Optical bias control of dispersive relaxations in α-SI:H

Relaxation of the photoinduced ir absorption band in a-Si:H was studied in the microsecond time domain as a function of cw bias illumination. The decays follow a power law t-a where the dispersion parameter a increases with bias illumination. At low temperatures, a increases linearly with the steady-state carrier density while at high temperatures it saturates at high illumination levels. These results are interpreted as evidence for the bias-controlled tunneling process at low temperatures and multiple trapping process with tail states under the saturation condition at high temperatures.

VOLUME 52, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1')84 Optical Bias Control of Dispersive Relaxations in a-Si:H D. Pfost, Z. Vardeny, (a) and J. Tauc Division of Engineering and Department of Physics, Brown University, Providence, Rhode Island 02912 (Received 5 December 1983) Relaxation of the photoinduced ir absorption band in a-Si:H was studied in the micro­second time domain as a function of cw bias illumination. The decays follow a power law t -'" where the dispersion parameter 0' increases with bias illumination. At low tem­peratures, 0' increases linearly with the steady-state carrier density while at high tem­peratures it saturates at high illumination levels. These results are interpreted as evi­dence for the bias-controlled tunneling process at low temperatures and multiple trapping process with tail states under the saturation condition at high temperatures. PACS numbers: 78.50.Ge, 72.80.Ng Illumination of amorphous silicon (a-Si:H) with supergap photon energy produces a transient mid­gap absorption (PA) band whose decay has been used for studying carrier recombination. 1, 2 The integrated P A band decay can often be described over several decades of time by a power law r'" where a was identified as the dispersion param­eter of carriers. At high temperatures, in sam­ples with a low density of gap states, the disper­sion process has been analyzed1, 2 in terms of the multiple-trapping (MT) model. 3,4 The dispersion parameter has been associated with the high­mobility carriers-electrons in a-Si: H 5-whose transport determines the recombination rate. When the distribution of traps below the mobility edge is exponential, the dispersion parameter is a o = T ITo where To is the width of the distribution. This model has provided good agreement with experimental data. However, Schiff6 has noted that this agreement cannot be interpreted as a proof of the MT model in the original version.3 ,4 This model assumes a small occupancy of the trap states while it is likely that with the illum­ination levels used in the reported experiments saturation of the traps occurs. 6,7 In this case, the effective carrier mobility is limited by re­combination rather than by trapping and thermal reexcitation. We will show that if the recombi­nation is bimolecular, the r"'o law still applies at long times as in the original MT model; how­ever, if the recombination is monomolecular, the decay is proportional to r"'o/(l-"'o). We measured the P A band decay in the presence of cw bias illumination. This illumination gener­ates a large steady-state density of electrons and holes and forces the recombination to be mono­molecular. We observed that at long times and high bias intensities the decay is indeed propor­tional to r exO /(l-exo ). We believe that this result is the first identification of saturation in the MT model. At low temperatures, it was proposed that the prevailing recombination mechanism is tunneling.8 The bias illumination method enabled us to vary the density of partners N H available for tunnel­ing recombination. Our data show that the change of a is proportional to N H in agreement with theory.9,10 For measuring the PA decay under bias illum­ination we used three different light sources. The transient excess carrier population N(t) was produced by a 14-Hz nitrogen-pumped dye laser with 10-ns pulses of 2.1 eV photon energy and 50 j1J energy per pulse. The steady-state car­riers, of