The acceptor binding energy is calculated to find out the best acceptor impurity in InN, GaN and AlN. Be is predicted to be the shallowest acceptor and the next are Mg and Zn. Group IV elements such as C or Si are very deep. Band lineup is calculated to be ΔEc : ΔEv = 2.1 eV : 0.76 eV = 0.73 : 0.27 = 2.8 : 1 for GaN/AlN and ΔEc : ΔEv = 0.88 eV : 0.66 eV = 0.57 : 0.43 = 1.3 : 1 for GaN/InN. GaN is grown on GaAs and GaP-coated Si substrate by MOCVD. GaAs intermediate layer gives better GaN compared to GaP intermediate layer. It is suggested that the lower bulk modulus of GaAs than that of GaP gives this difference.