Dependence of energy gaps with the stoichiometric deviation in a CuIn0.5Ga0.5Se2 ingot: A schematic band model

Abstract

The optical properties of a CuIn0.5Ga0.5Se2 ingot with strong stoichiometric deviations have been analyzed. The value of the first energy gap has been obtained by fitting the experimental reflectance data to the function R=A0+A1/(hν)2−A2/(hν)3, whereas the values of three other gaps were obtained through the fit of the absorption coefficient, obtained by photomodulated spectral ellipsometry, to the function (α*hν)m=B*(hν−Eg) (m=2 or 2/3 for the direct or forbidden gap). The four transition energy values have been found to be in the 1.251–1.294, 1.837–1.996, 2.963–3.052, and 3.365–3.419 eV ranges, respectively. A correlation has been found between the first energy gap and the Ga sublattice occupation while the other energy gap values have been found to be associated with the Se position in the unit cell, as determined by the relative coordinate of the anion. On its turn, this position depends on the point defect concentration in the lattice. The energy gaps increase with the force constants of the Ga–Se bond. Each gap has been assigned to a transition in the band structure. Eg2 corresponds to the transition from the Γ5v(2) level at the valence band to Γ1c, the conduction-band minimum. For Eg3 and Eg4, the transition are from Γ4v(2) (the maximum valence band) to Γ3c and Γ2c, respectively. The shifts in the valence- and conduction-band levels have been found by analyzing the differences between energy gaps and have been associated with changes in the structural properties. The Eg2−Eg1 difference is affected by stoichiometric deviations. The Γ5v(2) level is closer to Γ4v(2) in samples with vacancy concentrations higher than in the stoichiometric ones.