Electronic structure of semiconducting alkali-metal silicides and germanides

We present self-consistent linearized-muffin-tin-orbital calculations of the electronic structure of three alkali-metal germanides and silicides (KGe, NaGe, and NaSi). Like the alkali-metal–lead compounds investigated in our earlier work [M. Tegze and J. Hafner, Phys. Rev. B 39, 8263 (1989)] the Ge and Si compounds of the alkali metals form complex structures based on the packing of tetrahedral ${\mathrm{Ge}}_4$ and ${\mathrm{Si}}_4$ clusters. Our calculations show that all three compounds are narrow-gap semiconductors. The width of the energy gap depends on two main factors: the ratio of the intracluster to the intercluster interactions between the group-IV elements (which increases from Pb to Si) and the strength of the interactions between the alkali-metal atoms (which varies with the size ratio).