Question

An electric field is applied to a semiconductor. Let the number of charge carriers be $n$ and the average drift speed be $v$. If the temperature is increased,

• A. both $n$ and $v$ will increase
• B. $n$ will increase but $v$ will decrease
• C. $v$ will increase but $n$ will decrease
• D. both $n$ and $v$ will decrease

Answer 1

The correct option is B $n$ will increase but $v$ will decrease

When we increase the temperature, then more charge carriers are produced due to the breaking of covalent bands & average drift speed [(V${}_d$)${}_{avg}$] decreases with temperature due to increase of V${}_{rms}$ & decrease of relaxation time $\tau$.
$({\overrightarrow{V}}_d{)}_{av}=-\left(\frac{e\tau }{m}\right)\overrightarrow{E}$ & $\tau =\frac{\lambda }{v_{rms}}$
where $\lambda$ is mean free path, $v_{rms}=\sqrt{\frac{3KT}{m}}$