Spin–orbit splittings in AlN, GaN and InN

We have calculated the spin–orbit splittings of the top valence bands of AlN, GaN and InN crystallized in the zinc blende structure, using the LMTO–LDA method. Because of the large differences in the atomic splittings of cations and anions, and the core d levels of Ga and In, these materials are ideal to investigate anomalies in the valence band splittings. We have obtained strong deviations from the Δ1≃(2/3)Δ0 rule and extremely anomalous dependences of Δ1 and Δ0 on volume for GaN and InN. Such effects should also appear in the wurtzite counterparts of these nitride semiconductors.