Abstract
Optical absorption measurements [1] and theoretical calculations [2–9] have shown that the bandgap in silicon is not only temperature-dependent but is also influenced by the impurity concentration at higher values. Recent electrical measurements [10] of the pn-product in the base region of bipolar transistors made it possible to derive the bandgap narrowing quantitatively as a function of the impurity concentration. In this paper it will be shown that theoretical calculation of the pn-product as a function of temperature and impurity concentration can be approximated by the following relationship: pn = n ie 2( N, T) = CT 3 exp (− qV go ( N)/ kT) for temperatures between about 280 and 450°K. Moreover the calculated values for C and V go ( N) show surprisingly good quantitative agreement with the values derived from the above mentioned pn-measurements [10].
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