Doping dependence of electronic and mechanical properties of ${\text{GaSe}}_{1-x}{\text{Te}}_x$ and ${\text{Ga}}_{1-x}{\text{In}}_x\text{Se}$ from first principles

The electronic and mechanical properties of the hexagonal, layered GaSe doped with Te and In have been studied using first-principles pseudopotential method within density-functional theory. The calculated elastic constants of the end compounds GaSe and InSe compare well with the available experimental and theoretical values. As we go from GaSe to InSe, the elastic constants ${\text{C}}_{13}$, ${\text{C}}_{33}$, and ${\text{C}}_{44}$ increase while ${\text{C}}_{11}$ and ${\text{C}}_{12}$ decrease, suggesting that the crystal becomes stiffer in the direction perpendicular to the atomic layers and the softer in the direction parallel to the layers, as more substitutional In is incorporated in GaSe. The electronic structure and the formation energies of several defects and simple defect complexes are discussed and the calculated charge transition levels are compared to available experimental data. We demonstrate that In doping may play an important role in the observed enhancement in the structural properties of GaSe. Depending on the Fermi energy, In can either substitute for Ga $\left({\text{In}}_{\text{Ga}}\right)$ or occupy an interstitial position as a triply charged defect $\left({\text{In}}_i^{3+}\right)$. While the substitutional In does not change significantly the electronic and mechanical properties of the host, we find that the shear stiffness of GaSe is considerably increased when In is incorporated as charged interstitial impurity.

Figure 1

The calculated band structures of GaSe and InSe. $\text{A-}\Gamma$ and $\Gamma \text{-M}$ directions are perpendicular and parallel to the atomic layers, respectively.

Figure 2

(Color online) (a) and (b) Formation energies of Te impurity in GaSe under Ga-rich and Se-rich conditions, respectively. For all values of $E_F$ within the band gap, Te prefers to occupy the Se site. (c) Formation energies of In impurity in GaSe under Ga-rich conditions. When $E_F$ is very close to VBM, the In impurity becomes positively charged $\left(+3\right)$ and moves to the interstitial site. (d) Formation energies of In-related defects in GaSe under Se-rich conditions.

Figure 3

(Color online) The total DOS of GaSe with ${\text{In}}_i$ and the projected DOS of the $\text{In}s$ orbital, showing the positions of the HDDS $\left(-5.5\text{eV}\right)$ and DDS (just above $E_F$) introduced by the charged ${\text{In}}_i$ defect.

Figure 4

(Color online) Charge-density distribution associated with the localized band introduced by ${\text{In}}_i$ in the band gap of GaSe. The dominant contribution comes from the $\text{In}s$ orbital, hybridized with the NN $\text{Se}{p}_z$ orbitals.

Figure 5

The total density of states associated with ${\text{In}}_{\text{Ga}}{\text{-V}}_{\text{Ga}}$ defect complex, for different charge states. When the defect complex is triply negatively charged, the defect state is located in the gap (lower panel).

Figure 6

(Color online) Charge-density distribution associated with the localized band introduced by ${\text{In}}_{\text{Ga}}{\text{-V}}_{\text{Ga}}$ in the band gap of GaSe. The dominant contribution comes from the $\text{In}s$ orbital, hybridized with the NN $\text{Se}{p}_z$ orbitals.

Figure 7

(Color online) The DOS projected on the $\text{In}s$ orbital for the neutral and $-3$ charge state of the ${\text{In}}_{\text{Ga}}{\text{-V}}_{\text{Ga}}$ defect complex. The splitting between the bonding and antibonding states decreases mainly because the distance between the In and Se atoms increases.

Figure 8

(Color online) The energy barrier which must be overcome in order to cleave the GaSe crystal increases dramatically when In occupies the interstitial site compared to the case when In occupies substitutional site. For comparison the case of pure GaSe is also shown.