Non-geminate recombination in amorphous silicon

Solid State Communications, Vol. 44, No. 6, pp. 841-844, 1982. Printed in Great Britain.

0038-1098/82/420841-04503.00/0 Pergamon Press Ltd.

NON-GEMINATE RECOMBINATION IN AMORPHOUS SILICON F. Boulitrop and D.J. Dunstan* Centre d'Etudes Nucl6aires de Grenoble, LETI/CE and DRF/RM, 85X - 38041 Grenoble Cedex, France

(Received lO May 1982 by E.F. Bertaut) The excitation power dependence of the light-induced EPR signal in intrinsic a-Si: H is found to be sub-linear over the entire accessible range of excitation power. This result is shown to require a distant-pair model of the recombination of the carriers giving the LESR. If, as is thought, the same carriers give LESR and the 1.4 eV photoluminescence band, we show that the luminescence is also distant-pair. AT LOW TEMPERATURE, the dominant recombination mechanism in low spin-density a-Si: H is radiative and gives rise to a photoluminescence (PL) band at around 1.4 eV. It is generally agreed that the mechanism is radiative tunnelling between band-tail states [ 1-5], but the details of the mechanism are still controversial. Both distant-pair [4--6] and geminate [1,2] models have been proposed. Originally, the geminate model was advanced in order to explain the quenching signal observed in optically detected magnetic resonance (ODMR) experiments [7], and the electric field quenching of the luminescence [8], and has since been successfully used to interpret the PL decay and its temperature dependence observed in time-resolved spectroscopy (TRS) [1,2, 9]. On the other hand, many authors have interpreted their results in terms of a distant-pair model [4, 6, 10], and recently Depinna et al. [4] have shown that the waveform of the ODMR signal is consistent only with distant-pairs and not with geminate pairs. Furthermore, recent measurements of the lifetime distribution by frequency-resolved spectroscopy (FRS) [11 ] show not geminate, but distant-pair behaviour, and we have shown [12] that the TRS decay data [2] is fully consistent with a distant-pair model. The question whether the recombination is distantpair or geminate is of importance both for a fundamental understanding of amorphous semiconductors and for device applications, in view of its implications for the diffusion and trapping of excited carriers. In this paper, we report measurements of the excitation power dependence of the light-induced EPR (LESR) signal, over a wide range of excitation power. We find sub-linear behaviour that can be described by a power law over up to nine decades of excitation power density. This result is in agreement with previously reported measurements * Present address: Angewandte Physik, Johannes Kepler Universit~it, 4040 Linz, Austria. 841

[13, 14], but extends over a much wider range of excitation power and temperature. We compare this result with the predictions of the distant-pair and geminate pair models, and we find that only the distant-pair model gives a natural explanation of the power law. We show also that, if the PL and the LESR are due to the same carriers, then the PL must be due also to distant-pair recombination. The LESR signal observed in intrinsic a-Si : H consists of two lines, at g = 2.004 and g = 2.013 [ 13, 14 ], which are thought to be due to band-tail electrons and holes respectively [15]. The two lines show the same dependence on excitation power. Knights et al. [14] reported excitation power dependence following a power law over two decades of excitation power, with an exponent that varied between 1[3 and 1 in different samples, according to the dark EPR spin densities (i.e. defect densities). They explained their results in terms of optical saturation in a system with a wide range of lifetimes. The data of Friederich and Kaplan [13] also obeyed a power law (see Fig. 1). Recently, Street and Biegelsen [15] studied the temperature dependence of the LESR signal, and, by comparing it with the temperature dependence of the 1.4 eV PL decay, concluded that the same excited carriers are involved in the two phenomena. If this is indeed the case, then the excitation power dependence of the LESR will be determined by the recombination kinetics of this emission band. Our samples were prepared by sputtering in 70%H2-30%Ar at 250 W RF power onto quartz substrates held at 250°C. The dark EPR spin-densities are about 5 x 10 Is cm -3. The LESR spectra were recorded on a Varian X-band EPR spectrometer at 30, 77 and 130 K, using He-Ne 632 nm and Ar 514 nm laser excitation. Figure 1 shows the integrated intensities Lex of the spectra as a function of the excitation density; the points taken with 514 nm light have been corrected to

