Q. 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? ($kT =$ thermal energy, intrinsic carrier concentration $n_{i} = 1.4 \times \ 10^{10}$ ${cm}^{- 3}$ )
A) $\left( \frac{kT}{e} \right)$ ln (${4 \times 10}^{12}$)
B) $\left( \frac{kT}{e} \right)$ ln (${2.5 \times 10}^{23}$)
C) $\left( \frac{kT}{e} \right)$ ln ($10^{23}$)
D) $\left( \frac{kT}{e} \right)$ ln ($10^{9}$)
Explanation
(a) Constant potential at the junction
$V_{constant} = \frac{kT}{e}$ ln$\ \left( \frac{n_{a}n_{d}}{n_{i}^{2}} \right)$
$V_{constant} = \frac{kT}{e}$ ln$\ \left( \frac{10^{17} \times 10^{16}}{\left( 1.4 \times 10^{10} \right)^{2}} \right) = \frac{kT}{e}$ ln (${4 \times 10}^{12}$)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.