Question

The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is $6\times {10}^{19}$ per cubic metre. When some phosphorous impurity is doped into a germanium sample, the concentration of conduction electrons increases to $2\times {10}^{23}$ per cubic metre. The concentration of the holes in the doped germanium is $18\times {10}^x$. The value of $x$ is .(Integer only)

Answer 1

Initially, the number of conduction electron per cubic metre=$6\times {10}^{19}$

For an intrinsic semiconductor,

Number of holes per cubic metre=Number of electrons per cubic metre.

$n_e=n_h=6\times {10}^{19}$

Given that, after doping,

No. of conduction electrons per cubic metre,
$n_e^{\prime }=2\times {10}^{23}$

For an extrinsic semiconductor,

Concentration of holes $\times$ concentration of conduction electrons=constant.

$n_e\times n_h=n_e^{\prime }\times n_h^{\prime }$

$\Rightarrow (6\times {10}^{19})(6\times {10}^{19})=(2\times {10}^{23}\times n_h^{\prime })$

$\Rightarrow n_h^{\prime }=\frac{36\times {10}^{38}}{2\times {10}^{23}}=18\times {10}^{15}$

Comparing with the given value of $n_h^{\prime }=18\times {10}^x$

$\therefore x=15$