Question

An $n^{+}-n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1}=1\times {10}^{18}c{m}^{-3}$ and $N_{D2}=1\times {10}^{15}c{m}^{-3}$ corresponding to the $n^{+}$ and n regions respectively. At the operational temperature T, assume complete impurity ionization, $kT/q=25mV$ , and intrinsic carrier concentration to be $n_i=1\times {10}^{10}c{m}^{-3}$. What is the magnitude of the built-in potential of this device?

Answer 1

Ans : (d)

$V_o=V_T\ln \frac{n_1}{n_2}=V_T\ln \frac{N_{D1}}{N_{D2}}$
$=0.025\ln \frac{{10}^{18}}{{10}^{15}}=0.025\ln \left(1000\right)$
$=0.173V$