  Using first-principles calculations, we show that the conduction and valence
band energies and their deformation potentials exhibit a non-negligible
compositional bowing in strained ternary semiconductor alloys such as InGaAs.
The electronic structure of these compounds has been calculated within the
framework of local density approximation and hybrid functional approach for
large cubic supercells and special quasi-random structures, which represent two
kinds of model structures for random alloys. We find that the predicted bowing
effect for the band energy deformation potentials is rather insensitive to the
choice of the functional and alloy structural model. The direction of bowing is
determined by In cations that give a stronger contribution to the formation of
the In$_{x}$Ga$_{1-x}$As valence band states with $x\gtrsim 0.5$, compared to
Ga cations.
