Electronic Structure of AgInSe2and CuInSe2

Abstract

We report electroreflectance and photoluminescence studies of the chalcopyrite compounds AgIn${\mathrm{Se}}_{2}$ and CuIn${\mathrm{Se}}_{2}$. Observation of photoluminescence at low temperatures at the same energy as the direct energy gaps located by electroreflectance measurements confirms that both compounds have direct band gaps. At 300 \ifmmode^\circ\else\textdegree\fi{}K, the values for the energy gaps are 1.24 and 0.96 eV, respectively. The spin-orbit splittings of the uppermost valence bands as observed in electroreflectance measurements are considerably less than expected for $p$ levels, a result which we attribute to \ensuremath{\sim} 17% hybridization of Ag $4d$ levels, and \ensuremath{\sim} 34% hybridization of Cu $3d$ levels, with the otherwise $p$-like valence bands. An ultraviolet electroreflectance structure observed in CuIn${\mathrm{Se}}_{2}$ may result from transitions from the $d$ levels themselves to the lowest conduction-band minimum. The crystal-field and spin-orbit parameters for the uppermost valence bands of CuIn${\mathrm{Se}}_{2}$ disagree with values found in a recent energy-band calculation ignoring $d$ bands, a calculation which also predicted that CuIn${\mathrm{Se}}_{2}$ has an indirect energy gap. We also observe an anomalous temperature dependence of the energy gap in AgIn${\mathrm{Se}}_{2}$. Whereas the energy gap in CdSe (the binary analog of AgIn${\mathrm{Se}}_{2}$) decreases by approximately 80 meV as the temperature increases from 77 to 300 \ifmmode^\circ\else\textdegree\fi{}K, the energy gap of AgIn${\mathrm{Se}}_{2}$ is independent of temperature over this range within experimental error (\ifmmode\pm\else\textpm\fi{} 5 meV).