concentration N '" were produced by a cw Ar + laser with a controlled intensity up to 50 mW Icm2 • The probe source was an incandescent light with filters restricting the photon energy to between 0.8 and 1.4 eV and was used to measure the induced change in transmission t:.T associated with transient excess carriers. A fast Ge de­tector with an amplifier and a signal averager was used to measure t:.T(t). The steady-state in­duced change in transmission, t:.T", was meas­ured by a conventional phase detection technique. In all cases, at 10 j.1S, t:.T" was larger by at least an order of magnitude than t:.T. The sam­ple was a l-jJ.m-thick film of glow-discharge a­Si: H on a quartz substrate kept in a cryostat with controlled temperatures between 10 and 300 K. In Fig. 1 the transient relative change -t:.T(t)1 T is plotted versus the delay time following the 10-ns pump pulse, on logarithmic scales, at various temperatures and bias illuminations. In agreement with previous work1, 2, 5 we observed power-law decays rex in the time interval 10-5 to 10-3 s. The data for the no-bias case are shown in Fig. l(a) and in the inset. The dispersion pa­rameter a o increases slowly with temperature from a nonzero value at T = 0 K. This has been 376 © 1984 The American Physical Society VOLUME 52, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1984 L---------- ~------.------ - ~ I (a) 04~. _ ••• C·~- 10-2 r:J0 0 3 _;;; •• __ ~- 1=0 0.2 ----z; 0.1 0.0 W...LL..Li.LL.ul.L.LLLlLLuiLLLll_ o 100 200 300 T (K) __L ----L..~'~'U'--LLLl!1 _ _- -'-_'-----'~~'U'Ll'I _ _~ _~___j (b) T = 10 K XXxxxx x xxx XXxx I­...... I- <l 10-~ xxxx xXxx xxxxxxx 1=0 ao=0.21 x x x: x x x x x Xx Xx x x xxxx>s,:x x I x x x Xx x xxx>s<x. 1= 1.0 mW Xxx xxx . Xxx Xx Xx xXxxxx a= 0.26 xxxx ~xI=IOmW xxx"',\« a =0.32 I=40mW a=0.36 .1.__ J. ___ ~----1 ___ I_J~------.-l. ___ ~J. I I, "I ~ __ (c) x x x x xx x x Xx x T = 250 K xxxxxx 1=0 x Xx a= 0.34 o Xx Xxx x x xx x 1= 1.0 mW a =0.51 xxxx 10-5 Xx I=IOmW lLl.l_~~~~~ __~ ~~:J.:..5_7--,-,~~ ... ..J 10-4 I(s) 10-~ FIG. 1. Decays of induced absorption band in a-Si:H at different temperatures and different optical biasing levels I. interpreted as recombination by tunneling at low temperature with the MT recombination channel becoming progressively more important at high temperatures. 8 P A decays at various biasing illuminations (Bll are presented in Fig. 1(b) for 10 K and Fig. 1(c) for 250 K. At both temperatures a increases with the intensity Iof the cw laser. At 250 K the increase is more pronounced than at 10 K: O! in­creases from 0.2 to 0.3 at 10 K under BI of 10 mW Icm2 and under the same bias a increases <"J 0.1 o 250K 150K 10K ..--1.----_ ~ ____ J ___ .J_ J 1.0 2.0 3.0 4.0 5.0 6.0 70 8.0 61;/T (XIO') FIG. 2. flO' = a - 0'0 as a function of the strength of the P A band produced by optical biasing. from 0.37 to 0.58 at 250 K. The intensity I is not the directly relevant variable for studying the dependence of O! on biasing. A more meaningful variable is the steady-state excess carrier con­centration N" produced by the BI. This is be­cause N" depends sublinearlyll on I and also be­cause the same I produces different N" at dif­ferent temperatures as a result of the tempera­ture- dependent recombination rate.ll The steady­state change in transmission produced by BI, flT '" is proportional2 to N", For these reasons, we plot in Fig. 2 LlO! = a -O!o versus LlT "IT. We note a significant difference in the low- and high­temperature forms of this function. At 10 K, flO! is proportional to flT "IT (therefore N ,,); at high temperatures, a trend toward saturation is seen starting at low values of LlT "IT. We will show that these functional dependencies are in agreement with the tunneling model (applicable at low T) and MT model (at high T). At low temperatures, in the time range of our measurements, the photogenerated carriers are immobile and their recombination is governed by one -event tunneling. 