Optical constants of Cu(In, Ga)Se2 for arbitrary Cu and Ga compositions

Abstract

The optical constants of Cu(In, Ga)Se2 (CIGS)-based polycrystalline layers with different Cu and Ga compositions are parameterized completely up to a photon energy of 6.5 eV assuming several Tauc-Lorentz transition peaks. Based on the modeled optical constants, we establish the calculation procedure for the CIGS optical constants in a two-dimensional compositional space of (Cu, Ga) by taking the composition-induced shift of the critical point energies into account. In particular, we find that the variation of the CIGS optical constants with the Cu composition can be modeled quite simply by a spectral-averaging method in which the dielectric function of the target Cu composition is estimated as a weighted average of the dielectric functions with higher and lower Cu compositions. To express the effect of the Ga composition, on the other hand, an energy shift model reported earlier is adopted. Our model is appropriate for a wide variety of CIGS-based materials having different Cu and Ga compositions, although the modeling error increases slightly at lower Cu compositions [Cu/(In + Ga) < 0.69]. From our model, the dielectric function, refractive index, extinction coefficient, and absorption coefficient for the arbitrary CIGS composition can readily be obtained. The optical database developed in this study is applied further for spectroscopic ellipsometry analyses of CIGS layers fabricated by single and multi-stage coevaporation processes. We demonstrate that the compositional and structural characterizations of the CIGS-based layers can be performed from established analysis methods.