We have theoretically investigated, by ab initio techniques, the phonon properties of several semiconductors with chalcopyrite structure. Comparison with experiments has led us to distinguish between materials with $d$ electrons in the valence band (e.g., CuGaS${}_{2}$, AgGaS${}_{2}$) and those without $d$ electrons (e.g., ZnSnAs${}_{2}$). The former exhibit a rather peculiar nonmonotonic temperature dependence of the energy gap which, so far, has resisted cogent theoretical description. We analyze this nonmonotonic temperature dependence by fitting two Bose-Einstein oscillators with weights of opposite sign leading to an increase at low temperatures and a decrease at higher temperatures and find that the energy of the former correlates well with characteristic peaks in the phonon density of states associated with low-energy vibrations of the $d$-electron elements. We hope that this work will encourage theoretical investigations of the electron-phonon interaction in this direction, especially of the current ab initio type.

Temperature dependence of band gaps in semiconductors: Electron-phonon interaction

Raman investigation of chalcopyrite oxidation

Equilibrium isotopic fractionation of copper during oxidation/reduction, aqueous complexation and ore-forming processes: Predictions from hybrid density functional theory

We have theoretically investigated, by ab initio techniques, the phonon properties of several semiconductors with chalcopyrite structure. Comparison with experiments has led us to distinguish between materials with d electrons in the valence band (e.g., CuGaS2, AgGaS2) and those without d electrons (e.g., ZnSnAs2). The former exhibit a rather peculiar nonmonotonic temperature dependence of the energy gap which, so far, has resisted cogent theoretical description. We analyze this nonmonotonic temperature dependence by fitting two Bose-Einstein oscillators with weights of opposite sign leading to an increase at low temperatures and a decrease at higher temperatures and find that the energy of the former correlates well with characteristic peaks in the phonon density of states associated with low-energy vibrations of the d-electron elements. We hope that this work will encourage theoretical investigations of the electron-phonon interaction in this direction, especially of the current ab initio type.

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Synchrotron-based XPS and NEXAFS study of surface chemical species during electrochemical oxidation of chalcopyrite

To obtain a sound basis for calculations of the lattice dynamics of chalcopyrite type compounds the literature data for the vibrational frequencies of 14 chalcogenides and 8 pnictides crystallizing in this structure are critically analysed. This is done by introducing frequency ratios of those frequencies which can be derived from zone centre or zone boundary vibrations of the sphalerite lattice presuming similar bonding and normal co-ordinates in all compounds investigated. Based on the reliable spectra vibrational frequencies have been calculated for those compounds which have not yet been investigated or for which the results given in the literature are uncertain.

Lattice dynamics of chalcopyrite type compounds. Part I. Vibrational frequencies

The lattice dynamics of 12 chalcopyrite type compounds CuAlS 2 , CuGaS 2 ,CuInS 2 , AgGaS 2 , AgGaSe 2 , AgInSe 2 , ZnSiP 2 , ZnGeP 2 , CdSiP 2 , CdGeP 2 , CdSnP 2 , and CdGeAs 2 have been investigated based on 4 different short range force constant models. In all models a set of different solutions can be obtained which can be distinguished by their force constant patterns. For a comparison of the calculated force constants it is therefore necessary to use the data of the comparable minima. From the set of solutions one is selected by physical reasoning and complete results for a model with 8 force constants are given for this minimum for all 12 compounds. The calculated force constants, normal co-ordinates and potential energy distributions are compiled and discussed.

Lattice dynamics of chalcopyrite type compounds. Part II. Calculations in a short range force field model

The lattice dynamics of 12 chalcopyrite type compounds CuAlS 2 , CuGaS 2 , CuInS 2 , AgGaS 2 , AgGaSe 2 , AgInSe 2 , ZnSiP 2 , ZnGeP 2 , CdSiP 2 , CdGeP 2 , CdSnP 2 , and CdGeAs 2 have been investigated based on a rigid ion model. As the anisotropy of the dynamic charges is not very pronounced the calculations were done assuming isotropic charges. The calculated force constants, normal co-ordinates and potential energy distributions are compiled and discussed.

Lattice Dynamics of Chalcopyrite Type Compounds. Part III. Rigid Ion Model Calculations

The lattice dynamics of 12 chalcopyrite type compounds CuAlS 2, CuGaS 2, CuInS 2, AgGaS 2, AgGaSe 2, AgInSe 2, ZnSiP 2, ZnGeP 2, CdSiP 2, CdGeP 2, CdSnP 2, and CdGeAs 2, have been investigated based on a 5-parameter model involving two short range stretching force constants, an interaction constant, and the effective dynamic charges of the cations. The calculated force constants, normal co-ordinates and potential energy distributions are compiled and discussed.

H. Haeuseler

Papers

Lattice dynamics of chalcopyrite type compounds. Part I. Vibrational frequencies

Lattice dynamics of chalcopyrite type compounds. Part II. Calculations in a short range force field model

Lattice Dynamics of Chalcopyrite Type Compounds. Part III. Rigid Ion Model Calculations

Lattice dynamics of chalcopyrite type compounds. Part IV. Calculations of TO phonon modes in a reduced rigid ion model