Comprehensive study on band-gap variations in $sp^3$-bonded semiconductors: roles of electronic states floating in internal space

TL;DR

This study investigates how polytype variations influence the band gaps of $sp^3$-bonded semiconductors, revealing that internal electron states and channel properties are key factors affecting electronic properties.

Contribution

It uncovers the microscopic mechanism behind band-gap variations in $sp^3$-bonded semiconductors, emphasizing the role of floating electron states in internal channels.

Findings

Band-gap variation is common among $sp^3$-bonded semiconductors.

Specific polytypes exhibit minimum band gaps (e.g., SiC, AlN, BN in 3C; diamond in 2H).

Electron floating states and internal channel properties influence conduction band minimum energy.

Abstract

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.