Analysis of Resonant Tunneling for Parabolic Double Barrier Structure

Abstract

In this paper the resonant tunneling through the double barrier structure with the parabolic quantum well is studied theoretically. The transmission coefficient for such a structure as a function of applied voltage and the current-voltage characteristics are calculated and compared with those for the double barrier structure with the rectangular quantum well. The conclusion is that the resonant tunneling through parabolic double barrier structure can be used as a method of determination of the conduction band offset of the barrier and the well materials.PACS numbers: 73.40.Gk Recently, quantum structures with graded confining potential have received a great deal of interest, both from the point of view of their physical properties as well as from the point of view of their potential applications. The parabolic quantum-well structures were studied mainly by means of photoluminescence excitation spectroscopy [1]. This method allows us to determinate the partitioning of the energy gap discontinuities between the conduction and the valence bands. The resonant tunneling through the GaAs-AlGaAs double barrier structures (DBS) with a wide parabolic quantum well was also reported [2,3].Since its first observation in 1974 [4] the resonant tunneling has been studied theoretically only for the double barrier structures with a rectangular well between the barriers. The purpose of the present paper is an analysis of this phenomenon for the double barrier structures with the parabolic well. The considered one-dimensional potential profile is shown in Fig. 1 for unbiased and biased structures. The curvature of the well is determined by the height V0 of the barrier and the half-width w of the well.The global transmission coefficient, TG, for the structure under constant electric field, F, was calculated by the standard method, i.e., by matching the electron wave functions and their derivatives at the points of discontinuity of potential [5]. The electron wave functions were taken as linear combinations of the Airy functions in the barrier regions (379)