Based on the non-equilibrium Green's function (NEGF) formalism, we show a numerically efficient method to treat inelastic scattering in multi-dimensional atomistic codes. Using a simple rescaling approach, we detail the calculations of the lowest order approximation (LOA) 1 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 sp 3 d 5 s * 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, 3 rd 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.

International audienceThis paper presents an efficient direct quantum method to model inelastic scattering in nanoelectronic structures including degenerate band extrema. It couples the Born series expansion of the nonequilibrium Green's function (NEGF) to an analytic continuation based on the Pade approximant technique. Using a two-band k . p Hamiltonian, we analyze the electron transport through a linear chain in the presence of both optical and acoustic phonons. Results are consistently compared with the usual, computationally expensive, self-consistent Born approximation (SCBA). We find that our approach provides a much better convergence for both types of phonons in the presence of strong multiband coupling. The calculation of the current to the fifth order in the interactions is sufficient to reproduce the influence of all considered phonon interactions. We also show that the method can be applied to the calculation of the density of carriers which depicts however a slower convergence rate than the current. The capability to efficiently calculate both current and carrier density represents a clear advantage in a context of increasing request for atomistic quantum simulations