Band Gap II - Electrons in Molecular Bonds

Electrons in the outermost shell are called valence electrons.  A valence bond requires 1 valence electron, each from neighbouring atoms, to share its molecular orbital.  The molecular orbitals of the 4 valence electrons of silicon are shown in the diagram below.  These orbitals merge to form a tetrahedral like structure called the sp3 hybrid.

The orbitals of the an electron each from 2 atoms will merge when they bond, and they must satisfy the Pauli exclusion principle, meaning that one must spin up, while the other spin down.  At this bonding level (bonding state), the energy level is the lowest, more so than the original 2 individual sp3 levels.  This is the valence band level, and it is more stable.  The next energy level is the anti-bonding level, which is higher than the bonding level and the original sp3 level.  This is the conduction band level, and electrons prefer not to be in this state.  The smaller the structural gap between 2 atoms when bonded, the larger the energy required to split the 2 atoms, which means the bonding and anti-bonding levels will be further apart.  This difference in levels is called the band gap.  The valence band and conduction band, formed from the combine effects of many silicon to silicon bonding and anti-bonding levels, are discrete energy levels.

In chemistry, the valence band is also called the Highest Occupied Molecular Orbital (HOMO), while the conduction band is the Lowest Unoccupied Molecular Orbital.  In general, carbon, silicon and germanium are IV materials, but carbon is not a IV-semiconductor material because the bond length is much smaller, and hence the band gap is larger.  The lattice constant is defined as shown in the diagram below.

Materials with semiconductor properties can also be made from III-V materials like gallium arsenide (GaAs) and II-VI materials like cadmium-telluride (CdTe).  These also form the tetrahedral diamond cubic crystalline lattice.

Referencing:
2.2.2 Band Gap II - Electrons in Molecular Bonds, Delft University of Technology, https://www.youtube.com/watch?v=IFZeGsDOCi4