Multiscale electrostatic analysis of silicon nanoelectromechanical systems (NEMS) via heterogeneous quantum models

A multiscale method, seamlessly combining semiclassical, effective-mass Schrödinger (EMS), and tight-binding (TB) theories, is proposed for electrostatic analysis of silicon nanoelectromechanical systems (NEMS). By using appropriate criteria, we identify the physical models that are accurate in each local region. 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 EMS or TB model), 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 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 two NEMS examples, namely, a silicon fixed-fixed beam with hydrogen termination surfaces and another silicon beam switch with 90° single period partial dislocations. The accuracy and efficiency of the multiscale method are demonstrated.