Chemical trends of the band gaps in semiconducting silicon clathrates

We have calculated the band structures of (M: Na, K, Rb, and Cs) using the density-functional theory with the generalized gradient corrected local density approximation. They are indirect semiconductors with the calculated gaps from 0.45 to 0.89 eV, the gaps becoming wider with the promotion to the heavier encapsulated guest alkali atoms. These are comparable to the calculated gap of 0.65 eV of crystalline Si with the diamond structure.