2.3.3 Interpolation Schemes

Material parameters of Si, Ge, GaAs, InP, GaP, InAs, and InGaAs, as well as to some extent SiGe and AlGaAs, have received considerable attention in the past and many experimental data and theoretical studies for these parameters can be found in the literature. On the other hand, the band structure and transport related parameters of other III-V ternary and all quaternary materials has been the topic of few or no experimental/theoretical publications. These facts necessitate the use of some interpolation scheme, essentially based on known values of the physical parameters for the related basic materials and alloy materials. In the cases when experimental data scatters the most consistent or most recent published data has been adopted. In the cases when experimental data is inconsistent or missing Monte-Carlo (MC) simulation has been considered. Although the interpolation scheme is still open to experimental or MC verifications, it provides more useful and reliable material parameters for numerical device simulation over the entire range of alloy composition.

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.