A simple semiclassical treatment of the vertical transport in barrier-conductor structures is presented. The distribution function is constructed by fitting the solutions of the Boltzmann equation for the conductor parts with the barrier reflection and transmission probabilities. This semiclassical theory describes multiple reflection in a random phase approximation leaving out the fine structure associated with the quantum interference. As an application we analyze single and double barrier structures in detail. We study the high frequency behaviour of various diode structures. For the hot electron transistors (HET) we derive simple formulas for the base transport factor, transconductance and other elements of the ac-small signal equivalent circuit. The transistor model is also valid for the resonant hot electron transistor (RHET).
Juha A. T. Sinkkonen,
"Semiclassical Transport Theory For Quantum Barrier-Conductor Chains", Proc. SPIE 0943, Quantum Well and Superlattice Physics II, (18 August 1988); doi: 10.1117/12.947288; https://doi.org/10.1117/12.947288