Study of resonant tunneling structures: A hybrid incremental Airy function plane-wave approach

A numerical procedure for the calculation of the electron tunneling current through an arbitrary potential profile has been developed. It involves subdividing the profile into a number of strips for which a linear approximation of the potential is appropriate. A solution of the Schrödinger equation in the form of Airy functions is obtained. These functions are linked through boundary conditions at the interface of the strips. An expression for the transmission coefficient of the structure is obtained. The approach is found to accelerate the calculation of the electrical characteristic of resonant tunneling devices. An analysis is performed of tunneling through parabolic quantum-well and half-parabolic quantum-well structures in the presence of an electric field. The room-temperature current-voltage characteristic for the half-parabolic quantum-well structure is calculated and is found to be rectifying with multiple peaks and regions of negative differential resistance. It is also found to have a relatively high peak-to-valley ratio and high peak current density.