Abstract from Materials Technology'98, University of Waterloo, 13 June 1998
Serge Grabtchak and Michael Cocivera, Guelph-Waterloo Centre for Graduate Work in Chemistry, Guelph, Ontario N1G 2W1
Using Monte Carlo simulations it was shown previously by some authors [1] that a number of distributions could produce very similar power-law behavior under diffusion conditions specific for time-of-flight (TOF) experiments. On the other hand, the only model considering multiple trapping (MT) with a recombination term was developed solely for an exponential distribution [2]. Therefore, similarities and differences of various distributions under photoconductivity conditions were left unexplored.
A better understanding of MT can be obtained when both free and trapped electron densities can be observed and analyzed. Photoconductivity is related to free electrons. Direct information about trapped electrons can be obtained by photoadsorption (PA) and the advanced method of transient microwave photoconductivity (AMTMP) measurements. The time dependence of free and trapped electron densities based on MT rate equations were obtained and analyzed for exponential, rectangular, linear, Gaussian distributions. Continuous distribution functions were replaced by sets of discrete levels (up to 40) ensuring an adequate approximation of continuous distributions in a range of interest (10-11 - 10-1 s).
For exponential distribution we found that :(1) the form of transient peculiar to photoconductivity can be easily obtained as a solution of MT rate equations and does not need the more complicated theory developed by [2]; (2) detailed analysis of these rate equations gives the transient decay of total concentration of trapped electrons which can describe PA transients, (3) use of corresponding expression from [2] can lead to significant error (2 orders) in the estimation of recombination time.
For rectangular/linear distributions the following results have been obtained: (1) in contrast with results of the Monte Carlo simulation, these distributions do not generally provide a power law decay. Power law behavior occurs only under very limited conditions. Furthermore when it does occur, it is only over a limited time range, and unlike experimental observation it does not exhibit a transition to a second steeper power law at longer times. (2) in place of the second power law behavior these distributions cause an exponential decay related to the deepest level in the distributions when weak retrapping occurs. (3) as retrapping becomes stronger, the power law region shortens and eventually disappears. Although the exponential region remains at longer times, the time constant is a composite of several time constants. (4) the transition of the temporal behavior from weak to strong retrapping depends on the values of the recombination time, density of localized states and capture cross-section.
[1].J.M. Marshall, H. Michiel and G.J. Adriaenssens, Phil. Mag. B 47, (211) 1983
[2].J. Orenstein, M. A. Kastner and V. Vaninov, Phil. Mag. B 46, (23) 1982