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In the present paper, the lattice structure, band structure and density of state of LaAlO3 and LaAlO3:Mg are calculated by first-principle method based on density functional theory. Firstly, we select the different cutoff energy and k-point grid in the calculations, and obtain the most stable geometry structure of single crystal LaAlO3. The calculated lattice parameters are a=b=5.441 Å, c=13.266 Å, which matches with experimental values. To deeply understand the electronic structure of LaAlO3, a 2×1×1 super-cell structure is established and the doping concentration of Mg at Al sites is 25%. From the band structure and density of states, it can be seen that LaAlO3 has a direct band gap Eg=3.6 eV. However, LaAlO3:Mg has a larger band gap Eg=3.89 eV and the Fermi level enters into the valence band, which indicates the holes are introduced. The calculated results show that the conductivity of LaAlO3:Mg is better than pure LaAlO3, which is in good agreement with experimental results.

In the present paper, the lattice structure, band structure and density of state of pure and P-doped ZnO are calculated by first-principle method based on density functional theory. By analyzing the Mulliken charge overlap population and bond length, it is found that the bond of P-Zn is longer and stronger than O-Zn bond for PO-ZnO. But for PZn-ZnO, the O-P bond becomes shorter and more powerful than O-Zn bond. Also, weak O-O bonds are formed in this case. Our results show that the final total energy of PO-ZnO is lower than PZn-ZnO. The lattice structure of PO-ZnO is more stability than PZn-ZnO. For PO-ZnO, The Fermi level moves into the valence band, which expresses that the holes appear on the top of valence band and thus the PO-ZnO exhibits p-type conductivity. For PZn-ZnO, the Fermi level moves up to the conductor band and the total density of states shifts to the lower energy region, thus PZn-ZnO shows the n-type conductivity.

Density functional theory plane-wave pseudopotential with the general gradient approximation (GGA) was used to investigate electronic structural properties and the bulk spontaneous polarization (Ps) of PbZr0.4Ti0.6O3. It is found that there are strong hybridizations between Ti 3d states or Zr 4d states and O 2p states, which can reduce short-range repulsion in atoms and enhance the stability of the ferroelectric phase of PbZr0.4Ti0.6O3. Compared with cubic ideal structure, the calculated internal electronic structural data indicate that the slightly distorted O6 octahedrons around the central Ti and Zr atoms change to the Ti-O5 and Zr-O5 pyramid in the optimized structure, respectively. The major contribution to the spontaneous polarization along [001] comes from the stronger interaction along the c axis between the Ti and O rather than the Zr and O ions. The Pb atom’s relative displacement of oxygen octahedral implies that the Pb-O bonding interaction is also a key factor impacting the ferroelectricity of PbZr0.4Ti0.6O3. A theoretical spontaneous polarization of 0.78 C/m2 was computed in the tetragonal PbZr0.4Ti0.6O3 along [001] direction, consistent with the single crystal experimental data.