On Resonant Tunnelling in the Biased Double Delta-Barrier

Abstract

The solution of the one-dimensional Schrödinger wave equation is presented for the potential-energy function that describes a double delta-barrier under the application of a constant electrical field perpendicular to it. The transfer matrix technique is employed to determine the transmission coefficient in an analytical form. Some attributes of the transmission coefficient are established. The transmission coefficient is shown to exhibit maxima and minima, the conditions for maxima and minima in the transmission coefficient are discussed. The current-voltage characteristic of the biased double delta-barrier is calculated numerically. It is found to exhibit the same oscillatory behaviour as the transmission coefficient when the voltage applied to the double delta-barrier is increased. The width of the double delta-barrier is shown to modulate the peak-to-valley ratio in the current-voltage characteristic.

Effects of two successive parity-invariant point interactions on one-dimensional quantum transmission: Resonance conditions for the parameter space

“…Since the leading work in [39], the basic features had been investigated theoretically [40,41] and experimentally [42]. These studies have motivated various subsequent works; realistic effects on the resonant tunneling were discussed in [43,44,45,46,47,48,49], and some different theoretical methods which can deal with an arbitrary finite periodic potential were developed in [50,51,52,53,54,55]. Furthermore, the resonant tunneling is still an active area of research for the applications to high-frequency oscillators in recent years [56,57,58].…”

Relativistic two-particle equations with superposition of delta-shell potentials: scattering and bound states

“…Delta-function potentials attract much attention in the non-relativistic theory [9,10,11,12,13,14]. As a physical model, the delta-function potential is used to represent a potential whose spatial extension is very small compared to all other length scales.…”

Transmission Properties of the One-Dimensional Array of Delta Potentials

“…The problem of one-dimensional delta-function potential array has been studied in previus works 13,14,15,16,17 . In reference 13 they use a field-theoretic approach to obtain the transfer matrix in terms of a propagator.…”

“…The problem of one-dimensional delta-function potential array has been studied in previus works 13,14,15,16,17 . In reference 13 they use a field-theoretic approach to obtain the transfer matrix in terms of a propagator. In references 14,15,16,17 the case of two delta-function potentials is studied using a quantum-mechanical approach. We use a similar aproach to develop a convenient way to deal with the problem, based in a transfer matrix methodology.…”