Time-dependent boundary conditions with lead-sample Coulomb correlations: Application to classical and quantum nanoscale electron device simulators

Abstract

Standard boundary conditions (BCs) for electron-transport simulators are based on specifying the value of the scalar potential (or the electric field) and the charge density at the borders of the simulation box. Due to the computational burden associated to quantum or atomistic descriptions, the use of small simulation boxes that exclude the leads is a mandatory requirement in modern nanoscale simulators. However, if the leads (where screening takes place) are excluded, standard BCs become inaccurate. In this work, we develop analytical expressions for the charge density, the electric field, and the scalar potential along the leads and reservoirs. From these expressions, we present a (time-dependent) BCs algorithm that transfers the specification of the BCs at the boundaries of the simulation box to a deeper position inside the reservoirs. Numerical solutions of the time-dependent Boltzmann equation with our algorithm using large (reservoir, leads, and sample) and small (sample alone) simulation boxes are compared, showing an excellent agreement even at (far from equilibrium) high bias conditions. Numerical results demonstrating the limitations of standard BCs for small simulation boxes are presented. Finally, time-dependent simulations of a resonant tunneling diode (using a quantum trajectory-based simulator) are presented, emphasizing the ability of this BCs algorithm to ensure overall charge neutrality in simulation boxes much smaller than the total lead-sample-lead length. This BCs algorithm requires a minimum computational effort and it can be applied to study dc, ac, and current or voltage fluctuations in nanoscale devices.