3.5.3 Transfer-Matrix Method

The use of the transfer-matrix (TM) method for the calculation of the transmission coefficient of energy barriers is based on the work of TSU and ESAKI on electron tunneling through one-dimensional super lattices [99]. It has been used by numerous authors to describe tunneling processes in semiconductor devices [140,141,142,143,144]. The basic principle of the transfer-matrix method is the approximation of an arbitrary-shaped energy barrier by a series of piece-wise constant or piece-wise linear functions. Since the wave function in such barriers can easily be calculated, the total transfer matrix can be derived by a number of subsequent matrix computations. From the transfer matrix, the transmission coefficient can easily be derived.


A. Gehring: Simulation of Tunneling in Semiconductor Devices