Electronic structures and optical properties of HfO_2–TiO_2 alloys studied by first-principles GGA + U approach

The phase diagram of HfO_2–TiO_2 system shows that when Ti content is less than 33.0 mol%, HfO_2–TiO_2 system is monoclinic; when Ti content increases from 33.0 mol% to 52.0 mol%, it is orthorhombic; when Ti content reaches more than 52.0 mol%, it presents rutile phase. So, we choose the three phases of HfO_2–TiO_2 alloys with different Ti content values. The electronic structures and optical properties of monoclinic, orthorhombic and rutile phases of HfO_2–TiO_2 alloys are obtained by the first-principles generalized gradient approximation(GGA) +U approach, and the effects of Ti content and crystal structure on the electronic structures and optical properties of HfO_2–TiO_2 alloys are investigated. By introducing the Coulomb interactions of 5 d orbitals on Hf atom(U_1~d), those of 3 d orbitals on Ti atom(U_2~d), and those of 2 p orbitals on O atom(Up) simultaneously, we can improve the calculation values of the band gaps, where U_1~d, U_2~d, and Up values are 8.0 eV, 7.0 eV, and 6.0 eV for both the monoclinic phase and orthorhombic phase, and 8.0 eV, 7.0 eV, and 3.5 eV for the rutile phase. The electronic structures and optical properties of the HfO_2–TiO_2 alloys calculated by GGA +U_1~d(U_1~d= 8.0 eV) +U_2~d(U_2~d= 7.0 eV) +U~p(U~p= 6.0 eV or 3.5 eV) are compared with available experimental results.