Optical properties of Cu(In,Ga)Se2 and Cu2ZnSn(S,Se)4

doi:10.1016/j.tsf.2010.12.217

Thin Solid Films

Volume 519, Issue 21, 31 August 2011, Pages 7508-7512

https://doi.org/10.1016/j.tsf.2010.12.217 Get rights and content

Abstract

The optical properties of CuInSe₂, CuGaSe₂, Cu₂ZnSnS₄, and Cu₂ZnSnSe₄ are investigated using three different first-principles methods, namely the generalized gradient approximation by Perdew, Burke, and Ernzerhof (PBE), the hybrid Hartree–Fock-like functional by Heyd, Scuseria, and Ernzerhof (HSE), and a Green's function approach (GW). The density-of-states, the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω), and the optical absorption coefficient α(ω) are determined, providing fundamental understanding of these materials. We find that even though the PBE method generates fairly accurate effective crystal potentials, the HSE and GW methods improve considerably the band-gap energies E_g and also the localization of the semicore states, thereby describing the optical properties much better. Furthermore, we also present optimized convergence parameters for the self-consistent HSE calculation in order to reduce the computational time of this orbital-dependent method.

Introduction

The I–III–VI₂ ternary compounds CuInSe₂ (CISe), CuGaSe₂ (CGSe), and their alloys CuIn_xGa_1 − xSe₂ (CIGSe) are considered to be suitable absorber materials in low-cost and high-efficiency thin-film solar-cell technologies. To reduce the material costs, the expensive group-III elements (i.e., In and Ga) can be substituted by group-II-IV elements (e.g. Zn plus Sn), thereby forming the I₂–II–IV–VI₄ quaternary compound Cu₂ZnSnSe₄ (CZTSe) and its sulfide counterpart Cu₂ZnSnS₄ (CZTS). The band-gap energy E_g of the CIGSe alloy can be tuned from 1.04 to 1.68 eV and the gap energies of CZTS and CZTSe are around 1.0–1.5 eV, which is suitable for photovoltaic applications. Moreover, knowledge of the optical properties, such as the dielectric function and the optical absorption coefficient, is required to analyze optical measurements as well as to optimize the solar cell devices.

In this work, we study the optical properties of CISe, CGSe, CZTS, and CZTSe. Although the structural, electronic properties of these materials already have been investigated by first-principles calculations [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], only a few works were focused on the optical properties [8], [9], [10]. Most of the earlier theoretical studies rely on the local density approximation (LDA) or the generalized gradient approximation (GGA) within the density functional theory (DFT). These methods describe the crystalline and electronic structures well, but fail in predicting the band-gap energies. This is especially true for CISe and CZTSe for which LDA generates zero energy gaps. Thus, methods beyond the DFT-based LDA or GGA are needed to make more accurate analyses of the electronic band edges. The Hartree–Fock approximation is one approach for this purpose, involving an orbital-based and non-local exchange potential onto the average local Coulomb potential in order to take into account the self-interaction of the electrons. However, this method suffers from the unscreened nature of the Coulomb interaction and it therefore overestimates the gap energy [11]. Recently, Heyd, Scuseria, and Ernzerhof proposed a hybrid DFT functional with a partial Hartree–Fock screening [12], [13]. This so-called HSE functional has already been applied in calculations of CISe and CGSe [5], [10] as well as in calculations of CZTS and CZTSe [3], [10], and the results demonstrate more reliable band-gap energies. Furthermore, since the optical properties are related to excitation processes, methods beyond the ground-state DFT are called for in order to better describe the excitation effects. The unscreened Hartree–Fock can be improved in a rigorous way by using a dynamically screened Coulomb interaction. This leads to the Green's function (GW) approach [14], which is expected to generate more accurate results of many of the non-local optical properties.

In this work, we use the GW approach to calculate the density-of-states (DOS), the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω) and the optical absorption coefficient α(ω) of CISe, CGSe, CZTS, and CZTSe. The results from the GW calculations are compared with corresponding GGA and HSE calculations. Moreover, HSE is an orbital-dependent functional and the method is more time consuming compared with regular GGA, and it also requires larger computer memory. We therefore present optimized convergence parameters for the HSE functional in order to reduce the computational time for future large unit-cell investigations.

Section snippets

The crystal structures

CISe and CGSe are well know to crystallize in chalcopyrite (ch) structure with tetrahedral bonding character [15], [16]. The crystalline structure of CZTS and CZTSe are less established, but expected to crystallize in either kesterite (ke) or stannite (st) structure [17], [18], which are both similar to the chalcopyrite structure. Kesterite is expected to be the more stable than stannite structure at ambient pressure and moderate temperature. We consider six materials in the present study:

Electronic structures

The six materials considered here have all direct Γ-point band gaps, and the corresponding E_g are presented in Table 2. The PBE band gaps are underestimated by as much as 1 eV compared with the experimental values. These results are significantly improved by the HSE and GW calculations. In particular the GW method reproduces E_g well for CGSe and CZTS, which are only ~ 0.1 eV smaller than the experimental values. The present HSE and GW gap energies agree well also with earlier theoretical data (see

Conclusion

The dielectric functions and absorption coefficients of ch-CISe, ch-CGSe, ke-CZTS, ke-CZTSe, st-CZTS and st-CZTSe have been investigated using the first-principles PBE, HSE and GW methods. Although PBE generates very reasonable DOS, the HSE and GW provide better optical properties mainly due to a more accurate band gaps.

Test on the optimization of HSE calculation demonstrates that 3-step NSC calculation with lowered parameter setting is sufficient to provide fairly good band structures compared

Acknowledgements

This work is supported by the Swedish Energy Agency, the Swedish Research Council, and the computer centers NSC and HPC2N through SNIC/SNAC. H.Z. would like to express his thanks to Chen Jie for his helpful discussion on the GW calculations.

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Optical properties of Cu(In,Ga)Se2 and Cu2ZnSn(S,Se)4

Abstract

Introduction

Section snippets

The crystal structures

Electronic structures

Conclusion

Acknowledgements

J. Phys. Chem. Solids

J. Cryst. Growth

Thin Solid Films

Appl. Surf. Sci.

Rare Met.

J. Cryst. Growth

Phys. B

J. Appl. Phys.

Phys. Rev. Lett.

Appl. Phys. Lett.

Phys. Rev. B

Phys. Rev. Lett.

Jpn. J. Appl. Phys.

Appl. Phys. Lett.

J. Appl. Phys.

Phys. Rev. B

Z. Phys.

Optical properties of Cu(In,Ga)Se₂ and Cu₂ZnSn(S,Se)₄