Tunneling calculations for gallium-arsenide - aluminum(x)gallium(1-x)arsenide graded band-gap sawtooth superlattices

Quantum mechanical tunneling calculations for sawtooth and step-barrier AlGaAs superlattices are performed by means of a transfer matrix method, within the framework of the effective mass approximation. The transmission coefficient and tunneling current are computed for several representative structures. The Stark shift of bound states of single quantum wells is also calculated in order to clarify the effects of the spatial extent of applied electric fields on tunneling calculations.; Sawtooth and step-barrier superlattices are found to share some tunneling characteristics. Both structures can exhibit resonant tunneling, manifested by the correlation of peaks and regions of negative differential resistance in current-voltage curves with peaks in transmission resonance spectra. The shift of the resonances of step-barrier superlattices is a linear function of the field however, while in sawtooth superlattices the shift is not a simple function of the field. This is a consequence of the different ways in which the two structures deform under uniform electric fields: the sawtooth deforms into a staircase, at which field strength all barriers to tunneling are eradicated. The step-barrier superlattice always presents some barrier to tunneling no matter how high the electric field strength.; Effective mass variations in semiconductor heterostructures should not be neglected in tunneling calculations. Conventional wave function boundary conditions at interfaces must be modified to conserve the probability current density when the mass is discontinuous. The range of effective mass in AlGaAs heterostructures is found to affect the outcome of tunneling calculations significantly.; The applied electric field must be realistically modeled if the results of tunneling calculations are to apply to real superlattices. If the applied field is limited in extent to the area in and around a single quantum well, the Stark shift is linear in the field. If the field is assumed infinite in extent, the Stark shift obtained is quadratic. The same applies to the shift of resonances in step-barrier superlattices. Since experimental superlattices are subjected to localized fields, the assumption of infinitely extended fields should not be adopted in tunneling calculations for these structures.