Heavy doping effects in bipolar silicon transistors and p–n junction silicon solar cells

Abstract

The effects of heavy doping, bandgap narrowing ΔEg, and Fermi-Dirac statistics, on effective p–n junction silicon solar cells, are investigated with simplified models of an n-type heavily doped region of these semiconductor devices. It is suggested that, for a given high electron concentration n, the result of ΔEg, for the electrical bandgap is significantly larger than that for the optical bandgap, in good agreement with recent remarks of Marshak and Van Vliet and Tang, and that, while the ΔEg, effect leads to an increase in nie, the degeneracy given by the Fermi-Dirac statistics causes a decrease in nie, in accordance with recent works. For n higher than 1020 cm−3, nie saturates to its value approximately equal to 1011 cm−3, and for n lower than 1020 cm−3 the present results of nie are in good agreement with Tang's results. In the present theory, the characteristics of the above semiconductor devices agree with experiments of Tang for p–n–p bipolar silicon transistors, and with recent theoretical results of Shibib et al. for p–n junction silicon solar cells.