Current‐voltage characteristic for bipolar p‐n junction devices with drift fields, including correlation between carrier lifetimes and shallow‐impurity concentration

摘要

We present general analytic solutions for static current‐voltage characteristics of quasineutral regions of nonilluminated semiconductor bipolar devices under the following assumptions: (a) the quasineutral region has a graded shallow‐level impurity concentration producing a constant built‐in electric (drift) field; (b) minority carriers injected into this region stay at concentrations low enough to avoid violation of low‐injection conditions; (c) the minority‐carrier lifetime of this region depends on position in accordance with a power‐law dependence on the shallow‐level donor concentration, a dependence that is consistent with the longest minority‐carrier lifetimes measured and with the physical chemistry of divacancy‐donor reactions at high temperatures. The solutions presented are apparently the first that include assumption (c). Modified Bessel functions of the first and second kind appear in these solutions. From a pheonomenological standpoint, the solutions may account for defect centers associated with vacancy complexes and, in part, for the gettering observed in highly doped n‐type Si. Design implications for transistors, diodes, and solar cells are discussed quantitatively for a thin drift‐field Si p(x) junction solar cell.