Can wide-gap chalcopyrite be doped $n$-type

Wide-gap materials are more difficult to dope than their lower- gap counterparts, as evidenced by $n$-doping of Ge $\rightarrow$ Si $\rightarrow$ C or $p$-doping of GaN $\rightarrow$ AlN. Similarly, whereas CuInSe$_{2}$ (E$_{g}$ = 1.1eV) can be $n$- doped via stoichiometry control, its wider-gap counterpart CuGaSe$_{2}$ (Eg = 1.8eV) so far resisted $n$-type doping. Using the defect formation energies calculated from first-principles supercell calculations, we have studied theoretically doping of CuInSe$_{2}$ and CuGaSe$_{2}$ by Cl, Br, I (on Se-site) and Zn, Cd (on metal sites), as a function of chemical thermodynamic boundary conditions. We find that the bottlenecks are proportional to (a) the ease of forming V$_{Cu}$ (an electron killer) and (b) the ease of doping on the wrong site (e.g. Cd-on-In rather than Cd-on Cu). In CIS, halogen doping does not improve over intrinsic doping by InCu, which yields a net donor concentration of ~10$^{18}$cm$^{-3}$ at T = 800 K. A higher net donor doping can be achieved with Cd and Zn doping, but a high compensation ratio is always present. In CuGaSe$_{2}$, both anion-site and cation-site donor doping is intrinsically hampered by overcompensation due to V$_{Cu}$ formation.