842

NON-GEMINATE RECOMBINATION IN AMORPHOUS SILICON I

~

I

I

I

I

I

I

I

I

I

AU

30 ~ "~~ , ' ~ J

,~100

°*°

•

Vol. 44, No. 6

recombine in < ~ 130psec (compared with ~ 2 × 1017 cm -3 which are metastable). Since the experimental results Lex(Io) are power laws, we may readily correct for the attenuation of the excitation in the sample, to obtain L (G), where G is the pair creation rate, from Lex(Io). For the limiting cases a t < 1 and a t >> I, G = alo and G = alo exp (-- ax) respectively, where t is the thickness of the sample, x the depth in the sample, and Io is the excitation power. The LESR signal strength Le~ is given by

.d

1016

1018 1020 Pail" creation

1022 1024cn~3s1 rate aI 0

Fig. 1. LESR power dependence in two samples, A and B. All points were obtained with 514 nm excitation, except the squares which were obtained with 632 nm and have been corrected accordingly [equation (2)]. The solid curves are calculated from equation (3) (see text), then corrected for attenuation in the sample; they are labelled with the sample, the measurement temperature and the slope, or power law exponent p. The dots marked FK are the data of Friederich and Kaplan [13], for which G is in arbitrary units.

It x'° 1Orris B

I

I

Fig. 2. The decay of the LESR signal, measured using 1022 cm -3 sec -I of square-wave chopped excitation at 20 Hz. The resolution of the EPR spectrometer ( ~ 130 psec) is marked expanded by ten. The signal shown was accumulated 1000 times by a multi-channel analyser. The fast decrease A to B corresponds to about 1016 cm -3 spin, while the baseline (metastable LESR signal) is about 2 x 1017 crn -3. take account of the higher absorption coefficient a, as described below. We find very sub-linear behaviour, approximating to a power law LeA,to) ~ ~g with the exponent p varying slightly from sample to sample, and with temperature. The power law holds over the entire range of intensity that we could measure, nine decades of intensity to for the sample A at 77 K. We have also measured the decay of the LESR signal (Fig. 2); at high excitation power, ~ 1016 cm -3 spins

Lex(Io) = ; L(alo e-aX)dx

(1)

0

~dLex(Io)/dlo = L ( G ) / a G

for at>> 1

and by

Lex(Io) = tL(alo)

for at < 1

and so we have, for a power law L = cG v,

Lex(Io) = ct(alo) v

for a t < 1

c

Le~(Io) = ~p (alo) p

(2)

for at>> 1

and the experimental power law I~' gives for the true dependence L (G) the same power law G p. The 632 nm excitation corresponds to the case a t < 1 (a -1 ~ 5 p, t = 2 p), and the 514 nm to a t >> 1 (a -1 ~ 0.1 p, t = 2p), and so the correction factor for the 514 nm data is asl4pt, from equation (2). In the geminate model, photocreated electron-hole pairs are assumed to be trapped close to each other, at a range of separations which gives the range of lifetimes observed [1 ]. Thus each pair is independent of the others, and the LESR signal strength will, in general, be linearly dependent on the pair creation rate G. At high G, the pairs overlap [2], and the geminate model becomes identical to the distant-pair model. This point is important; we shall return to it later. The role of thermal diffusion in the geminate model depends on the temperature. At low temperature (< ~ 100 K) the Onsager radius is greater than the pair separations; diffusion tends to reduce the separations and so shorten the lifetimes. At higher temperatures, the Onsager radius becomes less than the pair separations and diffusion leads to ionisation of the pairs. This is supposed to be the rate-limiting step [1] in the thermally-induced nonradiative recombination; consequently pairs that undergo thermal ionisation contribute neither to luminescence nor to LESR. Our samples show thermal quenching from about 100-110 K; at 130 K the PL intensity is reduced by about a half. At 77 K, diffusion does not ionise a significant number of pairs, but changes the lifetime

Vol. 44, No. 6

NON-GEMINATE RECOMBINATION IN AMORPHOUS SILICON

distribution [2]; at 30 K there is not expected to be any appreciable diffusion. The geminate model accounts successfully for the temperature dependence and TRS (but not FRS) data on the PL. However, in order to explain the sub-linear power dependence of the LESR, it is necessary to postulate optical saturation of the longer-lived pairs [14], and, while this model may be satisfactory over the two decades of G observed by Knights et al. [14], it cannot explain the results we obtain over up to nine decades. This is because the required lifetime distribution would be roughly N ( Occ