12,13 The dispersive charac­ter of the recombination is due to a distribution of tunneling times as produced, for example, by the distribution of tunneling distances. Since N(t) «N" the recombination kinetics is mono­molecular. Under this condition a extracted from the decay curves can be directly related to the dispersion parameter, avoiding the complica­tion of the bimolecular recombination. 14. 15 There· fore the increase in a with I shows that the re­combination becomes less dispersive when I is increased. According to the theory9,10 the dis­persion parameter should be proportional to the density of N" as observed (Fig. 2). We note that the concentration of tunneling partners can be increased by doping as reported 377 VOLUME 52, NUMBER 5 PHYSICAL REVIEW LETTERS :J() JANUARY l')s4 in Ref. 8. However, by doping one introduces additional states in the gap that have a strong in­fluence on the recombination process. It is therefore no surprise that in this previously re­ported case a is not proportional to the carrier concentrations introduced by doping. However, the biasing experiment avoids the complication of new states being introduced in the gap by dop­ing. At high temperatures recombination by tunnel­ing is unlikely because carriers leave their sites very quickly. The results have been interpreted1 in terms of the MTmodel. The recombination rate is limited by electron transport which de­pends on the trapping in tail states below the mobility edge of the conduction band E e' assumed to have the distribution g(E) = (N /k To) expl-(E e - E) /k To] where Ntis the total density of states in the tail. The occupancy of these states by electrons is determined by the Fermi distribution with a de­marcation energy E a which separates states whose probability of thermal reexcitation is smaller or larger than t. The occupancy of the states below Ed depends on the competition be­tween the trapping and recombination processes. If recombination is neglected, trap saturation occurs6 at t = v-1(N sina 71/N a 71) -1/ CX o s 0 a to, where v is the attempt-to-escape frequency, ~ =T/To, and No is the total electron density. Satu­ration can occur if the recombination time T is longer than ts. We present an analysis which indicates that in our experiments saturation has occured before the time of measurement. We assume that the states below Ed are completely filled and that Ed sinks deeper with time by re­combination rather than by thermalization as in the MT model. The process is described by the following equations: j'Ea N = g(E)dE =N texp[ -(Ee -Ea)/kToJ, n=lg(EJ/g(Ea)]expl-(Ee-Ea)/kT L (1) (2) (3) where N is the time-dependent total electron den­sity in the tail, n, is the electron density in the conduction band (n «N), br is the recombination coefficient, N r is the density of recombination partners, and g(Ee) and g(Ea) are the densities of electron states at the bottom of the conduction 378 band Ee and at Ed' respectively. With the boundary conditions N(O) =No' one ob­tains for the monomolecular case (N r = const) N(t)=No/(l +t/TM)CXo/{l-cto) and for the bimolecular case (Iv r =N) N(t) =No/(l +t/T b)CXo, where the recombination times are T -l",b (l-a)N N N -l/cxoN{l-cxo)/cxo M r Oret 0 and (4) (5) where N e is the effective state density at the mobility edge of the conduction band IN c '" k Tg(E e)]. Equation (5) shows that at long times (t» T b) the decay of PA is proportional to rcxo, which is the same as when the traps are not saturated. Since the experiments are usually done in this time domain, the PA decay study cannot identify trap saturation if the recombination is bimolecu­lar. However, if the recombination is monomolecu­lar, long-time decay is proportional to r CXo/(I-'cto) [Eq. (4)] which we have actually observed by the optical biasing of P A at large BI (Fig. 3). This shows that the traps are saturated and that the biasing forces the recombination to be mono­molecular. 16 Experimental data show that 6.T" is at least ten times larger than 6.T(t) in the time range of measurement. This implies N r ~ N" »N(t) and monomolecular recombination should prevail. 