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We study the dielectric function of CuBrxI1−x thin film alloys using spectroscopic ellipsometry in the spectral range between 0.7 eV to 6.4 eV, in combination with first-principles calculations based on density functional theory. Through the comparison of theory and experiment, we attribute features in the dielectric function to electronic transitions at specific k-points in the Brillouin zone. The observed bandgap bowing as a function of alloy composition is discussed in terms of different physical and chemical contributions. The band splitting at the top of the valence band due to spin-orbit coupling is found to decrease with increasing Br-concentration, from a value of 660 meV for CuI to 150 meV for CuBr. This result can be understood considering the contribution of copper d-orbitals to the valence band maximum as a function of the alloy composition.