Coupled effects in quantum dot nanostructures with nonlinear strain and bridging modelling scales

Melnik, R.V.N. and Mahapatra, D.R.

Computers & Structures85 (11-14)698-711, 2007


We demonstrate that the conventional application of linear models to the analysis of optoelectromechanical properties of nanostructures in bandstructure engineering could be inadequate. Such linear models are usually derived from the traditional bottom-up approach applied to the analysis of nanostructure properties. At the same time, in the hierarchy of mathematical models for semiconductor device modelling constructed on the basis of the top-down approach, we deal predominantly with models where nonlinearity is essential. In this contribution, we analyze these two fundamental approaches in bridging the scales in mathematical models for the description of optoelectromechanical properties of nanostructures. The focus of the present paper is on a model based on the coupled Schrodinger-Poisson system where we account. consistently for the piezoelectric effect and analyze the influence of different nonlinear terms in strain components. The examples given in this paper show that the piezoelectric effect contributions are essential and have to be accounted for with fully coupled models. While in structural applications of piezoelectric materials at larger scales, the minimization of the full electromechanical energy is now a routine in many engineering applications, in bandstructure engineering conventional approaches are still based on linear models with minimization of uncoupled, purely elastic energy functionals with respect to displacements. Generalizations of the existing models for bandstructure calculations are presented in this paper in the context of coupled effects.