Electrical transport in semiconductor superlattices is studied within a fully self-consistent quantum transport model based on nonequilibrium Green functions, including phonon and impurity scattering. We compute both the drift velocity-field relation and the momentum distribution function covering the whole field range from linear response to negative differential conductivity. The quantum results are compared with the respective results obtained from a Monte Carlo solution of the Boltzmann equation. Our analysis thus sets the limits of validity for the semiclassical theory in a nonlinear transport situation in the presence of inelastic scattering.
The dc current in strongly coupled superlattices can either be described in a semiclassical picture in terms of miniband transport or in a quantum mechanical theory based on hopping transitions between the localized wave functions of the Wannier-Stark ladder. We demonstrate the equivalence of both models in the field regime of Bloch-oscillating electrons. Combining these two pictures we calculate the superlattice drift velocity resulting from microscopic phonon scattering between the Wannier-Stark levels. Our results show that previous discussions of the temperature dependence of the drift velocity have to be revised drastically.
͓S0163-1829͑99͒05011-0͔Electronic transport in man-made semiconductor superlattices offers a wide range of new high-field phenomena that cannot be observed in conventional bulk semiconductors: Due to the large superlattice constant d and the small width of the resulting minibands, electric fields F at which the potential drop per superlattice period eFd is comparable to or even larger than the miniband width can be easily obtained. Furthermore, scattering in these structures can be strongly reduced compared to bulk material by designing the miniband width ⌬ to be smaller than the optical-phonon energy. If the resulting scattering rate 1/ becomes lower than the Bloch frequency B ϭeFd/ប, the electrons perform Bloch oscillations in the mini-Brillouin zone.As Bloch-oscillating electrons do not contribute to a net current through the superlattice structure, negative differential conductivity ͑NDC͒ can be observed at moderately high fields. While this was explained as early as 1970 by Esaki and Tsu 1 within a semiclassical miniband model, Tsu and Döhler 2 soon afterwards proposed a quantum-mechanical explanation of this phenomenon, which is based on the fieldinduced localization of the superlattice wave functions. In analyzing their experimental results, 3,4 most of the authors came to the conclusion that the semiclassical momentum space picture ͑the Esaki-Tsu model or more sophisticated approaches 5,6 ͒ provides the correct description for wide minibands, whereas the quantum-mechanical real-space picture was assumed to be correct for narrow minibands only. Based on our recent detailed study of the hopping transport, 7 we claim that the applicability of this picture depends rather on the field range than on the miniband width.Our goal in this paper is to provide a consistent scheme for a quantitative description of transport in strongly coupled superlattices for the whole range of fields and temperatures, combining the semiclassical momentum space ͑or Boltz-mann͒ picture with the quantum-mechanical hopping picture. Taking advantage of the correspondence between the hopping picture and the semiclassical description in terms of electrons performing Bloch oscillations at moderately high fields, we are able to establish a link between the high-field hopping drift velocity and two fundamental quantities describing miniband transport, i.e., the momentum-relaxation time M and the energy-relaxation ti...
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