Analytical Determination of Generation-Recombination Rate in Amorphous Silicon
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ANALYTICAL DETERMINATION OF GENERATION-RECOMBINATION RATE IN AMORPHOUS SILICON JO7E FURLAN and SLAVKO AMON University of Ljubljana, Fak. za elektro., Tr~a~ka 25, Ljubljana, Yugoslavia ABSTRACT A general expression for generation-recombination rate in a-Si based on classical SRH theory including different electron and hole capture cross-sections for donor-like and acceptor-like centers inside the mobility gap is derived. Applying appropriate approximations and two-exponential model for localized states distribution two methods of analytical solution are presented and discussed. INTRODUCTION The theory of the generation-recombination process based on four basic events responsible for interactions of free carriers with localized states has been worked out by Shockley and Read /1/. This theory has been successful in explaining and describing a wide variety of phenomena in a single crystal silicon. The four processes through which free carriers can interact with localized states can be applied to amorphous silicon as well. The important difference between single crystal and a-Si is in the distribution of gap states. Due to compositional disorder the a-Si is characterized by a high density of localized states tailing from the conduction and valence bands and overlapping in the mobility gap /2/. It is believed that localized states distribution is composed of donor-like and acceptor-like states densities /3/. Assuming two-term exponential approximation for localized states distribution the SRH theory can be easily adopted to determine CR rate in a-Si. Basic equations governing generations and recombinations in general amorphous materials were given by Taylor and Simmons /4/. The treatment of recombinations in a-Si based on symmetrical distribution of localized states was presented by Card el al. /5/. In this paper the concept of SRH generations and recombinations will be applied to a-Si represented by an unsymmetrical exponential distribution of donor-like and acceptor-like localized states. Derivation of GR rate will be carried out assuming different electron and hole capture cross-sections for donor-like and for acceptor-like centers inside the mobility gap. GENERAL
EXPRESSION FOR GR RATE IN a-Si
The four electron and hole capture and emission transition processes in the energy range dE at energy E inside the mobility gap between Ev and E c, as shown in Fig.l, are described by dRn = dRnD + dRnA = vth n
dGn = dGnD
+
dGnA=
[
6
n
[ enD ftDgD
D(l-ftD)gD+ +
GnA(l-ftA)gA
efnAftAgA I dE
d
(2)
dRp = dRpD + dRpA = Vth p [ %DftDgD + OpAftAgA] dE
(3)
dGp = dG p
(4)
+ dGpA = [epo(l-ftD)gD + epA(l-ftA)gA]
Mat. Res. Soc. Symp. Proc. Vol 70.
1986 Materials Research Society
dE
150
where n is the free electron concentration in the extended states above E , p in the hole concentration in the extended states below, Ev, gD and gA are the densities of donor-like and acceptor-like states, f and ft are occupation probabilities, G-D' CnA' and 0 D' %A are elecEiron and t'ole capture crosssetos nD, e nA ande sections, en
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