A finite-difference technique for computation of electron states in core–shell quantum wires of different configurations

Abstract

In this paper, electron energies in core–shell quantum wires (CSQW) of rectangular, triangular, T-shaped, H-shaped and circular geometries are numerically computed by solving a time-independent Schrödinger equation using the finite difference technique. Computation is performed for both normal and inverted structures of CSQW, taking into account Kane-type nonparabolicity, conduction band discontinuity, and effective mass mismatch at the hetero-interface. Sparse, structured Hamiltonian matrices are produced for the calculation of energy eigenvalues and intersubband transition energies. Comparative study reveals that for a given core width of normal CSQW, the eigenenergy is the highest for the triangular geometry and the lowest for the rectangular geometry. For inverted CSQW, the ground-state energy of the triangular wire decreases with increasing core width, unlike other geometries. Studies on the intersubband transition energy show that for triangular and H-shaped inverted CSQW, it varies in a direction opposite to that of other inverted structures. Suitable tailoring of wire dimensions indicates the possibility of tuning the transition energy for photonic applications.