I–V characteristic of a truncated parabolic barrier

Transport in a nanostructure across a truncated parabolic barrier located along the width of a thin layer sandwiched by semiconductor reservoirs is examined. Contrary to the case of a square barrier upon application of dc voltage the height of the barrier diminishes. This peculiarity provides additional interest in the parabolic barrier study. Utilizing the combined barrier potential energy together with the one from the external field in the relevant Schrödinger equation we are able to obtain the corresponding scattering solution, in closed form, and thereby the transmission coefficient in terms of the applied voltage. Furthermore, applying the Tsu–Esaki formalism we are led to the required I – V characteristic, which exhibits regions of negative differential resistance. We consider cases whereby the carrier effective masses in the two reservoirs differ from each other, while the carrier effective mass in the thin obstructive layer is larger than each of them. With differing effective masses in the reservoirs larger peak to valley ratio is achieved. Also, larger peak to valley ratio results by narrowing the barrier layer thickness.