The dielectric functions of Cu(In, Ga)Se2(CIGS)-based polycrystalline layers with different Ga and Cu compositions have been determined by applying spectroscopic ellipsometry (SE) in a wide energy range of 0.7–6.5 eV. To suppress SE analysis errors induced by rough surface and compositional fluctuation, quite thin CIGS layers (<60 nm) with high uniformity toward the growth direction have been characterized using a self-consistent SE analysis method. We find that the optical model used in many previous studies is oversimplified particularly for the roughness/overlayer contribution, and all the artifacts arising from the simplified analysis have been removed almost completely in our approach. The CIGS dielectric functions with the variation of the Ga composition [x = Ga/(In + Ga)] revealed that (i) the whole CIGS dielectric function shifts toward higher energies with x, (ii) the band gap increases linearly with x without the band-gap bowing effect, and (iii) the overall absorption coefficients are significantly smaller than those reported earlier. Furthermore, the reduction of the Cu composition [y = Cu/(In + Ga)] leads to (i) the linear increase in the band-edge transition energy and (ii) the decrease in the absorption coefficient, due to the smaller interaction of the Cu 3d orbitals near the valence band maximum in the Cu-deficient layers. When y > 1, on the other hand, the free-carrier absorption increases drastically due to the formation of a semi-metallic CuxSe phase with a constant band gap in the CIGS component. In this study, by using a standard critical-point line-shape analysis, the critical point energies of the CIGS-based layers with different Ga and Cu compositions have been determined. Based on these results, we will discuss the optical transitions in CIGS-based polycrystalline materials.
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.
The dielectric functions of co-evaporated Cu2ZnSnSe4 (CZTSe) and Cu2SnSe3 (CTSe) polycrystalline layers are determined accurately from self-consistent spectroscopic ellipsometry analyses. To minimize the effects of the compositional modulation and light scattering induced by rough surfaces, quite thin CZTSe and CTSe layers (<50 nm) having the single-phase stoichiometric compositions are characterized. The dielectric functions of CZTSe and CTSe show rather similar spectral features with almost identical critical point energies for the transition peaks at 2.4 and 3.9 eV. The CTSe dielectric function, however, indicates strong free carrier absorption, expressed by the Drude model, due to high p-type conductivity in the layer. We find that CZTSe and CTSe show quite large absorption coefficients exceeding 105 cm−1 at 2.0 eV with band gap values of 0.91 ± 0.02 eV and 0.68 ± 0.05 eV, respectively. To characterize the optical transition in CZTSe in more detail, the dielectric response of each interband transition is calculated by applying density functional theory. The calculation result reveals that the strong visible light absorption in CZTSe is induced by the high joint density of states at the P point in the Brillouin zone. The optical constants of CZTSe and CTSe deduced in this study are further parameterized in an energy range up to 6.0 eV by expressing the transition peaks using the Tauc-Lorentz model. From the above results, we discuss the fundamental optical properties of (Cu,Se)-based compound semiconductors.
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