Commutativity and transitivity of GaAs-AlAs-Ge(100) band offsets

X-ray photoemission spectroscopy is used to measure the valence-band offset Δ$E_v$ for in situ molecular-beam-epitaxy–grown heterojunctions involving AlAs, GaAs, and Ge. Commutativity is found by the equivalence of the Al(2p)-Ga(3d) energy separation (54.65±0.05 eV) for the AlAs-GaAs(100) junction independent of the growth sequence. Transitivity is satisfied by the zero (0.05±0.15 eV) sum of the core-energy separations for AlAs/Ge, GaAs/AlAs, and GaAs/Ge junctions. The band offsets for GaAs-AlAs are more evenly divided between valence and conduction band than the conventional 15–85 % distribution, respectively.