Question

A semiconductor having electron and hole mobilities $\mu_{n}$ and $\mu_{p}$ respectively. if its intrinsic carrier density is $n_{i}$, then what will be the value of hole concentration $P$ for which the conductivity will be minimum at a given temperature?

• A. $n_{i} \sqrt{\frac{\mu_{n}}{\mu_{p}}}$
• B. $n_{h} \sqrt{\frac{\mu_{n}}{\mu_{p}}}$
• C. $n_{i} \sqrt{\frac{\mu_{p}}{\mu_{n}}}$
• D. $n_{h} \sqrt{\frac{\mu_{p}}{\mu_{n}}}$

Answer 1

Answer: (A)

$n_{i} \sqrt{\frac{\mu_{n}}{\mu_{p}}}$

Answer 2

The overall conductivity of a semiconductor is $\sigma=n_{e} e \mu_{e}+n_{p} e \mu_{p}$ $\sigma=e\left[\mu_{e} n_{e}+n_{p} \mu_{p}\right]$ Also $n_{e} n_{p}=n_{i}^{2}$ (For an intrinsic semiconductor) $n_{e}=\frac{n_{i}^{2}}{n_{p}}$ Now, $\sigma=e\left[\frac{n_{i}^{2}}{n_{p}} \mu_{n}+\mu_{p} n_{p}\right]$ On differentiating, $\frac{d \sigma}{d n_{p}} =e\left[\frac{n_{i}^{2}}{n_{p}^{2}} \mu_{n}+\mu_{p}\right]=0$ $\Rightarrow \mu_{p} =\frac{n_{i}^{2}}{n_{p}^{2}} \mu_{n}$ $\Rightarrow n_{p}=n_{i} \sqrt{\frac{\mu_{n}}{\mu_{p}}}$