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As mentioned often before, a knowledge of the pseudopotentials for superlattices is required at many more points than the small discrete set akin to bulk materials. With this aim, the pseudopotentials of Mader and Zunger [253], which have been shown to reproduce many experimentally measured parameters as well as the results of ab initio calculations, will be employed. The required continuous nature of these potentials is illustrated in Fig. 12.6 for both atomic species in GaAs and AlAs. Again, notice how the atomic potential of As in GaAs is different from that in AlAs. This difference, A V f ( q ) = VfsinGaAs(q) - V f A s i n A l A s (q), is plotted in Fig. 12.7, just

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Figure 12.6 The continuous atomic pseudopotentials of GaAs (left) and AlAs (right) of Mader and Zunger [253]

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to re-emphasise the point made in Section 11.8, namely that unfortunately, universal atomic potentials do not actually exist. Fig. 12.8 shows the band structures of bulk GaAs and AlAs, ignoring spin orbit coupling, as produced from the continuous potentials. Both band structures have been translated upwards in energy such that the top of the valence band of GaAs is at zero. At the same time, the top of the valence band for AlAs is at 0.51 eV, which gives the offset in the valence band as 33 % of the total, in line with experimentally determined values (see for example [14], p. 179), and recent calculations (see for example [256]). This illustrates an important point, namely that the correct choice of potentials can not only just be used to reproduce experimental data for bulk material, but in addition they can retain information on the alignment (or band offset) of two dissimilar materials.

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Figure 12.8 The bulk band structures of GaAs (left) and AlAs (right), illustrating the valence band offset built into the potentials of Mader and Zunger [253]

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