The p–n Junction

Introduction

Joining p-type and n-type semiconductor regions creates more than a seam. Electrons tend to diffuse from the n side toward the p side, while holes tend to diffuse in the opposite direction. Their early movement exposes fixed ionised dopant charges, and the resulting electric field opposes further net diffusion. The equilibrium structure is a depletion region with a built-in potential, the starting point for diodes, LEDs and solar cells.

Core explanation

Before contact, the n region has many electrons and the p region many holes. After contact, some electrons and holes cross the boundary and recombine. Near the interface, the n side is left with positively charged ionised donors and the p side with negatively charged ionised acceptors . These dopants are fixed in the lattice. The electric field points from positive n-side charge toward negative p-side charge, opposing further majority-carrier diffusion. At equilibrium, diffusion and drift currents cancel so total current is zero; microscopic carrier motion does not cease. MIT's junction-electrostatics lecture develops the built-in potential and depletion approximation.

The depletion approximation treats the space-charge region as mostly free of mobile carriers and the regions outside it as approximately neutral. If donor and acceptor concentrations are uniform, the exposed charges on each side must balance in magnitude: N D x n = N A x p for depletion widths x n and x p. The more lightly doped side therefore occupies more of the total depletion width. This is an ideal abrupt-junction model; real profiles and interfaces may be graded or contain traps. For nondegenerate, fully ionised, abrupt junctions at temperature T, the built-in potential magnitude is V bi = (k BT/e) ln(N A N D/n i²). It is a consequence of equilibrium carrier statistics and electrostatics, not a battery that can deliver continuous external power by itself.

On an energy-band diagram at thermal equilibrium, E c and E v bend across the junction, following local electrostatic potential. The equilibrium Fermi level remains flat because electron electrochemical potential is uniform. If the band edges were flat across dissimilar doped regions while E F stayed flat, their local carrier concentrations would not match the charge distribution required by contact. A voltmeter connected with ordinary metal leads cannot simply read V bi as a free external voltage in equilibrium, because contact potentials elsewhere in the closed measurement path also matter.

The junction stores charge in the depletion region and has a voltage-dependent capacitance. Forward bias reduces the effective barrier and narrows depletion; reverse bias raises it and widens the region, within the ordinary operating regime. The detailed current response involves carrier injection, diffusion and recombination and belongs to the next page. MIT's materials lecture on inhomogeneous semiconductors connects junction charge, potential and band diagrams.

Step-by-step reasoning

1. Label the p and n sides and their majority carriers before contact. 2. Show initial diffusion and recombination across the interface. 3. Mark fixed negative acceptors on p side and fixed positive donors on n side. 4. Draw the field from n to p and explain its opposition to majority diffusion. 5. At equilibrium, use charge balance and a flat Fermi level to check the diagram.

Visual explanation

Make three aligned panels against position: charge density, electric field and energy bands. Charge density is negative on the p-side depletion portion and positive on the n-side portion, with equal total area magnitudes. The field points from n to p. E c and E v bend across the space-charge region while E F remains a horizontal line.

Real-world analogy

Two crowded rooms connected by a doorway initially exchange people unevenly. As movement leaves behind opposite fixed charges—an effect absent from the room analogy—an electric “slope” develops that balances further net diffusion. The analogy explains how a concentration tendency can be countered, but the charges and field must be kept in the semiconductor picture.

Real-world example

A silicon p–n junction in a diode consists of doped regions grown or fabricated within one crystal. Its depletion zone may extend farther into the lightly doped side. If a designer wants a wide depletion region for a photodetector, adjusting doping is one route, though dark current, field strength and breakdown also impose limits.

Why?

Why is there no steady external current from the built-in field alone at equilibrium? The electric-field-driven drift current exactly balances diffusion current. The closed system has one Fermi level and no external energy source maintaining a difference in electrochemical potential. The internal field can separate newly generated carriers under illumination, but the illumination supplies energy.

Common misconception

“The depletion region contains no charges” is false: it is depleted of most mobile majority carriers but contains fixed dopant charges. “The junction field points from p to n” reverses the sign; it points from the exposed positive donors on n side toward exposed negative acceptors on p side.

Worked example

Suppose an abrupt junction has N D = 1 × 10¹⁶ cm⁻³ and N A = 4 × 10¹⁶ cm⁻³. Charge balance gives N D x n = N A x p, so x n/x p = N A/N D = 4 . Thus 80% of the total depletion width lies on the less heavily doped n side in this ideal approximation. This ratio does not require the absolute width or dielectric constant, but it assumes uniform complete ionisation and an abrupt interface.

Quick check

1. Which side of an abrupt junction has positive fixed charge in the depletion region? Answer: The n side, where ionised donor atoms remain after mobile electrons have diffused away.

Exam focus

Distinguish mobile and fixed charges. Show the electric-field arrow correctly and explain drift–diffusion balance. If using N D x n = N A x p, write the assumption of uniform dopants. A flat equilibrium Fermi level can coexist with bending band edges.

Advanced insight

Interface traps, band offsets in heterojunctions and degenerately doped regions require refinements beyond the ideal homojunction approximation. The depletion capacitance responds to voltage because charge separation width changes. Capacitance–voltage measurements can therefore provide information about doping profiles, provided interface and series-resistance effects are controlled.

Summary

A p–n junction forms when carrier diffusion exposes fixed dopant charges, creating a field and built-in potential. Its depletion region is wider on the more lightly doped side. At equilibrium drift balances diffusion, total current is zero and a single Fermi level remains flat across bent bands.

Practice questions

1. Which carrier initially diffuses from the n side toward the p side? Answer: Electrons, because their concentration is much higher on the n side. 2. If N A = 2N D, how do ideal depletion widths compare? Answer: x n = 2x p; the lightly doped n side occupies twice the width. 3. Why can an equilibrium junction not act as a battery solely from V bi? Answer: Drift and diffusion currents balance, and a closed equilibrium circuit has no sustained electrochemical-potential difference. 4. Is the depletion region completely empty of electrical charge? Answer: No. It contains exposed fixed donor and acceptor ions, though few mobile majority carriers.