Resonant states in quantum wells: theoretical analysis of the density of states and phase times

Abstract

The existence of sharp resonant states in a single quantum well separated from its semi-infinite substrate by a barrier layer is reported here. These resonances appear as well defined peaks in the density of states. The local and total densities of states are obtained from an analytical determination of the Green functions. The expressions of the transmission and reflection phase times are also derived and compared to the density of states. The positions of the peaks in the density of states enable us to study the energy levels of resonant states as a function of the thicknesses of the barrier and well layers. Specific applications of our analytical results are given in this paper for a bilayer sandwiched between two semi-infinite GaAs and media.

Partitioned densities of states in a resonant tunnelling structure

“…A typical characteristic is that at the resonant point the transmission density of states is almost located in the well. These results are confirmed by the explicit expression dn 21 (x)/dE = (T /2) dn(x)/dE given in reference [22], since at the resonant point the total density of states has a maximum peak in the well [23] as shown in figure 9, later. When the reflection probabilities increase, the LPDOS dn 11 (x)/dE becomes larger in the region I than those in the regions II and III .…”