T -(I+p)

over at least ten decades of 7-, which is quite unlike the experimental distributions [2, 11]. Furthermore, the explanation of the redistribution of lifetimes at intermediate temperatures (diffusion within the Onsager radius) requires that each pair has available to it both short and long lifetime states. Optical saturation of such a system will occur at all lifetimes together; to saturate the longer-lived components first would require a model in which different centres (pairs) each have a different available lifetime. Finally, our measurements extend both above and below the pair creation rate at which the pairs should begin to overlap, G ~ 1021 cm -3 sec -1 (the geminate-bimolecular transition). Above this transition, the behaviour of the system will in any case be given by the distant-pair model, in which the value of the exponent p is determined only by the separationindependent contributions to the pair inverse lifetime (thermal diffusion, non-radiative recombination). Below the transition, p would depend on the distribution of lifetimes in the geminate model. It is most unlikely that the lifetime distributions would be just such as to match the values o f p above and below the geminatebimolecular transition; yet none of the data in Fig. 1 shows any evidence of a change in slope around G = 1021 cm-3 sec -1. We consider, therefore, that the geminate model is not compatible with the results presented here. Thus if the LESR observes the carriers that subsequently recombine to give the PL [15], then the dominant recombination cannot be geminate. In contrast, if we assume distant-pair recombination, the sub-linear dependence arises naturally. The mean pair separation decreases as the excitation power is increased, and so the mean lifetime decreases. In consequence, although the PL intensity may vary linearly with G, the excited carrier density p and the LESR signal L ccp will vary sub-linearly with G at all power levels. The dependence L (G) is obtained from our theoretical calculation of the kinetics of recombination in a distant-pair system [12]. The pair decay rate is the sum of a separation-dependent rate and a

843

separation-independent rate: ~-(r) -I

ro 1 exp (--r/ro) + T n-1r •

-l (independent of r) includes both recombiThe rate Tnr nation (through defects) and redistribution (through thermal diffusion); the value of G is adjusted accordingly. Figure 3 shows solutions for the dependence of p on G using the parameters ro = 11 A, ro = 10 -s sec, from Tsang and Street [2] and the distribution of pair separations under continuous excitation G of [ 12]. Over considerable ranges of G the solutions are close approximations to power laws, with values o f p ranging from 1 (for dominant non-radiative recombination through defects, curve "c"), to 1/2 (for high temperatures where diffusion dominates and the kinetics are second-order, curve "b"), down to p ~ 1/6 when rnr-1 vanishes (curve "a"). Solid curves on Fig. 1 fit experimental results obtained with sample A using Tnr = 106 sec for recombination at 30 K, 20 sec and 2 x 10 -2 sec for redistribution at 77 and 130 K respectively. Thus the distant-pair model is consistent with the LESR data presented here and in the literature [14].

: "

16 10

' 18 20 22 10 10 10 Pair creation rate G

: c m - 3 s "-1

Fig. 3. Theoretical curves # (G) = L ( G ) are c~culated for 514nm. The rate rnr1 vanishes for curve ' a ;for curves " b " and "c" it has the value 1 0 3 s e c - 1 and corresponds respectively to diffusion and to recombination. We thus conclude that the LESR is due to carriers that subsequently undergo distant-pair recombination, and so that there is non-geminate recombination in a-Si : H. We now consider what information this result may give on the dominant low temperature recombination, the PL. There are three models to consider: (1) The LESR observes the carriers that subsequently recombine to give the PL; in this case it is clear that the PL must also have distant-pair kinetics. (2) The carriers giving the LESR and the PL are in the same states but are distinguished by the pair lifetime:

