Question

For an intrinsic semiconductor ($n_h$ and $n_e$ are the number of holes per unit volume and number of electrons per unit volume respectively)

• A. $n_h<n_e$
• B. $n_h = n_e$
• C. $n_h = \frac{n_e}{2}$
• D. $n_h>n_e$

Hint:

Logic Tip: In "intrinsic" (pure) semiconductors, balance is perfect ($n_e = n_h$). Extrinsic doping breaks this balance: N-type has excess electrons ($n_e>n_h$) due to donor impurities, and P-type has excess holes ($n_h>n_e$) due to acceptor impurities.

Answer 1

The Correct Option is B

Concept:
An intrinsic semiconductor is a pure semiconductor without any significant dopant species present. Its electrical conductivity is determined solely by its inherent properties.
Step 1: Understand the mechanism of charge carrier generation.
At absolute zero ($0\text{ K}$), an intrinsic semiconductor acts as a perfect insulator because all electrons are bound in covalent bonds in the valence band. As the temperature increases, thermal energy excites some electrons across the bandgap into the conduction band.
Step 2: Relate electron and hole populations.
Every time an electron is thermally excited into the conduction band, it leaves behind a vacancy in the valence band. This vacancy acts as a positive charge carrier and is called a "hole." Because these charge carriers are strictly generated in pairs (electron-hole pairs), the number density of conduction electrons ($n_e$) must exactly equal the number density of holes ($n_h$). $$n_e = n_h = n_i$$ where $n_i$ is the intrinsic carrier concentration.