Electronic and optical properties of native point defects in CuInS$_2$ and CuGaS$_2$

TL;DR

The study addresses intrinsic defects in CuInS2 and CuGaS2 and their impact on electronic and optical properties relevant to photovoltaics. It employs HSE hybrid functionals, optimizes alpha and omega to match band gaps and approximate generalized Koopmans' theorem, and computes defect formation energies, CTLs, and optical transition levels, including Franck-Condon lattice-relaxation effects. Key findings include deep CTLs for antisites and vacancies and amphoteric behavior for V_In, with optical transitions that align with photoluminescence peaks once lattice effects are included, improving the interpretation of PL in chalcopyrite absorbers. The work provides updated defect energetics, clarifies defect-PL connections, and offers data and methods for defect engineering in CuInS2 and CuGaS2.

Abstract

We present a detailed study of common intrinsic defects in CuInS$_2$ and CuGaS$_2$ using the Heyd, Scuseria and Ernzerhof (HSE) hybrid functional scheme. The impact of the two HSE parameters, $α$ and $ω$ on the band gap and compliance with the generalized Koopmans' theorem is investigated. Using the formation energy formalism and calculated thermodynamic charge-transition levels, we assess the electronic properties of the defects and explore the connection of charge-transition levels with optical-transition levels. Calculated Franck-Condon shifts for emission highlight the importance of lattice relaxation for the attribution of defects to luminescence peaks. Our results show that once these effects are included, predictions become closer to photoluminescence measurements available in literature.

Figures (7)

• Figure 1: Scheme of the parabolicity of (semi-)local functionals (blue) and Hartree-Fock (red) for partially removing an electron from the system. Dotted line indicates the linear behavior if the exact functional was known. (Semi-)local functionals show a positive parabolicity which can favor partially occupied states and delocalize the electron. Hartree-Fock shows a negative parabolicity and favors fully occupied states. Adapted from Freysoldt2014.
• Figure 2: Illustration of optical transition level (OTL) and charge transition level (CTL) within a configurational coordinate diagram. In this example, the transition is referenced to the conduction band. The right panel shows a band diagram with the positions of the transition levels. The color code of the left panel corresponds to those of the band diagram (CB = red, defect = green, VB = blue). i) E$^{(-/0)}_\text{opt}$: An electron in the defect state can absorb light, promoting it to the conduction band. This is described by a vertical transition in the atomic ground state (q=-1). ii) E$^{(0/-1)}_\text{opt}$: An electron in the conduction band can transition to a defect state by emitting light. Here the ground state geometry is defined by the neutral charge state. The difference between the vertical transition levels and the charge transition levels corresponds to the Franck-Condon shifts ($\text{d}^\text{e/g}_\text{FC}$), as indicated in the figure.
• Figure 3: Charge transition levels of the studied intrinsic defects in CuInS$_2$ and CuGaS$_2$. Defects are grouped by types. Antisites, the group three vacancies and the copper vacancies show deep charge transition levels. The S vacancy has no transition level within the band gap. The Cu$_\text{i}$ has a shows a charge transition level close to the conduction band.
• Figure 4: Franck-Condon shift as a function of the charge-transition level (CTL) position relative to midgap. CTLs closer to midgap induce larger lattice distortions upon changing the charge state. Blue dotted vertical lines mark the band edges of CuInS$_2$, and the x-axis limits correspond to those of CuGaS$_2$.
• Figure 5: Sketch of the optical/vertical transition levels within a configuration coordinate diagram. The color code of the parabolas describes the position of the electron and is consistent with the inset pictures (CB = red, defect = green, VB = blue). a corresponds to transitions from the conduction band to the defect, while in b the transition is between defect and valence band. Left displays to defects in Defects in CuInS$_2$ and right in CuGaS$_2$.