Date of Award
Master of Science
Department of Engineering Physics
T. E. Luke, PhD
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 τM:t ≪ τM;. The analytical solution properly predicts stratification conditions when the observation time is prior to τM; however, oscillatory behavior, characteristic of stratification, of the internal electric field occurs for times much greater than τM. During this regime the analytical solutions are invalid.
DTIC Accession Number
Dills, Anthony N., "Model of a Single Impurity in a Wide Bandgap Semiconductor Describing Electric Field Screening" (1994). Theses and Dissertations. 6361.