The Influence of Quantum Particle Mass on the Discrete Energy Spectrum of Multilayer Structures: A Fourier Transform Approach

Many optoelectronic devices contain multilayer structures with quantum wells, particularly semiconductor lasers and light-emitting structures based on organic semiconductors (OLEDs).The stationary Schrödinger equation must be solved to determine the discrete energy levels in quantum wells.This must account for the fact that the effective mass of carriers in different layers differs.The paper analyses a structure comprising three quantum wells of different widths, in which the charge-carrier effective masses differ.We propose a numerical method for solving the Schrödinger equation in the frequency domain.This method considers the different effective masses in quantum wells and barriers.The obtained discrete energy levels were compared with those calculated using the de Broglie wave method.This made it possible to determine the parameters of the numerical process required to achieve high accuracy.Studies have shown that the mass of particles in barriers has little effect on discrete energy levels, whereas the mass of particles in quantum wells has a significant impact.Numerical calculations have demonstrated that for an abrupt change in particle mass at the well-barrier interface, the first derivative of the wave function satisfies the BenDaniel-Duke boundary conditions.Wave function moduli in the coordinate domain have been constructed for the lowest energy levels.This indicates strong charge carrier localization in quantum wells.