Pn Junction Formation

14.5 The p-n Junction — Heart of Modern Electronics

A p-n junction is a single semiconductor crystal in which one region is doped p-type and the adjacent region is doped n-type, with a metallurgical junction in between. It is the building block of every diode, transistor, solar cell, LED and integrated circuit. Almost all the magic of solid-state electronics emerges from what happens at this junction.

14.5.1 How a Junction is Formed

A p-n junction is fabricated by converting part of a doped wafer to the opposite type. Practical methods include:

• Diffusion: heating the wafer in an atmosphere containing the desired dopant so atoms diffuse into the surface region.
• Ion implantation: firing dopant ions into the crystal at high energies.
• Epitaxial growth: depositing oppositely-doped layers on the surface.

Two physical processes drive the formation of the equilibrium junction: diffusion (driven by concentration gradients) and drift (driven by the resulting electric field).

Step 1 — Diffusion

Just after joining, the n-side has a huge surplus of electrons and the p-side has a huge surplus of holes. Random thermal motion drives:

• Electrons from n → p (where they are minority).
• Holes from p → n (where they are minority).

This concentration-gradient-driven motion is the diffusion current I_d, directed from p → n by convention.

Step 2 — Space charges and the depletion region

When an electron diffuses from n → p, it leaves behind an ionised donor with a fixed positive charge — these donors are bonded into the lattice and cannot move. Similarly, a hole crossing from p → n leaves behind an ionised acceptor with a fixed negative charge.

Result: a thin layer near the junction loses its mobile charge carriers, exposing the immobile ionised dopant cores. This depleted region — about 0.1 μm thick — is the depletion region:

• n-side of junction: positive space charge (ionised donors)
• p-side of junction: negative space charge (ionised acceptors)

Step 3 — Built-in electric field and drift

The two oppositely charged layers act like a parallel-plate capacitor. They produce an electric field E, directed from the n-side toward the p-side (i.e., from + to −). This field exerts forces opposing further diffusion: it pushes any electron that strays into the depletion region back to n, and any hole back to p. Minority carriers that wander into the depletion edge from either side are however swept across by the field, giving rise to a drift current I_dr (in the opposite direction to I_d).

Step 4 — Equilibrium

As more carriers diffuse, the depletion region grows; as the depletion region grows, the built-in field grows; as the field grows, drift current grows. Equilibrium is reached when

From this point on, the junction sits in a steady state with a fixed depletion-region width and a fixed potential difference across it.

Barrier Potential V₀

The depletion region's space charges set up not just a field but also a potential step across the junction — the n-side ends up at a higher potential than the p-side. This step is called the barrier potential or built-in potential V₀ and it opposes further diffusion of majority carriers.

Worked Example 14.3 (NCERT)

Width of Depletion Region — A Brief Note

The depletion-region width depends on doping levels: heavier doping → narrower depletion region (because fewer ionised cores are needed to set up the same V₀). Typical numbers:

• Light doping (10¹⁵ /cm³): depletion width ~ 1 μm
• Heavy doping (10¹⁸ /cm³): depletion width ~ 0.01 μm = 10 nm

The asymmetry between p and n doping decides how the depletion region distributes itself — the side with lighter doping has the wider depletion layer (it needs more space to accumulate enough charge to balance the heavier-doped side).

Interactive — p-n Junction Equilibrium Visualizer