The valence band offsets ΔE_v(x) as a function of the alloy compositon x of two typical lattice matched ternary alloy heterojunctions (AlP)_x(Si₂)_1-x/GaP and (GaP)_x(Si₂)_1-x/GaP are studied by using the average bond energy theory in conjunction with the cluster expansion method.It is shown that the variations of ΔE_v(x) at (AlP)_x(Si₂)_1-x/GaP and (GaP)_x(Si₂)_1-x/GaP are nonlinear and non monotonous.The calculated results of ΔE_v are in very good agreement with the data previously reported.

Based on an ab initio pseudopotentials band structure method,a theoretical approach of tak-ing the average-band energy as a energy reference is suggested to determine the valence-band offsets at Si/Ge heterojunctions under three different strain conditions:using Si as a substrate,using Ge as a substrate and Si-layer,Ge-layer deforming freely.The results are 0.731eV,0.243eV and 0.521eV respectively,in good agreement with relevant experimental values.