The electron and hole concentration in an extrinsic semiconductor in thermal equilibrium is given by:
Where \( n_e \) = electron density
\( n_h \) = hole density
\( n_i \) = intrinsic charge density
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( n_e \cdot n_h = n_i^2 \)
In thermal equilibrium the rate of generation of electron-hole pairs equals their rate of recombination. Doping raises one carrier concentration and lowers the other, but their product stays fixed at the intrinsic value (the mass action law):
\( \displaystyle n_e\,n_h = n_i^{2} \)
This holds for both n-type and p-type semiconductors at a given temperature.
NCERT (2026-27):
Extrinsic Semiconductor – “… The electron and hole concentration in a semiconductor in thermal equilibrium is given by
\( \displaystyle n_e n_h = n_i^2 \qquad (14.5) \)”