Experimentelle Untersuchungen zu Minoritätsträger-Diffusionskonstanten in Silizium

Abstract

In the present study the transportation parameter diffusion coefficient of minority carriers in silicon is determined experimentally. Measurements take place over a entire range of temperature and over a entire range of doping concentration of holes in n-silicon and of electrons in p-silicon. The results are compared with the usually used data. The mobility model according to D.B.M. Klaassen, used in many device simulators, is used as reference. The mobility values are converted into diffusion coefficients with the help of the einstein relationship. Special attention is given to the experimental method. Special value is put to determine the diffusion coefficient in a maximally direct way. The focus of the present study is the practical development and application of the experiment. The mobility model according to Klaassen is confirmed for high temperatures for all measured doping concentrations. With doping concentrations below the Mott-transition deviations exist between measurement results and converted mobilities according to Klaassen. The deviations increase with decreasing of temperature on the one hand, and with increasing of doping concentration on the other hand and can be explained with excitons. Therefor a weighted average diffusion coefficient is formed wich lies between the diffusion coefficient according to Klaassen and the diffusion coefficient of the excitons. The weighting factor is the relative exciton concentration. The comparison between this weighted averaged diffusion coefficient with the measurement results supplies a very good agreement over the entire range of temperature. With doping concentrations above the Mott-transition no excitons can form. Here, the measurement results are compared with converted mobilities according to Klaassen. The comparison between these two diffusion coefficients also results in a very good agreement over the entire range of temperature.