III-V semiconductor compounds - band gap approximations

Question

I'm looking for the most common and accurate approximation functions for III-V semiconductor compounds. So far, I found two (InGaAs as the sample compound):

1. The simplest one: $E(Ga_{1-x}In_xAs)=(1-x)E_{GaAs}+x \cdot E_{InAs}$

2. Binomial: $E(Ga_{1-x}In_xAs)=(1-x)E_{GaAs}+x \cdot E_{InAs} - b \cdot x \cdot (1-x)$

For InGaAs, b=1.44

Are there more? I mean the methods for which the parameters can be found in articles, not measured by myself. When using the first one is sufficient? Do the scientists bother to calculate next corrections? Are they useful?

Answer 1

I have been reading a bit about III-V compounds since I posted this question and it seems that the binomial approximation is sufficient in most, if not all, cases.