Fe-doped ${\mathrm{CuInSe}}_2$: An ab initio study of magnetic defects in a photovoltaic material

Iron substitution in ${\mathrm{CuInSe}}_2$ could have important implications either for photovoltaic or spintronic applications. To better understand the Fe effects, we have performed density functional calculations on the ${\mathrm{CuInSe}}_2$ chalcopyrite as well as on Fe-doped derivative compounds with different concentrations and geometries. The defect formation energies of ${\mathrm{Fe}}_{\mathrm{In}}$ and ${\mathrm{Fe}}_{\mathrm{Cu}}$ substitutions for different Fe/metal concentrations (6.25% to 100%) have been determined and we have shown that these energies fluctuate with the Fe content depending on concentration and magnetic ordering. In these Fe-substituted adamantine structures, the antiferromagnetic state has been found to be most of the time more stable than the ferromagnetic state. The magnetic moment of the iron atom was found to slightly decrease with the amount of substituted Fe. The antiferromagnetic to ferromagnetic transition temperatures have been determined by Monte Carlo methods and have been found to be around 100 K in most instances. The analysis of the densities of states was used to make predictions on the influence on photovoltaic performance improvement and on spintronic properties induced by substitutional Fe atoms. For the case of ${\mathrm{CuInSe}}_2$, Fe impurities are expected to impart to the material spintronic properties, depending on the site in which it is substituted, but to degrade its photovoltaic properties.

Figure 1

(a) Schematic electronic transition for an heterojunction, which can be seen as a ferromagnetic material. (1) $e^{-}\text{−}{h}^{+}$ pair generation, e.g., via phonon absorption, (2) $e^{-}$ transport, (3) (3’)$e^{-}\text{−}{h}^{+}$ recombination, (3”) $e^{-}\text{−}{h}^{+}$ recombination inhibited, (4’) current injection. (b) Schematic electronic transition of a model magnetic system. The symbols on the arrows are as follows: crosses correspond to small recombination matrix elements, open (filled) circles for low initial state electron (final state hole) occupation probability. The horizontal arrows represent the current flow in an operating device.

Figure 2

Variation of the $\angle \mathrm{Se}\text{−}\mathrm{Fe}\text{−}\mathrm{Se}$ angles with (a) ${\mathrm{Fe}}_{\mathrm{In}}$ and (b) ${\mathrm{Fe}}_{\mathrm{Cu}}$ concentration (FM state). For pure ${\mathrm{CuInSe}}_2$, the Se-In-Se angles are 108° and 112.5°, the Se-Cu-Se angles are 106° and 111.2°.

Figure 3

Evolution of the $a$ and $c$ lattice parameters as a function of Fe substitution content on Cu and In sites (FM state).

Figure 4

Variation of mixing energy (eV) with Fe magnetic center concentrations. (a) ${\mathrm{Fe}}_{\mathrm{In}}$ substitution: $\Delta E=E_{{\mathrm{CuIn}}_{1-x}{\mathrm{Fe}}_x{\mathrm{Se}}_2}-x{E}_{{\mathrm{CuInSe}}_2}-(1-x)E_{{\mathrm{CuFeSe}}_2}$. (b) ${\mathrm{Fe}}_{\mathrm{Cu}}$ substitution: $\Delta E=E_{{\mathrm{Cu}}_{1-x}{\mathrm{Fe}}_x{\mathrm{InSe}}_2}-x{E}_{{\mathrm{CuInSe}}_2}-(1-x)E_{{\mathrm{FeInSe}}_2}$. For both ${\mathrm{CuFeSe}}_2$ and ${\mathrm{FeInSe}}_2$ the reference energy (0) is the AFM state.

Figure 5

Antiferromagnetic configurations (32-atom supercell represented and we only present one cation type). The figures of the In and Cu cation substitutions are similar with $(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ translation.

Figure 6

Density of states of ${\mathrm{CuIn}}_{1-x}{\mathrm{Fe}}_x{\mathrm{Se}}_2$ (FM state).

Figure 7

Density of states of ${\mathrm{Cu}}_{1-x}{\mathrm{Fe}}_x{\mathrm{InSe}}_2$ (FM state).

Figure 8

Partial density of states of (a) ${\mathrm{CuIn}}_{15∕16}{\mathrm{Fe}}_{1∕16}{\mathrm{Se}}_2$ and (b) ${\mathrm{Cu}}_{15∕16}{\mathrm{Fe}}_{1∕16}{\mathrm{InSe}}_2$ (FM state).

Figure 9

Density of states of (a) ${\mathrm{CuIn}}_{7∕8}{\mathrm{Fe}}_{1∕8}{\mathrm{Se}}_2$ and (b) ${\mathrm{Cu}}_{7∕8}{\mathrm{Fe}}_{1∕8}{\mathrm{InSe}}_2$ (FM and AFM states).

Figure 10

Schematic electronic transition of Fe-doped ${\mathrm{CuInSe}}_2$ for ${\mathrm{Fe}}_X$. If $X=\mathrm{Cu}$ the Fermi level is above the Fe states, and if $X=\mathrm{In}{E}_F$ is below the Fe states.