Influence of nonradiative and nongeminate processes on a lifetime distribution of photoexcited carriers in amorphous semiconductors at low temperatures

JOURNA L OF

Journal of Non-Crystalline Solids 137&138 (1991) 567-570 North-Holland

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I N F L U E N C E OF N O N R A D I A T I V E AND N O N G E M I N A T E P R O C E S S E S ON A L I F E T I M E DISTRIBUTION OF P H O T O E X C I T E D C A R R I E R S IN A M O R P H O U S S E M I C O N D U C T O R S AT LOW T E M P E R A TURES S.D. B A R A N O V S K I I t, Rosari SALEH, P. T H O M A S and H.VAUPEL Fachbereich Physik und Wissenschaftliches Zentrum fiir Materialwissenschaften, Philipps-Universitgt Marburg, Renthof 5, W-3550 Marburg, FRG and H. F R I T Z S C H E The James Franck Institute, The University of Chicago, Chicago, IL 60637, USA The influence of nonradiative and nongeminate radiative processes on the lifetime distribution of photoexcited carriers is studied in a simple computer simulation. The lifetime distribution was simulated recently for geminate radiative processes, and turned out to be much broader than that observed by experiment. The aim of the present simulation is to clarify whether nonradiative or nongeminate radiative processes could lead to the observed narrowing of the distribution. The results show that nonradiative processes lead to a narrowing only with an appreciable and unrealistic shift of the distribution to shorter times. Nongeminate radiative processes lead to a narrowing of the distribution with a weaker and more reasonable shift.

ward in energy to another localized tail state at a dis-

1. I N T R O D U C T I O N Recent measurements I of the lifetime distribution of

tance r, with a rate

the photoluminescence using frequency resolved specuh(r) = vo exp (-2r/c~),

troscopy (FRS) and measurements 1 of the excess carrier

(1)

concentration by light-induced electron spin resonance

where a is the localization radius, and ~o ~ 1012s-1.

(LESR)

The second possibility for the electron is to recombine

within

a wide range

of generation

rates

( 101%m-as -1 _< G < 1022cm-as -1) have provoked a

radiatively with the hole at a rate

renewed interest in the recombination mechanisms of photoexcited carriers in undoped

ugr(R) = r o 1 exp ( - 2 R / a ) ,

a-Si:H at low

(2)

temperatures. Before these measurements were carried out, the situation seemed to be relatively clear, and a quanti-

where /{ is the distance to the hole, and r0 ,-~ 10-as. The prefactors Uo and ro define a characteristic length

tative theory was suggested 2'a for the behavior of excess carriers in the bandtails.

Rc = ( 2 ) in (u0r0).

(3)

We give here a brief review

of the theory in order to emphasize the point where it

A pair survival probability ~/(R) to a distance R and a

disagrees with the new experimental data 1.

geminate recombination density P(R) = -&l/dR were

Let us consider the fate of an electron-hole pair generated by light at or just below the mobility edge.

introduced and calculated 2'a. For R >> Rc it was found that

The hole is assumed to be immobile (movement of the hole does not change the results significantly4).

,(R) : c

(4)

The

electron has two possibilities. First it can hop down-

with fl = 1.16 4- 0.01 and C = 3.0 4- 0.1 . The function P(R) has a maximum at R ~ Re, and decreases in the

t

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S.D. Baranovskii et al. / Influence of nonradiative and nongeminate processes

568

range R >> Rc as (~c//l~) #+1.

~

0.4

For the geminate recombination process the function

I

P(/~) is to be compared with the distribution of the logarithms of lifetimes 2'3. The comparison shows 1 however that the experimental lifetime distribution is on a

0.3-

logarithmic scale about third as wide as the theoretisome processes which were not taken into account in cal-

131

culating P ( R ) play a significant role at the experimental

13.

I

'

I

'

)(-\\ 10 -3

r

cal geminate function P ( R ) . This probably means that

•

N n,r = 10 - 2

/ 1...., \' ,

0.2

/ i/1 "'""

conditions. We study here the influence of nonradiative processes and nongeminate radiative processes on the lifetime distribution in a simple computer simulation.

