Unit cell restricted Bloch functions basis for first-principle transport models: Theory and application

Abstract

We present the theory and the application of a first-principle transport model employing a basis set obtained directly from the ab initio Bloch functions. We use a plane-wave density functional theory Hamiltonian and show that a judicious choice of the reduced basis set can effectively suppress the potentially thorny problem of the unphysical solutions. Our methodology enables ab initio transport simulations with a huge reduction of the size of the problem compared to the original ab initio formulation. Moreover, the approach can also be used for local and nonlocal empirical pseudopotential Hamiltonians, thus promising a wide range of possible applications. We report results for ab initio simulations of ${\mathrm{MoS}}_{2}$ field effect transistors, where the transport and electrostatics equations are solved self-consistently for channel lengths up to about 20 nanometers. The simulation results rapidly converge with the size of the basis set, so that the blocks of the Hamiltonian matrix can be reduced to a size below 100. Our methodology is a viable approach for ab initio and semiempirical quantum transport simulations and, in particular, it offers an alternative to the use of maximally localized Wannier functions.