case of negaive one is, when he oher polarisaion condiions he emperaure, duraion of polarisaion as well as poling elecrical field volage) o mainain he same. The dependencies of raio jus noed on he sample hickness are more pronounced in he posiive surface charge case, also: he raio decreases by 3 imes 1.4 imes in he case of negaive charge), when layer hickness has been increased from 1.5 o 7.8 mm. These dependencies indicae ha he polarisaion effecs are he case in he near-elecrode regions of polycrysalline layer. The occurrence and he significance of hese near-elecrodes regions has been also subsaniaed by analysis of peculiariies of longiudinal kineics of phooconduciviy as well as by resuls of invesigaions of he same samples by means of TSD. The dependency of he raes of hermodepolarisaion on he emperaure in he Zn 0.7 Cd 0.3 S layers has been presened in Fig. 2 and shows linear run. Fig. 2. Dependencies of he raes of hermodepolarisaion on he emperaure in he Zn 0.7 Cd 0.3 S layers ) as well as he resuls of compuer simulaion. I has been supposed in he model, ha he effecive densiy of saes in he conduciviy zone N c is equal o: ), ), m 3 3); recombinaion imes: r = ), ) and 10 6 s 2 ); poling elecrical field E = 5 V/µm; acivaion energy W = 0.5 ev. The peculiariies of TSD on he elecrode maerials and on he polariy of iniial charge as well as known informaion on he similar o Zn 0.7 Cd 0.3 S sruc- 80

5 The Simulaion of Elecre Effec ures suppose o he possibiliy of monomolecular recombinaion ype in he layers under invesigaion. In such a case i) blocking elecrodes ion canac mode), ii) near-elecrode polarisaion process and iii) monomolecular recombinaion ype he general equaion for depolarisaion curren, equaion 2) can be simplified and expressed explicily by expressions for he displacemen curren densiy [1], where: jt) = eµτ r ω E 0 n 0 exp W T kt T 0 ω β exp W ) ) dt kt 3) in he case of weak secondary capure τ r τ, τ τ r ), and jt) = eµτ ω E 0 n 0 exp W T kt T 0 ω τ exp W ) ) dt βτ r kt 4) in he case of srong τ τ r, τ τ ) one he case can be realised when he rap levels are hinly occupied, i.e., n N. Here E 0 is he poling elecrical field volage, n 0 iniial concenraion of rapped elecrons, ω = N 0 S ν T frequency facor, N c and N effecive densiy of saes in he conduciviy zone and in he rap levels, S cross-secion of capure ceners, ν T dark velociy of he free elecron, T 0 iniial emperaure so, emperaure T = T 0 + β), W acivaion energy, k Bolzman consan. The τ, i.e., he ime consan of he capure o he ceners, possessing energy W and τ r ime consan of recombinaion can be expressed as follows: τ = 1 N n )S ν T, τ r = 1 p r S r ν T, 5) where S r is he recombinaion cross-secion. Boh cases of weak and srong secondary capure have been examined, fiing o he experimenal resuls. The acivaion energy has been chosen from presen and earlier experimenal invesigaions e.g., 0.4 ev, if E 0 = 23 V/µm and 0.5 ev a E 0 = 5 V/µm [2]). The oher parameers have been chosen o be adequae o hose of he relaed compounds and have been calculaed by means of approximaion of experimenal resuls by expressions 3), 4), using he leas-square echnics. The calculaed 81

6 F. Kuliešius, S. Tamoši ūnas, A. Žindulis resuls, when he model of weak secondary capure has been used, were no succeeded o mach wih he experimenal ones. The bes coincidence of experimenal and calculaed resuls has been obained in he case of srong secondary capure Fig. 2, curve 2), when τ r = s and N c = 2 10 m 3 have been aken. I mus be sressed, ha N c ac only as he scaling facor, bu he diminishing of recombinaion ime τ r leads o he sublinear deflecion from linear emperaure dependence of hermodepolarisaion rae. The effec become more pronounced, when elevaing he emperaure. 5 Conclusions The polarisaion phenomena ake place in he near-elecrod region of Zn 0.7 Cd 0.3 S layers. The hermodepolarisaion processes in Zn 0.7 Cd 0.3 S layers can be described by he model, based on he srong secondary capure and monomolecular recombinaion. The parameers, effecive densiy of saes in he conduciviy zone N c = m 3 and he recombinaion ime τ r = s, has been obained. References 1. Yu. Gorokhovasky, G. Bordovsky. Thermoacivaed curren specroscopy of highresisiviy semiconducors and dielecrics, Nauka, Moscow, p. 249, 1991 in Russian). 2. F. Kuliešius, S. Tamoši ūnas, A. Žindulis. Regulariies of elecre volage in Zn 0.7 Cd 0.3 S layers, in: Proc. SPIE, 3181, p. 82, V. Krišči ūnas, S. Tamoši ūnas, G. Bajoras. The dependence of darkdischarge of polyepoxypropylcarbazole layers on emperaure, J. Sci. and applied phoography and cinemaography, 27, p. 426, 1982 in Russian). 82