The conventional drift-diffusion equation is inadequate to analyze ballistic effects. In most device analysis, thermoelectric effects associated with gradients in the carrier temperature are assumed to be small. The base thickness dependence of current gain as a result of non-equilibrium transport of electrons in the base was experimentally shown by many researchers. We present a simulation to analyze the electron transport in the base region of an HBT based on the carrier density balance, momentum balance, and energy balance equations. Transistors with base thickness of 1000 Å and 2500 Å are investigated. Simulation results of electron transport in the base region indicates that tunneling electrons give rise to unique transport characteristics in the base of HBTs. The density profile is found as a result of transition from ballistic to diffusive transport in the base region. The range of observed non-equilibrium transport and the carrier density and temperature profiles in the base region are functions of average momentum and energy relaxation times. The non-equilibrium effects are shown to exist up to 1000 Å in the base region of AlGaAs/GaAs HBTs. The simulation results are in good agreement with experimental data.
Özaydin, M., & Eastman, L. F. (1996). Non-equilibrium carrier transport in the base of heterojunction bipolar transistors. Solid-State Electronics, 39(5), 731–735. https://doi.org/10.1016/0038-1101(95)00159-X