We present a nearest neighbor sp3d5 tight binding study on the external pressure, lattice mismatch and thermal expansion gradient induced interface strain effects on band offsets in II-VI/III-V heterostructures with normal interfaces (e.g., ZnSe/GaAs and HgTe/CdTe) and inverted interfaces (e.g., GaAs/ZnSe and CdTe/HgTe). We screen the valence band energies by the optical dielectric constants of semiconductors at any temperature, pressure, strain,, and alloy composition and then find the band offsets are obtained by matching an average sp3d5 tight binding midgap level, at which the antibonding and bonding states are equal at heterointerface. The sp3 tight binding midgap level is defined at a special point (Baldereschi special point) in the forbidden gaps of constituents. This allows the inclusion of the effects of high symmetry point conduction and valence energy band structure band minimums on defining the thermal equilibrium across the heterointerfaces. Model predictions compare well with the experiment for the band offsets of many lattice matched and mismatched II-VI/II-VI isovalent and II-VI/III-V heterovalent heterostructures. The model predicts that the growth orientation dependence of band offsets for lattice matched heterostructures is due to the change in sign of lattice thermal expansion gradient induced strain across the interface and that in mismatched heterostructures is due to the change in sign of lattice mismatch strain. The electron-phonon interaction has very little effect on the valence band offsets but some effects on conduction band offsets as temperature is increased. Furthermore, the model also predicts that there is a crossover for the band offsets at HgTe/CdTe at pressures about 50 Kbar; becomes smaller than above 50 Kbar.

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