Comprehensive study on band-gap variations in sp³-bonded semiconductors: roles of electronic states floating in internal space

We have performed electronic structure calculations to explore the band-gap dependence on polytypes for $sp^3$-bonded semiconducting materials, i.e., SiC, AlN, BN, GaN, Si, and diamond. In this comprehensive study, we have found that band-gap variation depending on polytypes is common in $sp^3$-bonded semiconductors; SiC, AlN, and BN exhibit smallest band gaps in $3C$ structure, whereas diamond does in $2H$ structure. We have also clarified that the microscopic mechanism of the band-gap variations is attributed to peculiar electron states $floating$ in internal channel space at the conduction-band minimum (CBM), and that internal channel length and the electro-static potential in channel affect the energy level of CBM.