Electronic structure and transport properties of GaAs-GaAlAs superlattices in high perpendicular electric fields

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Abstract
We present a study of the effect of high (∼1×105 V/cm) perpendicular electric fields on the electronic structure of a GaAs-Ga0.7Al0.3As superlattice represented by five quantum wells separated by 70-Å barriers. An exact solution is obtained by using the transfer-matrix technique to match the Airy functions at the interfaces. The method of phase-shift analysis is employed to evaluate the energy levels, the width of the Stark resonances, the real-space wave functions, and the time of flight associated with the field-induced phenomena. Wells of 50- and 70-Å width are used to elucidate the relationship between level depth and field. The quantum states above the semiclassical confining barrier, which have so far been represented by a continuum, are correctly accounted for. These states are mainly localized in the barrier material. It is shown that the real-space localization and bandwidth of these states are significantly altered by the external field. In particular, we evaluate the time delay for electrons above the barrier due to the field-induced change in the density of states, which is related to the presence of the above higher-lying confined states and which would be observed in current–voltage measurements.