250 K 0.5 ~ 04,f"c< 150 K 0.1 - 00 5.0 10.0 15.0 20.0 25,0 30.0 35.040.0 I(mW) FIG. 3. Dispersion parameter 0' as a function of bias-light intensity. The dotted lines are asymptotes at T = 150 and 250 K corresponding, within the accu­racy of the measurement, to 0' = 0'01 (I-ao) where 0'0 = 0' (I = 0). VOLUME 52, NUMBER 5 PHYSICAL REVIEW LETTERS 30 JANUARY 1984 However, it is difficult to understand how this condition is realized. In our experiments, No "" 1 018 cm -3 and the cw carrier generation rate is about 1022 cm -3 s -1 giving as a rough estimate N,,""10 16 cm-3 (if br =10-10 cm-3 S-l). Another difficulty is to explain why under biasing the re­combination of holes is still dominated by elec­trons produced by the pulse rather than by the high concentration of cw electrons. These discrepancies are removed if we as­sume that below the band tail of the conduction band there are deeper electron traps. Electrons in these traps do not contribute to the recombina­tion of holes via transport in the conduction band. The presence of these states has the following consequences. All or most of the electrons pro­duced by biasing are in the deep traps; there­fore the cw hole densities can be significantly larger than the above estimate of 1016 cm -3. The hole recombination rate and therefore t::,T(t) are determined by the transient electron density. During the thermalization process, electron trapping in the deep states competes with the MT mechanism and delays the onset of saturation?; therefore filling of these states by biasing facili­tates saturation of the tail states. These deep electron traps are probably the dangling bonds that have been observed in many studies1?-19; when they are doubly occupied (n-), their ener­gy is approximately 0.7 eV below the bottom of the conduction band. In conclusion, we found that optical biasing of a-Si:H leads to an increase of the dispersion pa­rameter. At low temperatures, the change of the dispersion parameter is proportional to the steady-state population of carriers in agreement with the tunneling mechanism of recombination. At high temperatures, the biasing induces mono­molecular kinetics which reveals the tail-state saturation identified by the change of the disper­sion parameter from the zero-bias value a o to the high-bias value a o/(l - a o). We acknowledge very helpful discussions with H. Scher. We also thank B. Abeles and his collab-orators at Exxon Research for providing samples for this work, and H. A. Stoddart and T. R. Kirst for technical assistance. The work was supported in part by National Science Foundation Grant No. DMR 8209148 and benefited from extensive use of the Optical Central Facility supported by the National Science Foundation Materials Research Laboratory Program at Brown University. (a)Permanent address: Solid. State Institute, Technion, Haifa, Israel. lZ. Vardeny, P. O'Connor, S. Ray, and J. Tauc, Phys. Rev. Lett. 44, 1267 (1980). 2J. Tauc, Festkorperprobleme: Advances in Solid State Physics, edited by P. Grosse (Vieweg, Braunsch­weig, 1982), Vol. XXII, p. 85. 3J. Orenstein and M. A. Kastner, Phys. Rev. Lett. 43, 161 (1981). -4T. Tiedje and A. Rose, Solid State Commun. 37, 49 (1981). 5p. B. Kirby, W. Paul S. Ray. and J. Tauc, Solid State Commun. 42, 533 (1982). "E. A. Schiff, Phys. Rev. B 24, 6189 (1981). 7J. Orenstein and M. A. Kastner, Solid State Commun. 40, 85 (1981). -3D. Pfost and J. Tauc, Solid State Commun. 48, 195 (1983). 8M. Scher and E. W. Montroll, Phys. Rev. B 12,2455 (1975). loH. Scher and M. Lax, Phys. Rev. B 7, 4502 (1973). IIp. O'Connor and J. Tauc, Phys. Rev-:- B 25, 2748 (1982). 12D. K. Biegelsen, R. A. Street, and W. B. Jackson, Physica (utrecht) 117B& 118B, 899 (1983). 13D. J. Dunstan, Philos. Mag. B 46, 579 (1982). 14M. Scher, J. Phys. (Paris), Colloq. 42, C4-547 (1981). 15A. Blumen, J. Klafter, and G. Zumfen, Phys. Rev. B 27, 3429 (1983). 16R. Pandya and E. A Schiff, in Proceedings of the International Conference on Amorphous and Liquid Semiconductors, TOkyo, 1983 (to be published). 17R. A. Street, Adv. Phys. 30, 593 (1981). 13J. D. Cohen, J. P. Harbison, and K. W. Wecht, Phys. Rev. Lett. 48, 109 (1982). 191. Hirabayashi and K. Morigaki, in Ref. 16. 379