n -type doping of CuInSe2 and CuGaSe2

The efficiency of $mathrm{CuIn}{mathrm{Se}}_{2}$ based solar cell devices could improve significantly if $mathrm{CuGa}{mathrm{Se}}_{2}$, a wider band gap chalcopyrite semiconductor, could be added to the $mathrm{CuIn}{mathrm{Se}}_{2}$ absorber layer. This is, however, limited by the difficulty of doping $n$-type $mathrm{CuGa}{mathrm{Se}}_{2}$ and, hence, in its alloys with ${mathrm{CuInSe}}_{2}$. Indeed, wider-gap members of semiconductor series are often more difficult to dope than lower-gap members of the same series. We find that in chalcopyrites, there are three critical values of the Fermi energy ${E}_{F}$ that control $n$-type doping: (i) ${E}_{F}^{n,mathrm{pin}}$ is the value of ${E}_{F}$ where the energy to form Cu vacancies is zero. At this point, the spontaneously formed vacancies ($=$acceptors) kill all electrons. (ii) ${E}_{F}^{n,mathrm{comp}}$ is the value of ${E}_{F}$ where the energy to form a Cu vacancy equals the energy to form an $n$-type dopant, e.g., ${mathrm{Cd}}_{mathrm{Cu}}$. (iii) ${E}_{F}^{n,text{site}}$ is the value of ${E}_{F}$ where the formation of Cd-on-In is equal to the formation of Cd-on-Cu. For good $n$-type doping, ${E}_{F}^{n,mathrm{pin}}$, ${E}_{F}^{n,mathrm{comp}}$, and ${E}_{F}^{n,text{site}}$ need to be as high as possible in the gap. We find that these quantities are higher in the gap in $mathrm{CuIn}{mathrm{Se}}_{2}$ than in $mathrm{CuGa}{mathrm{Se}}_{2}$, so the latter is difficult to dope $n$-type. In this work, we calculate all three critical Fermi energies and study theoretically the best growth condition for $n$-type $mathrm{CuIn}{mathrm{Se}}_{2}$ and $mathrm{CuGa}{mathrm{Se}}_{2}$ with possible cation and anion doping. We find that the intrinsic defects such as ${mathrm{V}}_{mathrm{Cu}}$ and ${mathrm{In}}_{mathrm{Cu}}$ or ${mathrm{Ga}}_{mathrm{Cu}}$ play significant roles in doping in both chalcopyrites. For group-II cation (Cd, Zn, or Mg) doping, the best $n$-type growth condition is $mathrm{In}∕mathrm{Ga}$-rich, and maximal Se-poor, which is also the optimal condition for stabilizing the intrinsic ${mathrm{In}}_{mathrm{Cu}}∕{mathrm{Ga}}_{mathrm{Cu}}$ donors. Bulk $mathrm{CuIn}{mathrm{Se}}_{2}$ can be doped at equilibrium $n$-type, but bulk $mathrm{CuGa}{mathrm{Se}}_{2}$ cannot be due to the low formation energy of intrinsic Cu-vacancy. For halogen anion doping, the best $n$-type materials growth is still under $mathrm{In}∕mathrm{Ga}$-rich, and maximal Se-poor conditions. These conditions are not best for halogen substitutional defects, but are optimal for intrinsic ${mathrm{In}}_{mathrm{Cu}}∕{mathrm{Ga}}_{mathrm{Cu}}$ donors. Again, $mathrm{CuGa}{mathrm{Se}}_{2}$ cannot be doped $n$-type by halogen doping, while $mathrm{CuIn}{mathrm{Se}}_{2}$ can.