p-n Junction

Formation of a p-n Junction

A p-n junction is the fundamental building block of almost all semiconductor devices — diodes, transistors, solar cells, LEDs, and integrated circuits. Understanding how this junction behaves is essential before you can analyse any of those devices.

When a piece of p-type semiconductor and a piece of n-type semiconductor are brought into intimate contact, a p-n junction is formed. In practice, this is done by doping one side of a single crystal with acceptor impurities and the other side with donor impurities, so the entire structure remains one continuous crystal. The plane where the two regions meet is called the metallurgical junction.

What Happens at the Junction — The Depletion Region

Immediately after the junction is formed, a dramatic redistribution of charges begins.

On the p-side, the majority carriers are holes (positive charge). On the n-side, the majority carriers are electrons (negative charge). Right at the junction, there is a huge concentration gradient: holes are abundant on the p-side and scarce on the n-side, and vice versa for electrons. Consequently, holes from the p-side begin to diffuse across the junction into the n-side, and electrons from the n-side diffuse into the p-side.

As a hole leaves the p-side, it leaves behind a fixed, negatively charged acceptor ion (a trivalent impurity atom that has accepted an electron). As an electron leaves the n-side, it leaves behind a fixed, positively charged donor ion (a pentavalent impurity atom that has donated an electron). These fixed ions are immobile — they are locked in the crystal lattice.

This creates a thin layer on either side of the junction that is depleted of mobile charge carriers (free electrons and holes). This region is called the depletion region or depletion layer.

Because the p-side of the depletion region now has a net negative charge (fixed acceptor ions) and the n-side has a net positive charge (fixed donor ions), an electric field is established across the depletion region, directed from the n-side toward the p-side. This electric field opposes further diffusion of majority carriers — it pushes holes back into the p-side and electrons back into the n-side.

The diffusion of carriers and the drift due to the electric field eventually reach a dynamic equilibrium. At equilibrium, the net current across the junction is zero.

The Built-in Potential Barrier

The electric field in the depletion region corresponds to a potential difference across the junction. This potential difference is called the built-in potential or barrier potential, denoted by $V_0$. For a silicon p-n junction at room temperature, $V_0$ is approximately 0.7 V; for germanium, it is about 0.3 V.

This potential barrier prevents the majority carriers from crossing the junction under equilibrium conditions. Only those carriers with enough energy to overcome this barrier can diffuse across.

Biasing a p-n Junction

Applying an external voltage across a p-n junction is called biasing. The behaviour of the junction changes dramatically depending on the polarity of the applied voltage.

Forward Bias

When the positive terminal of the battery is connected to the p-side and the negative terminal to the n-side, the junction is said to be in forward bias.

The applied voltage $V$ opposes the built-in potential $V_0$. The net potential barrier across the depletion region becomes $V_0 - V$. As $V$ increases, the barrier height decreases. This allows more majority carriers (holes from p-side, electrons from n-side) to diffuse across the junction.

The width of the depletion region decreases under forward bias because the applied field pushes majority carriers toward the junction, where they recombine with the fixed ions, neutralising them.

When the applied voltage exceeds the built-in potential (i.e., $V > V_0$), the barrier essentially disappears, and a large forward current flows easily. This is why a forward-biased diode conducts strongly above a threshold voltage (about 0.7 V for silicon).

Reverse Bias

When the positive terminal of the battery is connected to the n-side and the negative terminal to the p-side, the junction is in reverse bias.

The applied voltage $V$ now adds to the built-in potential. The net barrier becomes $V_0 + V$, which is larger than the equilibrium barrier. This makes it even harder for majority carriers to diffuse across.

The width of the depletion region increases under reverse bias because the applied field pulls majority carriers away from the junction, exposing more fixed ions.

Under reverse bias, only a very small current flows — this is the reverse saturation current, $I_0$, which is due to the drift of minority carriers (electrons from the p-side and holes from the n-side) across the junction. This current is typically in the microampere or nanoampere range and is almost independent of the applied reverse voltage (until breakdown occurs).

The p-n Junction as a Rectifier

The most important property of a p-n junction is that it allows current to flow easily in one direction (forward bias) and almost not at all in the opposite direction (reverse bias). This property is called rectification. A p-n junction diode acts as a rectifier — it converts alternating current (AC) to direct current (DC).

Summary of Junction Behaviour Under Bias

The Depletion Region Width

The width of the depletion region $W$ depends on the doping concentrations on both sides. For an abrupt junction (where doping changes sharply at the junction), the depletion width is given by:

where:

• $\epsilon$ is the permittivity of the semiconductor material.
• $N_A$ is the acceptor concentration on the p-side.
• $N_D$ is the donor concentration on the n-side.
• $V$ is the applied voltage (positive for forward bias, negative for reverse bias). …