Bowing in quaternary alloys

Band gap bowing occurs in ternary and quaternary alloys as it does in binary and pseudobinary alloys. The behavior of quaternary alloys and can be treated in the same way. For a typical quaternary of the form Ai xBxCyDi y, Equation 6.13 for the energy of a specific part of the band stractrrre (for example, the direct gap) can be generalized to [2]  

Here Eabcd is the energy of a given band in the quaternary and Eabd, Eabc, Eacd and Ebcd are the energies of the same band that would have been detErmined from Equation 6.13 for each individual pseudobinary alloy. Thus, Equation 6.17 is a linear interpolation of the pseudobinary alloy values. This approach produces a reasonable estimate of the gap values. [2] There are other methods for estimating the alloy energy gap that increase the effective bowing but the performances of these methods are not particularly improved. 

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