P-N Junction Equilibrium: Current Balance

In a semiconductor p-n junction, when there is no external voltage applied, the junction is said to be in a state of thermal equilibrium. In this equilibrium condition, there is a fundamental balance between two opposing types of charge carrier movements: diffusion and drift.

Diffusion Current in P-N Junction

Diffusion current occurs due to the concentration gradient of charge carriers. In a p-n junction:

• On the p-side, there is a high concentration of holes. These holes tend to move (diffuse) from the p-side to the n-side where hole concentration is low.
• On the n-side, there is a high concentration of electrons. These electrons tend to move (diffuse) from the n-side to the p-side where electron concentration is low.

This movement constitutes the diffusion current, for both holes and electrons, flowing across the junction.

Drift Current in P-N Junction

As diffusion occurs, a depletion region (or space-charge region) forms at the junction. Within this depletion region, an electric field is established, directed from the n-side to the p-side. This electric field causes drift current:

• Any minority electrons that wander into the p-side (from thermal generation) are swept by the electric field towards the n-side.
• Any minority holes that wander into the n-side (from thermal generation) are swept by the electric field towards the p-side.

This movement of minority carriers due to the electric field is the drift current.

Equilibrium Current Components Sum to Zero

When the p-n junction is in equilibrium (i.e., no external voltage is applied), the net current flowing across the junction is zero. This happens because the diffusion current and the drift current for each type of carrier exactly balance each other out.

Consider the individual carrier currents:

• For holes: The hole diffusion current \(I_{p,\text{diffusion}}\) (from p to n) is exactly balanced by the hole drift current \(I_{p,\text{drift}}\) (from n to p). Therefore, the net hole current \(I_p\) is: \[I_p = I_{p,\text{diffusion}} + I_{p,\text{drift}} = 0\] This implies \(I_{p,\text{diffusion}} = -I_{p,\text{drift}}\).
• For electrons: Similarly, the electron diffusion current \(I_{n,\text{diffusion}}\) (from n to p) is exactly balanced by the electron drift current \(I_{n,\text{drift}}\) (from p to n). Therefore, the net electron current \(I_n\) is: \[I_n = I_{n,\text{diffusion}} + I_{n,\text{drift}} = 0\] This implies \(I_{n,\text{diffusion}} = -I_{n,\text{drift}}\).

Since both the net hole current and the net electron current are zero separately, the total current across the junction is also zero:

Therefore, in a p-n junction with no externally applied voltage, the drift and diffusion components of the hole and electron currents sum to zero, ensuring no net flow of charge and maintaining thermal equilibrium.