Derivative of Electron Density in Non-Equilibrium Green's Function Technique and Its Application to Boost Performance of Convergence

Abstract

The non-equilibrium Green's function (NEGF) technique provides a solid foundation for the development of quantum mechanical simulators. However, the convergence is always of great concern. We present a general analytical formalism to acquire the accurate derivative of electron density with respect to electrical potential in the framework of NEGF. This formalism not only provides physical insight on non-local quantum phenomena in device simulation, but also can be used to set up a new scheme in solving the Poisson equation to boost the performance of convergence when the NEGF and Poisson equations are solved self-consistently. This method is illustrated by a simple one-dimensional example of an N++ N+ N++ resistor. The total simulation time and iteration number are largely reduced.