Advanced Algorithms for Ab-initio Device Simulations

Numerical algorithms dedicated to large-scale quantum transport problems from first-principles are presented in this paper. They can be decomposed into three main categories: (i) the calculation of the open boundary conditions that connect the simulation domain and its environment, (ii) the solution of the resulting Schrödinger equation in the ballistic limit of transport, and (iii) the extension of this case to situations involving scattering, e.g. electron-phonon interactions. It will be shown that ab-initio device simulations require algorithms specifically developed for that purpose and that graphics processing units (GPUs) can bring significant speed ups as compared to solvers based on CPUs only. As an illustration, the computational times coming from the investigation of a realistic conductive bridging random access memory cell will be reported.