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Model of a Single Impurity in a Wide Bandgap Semiconductor Describing Electric Field Screening.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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A mathematical model of the influence on electric field screening arising from a single impurity in a wide bandgap semiconductor has been numerically investigated and compared with analytically derived solutions. The parameter set chosen to perform the comparison of analytical solution and numerical solution is based upon a bismuth silicate crystal. Both the analytical calculations and the numerical calculations are an attempt to mathematically model the internal electric field within a semiconductor. Two types of impurities were looked at a single donor level and a single trap impurity level. In general, after an abrupt application of a voltage across the semiconductor, net charge regions begin to redistribute and create internal electric fields that screen the applied field. A trap impurity is found to be more self-consistent with the analytical solutions than a donor impurity the former satisfying the assumption of a constant free electron lifetime. The analytical solutions are valid for observation times much less than the Maxwellian relaxation time tau sub M t tau sub M. The analytical solution properly predicts stratification conditions when the observation time is prior to tau sub M however, oscillatory behavior, characteristic of stratification, of the internal electric field occurs for times much greater than tau sub M. During this regime the analytical solutions are invalid.
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