The common diagram of semiconductor band energies as a function of alloy lattice constant doesn’t apply to a heterostructure with lattice mismatched materials. In the graph below, the grey curves give the band energies for bulk materials, while the colored curves indicate the band energies for a slab of material, when strained to a substrate with a lattice constant indicated by the solid vertical line (from C. Pryor and M.-E. Pistol, Phys. Rev. B 72, 205311 (2005) ).
These are full sized pdf’s of the band diagrams for substrates with binary composition:
GaAs substrate
GaP substrate
GaSb substrate
InAs substrate
InP substrate
InSb substrate