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According to the Wikipedia's graph of electric field in a p-n junction, there is no electric field outside the deletion region and hence no minority charge carriers move into the other side. Also, the minority charge carriers which cause the drift current are swept off. So there are no more free charge carriers in the depletion region. Then the drift current will stop whereas the diffusion current will not. So how is the equilibrium maintained in a p-n junction ? Graph

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The free carriers leave behind charged atoms of opposite sign; they provide an electric field that balances the diffusion current. Specifically, as the electrons drift into the p-region positively charged atoms are created and similarly when holes are swept to the n-side negatively charged atoms are created. So an electric field is setup between these fixed charges that oppose the diffusion current.

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There is only drift and diffusion at the edge of the depletion region. The drift and diffusion of carriers are equal and opposite so there is no net current. In the centre of the depletion region there is no drift or diffusion, and also no net current.

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The short answer is: drift current never stops.

Drift current is always present in the depletion region, but it is compensated by diffusion current, so that the result is a void net current.

$$\vec{J}_A=-\vec{J}_D$$ where $A$ refers to drift component and $D$ to diffusion component.

In other words, it is a dynamic equilibrium: it's not they dissapear, they continue flowing all the time, but they are compensating each other so that the net effect is 0. There are as many charges moving leftwards as moving rightwards. So:

$$\vec{J}=\vec{J}_A+\vec{J}_D=\vec{0}$$

This, of course, refers to the equilibrium reached after a transient time. This is stationary regime. IF you plugged a P semiconductor to a N semiconductor, it would need some time (Transient) to reach this situation, but once it is reached, $J=0$.

This happens in the depletion region. The P and N regions are neutral regions (or quasi-neutral), and they have no electric field inside or moving charges. (They've got them, but they are negligible). Pretty much the same as a metal in equilibrium.

This happens in thermal equilibrium conditions. The situation will change if you disturb the equilibrium by, for example, applying an external potential $V$

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