Question

Write the two processes that take place in the formation of a $p-n$ junction. Explain with the help of a diagram, the formation of depletion region and barrier potential in a $p-n$ junction.

Answer 1

The two process that takes place in the formation of a p-n junction are- Diffusion and drift.

1. When a p-n junction is being formed, holes diffuse from the p-side to the n-side$(p\to n)$ while elctrons diffuse from n-side to the pside $(n\to p)$.

2.This happens due to the concentration gradient across p and n sides.

3. This gives rise to a diffusion current across the junction.

4. Diffusion current density is given by

$J_{n\left(diff\right)}=q{D}_n\frac{dn\left(x\right)}{dx}$ ; $J_{p\left(diff\right)}=-q{D}_n\frac{dp\left(x\right)}{dx}$

where,

$J_{n\left(diff\right)}\to$diffusion current density due to electrons.

$J_{p\left(diff\right)\to }$diffusion current density due to holes.

$D_n\to$electrons diffusion coefficient.

$D_p\to$holes diffusion coefficient.

$n_{(}x)\to$ profile of $e_s$ withb respect to $x$

$P_{(}x)\to$profile of holes with respect to $x$.

5. The thickness of the depletion region is merely around one-tenth of a micrometer.Also, an electric field develops, this electric field is responsible for the movement of electrons from the p-side to the n-side and holes from the n-side to p-side.

6. This motion of charged carrier due to the electric field is called drift.

7. Hence, a drift current starts which is opposite inn direction to the diffusion current.

8. Drift current is given by

$J_{n\left(drift\right)}=nq{\mu }_{n}E$ ; $J_{p\left(drift\right)}=nq{\mu }_{n}E$.

where

$J_{n\left(drift\right)}\to$ Drift current density due to electrons.

$J_{p\left(drift\right)}\to$ Drift current density due to holes.

$n,p\to$Concentration of electron and holes respectively.

$E\to$Applied Electric Field.

9. With the formation of p-n junction, the holes from p-region diffuse into n-region and electrons from n-region diffuse into p-region and electrons hole pair combine and get annihilated.

10. This in turn, produce potential barrier voltage across the junction which oppose the further diffusion through the junction.

11. Thus, small region forms in the vecinity of the junction which is depleted of free charge carrier and has only immobile ions is called the depletion regions.

12. Since, the n-side loses electrons and p-side gains electrons a potential difference is developed across the junction of the two region.

13. This potential difference tends to oppose further motion of electrons from the n-region into the p-region.The same happens for holes too.

14.The reverse polarity of this potential oppose further flow of carrier and is thus called the barrier potential.