Question

Explain the difference between conductors and semiconductors on the basis of energy bands in solids.

Hint:

Compare the forbidden energy gap: conductors have overlapping valence and conduction bands (no gap), semiconductors have a small gap of about 1 eV.

Answer 1

Step 1: Recall the band picture of solids.
In a solid the closely packed atoms make the electron energy levels spread into bands. The highest band that is filled with valence electrons is the valence band, and the next higher band into which electrons must go to conduct is the conduction band. The gap between them is the forbidden energy gap \(E_g\).

Step 2: Conductors (metals).
In a conductor the valence band and conduction band overlap, so \(E_g \approx 0\). A very large number of free electrons is available in the conduction band even at room temperature, so a conductor conducts electricity easily.

Step 3: Semiconductors.
In a semiconductor the valence band is full and the conduction band is empty at 0 K, and they are separated by a small forbidden gap (about \(E_g \approx 1\ \text{eV}\), e.g. \(1.1\ \text{eV}\) for silicon and \(0.7\ \text{eV}\) for germanium). At 0 K it behaves like an insulator, but at room temperature some electrons gain enough thermal energy to jump the gap into the conduction band, so it conducts a little; its conductivity increases with temperature.

Step 4: State the key difference.
The distinction is the size of the forbidden gap and the availability of conduction electrons: a conductor has zero (overlapping bands) gap and plenty of free electrons, while a semiconductor has a small gap and only a few thermally excited electrons.
\[\boxed{\text{Conductor: } E_g \approx 0 \text{ (overlap)};\quad \text{Semiconductor: } E_g \approx 1\ \text{eV (small gap)}}\]