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A new method for simultaneous measurement of bandgap narrowing and diffusion length in a heavily doped n + substrate is proposed. The method uses planar test pattern at the front side of the substrate to determine the hole minority-carrier current injected from a p-type emitter and diodes at the rear side to measure diffusion lengths. The method can be generalized such that the minority-carrier diffusion constant can be estimated and the use of extrapolated literature data can be avoided. Results of measured values of bandgap narrowing and diffusion length versus impurity concentration are given for n-type material.
Mertens et al. (1980) studied this question.