Resonant tunneling: A method for simultaneous determination of resonance energy and energy eigenvalue

Assuming an effective mass approximation and using Bastard's boundary conditions, a simple method for simultaneous determination of the energy levels forming the sub-band structure and the transmissions coefficient of non-symmetrical, non-periodical potential semiconducting heterostructure is being proposed. The method can be applied on a multilayer system with varying thickness and effective mass of the layers, and with potential that is neither periodical nor symmetrical. To illustrate the feasibility of the proposed method, cases of symmetrical rectangular triple-barrier structure with constant effective mass, multi-barrier semiconductor heterostructure (nine barriers–eight-wells), and monomer height barrier superlattices (300 barriers) systems have been examined. Findings show very good agreements with previously published results obtained by different methods on similar systems. The proposed method was found to be useful for any number of semiconducting layers arranged in any random way making it more realistic, simple, and applicable to superlattice analysis and for devices design.