On the basis of detailed ab initio studies the influence of strain on the anisotropy of the transport distribution of the thermoelectrics Bi_2Te_3 and Sb_2Te_3 was investigated. Both tellurides were studied in their own, as well as in their co-partners lattice structure to gain insight to the electrical transport in epitaxial heterostructures composed of both materials. It is shown, that the anisotropy of the transport distribution overestimates the experimental findings for Bi_2Te_3, implying

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... nisotropic scattering effects. An increase of the in-plane lattice constant leads to an enhancement of the transport anisotropy for p-doping, whereas the opposite occurs for n-doping. The recent findings and special features of the transport distribution are discussed in detail in relation to the topology of the band structures.