Three-dimensional scattering matrix simulation of resonant tunnelling via quasi-bound states in vertical quantum dots

Abstract

This paper presents a numerical simulation technique for quantum-dot-based electronic devices based on the three-dimensional (3D) scattering matrix (S-matrix) theory. Starting from the 3D time-independent Schrödinger equation with scattering boundary conditions, the multi-mode S-matrix and transmission rates are derived and the tunnelling current is calculated based on the global coherent tunnelling model. The present simulation technique is applied for zero-dimensional (0D) resonant tunnelling diodes (RTDs). The effects of a complex mixture of lateral mode conserving and non-conserving tunnelling processes on the I– V characteristics are investigated in terms of multi-mode transmission rates and quasi-bound electronic states at resonance. The simulation is also used for analysing resonant tunnelling (RT) assisted by ionised impurities in a quantum dot. By introducing ionised impurities in the quantum dot region, a new type of RT via single-impurity-induced quasi-bound states is investigated.