# p-n junction depletion region

During forward biasing, holes move towards n side and electrons move towards p side. The diffusion of electrons and holes into the depletion layer decreases its width.

If more holes and electrons will diffuse, wouldn't they form more immobile ions i.e. increase the width of depletion region. How come this decreases its width?

You can easily show that the width of the depletion layer is given by $$W=\sqrt{\frac{2\varepsilon}{q}\left(\frac{N_a +N_d}{N_a N_d}\right)V_{bi}},$$ where $N_i$ is the acceptors/donors atoms density and $V_{bi}$ is the built-in voltage. If you forward bias the p-n junction, equation above modifies as follows: $$W=\sqrt{\frac{2\varepsilon}{q}\left(\frac{N_a +N_d}{N_a N_d}\right)\left(V_{bi}-V\right).}$$ So you can see that high forward bias voltage $V$ means decreasing of $W$.
• So depletion region disappears when $V>V_{b}i$? – Stacy Barrymore Feb 15 '18 at 12:17