The nonlinear partial differential equations which describe transient photoconductivity in insulators are solved numerically. Trapping and recombination are included which allows photoconduction to be studied in the presence of large space charge. Use of methods for ‘‘stiff’’ differential equations insures stable time dependent solutions even for problems which have widely different time constants. The program is applied to a thin film (1000 Å) of silicon dioxide to illustrate the salient features of the numerical solutions and the capabilities of the program.
Exact solutions for the photoconductivity of insulators with space charge (caused by deep trapping) and recombination require numerical methods for solving coupled, nonlinear differential equations. A method for obtaining computer solutions is outlined and the parameters required for fitting existing data for the photoconductor PbO are given. The carrier lifetimes are found to be much longer than previously assumed and the recombination coefficients for free with trapped carriers are found to be very large, close to diffusion controlled. The predictions for the time required to achieve steady state were found to be unexpectedly long, a result of the feedback between trapping and recombination.
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