Strong Interplay between Structure and Electronic Properties in $\mathrm{CuIn}(\mathbf{S},\mathrm{Se}{)}_2$: A First-Principles Study

We present a first-principles study of the electronic properties of $\mathrm{CuIn}(\mathrm{S},\mathrm{Se}{)}_2$ (CIS) using state-of-the-art self-consistent $GW$ and hybrid functionals. The calculated band gap depends strongly on the anion displacement $u$, an internal structural parameter that measures lattice distortion. This contrasts with the observed stability of the band gap of CIS solar panels under operating conditions, where a relatively large dispersion of values for $u$ occurs. We solve this apparent paradox considering the coupled effect on the band gap of copper vacancies and lattice distortions. The correct treatment of $d$ electrons in these materials requires going beyond density functional theory, and $GW$ self-consistency is critical to evaluate the quasiparticle gap and the valence band maximum.

Figure 1

Photoemission band gap vs the anion displacement $u$ for ${\mathrm{CuInS}}_2$. The vertical (horizontal) shaded areas give the spread of experimental data for $u$ (band gap). Left panel: calculations using DFT-LDA, $G_0{W}_0$, sc-COHSEX, and $\mathrm{sc}\mathrm{\text{−}}\mathrm{COHSEX}+G_0{W}_0$. The dotted line is from Ref. 7. Right panel: $\mathrm{sc}\mathrm{\text{−}}\mathrm{COHSEX}+G_0{W}_0$ and calculations using HSE06 and a modified HSE06 (see the text).

Figure 2

The VBM shift $\Delta E_v$ of ${\mathrm{CuInS}}_2$ with respect to the LDA band edge versus the anion displacement $u$. We compare results for sc-COHSEX with self-consistency only in energy (dashed curve) and in both wave functions and energies (continuous curve). The horizontal blue line represents $\Delta E_v$ given by $\mathrm{DFT}+U_d$ [34] where $U$ is set to 6 eV.

Figure 3

Scheme of the feedback loop that stabilizes the gap.