  We propose a simple and effective approach to construct the empirical
tight-binding parameters of ternary alloys in the virtual crystal
approximation. This combines a new, compact formulation of the strain
parameters and a linear interpolation of the hamiltonians of binary materials
strained to the alloy equilibrium lattice parameter. We show that it is
possible to obtain a perfect description of the bandgap bowing of ternary
alloys in the InGaAsSb family of materials. Furthermore, this approach is in a
good agreement with supercell calculations using the same set of parameters.
This scheme opens a way for atomistic modeling of alloy-based opto-electronic
devices without extensive supercell calculations.