844

NON-GEMINATE RECOMBINATION IN AMORPHOUS SILICON

the short-lived pairs giving PL and the long-lived, LESR. (3) The carriers giving PL and those giving LESR are trapped in different states. Note that in the models 2 and 3 the kinetics of the PL and of the LESR need not be in any way related. Street and Biegelsen have recently suggested, on the basis of experiments in which they study the intensity of PL and of LESR during the first few pulses of excitation in an annealed sample, that model 2 is correct [16]. They estimate that "~ 95% of the photocreated pairs give PL with geminate kinetics, while ~ 5% have separations too great to recombine and so accumulate, giving the LESR signal, until they can recombine with bimolecular kinetics. This model cannot, however, possibly account for the results we present here, because at high excitation power the density of longlived carriers vanishes [12]. If the LESR does not observe short-lived carriers (r < ~ 1 msec) because, for example, their spins have not yet had time to thermalise, the LESR signal L(G) should decrease at high G, for which there is no evidence in the data (Fig. 3). Furthermore, Fig. 2 shows that the LESR does observe shortlived carriers; thus if the PL and the LESR are due to carriers in the same states then model 1 applies and the dominant recombination must be distant-pair, at least in a sample that has been illuminated for sufficient time for the carriers concentrations and separation distributions to have reached their equilibrium values. There remains the possibility that the carriers giving LESR and to PL are not in fact trapped in the same states (model 3). It would be hard to understand the results of [15] in this case; also the evidence suggests independently that the LESR [15], and the PL [1 ], are each due to carriers trapped in the band-tail states. Nevertheless, this possibility cannot be ruled out; it is known that there are deep states some 2 0 0 4 0 0 meV below the band edges (Chenevas-Paule and Dijon [I 7]), i.e. among the tail states, but it is not yet clear what role they may play in either the PL or the LESR. Further ODMR studies, and thermally-stimulated EPR experiments, may resolve this point. In summary, we have shown conclusively that the LESR in a-Si: H displays distant-pair kinetics, and so that there is non-geminate recombination. We argue that this applies also to the PL band at 1.4 eV, provided that the carriers involved in the two phenomena are the same.

Vol. 44, No. 6

This is in agreement with the data on the decay of this PL band from TRS [2] and FRS [11 ], and with ODMR data [4]; it is not in agreement with the remits of [16] and it remains to be seen whether this is a consequence only of the accumulated long-lived population in most optical experiments, or whether, in fact, LESR and PL observe carriers in completely different states.

Acknowledgements - We are grateful to Dr J. Glover for the deconvolution of the exponential attenuation of the excitation in the sample, and to Dr S. Depinna for useful discussions. We thank Dr A. Chenevas-Paule for providing the samples, Dr R.A. Street and Dr D.K. Biegelsen for preprints and discussion of their recent work, and the COMES for financial support. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

R.A. Street, Adv. Phys. 30, 593 (1981). C. Tsang & R.A. Street,Phys. Rev. BI9, 3027 (1979). T.M. Searle, T.S. Nashashibi, I.G. Austin, R. Devonshire & G. Lockwood,Phil. Mag. B39,389 (1979). S. Depinna, B.C. Cavenett, I.G. Austin, T.M. Searle, M.J. Thompson, J. Allison & P.G. LeComber, Phil. Mag. (to be published). D.J. Dunstan & F. Boulitrop, J. Phys. (Paris) 42, C4 331 (1981). K. Morigaki, D.J. Dunstan, B.C. Cavenett, P. Dawson, J.E. Nicholls, S. Nitta & K. Shirnakawa, Solid State Commun. 26,981 (1978). D.K. Biegelsen, J.C. Knights, R.A. Street, C. Tsang & R.M. White,Phil. Mag. B37,477 (1978). R.A. Street,Phil. Mag. B37, 35 (1978). J. Noolandi, K.M. Hong & R.A. Street, J. NonCryst. Solids 35/36,669 (1980). I.G. Austin, T.S. Nashashibi, T.M. Searle, P.G. LeComber & W.E. Spear, J. Non-Cryst. Solids 32, 373 (1979). D.J. Dunstan, S. Depinna & B.C. Cavenett, J. Phys. C 15, L425 (1982). D.J. Dunstan,Phil. Mag. (in press). A. Friederich & D. Kaplan, Z Elect. Mat. 8, 79 (1979). J.C. Knights, D.K. Biegelsen & I. Solomon, Solid State Commun. 22,133 (1977). R.A. Street & D.K. Biegelsen, J. Non-Cryst. Solids 35/36,651 (1980). R.A. Street & D.K. Biegelsen, Solid State Commun. (to be published). A. Chenevas-Paule & J. Dijon, 3". Phys. (Paris) 42, C4,605 (1981).