| Summary: | Using first-principles approach, we calculated the band gaps of wurtzite $ {\rm Be}_{1-x} $ Cd $ _x{\rm O} $ ternary alloy and the band offset of the lattice matched $ {\rm ZnO}/{\rm Be}_{0.44}{\rm Cd}_{0.56}{\rm O}[1\,1\,\overline {2}\,0] $ heterojunction, where the modified Becke–Johnson semi-local exchange was used to determine the band gap and the coherent potential approximation was applied to deal with doping effect in disordered alloys. The $ {\rm ZnO}/{\rm Be}_{0.44}{\rm Cd}_{0.56}{\rm O} $ heterojunction was determined to have a type II band alignment, with valence and conduction band offset being 0.28 and 0.50 eV, respectively. The calculation approach and procedure demonstrated here can be used to predict the band offset of more lattice matched semiconductor heterojunctions.
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