Single and multiband modeling of quantum electron transport through layered semiconductor devices

TLDR

The study formulates a non‑equilibrium Green function theory to address self‑consistent charging, incoherent and inelastic scattering, and band‑structure challenges in high‑bias quantum device modeling. The authors develop the theory in a localized orbital basis for zinc blende lattices, derive a Dyson‑equation tunneling formula with a generalized Fisher‑Lee transmission, and incorporate scattering through self‑energies for phonons, alloy fluctuations, interface roughness, and dopants, offering both self‑consistent Born and multiple sequential scattering treatments. Numerical comparisons show that the multiple sequential scattering algorithm converges to the self‑consistent Born results, establishing its reliability.

Abstract

Non-equilibrium Green function theory is formulated to meet the three main challenges of high bias quantum device modeling: self-consistent charging, incoherent and inelastic scattering, and band structure. The theory is written in a general localized orbital basis using the example of the zinc blende lattice. A Dyson equation treatment of the open system boundaries results in a tunneling formula with a generalized Fisher-Lee form for the transmission coefficient that treats injection from emitter continuum states and emitter quasi-bound states on an equal footing. Scattering is then included. Self-energies which include the effects of polar optical phonons, acoustic phonons, alloy fluctuations, interface roughness, and ionized dopants are derived. Interface roughness is modeled as a layer of alloy in which the cations of a given type cluster into islands. Two different treatments of scattering; self-consistent Born and multiple sequential scattering are formulated, described, and analyzed for numerical tractability. The relationship between the self-consistent Born and multiple sequential scattering algorithms is described, and the convergence properties of the multiple sequential scattering algorithm are numerically demonstrated by comparing with self-consistent Born calculations.