Electronic structure and transport in type-I and type-VIII clathrates containing strontium, barium, and europium

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Abstract
The thermoelectric properties of filled gallium-germanium clathrates are analyzed from a band-structure point of view. Using the virtual crystal approximation the undoped clathrates are calculated to be semiconductors with band gaps around 0.6–0.9 eV. The conduction bands hybridize with the unoccupied d states of the guest atoms. This means that the thermoelectric properties of n-doped type-I clathrates depend strongly on the guest atom while p doped clathrates are relatively unaffected. The type-VIII structures have disperse bands centered around the voids in the framework structure. This explains the low effective masses observed for n-doped type-VIII structures. It also means that the electronic structure and thermoelectric properties are relatively independent of the guest atom and that p-doped should have favorable thermoelectric properties while n-doped type-VIII structures have poor properties. We estimate a figure of merit of 1.2 at 400 K for an optimally p-doped europium-VIII clathrate. In addition we predict that the strontium-VIII clathrate should be stable.