9.1.3.5. p-n Junctions

Table of Contents

Forming the Junction

A p-n junction is created when a p-type semiconductor and an n-type semiconductor are joined together in a single crystal. The p-type side has many holes as majority charge carriers, while the n-type side has many electrons as majority charge carriers. The junction is the boundary region where these two differently doped materials meet.

When they are first brought into contact, the charge carriers do not stay separated. Because the concentration of electrons is much higher on the n-side than on the p-side, electrons diffuse from the n-side into the p-side. In the same way, holes diffuse from the p-side into the n-side. This diffusion is driven by the difference in carrier concentration.

What Happens Near the Boundary

As electrons leave the n-side, they expose positively charged donor ions that cannot move. As holes leave the p-side, they expose negatively charged acceptor ions that also remain fixed in place. These fixed ions create a region near the junction that has very few mobile charge carriers.

This region is called the depletion region, or depletion layer, because it is depleted of free electrons and holes.

Rendering scientific sketch…

A simple p-n junction and depletion region

Built-In Electric Field

The fixed positive ions on the n-side edge and fixed negative ions on the p-side edge produce an electric field inside the depletion region. This field points from the positive charges toward the negative charges, which means from the n-side toward the p-side.

This electric field opposes further diffusion. Electrons trying to diffuse from n to p are pushed back by the field, and holes trying to diffuse from p to n are also pushed back. Very quickly, an equilibrium is reached where diffusion and electric effects balance.

In equilibrium, the p-n junction develops a depletion region and a built-in electric field that opposes further carrier diffusion.

Barrier Potential

The electric field in the depletion region creates a potential difference across the junction. This is called the built-in potential, junction potential, or barrier potential. It acts like an energy barrier that carriers must overcome to cross the junction.

Typical values are about $0.7 \, \text{V}$ for silicon and about $0.3 \, \text{V}$ for germanium, though the exact value depends on doping and temperature.

The barrier potential is not an externally applied voltage. It forms naturally because of carrier diffusion and charge separation at the junction.

Equilibrium Condition

At equilibrium, there is no net current across the junction. This does not mean that charges stop moving completely. Electrons and holes still have thermal motion, but the diffusion current and the drift current cancel each other.

The diffusion current comes from carriers moving from high concentration to low concentration. The drift current comes from the electric field in the depletion region.

$$
I_{\text{net}} = I_{\text{diffusion}} + I_{\text{drift}} = 0
$$

This balance is the key feature of an unbiased p-n junction.

Forward Bias

If an external voltage is applied so that the p-side is connected to the positive terminal and the n-side to the negative terminal, the junction is forward biased.

The external field opposes the built-in field, which reduces the barrier potential and narrows the depletion region. As a result, majority carriers can cross the junction more easily. Electrons from the n-side move into the p-side, and holes from the p-side move into the n-side. A large current can then flow.

Rendering scientific sketch…

Forward biased p-n junction

Reverse Bias

If the external voltage is applied in the opposite way, with the p-side connected to the negative terminal and the n-side to the positive terminal, the junction is reverse biased.

Now the external field adds to the built-in field. The barrier potential increases and the depletion region widens. Majority carriers are pulled away from the junction, so current is strongly reduced.

A very small reverse current can still exist because of minority carriers, but for ordinary reverse bias it is much smaller than the forward current.

Forward bias decreases the barrier and allows strong current flow. Reverse bias increases the barrier and suppresses current.

Rendering scientific sketch…

Reverse biased p-n junction

Why the Junction Conducts in One Direction

This one-way behavior is what makes the p-n junction the basic element of a diode. In forward bias, the junction allows current easily. In reverse bias, it resists current. This is called rectifying behavior.

The reason is not that the material suddenly changes, but that the depletion region and barrier potential respond strongly to the direction of the applied voltage.

Current Voltage Behavior

The current through an ideal p-n junction diode follows an exponential relation with applied voltage:

$$
I = I_S \left(e^{\frac{qV}{kT}} - 1\right)
$$

Here, $I$ is the diode current, $I_S$ is the reverse saturation current, $q$ is the elementary charge, $V$ is the applied voltage across the junction, $k$ is Boltzmann's constant, and $T$ is the absolute temperature.

This equation shows that a small increase in forward voltage can produce a large increase in current.

For an ideal diode junction,
$$
I = I_S \left(e^{\frac{qV}{kT}} - 1\right)
$$
Forward current rises rapidly with voltage, while reverse current remains approximately equal to $-I_S$ until breakdown.

Breakdown

If the reverse voltage becomes very large, the junction can enter breakdown. In this region, the reverse current increases sharply. Two main mechanisms are commonly discussed, Zener breakdown and avalanche breakdown, but the detailed treatment belongs to diode behavior more broadly.

For beginners, the important point is that ordinary reverse bias gives only a tiny current, but sufficiently high reverse bias can cause a sudden large current.

Summary Table

Condition	Barrier potential	Depletion region	Current
No external bias	Natural built-in value	Normal width	Net current zero
Forward bias	Decreases	Narrows	Large current
Reverse bias	Increases	Widens	Very small current
Reverse breakdown	Effectively overcome	Strong conduction begins	Large reverse current

Physical Picture to Remember

The p-n junction is best understood as a boundary where diffusion first mixes carriers, then fixed ions create an electric field, and that field builds a barrier. The balance of diffusion and electric forces creates equilibrium. External voltage changes that balance. One direction lowers the barrier, the other raises it.

Key ideas of a p-n junction:
$$
\text{diffusion} \rightarrow \text{depletion region} \rightarrow \text{electric field} \rightarrow \text{barrier potential}
$$
This sequence explains why the junction rectifies current.

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9.1.3.5. p-n Junctions

Forming the Junction

What Happens Near the Boundary

Built-In Electric Field

Barrier Potential

Equilibrium Condition

Forward Bias

Reverse Bias

Why the Junction Conducts in One Direction

Current Voltage Behavior

Breakdown

Summary Table

Physical Picture to Remember

Comments

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