Question

The drift current in a p-n junction is 20.0 µA. Estimate the number of electrons crossing a cross section per second in the depletion region.

Answer 1

Given:
Drift current, i_d = 20 µA = 20 × 10⁻⁶ A
Both holes and electrons are moving and contributing to the current flow.
We know that current is the rate of the flow of charge.
Thus, we need to find the number of electrons crossing unit area per second.
Now,
t = 1 s
$$\begin{gathered} i_d=\frac{Q}{T} \\ \because T=1\mathrm{s} \\ \therefore i_d=Q=ne \\ \Rightarrow n=\frac{i_d}{e} \end{gathered}$$
So, the total number of charge carriers crossing the depletion region is given by
$$\begin{gathered} n=\frac{20\times {10}^{-6}}{2\times 1.6\times {10}^{-19}} \\ \Rightarrow n=6.25\times {10}^{13} \end{gathered}$$
Also, the number of electrons crossing the depletion region is given by
$$\begin{gathered} n_e=\frac{n}{2}=\frac{6.25\times {10}^{13}}{2} \\ \Rightarrow n_e=3.1\times {10}^{13} \end{gathered}$$