Combined semiclassical and effective-mass Schrödinger approach for multiscale analysis of semiconductor nanostructures

Abstract

A multiscale model, seamlessly combining semiclassical and quantum-mechanical theories, is proposed for electrostatic analysis of semiconductor nanostructures. A quantum potential criterion is used to determine if a local region in the semiconductor is semiclassical or quantum mechanical. If the local physical model is semiclassical, the charge density is directly computed by the semiclassical theory. If the local physical model is quantum mechanical, the charge density is calculated by using the theory of local density of states (LDOS). The LDOS is efficiently calculated from the Green's function by using Haydock's recursion method where the Green's function is expressed as a continued fraction based on the local effective-mass Schr\odinger Hamiltonian. Once the charge density is determined, a Poisson equation is solved self-consistently to determine the electronic properties. The accuracy and efficiency of the multiscale method are demonstrated by considering examples from nanoelectromechanical systems (NEMS) and nanoelectronics. Furthermore, the regions where quantum-mechanical effects are significant are identified for the NEMS and nanoelectronic device structures.