Diffused Junction Depletion Layer Calculations

The dependence of depletion layer properties on voltage is important in the design of many semiconductor devices. Some of these properties, such as total depletion layer thickness, are accurately predicted by the commonly used step and graded junction approximations over fairly wide voltage ranges. However, the ranges in which the approximations are applicable have not been established previously. The present work establishes the regions in which these approximations are valid and supplies data for the entire voltage range of interest. Both the complementary error function distribution and the gaussian distribution have been treated. Total depletion layer thickness, peak electric field, capacitance per unit area and the fraction of the depletion layer on each side of the junction have been calculated for wide ranges of voltage, junction depth, background impurity concentration and 389 390 T H E B E L L SYSTEM TECHNICAL J O U R N A L , MARCH 1900 surface concentration. Results are given for silicon and germanium and can readily be extended to other materials.