SEM images of the CIGS layers (x = 0.34 and y = 0.88) with a thickness of (a) 50 nm and (b) 360 nm.
SE analysis procedure in the global error minimization. This analysis is consisting of two steps with (i) mathematical inversion for a thin layer and (ii) ellipsometry fitting for a thicker layer.
(a) Dielectric function of the CIGS layer (x = 0.38 and y = 0.90) extracted directly from a thin layer (∼25 nm) using the mathematical inversion and (b) (ψ, Δ) spectra obtained from a thick CIGS layer (∼40 nm) deposited with the identical growth conditions. For the experimental data of (b), only one out of every five data points is shown for clarity.
Cross-sectional TEM image obtained from the CIGS/Si(100) structure. The SE analysis of this sample is shown in Fig. 3(b) .
(ψ, Δ) spectra obtained from the CIGS(360 nm)/Si(100) sample shown in Fig. 1(b) (open circles) and the result of the fitting analysis (solid lines). The inset shows the optical model, consisting of five surface roughness layers with different fvoid on the CIGS bulk layer, used in the SE analysis. For the experimental data, only one out of every five data points is shown for clarity.
Dielectric functions of the CIGS layers with different x ranging from x = 0.00 (CIS) to x = 1.00 (CGS) with a constant y ∼ 0.9 (sample A-D in Table I ), determined from the SE analyses using the global error minimization.
α spectra of the CIGS layers with different x. These spectra were obtained directly from the dielectric functions shown in Fig. 6 .
(αhν)2 obtained from the CIGS layers, plotted as a function of photon energy. Solid lines show linear fits to the experimental data. The intercept at (αhν)2 = 0 shows the band gap Eg of the CIGS layers.
Dielectric functions of the CIGS-based layers having different y in a range of 0.36 ≤ y ≤ 1.34 with a constant x ∼ 0.4 (samples E-H in Table I). The ε2 spectrum for y = 1.34 is sifted vertically by +2 for clarity.
α spectra of the CIGS-based layers with different y. These spectra were obtained directly from the dielectric functions shown in Fig. 10 .
Band gap Eg estimated from the energy positions of (αhν)2 = 0 in the (αhν)2-E analysis and α = 103 cm−1, plotted as a function of y in the various CIGS-based layers.
ε2 spectrum of the CIS obtained experimentally (open circles) and the result of the dielectric function modeling using the Lorentz oscillators (solid lines). For the experimental data, only one out of every two data points is shown for clarity.
Second-derivative ε1 and ε2 spectra calculated from the modeled dielectric function shown in Fig. 13 (open circles) and the fitted spectra calculated from the CP analysis assuming the excitonic transitions (solid lines).
Transition energies obtained from the CP analysis, plotted as a function of x in the CIGS layers.
Transition energies obtained from the CP analysis, plotted as a function of y in the CIGS-based layers.
Band structure of CIS. The optical transitions in the chalcopyrite BZ are indicated by arrows. For the energy levels and the transitions, the notations used by Alonso et al. (Ref. 4 ) were adopted.
Valence band structure of CIGS-based materials. By the interaction between the anion p and cation d states, the bonding and antibonding bands are formed. In this figure, ΔEp-d represents the energy separation between the p-d states.
α spectra of CIS deduced in this study and reported previously in other studies (Refs. 1, 2, and 6 ).
Chemical compositions of the selected CIGS-based layers estimated from EPMA. In the samples A-D, the Ga composition x = Ga/(In + Ga) was changed with a constant Cu composition y = Cu/(In + Ga) of ∼0.9, whereas y changes with x ∼ 0.4 in the samples E-H.
Optical transition energies in single-crystalline and polycrystalline CIS semiconductors. For the energy levels and transitions in the chalcopyrite BZ, the notations used by Alonso et al. (Ref. 4 ) were adopted. The energy levels and some of the transitions are also depicted in Fig.17. In the case of the CIS single crystal, the optical transitions for the extraordinary ray (E//c) and ordinary ray (E⊥c) are shown.
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