I-II-V half-Heusler compounds for optoelectronics: Ab initio calculations

Half-Heusler compounds $XYZ$ crystallize in the space group $F\overline{4}3m$ and can be viewed as a zinc-blende-like ${\left(YZ\right)}^{-}$ lattice partially filled with He-like $X^{+}$ interstitials. In this work, we investigated I-II-V (eight-electrons) half-Heusler compounds by first-principles calculations in order to find suitable semiconductors for optoelectronics such as Cd-free buffer layer materials for chalcopyrite-based thin-film solar-cell devices. We report a systematic examination of band gaps and lattice parameters, depending on the electronegativities and the ion radii of the involved elements. Half-Heusler buffer materials should have a band gap of more than 2 eV to avoid absorption losses and a lattice constant of about $5.9\text{Å}$ to match the crystal structure of the absorber material. With these criteria we selected seven half-Heusler compounds as candidates for a buffer layer material.

Figure 1

(Color online) (a) $XYZ$ half-Heusler crystal structure (space group $F\overline{4}3m$) with $X$ at ${\mathbf{r}}_{\mathbf{1}}=\left(0.5,0.5,0.5\right)$ (black), $Y$ at ${\mathbf{r}}_{\mathbf{2}}=\left(0,0,0\right)$ (gray), and $Z$ at ${\mathbf{r}}_{\mathbf{3}}=\left(0.25,0.25,0.25\right)$ (red/dark gray). Note the zinc-blende-like ${\left(YZ\right)}^{-}$ lattice partially filled with He-like $X^{+}$ interstitials. (b) CdS in the zinc-blende structure (space group $F\overline{4}3m$) with Cd (gray) at (0,0, 0) and S (green/dark gray) at (0.25, 0.25, 0.25). (c) Chalcopyrite crystal structure of ${\text{CuInSe}}_2$ (space group $I42d$). Cu (black) is located at (0, 0, 0), In (dark blue/dark gray) at (0, 0, 0.5) and Se (green/gray) at $\left(z,0.25,0.125\right)$. (The figure is in color only in the electronic version.)

Figure 2

(Color online) Band diagram of the half-Heusler compounds (a) LiMgP, (b) NaMgP, (c) of the III-V semiconductor GaP, and (d) of CdS in the zinc-blende structure. Calculations were done with the WIEN2K code. (The figure is in color only in the electronic version.)

Figure 3

Dependence of the band gaps (WIEN2K) of $XYZ$ compounds ($X=\text{Li}$, Na, and K) on the Pauling electronegativity difference between the element $Z=\text{P}$ and $Y=\text{Mg}$, Ca, and Zn, respectively.

Figure 4

Lattice constants of $XYZ$ compounds plotted against the sum of the ion radii of element $X$ and $Y$ (ion radii for ions with removed valence electrons).