If the temperature of a semiconductor is increased from room temperature, then the number density of free electrons and the resistivity _______ and _________, respectively.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → increases, decreases
In a semiconductor the valence and conduction bands are separated by a small energy gap. When the temperature rises, more covalent bonds break and more electrons are thermally excited into the conduction band, so the number density of free electrons (and holes) increases sharply.
The conductivity depends on the carrier densities, so it rises with them and the resistivity falls.
\( \displaystyle \rho = \frac{1}{e\,(n_e\mu_e + n_h\mu_h)} \)
So a semiconductor has a negative temperature coefficient of resistivity.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… Unlike metals, the resistivities of semiconductors decrease with increasing temperatures. A typical dependence is shown in Fig. 3.10.”
Temperature Dependence of Resistivity – “… For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in \( \tau \) in Eq.(3.23) so that for such materials, \( \rho \) decreases with temperature.”