Emitter-collector reciprocity of double heterojunction bipolar transistors: A three-dimensional analysis and proof for transistors with heavily doped and degenerate base regions

Abstract

A three-dimensional analysis of the validity of emitter-collector reciprocity of double heterostructure bipolar transistors with heavily doped and degenerate base regions has been carried out. The analysis is based on current-density relations of Marshak and Van Vliet [Solid-State Electron. 21, 429 (1978)], an effective intrinsic carrier concentration derived in terms of band-gap narrowing and the effect of Fermi–Dirac statistics, and p-n product derived by considering potential barriers and related properties of heterostructures. The analysis indicates that the bipolar reciprocity holds under low-level injection even when parameters such as band-gap narrowing of the band, and mobility, diffusivity, lifetime, and recombination velocity, etc., of the carriers depend on spatial coordinates, and the carrier concentrations are described by Fermi–Dirac statistics. The analysis is general enough to be applicable to both n-p-n and p-n-p heterostructure and homostructure bipolar transistors.