Finite-element calculation of the transmission probability and the resonant-tunneling lifetime through arbitrary potential barriers

A numerical method for the calculation of the transmission probability through a potential barrier or structure and of the lifetime of a resonant state in a double- or multiple-barrier structure is presented. This method is based on a combination of the finite-element method and the analytical approach. A generalized boundary condition of the heterointerface is introduced by use of the interface matrix, and thus the method is applicable to the potential barriers made of arbitrary semiconductors. The validity of the method is confirmed by calculating the transmission probability of rectangular potential barriers and double barrier structures. Numerical results on sinusoidal barriers and voltage-applied barriers are also presented.>