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Nonexponential photoionization of the DX related centers in indium doped Cd_{1x}Mn_{x}Te. On the relationship between the stretched exponential and twoexponential relaxation models. 
Justyna Trzmiel ^{1}, Karina Weron ^{1}, Ewa Popko ^{1}, Piotr Becla ^{2} 
1. Wroclaw University of Technology, Institute of Physics, Wybrzeże Wyspiańskiego 27, Wrocław 50370, Poland 
Abstract 
The kinetics of phototransients due to the presence of defects in semiconductors is commonly analyzed in the terms of the multiexponential fitting or by means of the stretched exponential function.The motivation of this paper is to explain the relationship between both models.For this purpose the kinetics of phototransients due to DX centers in indium doped Cd_{0.93}Mn_{0.07}Te crystals grown by the Bridgman method were studied.Photoconductivity transients, measured at 77K for different photon fluxes with fixed photon energy,were analyzed. The obtained data can be well fitted with the stretched exponential function.On the other hand, it appears that the transients are also well fitted by a superposition of two weighted exponents with the short and long time constants b1and b2, respectively.To explain the result we propose the probabilistic representation of the relaxation function Φ(t)=<e^{βt}>, given by a weighted average of the exponential decay with respect to the distribution of the random relaxation rate β,representing the intrinsic nonexponential behavior of the entire system.As it is wellknown from probability theory, such an average can be expressed either as a sum of weighted exponentials Σp_{i}e^{bit},if β takes positive discrete values b_{i} with probabilities p_{i},or as the integral ∫e^{bt}ρ(b)db,if β takes values from [0,∞) with probability ρ(b)db.This "dual" representation of the relaxation function explains a relationship between the stretched exponential pattern and the twoexponential fitting.In the studied case the probabilities p_{1},p_{2} of taking two different time constans b_{1},b_{2} attributed to the twostep photoionization of the DX centers, are shown to be in agreement with the longtailed stable distribution of the effective relaxation rate corresponding to the stretched exponential relaxation response. 
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Presentation: Oral at EMRS Fall Meeting 2006, Symposium F, by Justyna Trzmiel Submitted: 20060513 18:14 Revised: 20090607 00:44 