No abstract

A fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrödinger’s and Poisson’s equations is presented. Using quantum mechanical perturbation theory, a simple expression describing the dependence of the quantum electron density on the electrostatic potential is derived. This expression is then used to implement an iteration scheme, based on a predictor-corrector type approach, for the solution of the coupled system of differential equations. We find that this iteration approach simplifies the software implementation of the nonlinear problem, and provides excellent convergence speed and stability. We demonstrate the approach by presenting an example for the calculation of the two-dimensional bound electron states within the cross section of a GaAs-AlGaAs based quantum wire. For this example, the convergence is six times faster by applying our predictor-corrector approach compared to a corresponding underrelaxation algorithm.

nextnano is a simulation tool that aims at providing global insight into the basic physical properties of realistic three-dimensional mesoscopic semiconductor structures. It focuses on quantum mechanical properties such as the global electronic structure, optical properties, and the effects of electric and magnetic fields for virtually any geometry and combination of semiconducting materials. For the calculation of carrier dynamics, two models are currently implemented that provide results for the limiting cases of highly diffusive or purely ballistic quantum-mechanical transport. In this paper, we present an overview of nextnano's present and future capabilities and discuss some key concepts in the areas of code structure, numerical techniques, and electronic structure principles.

nextnano3 is a simulation tool that aims at providing global insight into the basic physical properties of realistic three-dimensional mesoscopic semiconductor structures. It focuses on quantum mechanical properties such as the global electronic structure, optical properties, and the effects of electric and magnetic fields for virtually any geometry and combination of semiconducting materials. For the calculation of the carrier dynamics a drift--diffusion model based on a quantum-mechanically calculated density is employed. In this paper we present an overview of the capabilities of nextnano 3 and discuss some of the main equations that are implemented into the code. As examples, we first discuss the strain tensor components and the piezoelectric effect associated with a compressively strained InAs layer for different growth directions, secondly, we calculate self-consistently the quantum mechanical electron density of a Double Gate MOSFET, then we compare the intersubband transitions in a multi-quantum well structure that have been obtained with a single-band effective mass approach and with an 8-band k · p model, and finally, we calculate the energy spectrum of a structure in a uniform magnetic field.