Monte-Carlo Simulation of Energy Relaxation of Interacting Carriers in a-Si:H Under Arbitrary Electric Fields
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MONTE-CARLO SIMULATION OF ENERGY RELAXATION OF INTERACTING CARRIERS IN a-Si:H UNDER ARBITRARY ELECTRIC
FIELDS B. CLEVE, R. HESS, S.D. BARANOVSKII, AND P. THOMAS Fachbereich Physik und Wiss. Zentrum fuir Materialwissenschaften, Renthof 5, W-3550 Marburg, FRG. ABSTRACT A new Monte-Carlo simulation algorithm has been applied to verify the concept of the effective temperature recently suggested as a description of energy relaxation of carriers in band tails of amorphous semiconductors under the presence of an applied electric field. The algorithm allows the simulation with arbitrary applied field and finite temperature. The results of the simulation agree favourably with the theoretical prediction. INTRODUCTION The dynamics of nonequilibrium carriers in disordered semiconductors has been studied for many years both experimentally and theoretically. Whereas theoretical concepts for the interpretation of low-field transport such as dark conductivity, time-of-flight drift mobility, and stationary photoconductivity have been developed and successfully applied, a consistent theory which describes the non-linear field dependence of the conductivity and the drift mobility does not yet exist. The most fruitful concept used so far, which describes the combined action of an electric field and of finite temperature on nonequilibrium carriers is that of the "effective temperature", introduced by Marianer and Shklovskii [1]. They consider the relaxation of nonequilibrium carriers in exponential band tails of amorphous semiconductors, given by N,,(E) = N-exp -.E E < 0,(1 N is the spatial density of states in the tails and f0, is the exponential energetic slope of the tail (u = c, v refers to the conduction band tail or to the valence band tail). Their analysis in terms of a numerical solution of linear balance equations yields the
heuristic formula t
2
= T +y
eFa,)2
kB
(2)
where e is the elementary charge, F the applied electric field, and y is a numerical factor which turned out to be 7 = 0.67. This prediction also implies that the effective temperature does not depend on the tailing parameter f0. Recently, we have developed a new Monte-Carlo simulation algorithm which allows the study of the dynamics of optically generated electron-hole pairs in amorphous semiconductors under a wide variety of experimental conditions. Hopping, multipletrapping, and radiative recombination are the microscopic processes underlying the simulation. Arbitrary density of states functions, finite temperature and an applied electric field of arbitrary strength can be considered. The Coulomb interaction between carriers is restricted to the intra-site contribution, i.e. double occupancy of a given localized state is not allowed. Inter-site Coulomb interaction beyond this intrasite interaction is ignored. In this contribution we present, as a particular application of our algorithm, a test of the prediction of Marianer and Shklovskii. We concentrate on the relaxation of nonequilibrium carriers in amorphous semiconductors under an applied electric fi
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