Efficient GPU implementation of a Boltzmann-Schrödinger-Poisson solver for the simulation of nanoscale DG MOSFETs

Abstract A previous study by Mantas and Vecil (Int J High Perform Comput Appl 34(1): 81–102, 2019) describes an efficient accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of Boltzmann equations, was ported to GPU using CUDA extensions, but computation system’s eigenstates, solution Schrödinger-Poisson block, parallelized only OpenMP due its complexity. This work fills gap describing port block. new proposal implements Scheduled Relaxation Jacobi method solve sparse linear systems which arise in 2D Poisson equation. 1D Schrödinger equation is solved adapting multi-section iteration Newton-Raphson algorithm approximate energy levels, Inverse Power Iterative Method used wave vectors. We want stress that this block can be thought as module independent phase (Boltzmann) solvers different levels description electrons; therefore, it particular interest because adapted other macroscopic, hence faster, confined devices exploited at industrial level.