Junction capacitance and related characteristics using graded impurity semiconductors

The transition capacitance of a junction of semiconductors with constant impurity density is well-known and varies inversely with the square root of the bias voltage. This paper analyzes the variation of transition capacitance with bias voltage of a junction of semiconductors with graded impurity densities; i. e., densities which are an arbitrary function of position. It is found that the transition capacitance can be simply related to a depletion width and that, in turn, depletion width can be related to the bias voltage. An analysis is also carried out for the impurity grading to produce a specified transition capacitance variation, as for instance, a linear variation of capacitance with bias voltage. It is also possible to determine impurity gradings to satisfy certain special conditions. An example of this type that is considered in some detail is the determination of the impurity grading which will produce avalanche breakdown simultaneously throughout the semiconductor. An important result of the analysis is that the capacitance vs bias voltage relation can be favorably modified by suitable choice of impurity grading (see Fig. 7). The practical realization of the various characteristics considered in this article is contingent upon techniques for fabricating semiconductors with specified impurity gradings.