The effect of level broadening on the tunneling of electrons through semiconductor double-barrier quantum-well structures

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Abstract
Scattering and well-width nonuniformities in double-barrier structures introduce level broadening, particularly in the quantum-well region, and the effect of this level broadening on coherent and sequential transmission of electrons through these structures has been examined. First, it is shown that resonant energies are eigenenergies of the overall system, so that it is the same energy level which is involved in both tunneling mechanisms. This explains why the negative differential resistance (NDR) peak occurs at the same voltage for coherent and sequential tunneling. Expressions for the transmission coefficients and, consequently, for the current density are derived, and it is shown that the effect of broadening is to reduce the peak current and the peak-to-valley ratio for both tunneling processes, this reduction being quite remarkable for the case of coherent tunneling through the structures with thick barriers. Based on this, ways are suggested to distinguish between the two tunneling phenomena. This broadening-induced reduction in peak current and peak-to-valley ratio leads to a reduction in the NDR-related maximum operating frequency in these structures. On the other hand, the effect of broadening on coherent tunneling itself is to reduce the resonant tunneling time, thus allowing higher-frequency operation in optical devices. Above a critical amount of broadening the assumption of coherent tunneling breaks down, and sequential tunneling takes over. Critical broadenings for a number of cases are estimated. It is emphasized that the form of the NDR and hence the frequency response is dependent on whether the emitter density of states is two- or three-dimensional-like.