Question

Pure silicon crystal of length $l\left(0.1m\right)$ and area $A$(${10}^{-4}{m}^2$) has the mobility of electrons (${\mu }_e$) and holes (${\mu }_h$) as $0.135m^2/Vs$ and $0.048m^2/Vs$ , respectively. If the voltage applied across it is $2V$ and the intrinsic charge concentration is $n_i=1.5\times {10}^6{m}^{-3}$, then the total current flowing through the crystal is

• A. $8.78\times {10}^{-17}A$
• B. $6.25\times {10}^{-17}A$
• C. $7.89\times {10}^{-17}A$
• D. $2.456\times {10}^{-17}A$

Answer 1

The correct option is A $8.78\times {10}^{-17}A$

Given:
$l=0.1m$
$A={10}^{-4}{m}^{-2}$
${\mu }_e=0.135m^2(Vs{)}^{-1}$
${\mu }_h=0.048m^2(Vs{)}^{-1}$
$n_i=1.5\times {10}^6{m}^{-3}$
$E=2V$

The conductivity is:

$\sigma =n_i({\mu }_e+{\mu }_h)e$
$\sigma =1.5\times {10}^6(0.135+0.048)1.6\times {10}^{-19}$
$\sigma =1.5\left(0.183\right)1.6\times {10}^{-13}$
$\sigma =0.4392\times {10}^{-13}S{m}^{-1}$

Now, the resistance is given by,
$R=\frac{l}{\sigma \left(A\right)}$
$R=\frac{0.1}{0.4392\times {10}^{-13}\left({10}^{-4}\right)}$
$R=0.2276\times {10}^{17}\Omega$

Hence, the current is:
$I=\frac{V}{R}=\frac{2}{0.2276\times {10}^{17}}$
$I=8.787\times {10}^{-17}A$