0.1 /

2.1.Influence of nonradiative processes We consider the influence of nonradiative processes on the lifetime distribution of a geminate electronhole pair

in the

./ ]

\

!,,// \

2. C O M P U T E R SIMULATION

0.0 0

\

I

I

I

1

2

3

,,

simplest model for nonradiative

recombination s. Defects, which provide nonradiative re-

R/R c

combination, are assumed to be randomly distributed in space with concentration N,~, and capture of an electron by a defect occurs by tunneling with a rate

~.,(n) = ,o e~p (-2n/,),

(5)

where R is the distance to the defect and Vo ~ 1012s-1.

FIGURE 1 Influence of nonradiative processes on the geminate distribution P(R) at R~ = 2. Concentration of nonradiatire defects: 10 -4 (dashed-dotted line), 10 -3 (dashed line), 10 -2 (solid line).

quantity R and the time of the process ~-(R)

=

The simulation algorithm is similiar to that used

uo 1 exp (2R/a). The distribution function P(R) is cal-

previously 3 but in addition to the two possibilities of

culated by averaging over 105 electron-hole pairs. It was

a hop with a rate (1) and a geminate radiative recom-

checked that hopping of the electron in bandtail prior to

bination with a rate (2), an electron now has the third

recombination is so fast that it does not contribute to

possibility to tunnel to the nearest defect with a rate

lifetime which is given by the last slow process of recom-

(5). There are three spatial scales in the problem: Re,

bination. Simulations were carried out for /{c = 2, 3, 4

N~l/a, and NU l/s, where Nt is the total concentration

and N,~ = 10 -5, 10 -4, 10 -3, 10 -2 for each value of Re. In

of the bandtail states. In the following we measure all

Figure 1 the corresponding curves are shown for Rc = 2

concentrations in the units of N,. A series of simula-

and Nn, = 10 -4, 10 -3, 10 -2. For the low concentration

tions was carried out for different sets of parameters Re

of nonradiative centers N,~ = 10 -4, the distribution

and N~T. For each set of parameters, the fate of l0 s

P ( R ) is very close to the purely radiative geminate dis-

electron-hole pairs are simulated. If an electron recom-

tribution as one should expect s . For higher concentra-

bines nonradiatively by tunneling to a defect at a dis-

tions N ~ , nonradiative processes become more impor-

tance /~, the distance R = /~ is stored. If an electron

tant, and the distribution P ( R ) shifts to shorter times

recombines radiatively with a hole at a distance r, the

becoming much narrower. The corresponding quantum

quantity R = r + R~ is stored. Here R~ is added in order

efficiency of the photoluminiscence decreases from 78%

to have the universal relation between the stored

for N,~ = 10 -4 to 6% for Nnr = 10 -2. The width of the

S.D. Baranovskii et al. / Influence of nonradiative and nongeminate processes

569

distribution P(R) at Nn~ = 10 -2 is not too far from !

that observed in the FRS experiment 1, but the position

I

_ Nng=10-2

-0;

of the m a x i m u m r , ~ , at R ~ R~ corresponds (in our

I

units) to the time r(R~) = Uo1 exp (2Ro/a), which, using (3), gives r , ~

~ % ~ 10-Ss. That obviously is too

far from the experimental value 1 r , ~ , ~ 10-as.

-0.3

This

means that nonradiative processes, at least as tong as they are treated in such a simple model, cannot account rr"

for the lifetime distribution observed in FRS 1.

]O-3

~- 0.2

2.2. Influence of nongeminate radiative processes The influence of nongeminate processes is studied in the framework of the same algorithm as the influence of

" " ""

01

nonradiative defects, but the rate of nongeminate radia-

...h

tive recombination is

(6)

~..(R) = ~o ~ exp ( - 2 R / ~ ) ,

I

0 where r0 ~ 10-ss, and R is the distance from the electron to the nearest nongeminate hole.

Nongeminate

holes are assumed to be randomly distributed in space

1

I

2 R/R c

!

