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difference in energy between the several tetrahedral types is much greater than kT for many types of tetrahedrals. Taking into account the effects of the resulting short-range order (SRO) makes the calculation of the mixing enthalpy difficult, since it couples the two factors [Ich86]. These problems can be surmounted by considering a large ensemble of several hundred atoms with the positions of each allowed to relax while maintaining a relatively simple calculation by considering only the dilute limit, where the effect of the SRO is negligible [Sch91, Ho96]. This approach was developed specifically for dealing with systems with very low solubility limits, in particular for the solubility of the very small N atom in conventional III/V semiconductors such as GaAs, InP, GaP, and so forth.

2.2.1.5 First-Principal Models

Advances in fundamental insight for the energy of a semiconductor lattice and the methodology of solving mathematical problems of large matrices have been achieved recently due to the availability of high-powered computers.

These achievements can make possible the first-principle local density selfconsistent total energy minimization calculations in semiconductor alloy systems [Zun94]. Using these quantum mechanical calculations, the thermodynamics of semiconductor solid solutions can be calculated without any of the extreme simplifying approximations necessary to obtain simple analytic models.

The total energy minimization calculations are based on the entire complex band structures. The results from such calculations are included in Table 2-4. The mixing enthalpies have also been calculated for InxGa1-xN, InAlN, and AlGaN alloys using a pseudopotential perturbation approach [Ito97].