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: Set up the comparison using the forbidden gap.
Whether a solid conducts is decided by how easily electrons can reach the conduction band from the valence band, which depends on the width of the forbidden energy gap \(E_g\) that lies between these two bands.

Step 2: Describe a conductor.
In metals the conduction band and valence band are not separated at all, they overlap. There is effectively no forbidden gap (\(E_g = 0\)), so electrons are already free to move and even a tiny voltage produces a large current. This is why the resistance of a metal is low and rises slightly with temperature.

Step 3: Describe a semiconductor.
In a semiconductor the two bands are separate but the gap is narrow, of the order of \(1\ \text{eV}\). At absolute zero no electron is in the conduction band, so it is an insulator; as the temperature rises, thermal energy lifts a few electrons across the gap, leaving holes behind, and both the electrons and holes carry current. Its conductivity therefore increases as temperature increases.

Step 4: Summarise with numbers.
Conductor: bands overlap, \(E_g \approx 0\), many free electrons, high conductivity. Semiconductor: small gap \(E_g \approx 0.7\) to \(1.1\ \text{eV}\), few free carriers at room temperature, moderate and temperature-sensitive conductivity.
\[\boxed{\text{Overlapping bands} \Rightarrow \text{conductor};\ \text{small gap} \Rightarrow \text{semiconductor}}\]