MODELING HETEROSTRUCTURES WITH SCHRÖDINGER–POISSON–NAVIER ITERATIVE SCHEMES, EFFECT OF CARRIER CHARGE, AND INFLUENCE OF ELECTROMECHANICAL COUPLING

Abstract

This paper presents a detailed investigation of the effects of piezoelectricity, spontaneous polarization and charge density on the electronic states and the quasi-Fermi level energy in wurtzite-type semiconductor heterojunctions. This has required a full solution to the coupled Schrödinger–Poisson–Navier model, as a generalization of earlier work on the Schrödinger–Poisson problem. Finite-element-based simulations have been performed on a AlN/GaN quantum well by using both one-step calculation as well as the self-consistent iterative scheme. Results have been provided for field distributions corresponding to cases with zero-displacement boundary conditions and also stress-free boundary conditions. It has been further demonstrated by using four case study examples that a complete self-consistent coupling of electromechanical fields is essential to accurately capture the electromechanical fields and electronic wavefunctions. We have demonstrated that electronic energies can change up to approximately 0.5 eV when comparing partial and complete coupling of electromechanical fields. Similarly, wavefunctions are significantly altered when following a self-consistent procedure as opposed to the partial-coupling case usually considered in literature. Hence, a complete self-consistent procedure is necessary when addressing problems requiring more accurate results on optoelectronic properties of low-dimensional nanostructures compared to those obtainable with conventional methodologies.