Self-consistent time-dependent boundary conditions for static and dynamic simulations of small electron devices

A quasi-analytical self-consistent and time-dependent boundary conditions algorithm for micro- and nanoscale electron transport simulators is presented and discussed. The algorithm is the result of imposing overall charge neutrality and current conservation along the reservoirs, the leads and the active region. Only an explicit numerical simulation of the active region is required. By means of analytical solutions of the spatial distribution for the charge density, electric field and potential energy along the leads, the algorithm is able to self-consistently translate standard “metallic” boundary conditions in the reservoirs into intricate constraints at the borders of the active region. The algorithm is robust, requires small computational effort and it is suitable for any (classical or quantum) electronic device simulator for stationary (DC) and dynamic (transients, noise and AC) regimes up to several THz. The algorithm is specially welcomed for dynamical regime simulations, where the predictions of the time-evolution of the electrostatic potential, electric field and charge density at the borders of the active region are rather complicated.