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By using first-principles plane-wave ultrasoft pseudopotential method based on the density functional theory, the maximally localized Wannier functions of N vacancy and Al vacancy with different charge states in wurtzite AlN are calculated. With the shape and center of the computed Wannier function, the electronic structure and the spontaneous polarization of vacancy are studied respectively. The results show that N–Al bond possesses a large ionicity. It is found that the electrons of the dangling bonds displace to the positions of vacancies in N vacancy structure, while in Al vacancy structure the electrons of dangling bonds keep away from vacancies and move to the other side of N atoms. Since the vacancy breaks the centrosymmetry of the [1010] and [1210] orientations, the polarization will be induced in these two directions, and the polarization will increase as the charge increases. In the [0001] orientation, the spontaneous polarization in N vacancy will reverse as charge increases because of the dramatic variation of the electronic structure. Contrary to N vacancy, the reversion does not occur although the spontaneous polarization of Al vacancy increases as charge increases.

The stability and electronic structures of AlN nanowires with and without N-vacancy are investigated using first-principles calculations. We find that there is an inverse correlation between formation energy and diameter in ideal AlN nanowires. After calculating the formation energies of N-vacancy at different sites in AlN nanowires with different diameters, we find that the N-vacancy prefers to stay at the surface of the nanowires and it is easier to fabricate them under Al-rich conditions. Through studying the electronic properties of AlN nanowires with N-vacancies, we further find that there are two isolated bands in the deep part of the band gap, one of them is fully occupied and the other is half occupied. The charge density indicates that the half-fully occupied band arises from the Al at the surface, and this atom becomes an active centre.

The change of atom configuration in hexagonal AlN, caused by native point defects (N and Al vacancies, N and Al antisites, N and Al interstitials), are calculated firstly by plan-wave pseudopotential method with the generalized gradient approximation in the frame of density functional theory, and the most stable structure are obtained. Then the formation energy of each kind of native point defect is calculated, by which the possibilities of the six kinds of native defects to be formed during crystal growth are analyzed. Finally, the defect energy levels responding to every kind of native point defect and their electron occupancy are analyzed from the aspect of density of states. The results show that all the native defects form very deep energy levels in the band gap except N vacancy, and foreign impurities are needed to realize n- or p-type AlN. The values of defect energy levels obtained will be helpful in ascertaining the luminescence mechanism of some AlN non-band-edge emissions.