Analytical approach for transient photoconductivity in undoped a-Si:H
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M. Goerlitzer, P. Pipoz, H. Beck*, N. Wyrsch, A. V. Shah Institut de Microtechnique, *Institut de Physique, Universitd de Neuchdtel, 2000 Neuchdtel, Switzerland. ABSTRACT Transient photoconductive response of undoped a-Si:H has been studied; the changes were analysed between two slightly different steady-state illumination conditions, at room temperature. A theoretical model is developed to describe transient photoconductivity; it yields good agreement with the measured curves for a whole range of light intensities. Numerical evaluations allows one to extract the recombination time of electrons. Comparison with steadystate photoconductivity yields a band mobility of free electrons between 0.1 and 6 cm 2 V-ls-1 , depending upon sample quality.
INTRODUCTION . We present here a theoretical model for transient photoconductivity in undoped a-Si:H. Several studies have already been published on the subject [1,2,31. Here we will analyse the special case of a small step in generation between two steady-states, and we will look at recombination via dangling bond states; furthermore, we will obtain an analytical form for the evolution of free carriers [4]. The general outline of our model will be discussed; then, the correspondence between theory and measurements will be analysed, and finally a comparison between transient and steady-state photoconductivity will be made; this last step allows us to evaluate the band mobility of electrons, for a whole series of samples deposited at different temperatures.
THEORY This model describes the time response of undoped a-Si:H for a small variation in bias illumination, at room temperature. The multiple-trapping model [5,6] for a step in generation between two steady-states is used. We consider interband generation and monomolecular recombination of free carriers via dangling bond states. Thermal emission from and capture via traps in bandtail states are assumed. The evolution equations of the density of free and trapped electrons are: dn(t) = G(t) -
dt
d n(t) -vthn(t)(cN°(t) + 'N(t))
(1)
dt d ni d(t) = wN (Ni - ni (t))n(t) - eini (t)
dt
(2)
where wi is the mobile carrier capture coefficient of the traps, ei the coefficient of thermal release from these traps, G the generation rate and Ni, ni are the total density and the occupied density, respectively, for a trap of energy Ei. 503
Mat. Res. Soc. Symp. Proc. Vol. 377 01995 Materials Research Society
The last two terms in equation (1) represent the recombination of mobile carriers via dangling bonds with the thermal velocity Uth, the capture cross-section an of a dangling bond of charge 0 (the dangling bonds are taken here to have three states of' charge: positive, neutral and negative), for electrons or holes, and with dangling bond densities N 9 . For N- we have:
d N-(t) dt
=
-VthanN-(t)p(t) + vha°,N°(t)n(t)
(3)
Analogous equations can be written for holes and for positively charged dangling bonds. Introducing a small step in the generation rate, G(t) = GO + 8G(t), we linearise the above equations; afterwards, the La
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