Accelerated boundary integral analysis of energy eigenvalues for confined electron states in quantum semiconductor heterostructures

Abstract

This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding their optical and electronic properties, making it a key challenge in semiconductor physics. The proposed method is based on utilizing series expansions of zero-order Bessel functions to numerically solve the Schr\"odinger equation using boundary integral method for bound electron states in a computationally efficient manner. To validate the proposed technique, we applied it to address previously explored issues by other research groups. The results clearly demonstrate the computational efficiency and high precision of our approach. Notably, the proposed technique significantly reduces the computational time compared to the conventional method for searching the energy eigenvalues in quantum structures.