Controlled electron transmission by lead chalcogenide barrier potential

Transmission of electrons across a rectangular barrier of IV-VI semiconductor compounds is considered. Conduction electrons arrive at the barrier and are reflected or transmitted through it depending on the relative values of the barrier potential $V_b$ and the electron energy $E$. The theory, in close analogy to the Dirac four component spinors, accounts for the boundary conditions on both sides of the barrier. The calculated transmission coefficient $T_C$ is an oscillatory function of the barrier voltage varying between zero (for full electron reflection) and unity (for full electron transmission). Character of electron wave functions outside and inside the barrier is studied. There exists a total current conservation, i. e. the sum of transmitted and reflected currents is equal to the incoming current. The transmission $T_C$ is studied for various barrier widths and incoming electron energies. Finally, the transmission coefficient $T_C$ is studied as a function of $V_b$ for decreasing energy gaps $E_g$ of different Pb$_{1-x}$Sn$_x$Se compounds in the range of 150 meV $\geq E_g \geq$ 2 meV. It is indicated that for very small gap values the behaviour of $T_C$ closely resembles that of the chiral electron tunneling by a barrier in monolayer graphene. For $E_g$ =0 (Pb$_{0.81}$Sn$_{0.19}$Se) the coefficient $T_C$ reaches the value of 1 independently of $V_b$.