Exercise 1
The conductivity of a semiconductor increases with increase in temperature because
(a)
number density of free current carriers increases.
(b)
relaxation time increases.
(c)
both number density of carriers and relaxation time increase.
(d)
number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density.
NCERT’s answer
(d)
(d) Carrier density rises sharply with temperature; relaxation time falls only slightly, so conductivity rises.\[\sigma=\frac{n e^{2}\tau}{m} \]\[T\uparrow \Rightarrow n\uparrow\ \text{(more bonds break)},\qquad \tau\downarrow\ \text{(more lattice collisions)} \]\[\frac{\Delta n}{n}\gg\frac{\lvert\Delta\tau\rvert}{\tau} \Rightarrow \sigma\uparrow \]