For many parameters, such as various lattice parameters, a linear interpolation
is sufficient. Some parameters, like the electronic bandgap exhibit a strong
non-linearity with respect to the alloy composition which arises from the
effects of alloy disorder. In such cases, a quadratic interpolation is used and
a so-called bowing parameter is introduced. For other parameters, such as
carrier mobility, a linear interpolation of the inverse values - Mathiessen
rule - is used. Finally, there are parameters, such as thermal conductivity,
for which none of the interpolation schemes mentioned so far is sufficient, and
a quadratic interpolation of the inverse values together with an inverse
bowing factor is proposed.
The bandgap bowing parameters of InAsP and GaAsP are believed to be much
smaller than those of InGaP and InGaAs [73,74]. Similarly, for
parameters where data are lacking no bowing factors are assumed.
In the following chapter, the choice of interpolation formula will largely depend on factors such as required accuracy, the physical nature of the parameter, and available experimental or MC data. For example, the bandgap energy is the most critical parameter in device modeling and a slight variation in this parameter can significantly affect the terminal characteristics of the semiconductor device.