First-principles investigation of isolated band formation in half-metallic ${\mathrm{Ti}}_x{\mathrm{Ga}}_{1-x}\mathrm{P}(x=0.3125–0.25)$

Several alloy semiconductors containing a transition metal atom of the type $M{\mathrm{Ga}}_4{X}_3$ with $X=\mathrm{As}$ or P and $M=\mathrm{Sc}$ or Ti have been found previously to present an isolated partially filled intermediate band within the usual band gap of the host semiconductors and have been proposed as highly efficient photovoltaic materials. In this paper, we carry out an ab initio investigation of band structures and electronic properties for the more chemically stable ${\mathrm{Ti}}_x{\mathrm{Ga}}_{1-x}\mathrm{P}$ compound as a candidate for isolated intermediate band formation. We have calculated the electronic structures using self-consistent density functional theory method in both local density approximation and generalized gradient approximation (GGA) approaches and compared the GGA results with those obtained with the exact exchange method that we have implemented in the code SIESTA. Using spin-polarized localized wave functions to represent the valence electrons states and nonlocal pseudopotentials for the core electrons, we have also studied in detail the ${\mathrm{Ti}}_x{\mathrm{Ga}}_{1-x}\mathrm{P}$ compounds at different dilution levels of the Ti transition metal atom $(x=3.125\%,6.25\%,12.5\%,25.0\%)$ and for two (cubic and tetragonal) different crystal cells. Results at the different dilutions show in all cases a fully spin-polarized structure and, except for the case of immediate Ti neighbors, indicate a rather small spin coupling between Ti atoms and confirm the presence of the isolated narrow partially filled intermediate band for this compound. They also show the higher suitability of isotropic crystal structures for obtaining in these materials the intermediate band with the desired small band width.

Figure 1

$\mathrm{Ti}{\mathrm{Ga}}_3{\mathrm{P}}_4$ total density of states (solid lines) and Ti $d$ orbital-projected partial density of states (dotted lines), for (a) spin nonpolarized and (b) spin-polarized fully relaxed GGA calculations. Energies are measured in eV and Fermi levels have been set at the energy zero.

Figure 2

Nonpolarized electronic band structure for $\mathrm{Ti}{\mathrm{Ga}}_3{\mathrm{P}}_4$ calculated with GGA (a) and EXX (b) method displayed in the main directions of the Brillouin zone of the parent fcc structure. The horizontal line denotes the position of the Fermi level $(E_F=0\mathrm{eV})$.

Figure 3

Polarized band structure of 25% Ti atom dilution, as calculated with an eight-atom cubic cell using LDA (upper panel) and GGA (lower panel) represented in the corresponding fcc directions. In both cases, the majority spin is displayed on the left and the minority on the right sides. Fermi level is displayed by a horizontal line and set at the energy zero.

Figure 4

Total density of states (solid lines) and Ti atoms $d$ orbitals projected density (dashed lines) obtained for calculations on the 64-atom cell: (a) $\mathrm{Ti}{\mathrm{Ga}}_{31}{\mathrm{P}}_{32}$,; (b), (c), (d), and (e) ${\mathrm{Ti}}_2{\mathrm{Ga}}_{30}{\mathrm{P}}_{32}$ with Ti orderings of CC, FC, EC, and CP types, respectively.

Figure 5

GGA full relaxed spin polarized band diagrams of the majority (solid lines) and minority bands (dashed lines) obtained for (a) $\mathrm{Ti}{\mathrm{Ga}}_7{\mathrm{P}}_8$ and (b) ${\mathrm{Ti}}_2{\mathrm{Ga}}_6{\mathrm{P}}_8$ (16-atom tetragonal cells) displayed in directions corresponding to those of high symmetry in the Brillouin zone of the parent fcc structure. The horizontal line denotes the position of the Fermi level $(E_F=0\mathrm{eV})$.