Quantum treatment of phonon scattering for modeling of three-dimensional atomistic transport

Based on the nonequilibrium Green's function formalism, we show a numerically efficient method to treat inelastic scattering in multidimensional atomistic codes. Using a simple rescaling approach, we detail the calculations of the lowest-order approximation (LOA) [Y. Lee et al., Phys. Rev. B 93, 205411 (2016)2469-995010.1103/PhysRevB.93.205411] series to the usual, computationally intensive, self-consistent Born approximation (SCBA). This, combined with the analytic continuation technique of Padé approximants, is applied to an atomistic code based on a tight-binding sp3d5s∗ model for electrons and holes, and a modified valence-force-field method for phonons. Currents in Si and Ge gate-all-around nanowire transistors are then computed considering the main crystallographic transport directions ((100), (110), (111)) for both n-type and p-type devices. Our results show that in most configurations, third-order LOA currents are enough to achieve a high agreement with SCBA results, while reducing the calculation time by about one order. In addition, we propose a criterion to determine the validity of such expansion techniques