In a semiconductor let the number of charge carriers be n and the average drift speed be v. An electric field is applied to it. If we increase the temperature of this semiconductor then:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → n will increase but v will decrease
Two effects act when a semiconductor is heated.
Number of carriers n: more covalent bonds break, so more electron–hole pairs are produced and n increases.
Drift speed v: the atoms vibrate more, so the carriers collide more often and the relaxation time \( \tau \) falls. Since \( v_d = \frac{eE\tau}{m} \), the drift speed decreases.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… As we increase temperature, average speed of the electrons, which act as the carriers of current, increases resulting in more frequent collisions. The average time of collisions τ, thus decreases with temperature. … For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in τ in Eq.(3.23) so that for such materials, ρ decreases with temperature.”