Rigid band analysis of heavily doped semiconductor devices

Abstract

The conventional carrier transport equations used in device analysis must be modified for heavily doped semiconductor regions. The modifications to Shoekley's auxiliary equations relating the carrier densities to their corresponding quasi-Fermi levels are derived for the rigid band model. We include the effects of asymmetric bandgap narrowing and of carrier degeneracy (Fermi-Dirac statistics). Emphasis is placed on writing the equations in a simple form that indicates the effect of changes in the band structure due to heavy doping. In this form they can serve as a basis for computer-aided analysis and design. We show that, in general, the effective intrinsic carrier density n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ie</inf> as well as the electron and hole current densities depend on the asymmetry in bandgap narrowing. However, for the special case of low-level injection, n <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ie</inf> and the minority current density depend only on the total bandgap narrowing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaE_{g}</tex> . Furthermore, we indicate that interpretation of experiments with theory using Boltzmann statistics, instead of Femi-Dirac statistics, will underestimate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\DeltaE_{g}</tex> in degenerate material.