3

FIGURE 2 Influence of nongeminate processes on the distribution P(R) at Rc = 2. Concentration of the excess holes: 10 -1 (dashed-dotted line), 10 .3 (dashed line), 10 .2 (solid line).

with a concentration N,,g. Simulations are carried out for R~ = 2, 3, 4 and N,~g = 10 -5, 10 -4, 10 -3,10 .2 for each value of Re. In Figure 2 the corresponding distributions P ( R ) are shown for Rc = 2 and N,,g = 10 -4, 10 -3 and 10 -2. The curve for Nog = 10 .4 coincides with that for a purely geminate processes as expected 3. For higher N~g the relative contribution of nongeminate processes increases. At N,~g = 10 .4 only 6% of electrons recombine nongeminately, whereas at Nna = 10 .2 more than 60% of electrons recombine by these processes. It is seen in Figure 2 that nongeminate radiative processes lead to a narrowing of the distribution P ( R ) compared to the geminate case with a much weaker shift of the maximum than in nonradiative processes. Therefore nongeminate processes seem to be better candidates to account for the experimentally observed lifetime distribution.

bution observed in the FRS measurements 1, whereas nongeminate radiative processes may account for the experimental observations. However, the concentration of nongeminate holes Nna = 10-2N~ at which we obtain a sufficiently narrow lifetime distribution seems to be too high for the reported experimental conditions. This may be due to the fact that in our simple simulation we do not take into account spatial correlations between positions of holes and electrons, which should lead to a further narrowing of the lifetime distribution s. It was argued recently 7 that the LESR spin density and the radiative lifetime distribution can be understood in a model with only one channel of recombination, i.e. nongeminate radiative recombination. An analytical theory for photoluminiscence and photoconductivity

3. DISCUSSION

was developed s taking into account only such processes.

Our simple computer simulation of the recombina-

The question has been studied in detail in a more accu-

tion of electron-hole pairs has shown that nonradiative

rate and sophisticated computer simulation 9 of radiative

processes cannot account for the narrow lifetime distri-

processes, and it is shown there that nongeminate re-

570

S.D. Baranovskii et al. / Influence of nonradiative and nongeminate processes

combination should dominate over the whole range of experimentally achieved generation rates. It should be pointed out however that there is another experimental observation besides the narrowness of the radiative lifetime distribution which need be explained, the position of the maximum r , ~ of the lifetime distribution. According to the recent FRS experiments 1 as well as earlier pulse excitation measurements 1°, this maximum ~m~ is essentially independent of the generation rate G for G less than 101%m-3s-1. In contrast our corn-

REFERENCES 1. M. Bort, W. Fuhs, S. Liedtke, R. Stachowitz and R. Carius, Geminate recombination in a-Si:H, this volume. 2. S.D. Baranovskii, H. Fritzsche, E.I. Levin, I.M. Ruzin and B.I. Shklovskii, Soy. Phys. JETP 69 (1989) 773. 3. B.I. Shklovskii, H. Fritzsche, and S.D. Baranovskii Phys. Rev. Left. 62(1989)2989.

purer simulations yield a shift of ~-,~ax to lower values

4. S.D. Baranovskii and E.I. Levin, to be published.

with decreasing G as long as nongeminate recombination

5. C. Tsang and R.A. Street, Phil. Mag. B37 (1978) 601.

dominates. In the limit of small G the simulations yield a constant ~-,~a~but the broad distribution of geminate

6. D.J. Dunstan, Phil. Mag. B52 (1985) 111.

recombination lifetimes. This discrepancy needs further study.

ACKNOWLEDGEMENTS We are grateful to B.I. Shklovskii, W. Fuhs, M. Bort, S. Liedtke and R. Stachowitz for useful discussions and for sending us their theoretical and experimental results prior to publication and to R. Heft for his help in calculations. The work was supported by the Alexander yon Humboldt Foundation.

7. T.M. Searle, Phil. Mag. Lett. 61 (1990) 251. A.G. Abdukadirov, S.D. Baranovskii and E.L. Ivchenko, Soy. Phys. Semicond. 24 (1990) 82. 9. E.I. Levin, S. Marianer, B.I. Shklovskii and H. Fritzsche, Luminiscence lifetime distribution in amorphous semiconductors, this volume. 10. C. Tsang and R.A. Street, Phys. Rev. B19 (1979) 3027.