Semiconductor Quantum Wells with BenDaniel-Duke Boundary Conditions and Janus Nanorods

Abstract

The energy levels of bound states of an electron in a quantum well with BenDaniel-Duke boundary condition are studied. Analytic, explicit, simple, and accurate formulae have been obtained for the ground state and the first excited state. In our approach, the exact, transcendental eigenvalues equations were replaced with approximate, tractable, algebraic equations, using algebraic approximations for some trigonometric functions. Our method can be applied to both type I and type II semiconductors and easily extended to quantum dots. The same approach was used for the semi-quantitative analyze of two toy models of Janus nanorods.

Asymmetric quantum wells and the solotone effect: towards an inverse method

“…This is the eigencondition for an asymmetric infinite square well with position dependent mass and E > V 0 . A similar derivation may be found in [17] and it is not difficult to show that this eigencondition is equivalent to equation (82) on p 63 of [17] (with V 0 = h2 k 2 0 /2m 1 and a = b = L/2). We now consider the first of three special cases: an asymmetric infinite square well containing a particle with constant mass.…”