Question

Sn,C,Si and Ge are all group $XIV$ elements. Yet, $Sn$ is a conductor, $C$ is an insulator while $Si$ and $Ge$ are semiconductor. Why?

Answer 1

Semiconductors are the materials which have a conductivity between conductors (generally metals) and nonconductors or insulators (such as most ceramics). Semiconductors can be pure either elements, such as silicon or germanium, or compounds such as gallium arsenide or cadmium selenide.

Complete step by step answer:
The high conductivity in a material is defined by it having many partially filled states and much electronic state delocalization. Metals are good electrical conductors and have many partially filled electronic micro states with energies near their Fermi level. Insulators, by contrast, have few partially filled states, their Fermi levels sit within band gaps with few energy states to occupy. The conductivity of conductors, insulators and semi- conductors depend upon the band gap of the materials. The lower the band gap, the higher is the conductivity of the material. This means the order of band gap of conductor; semi- conductor and insulator is in the order of:
Conductor < Semi- conductor < Insulator
$Sn$ is a conductor because the band gap in tin is $0eV$ and there is no gap between the valence and conduction band.
$C$ is an insulator because the gap in carbon is $5.4eV$ and there is so much gap between the valence and conduction band that it is difficult for the electron to jump from valence to conduction band and conduct electricity.
$Si$ and $Ge$ are semiconductor because they have an intermediate band gap of values $1.1eV$ and $0.7eV$ respectively.

Note:
Importantly, an insulator can be made to conduct electricity by increasing its temperature, i.e. heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath the band gap (valence band) and the band of states above the band gap (conduction band). An (intrinsic) semiconductor has a band gap that is smaller than that of an insulator and at room temperature significant numbers of electrons can be excited to cross the band gap.