Calculating Transmission Coefficient on Superlattice Structure Using Propagation Matrix Method

Abstract

The tunneling effect is a phenomenon where the particle can penetrate the barrier potential even though the particle energy is smaller than the barrier potential value. The probability of an electron to penetrate the barrier potential depends on the transmission coefficient. This study aims to investigate the transmission coefficient on the superlattice structure. The studied superlattice structure is formed from 12 potential barriers which are divided into two types of barriers (barrier A and barrier B). Thus, the periodicity of this superlattice is the periodicity of the two types of barrier potentials that align to each other. The transmission coefficient was calculated numerically using the matrix propagation method with the support from MATLAB R2009a software. The variations in the value of the barrier potential A are 5 eV, 10 eV, and 15 eV, while the variations in the value of the barrier potential B are 5 eV and 10 eV. Subsequently, the concept of electron effective mass is also included once in the state of barrier potential A (B) of 5 eV (10 eV). To observe clearly the miniband and minigap, the electron energies were varied from 0 eV―15 eV. The exception is when it involves the concept of electron effective mass where the electron energy is varied from 0 eV―30 eV. Based on the results of numerical computations, the graph of relation between transmission coefficient and electron energy showed that minigap and miniband are also formed in this structure. The width of the minigap from the first to next does not increase continuously, but changes iteratively from small to large and so on. When the concept of effective mass of electrons is taken into account, the electron energy range under test must be set higher so that it is clear whether the miniband and minigap are alternately formed.