Energy band and acceptor binding energy of GaN and Al_xGa_1-xN

The hole effective-mass Hamiltonian for the semiconductors of wurtzite structure is established, and the effective-mass parameters of GaN and Al_xGa_1-xN are given. Besides the asymmetry in the z and x, y directions, the linear term of the momentum operator in the Hamiltonian is essential in determining the valence band structure, which is different from that of the zinc-blende structure. The binding energies of acceptor states are calculated by solving strictly the effective-mass equations. The binding energies of donor and acceptor for wurtzite GaN are 20 and 131, 97 meV, respectively, which are inconsistent with the recent experimental results. It is proposed that there are two kinds of acceptors in wurtzite GaN. One kind is the general acceptor such as C, substituting N, which satisfies the effective-mass theory, and the other includes Mg, Zn, Cd etc., the binding energy of which deviates from that given by the effective-mass theory. Experimentally, wurtzite GaN was grown by the M BE method, and the PL spectra were measured. Three main peaks are assigned to the DA transitions from the two kinds of acceptor. Some of the transitions were identified as coming from the cubic phase of GaN, which appears randomly within the predominantly hexagonal material. The binding energy of acceptor in AlN is about 239, 158 meV, that in Al_xGa_1-xN alloys (x ≈ 0.2) is 147, 111 meV, close to that in GaN.