Question

A $p-n$ junction has acceptor impurity concentration of $10^{17}\, cm ^{-3}$ in the $P$ side and donor impurity concentration of $10^{16} cm ^{-3}$ in the $N$ side. What is the contact potential at the junction? $(k T=$ thermal energy, intrinsic carrier concentration $\left.n_{i}=1.4 \times 10^{10}\, cm ^{-3}\right)$

• A. $( kT / e ) \ln \left(4 \times 10^{12}\right)$
• B. $( kT / e ) \ln \left(2.5 \times 10^{23}\right)$
• C. $(k T / e) \ln \left(10^{23}\right)$
• D. $( kT / e ) \ln \left(10^{9}\right)$

Answer 1

Answer: (A)

Constant potential at the junction
$ V_{\text {constant }} \frac{k T}{e} \ln \left(\frac{n_{a} n_{d}}{n_{i}^{2}}\right) $
$\therefore V_{\text {constant }} =\frac{k T}{e} \ln \left(\frac{10^{17} \times 10^{16}}{\left(1.4 \times 10^{10}\right)^{2}}\right) $
$=\frac{k T}{e} \ln \left(4 \times 10^{12}\right) $