9 min readPathway sheet2-mark diffusion and drift, 3-mark formation of the depletion region and barrier potential with a diagram; also a NEET favourite

Formation of a p-n junction

At a p-n junction, diffusion of holes and electrons leaves a depletion region of fixed ions. Its field sets up a barrier potential and a drift current that balances diffusion.

Depletion regionA thin layer at the junction with fixed ions but almost no free carriers; about one-tenth of a micrometre thick

Barrier potential V₀The potential difference across the depletion region, with the n-side higher; a few tenths of a volt

Diffusion currentMajority carriers moving from high to low concentration; conventional direction p to n

Drift currentMinority carriers pushed by the junction field; direction n to p. At equilibrium it equals the diffusion current

How the junction forms

1
The p-side has many holes; the n-side has many free electrons.
2
Because of the concentration difference, holes diffuse from p to n and electrons from n to p. This gives a diffusion current from p to n.
3
Each electron leaving the n-side leaves behind a fixed positive donor ion. Each hole leaving the p-side leaves a fixed negative acceptor ion.
4
The layer of + ions on the n-side and − ions on the p-side has no free carriers. It is the depletion region.
5
These ions set up an electric field from n to p. The field pushes minority carriers across: a drift current from n to p.
6★
Diffusion current falls and drift current grows until they are equal. Then no net current flows. The potential difference across the depletion region is the barrier potential V₀, with the n-side positive.

★ key step

The chain of causes at a p-n junction

Diffusion current and drift current

Diffusion currentCaused by a concentration difference. Carried by majority carriers. Conventional direction p to n. It falls as the depletion region builds up.

Drift currentCaused by the electric field of the junction. Carried by minority carriers. Direction n to p. It grows until it equals the diffusion current.

How to draw the junction and the barrier

Draw a rectangle; label the left half p and the right half n.
In the middle, mark the depletion region: circled − signs on the p-side and circled + signs on the n-side.
Show small open circles (holes) in the rest of the p-side and dots (electrons) in the rest of the n-side.
Draw an arrow labelled E from the n-side to the p-side across the depletion region.
Below it, draw a graph of potential V against distance x: flat and low on the p-side, rising across the depletion region, flat and high on the n-side. Mark the rise as V₀.

Worked example: the field in the depletion region

Problem

A silicon p-n junction has a barrier potential of 0.7 V and a depletion region 0.1 μm (1 × 10⁻⁷ m) wide. Estimate the electric field in the depletion region, taking it as uniform.

Working

Formula: E = V/d.
E = 0.7 V ÷ 1 × 10⁻⁷ m = 7 × 10⁶ V m⁻¹.
This is a very strong field, even though the voltage is small, because the layer is so thin.

Answer

About 7 × 10⁶ V m⁻¹

In real life

Every LED bulb, phone charger and solar cell has at least one p-n junction. In a solar cell, the field of the depletion region separates the electrons and holes made by sunlight, which drives a current.

Exam angle

2 marks: “Define the depletion region and the barrier potential of a p-n junction.” Depletion region: a thin layer at the junction with fixed ions and no free carriers. Barrier potential: the potential difference across it, which stops further diffusion.

3 marks: “Explain, with a diagram, how the depletion region and barrier potential are formed in a p-n junction.” Holes and electrons diffuse across, leaving fixed − ions on the p-side and + ions on the n-side. Their field from n to p causes drift; equilibrium when drift = diffusion. Labelled diagram.

2 marks: “Distinguish between diffusion current and drift current in a p-n junction.” Diffusion: majority carriers, due to concentration difference, p to n. Drift: minority carriers, due to the junction field, n to p.

Remember it

Diffuse, Deplete, Drift, Draw level: carriers diffuse, ions are left (depletion), the field makes drift, and the two currents become equal.