Animated Solution for Physics - Semiconductors: In a $p$-$n$ junction diode not connected to any circuit

Have you ever wondered what happens inside a semiconductor diode when it's just sitting on a table, completely disconnected from any circuit? It might seem like nothing is going on, but at the microscopic level, a fascinating balancing act is taking place. Let's dive into the physics of an unbiased $p$-$n$ junction.

When a $p$-type semiconductor is joined to an $n$-type semiconductor, we create a $p$-$n$ junction. The $p$-side is teeming with holes (majority carriers), while the $n$-side is packed with electrons. Nature loves balance, so due to this massive concentration gradient, charge carriers begin to move.

Holes from the $p$-side diffuse across the junction into the $n$-side, and electrons from the $n$-side diffuse into the $p$-side. This process is known as diffusion.

As these charge carriers cross the junction, they leave something behind. When an electron leaves the $n$-side, it leaves behind a positively charged donor ion. Similarly, when a hole leaves the $p$-side, it leaves behind a negatively charged acceptor ion.

Unlike the electrons and holes, these ions are locked in the crystal lattice and cannot move. They accumulate near the junction, creating a region devoid of free charge carriers. This region is aptly named the depletion region.

Now, we have a layer of positive ions on the $n$-side of the junction and a layer of negative ions on the $p$-side. What happens when you have separated positive and negative charges? You get an electric field!

An internal electric field $\vec{E}$ is established within the depletion region. By convention, the direction of an electric field is always from positive to negative. Therefore, this internal electric field is directed from the $n$-side to the $p$-side.

Because there is an electric field pointing from the $n$-side to the $p$-side, it means that work must be done to move a positive charge from the $p$-side to the $n$-side. In terms of electric potential, the $n$-side is at a higher potential than the $p$-side.

This potential difference is known as the barrier potential ($V_0$). It acts as a hill that stops further diffusion of majority carriers, bringing the system into a state of dynamic equilibrium.

So, even without any external battery, an unbiased $p$-$n$ junction hosts a built-in electric field directed from the $n$-side to the $p$-side, keeping the microscopic world in perfect harmony!