# P–n junction and depletion region

Canonical: https://semiaifoundry.com/learn/atlas/pn-junction/
Revision: 2026-10-07
Rights: https://semiaifoundry.com/ai-atlas/licenses.html

Device physics · Atlas v1.3.0

# P–n junction and depletion region

Creates an internal electric field between differently doped regions.

[Explore in Atlas](https://semiaifoundry.com/ai-atlas/#pn-junction)Device-scale junction; width is illustrative and bias-dependent

Learning objectiveExplain how junction concentration sets a built-in potential.

## The mechanism

When p-type and n-type regions meet, carrier concentration differences drive diffusion. Mobile charge redistributes near the interface, leaving a region whose fixed ionized dopants produce an electric field. At thermal equilibrium, drift and diffusion balance, so the internal field does not provide a perpetual power source. The depletion approximation models this region as mostly depleted of mobile carriers and makes its electrostatics easier to understand. Applied voltage changes the barrier and charge distribution. Junctions appear in transistor bodies and isolation structures as well as diodes. They help explain why a transistor is more than three metal terminals attached to an otherwise featureless silicon block.

1.  Bring differently doped p-type and n-type regions into contact.
2.  Let carriers redistribute until fixed dopant charge creates an opposing electric field.
3.  At equilibrium, balance carrier diffusion with field-driven drift; applied bias shifts that balance.

## Science and assumptions

### Built-in junction potential

$$
V_{\mathrm{bi}}=\frac{k_B T}{q}\ln\!\left(\frac{N_A N_D}{n_i^2}\right)
$$

Built-in potential equals thermal voltage times the natural logarithm of the acceptor–donor density product divided by intrinsic carrier density squared.

Symbols and units

V\_bi

Built-in potential

V

k\_B

Boltzmann constant

J/K

T

Absolute temperature

K

q

Positive elementary charge

C

N\_A

Effective ionized acceptor density

cm⁻³

N\_D

Effective ionized donor density

cm⁻³

nᵢ

Intrinsic carrier density

cm⁻³

The internal potential follows from the different equilibrium carrier populations. $N_{A}$ and $N_{D}$ are acceptor and donor densities, while $k_{B}$ T / q is the thermal voltage.

Assumptions Ideal equilibrium junction with nondegenerate regions and effective ionized doping densities; this is not an externally available battery voltage.

## Engineering example

Increasing the product $N_{A}$ $N_{D}$ increases the logarithm in $V_{bi}$ at fixed T; series resistance and breakdown are separate design constraints.

## Distinctions and tradeoffs

The built-in junction field is not a battery that can supply unlimited power to an external circuit.

Junctions provide useful isolation. Their capacitance and leakage add delay and power costs.

Electrical isolation keeps nearby circuit functions independent. Its nonideal behavior contributes to chip power and timing limits.

## Specifications and interfaces

Equilibrium

Drift balances diffusion

No net equilibrium current.

Depletion region

Bias-dependent width

Also depends on doping and material properties.

Built-in potential

Internal electrostatic barrier

Not a free external voltage source.

### Interfaces

P and N regions Input

Carrier concentration difference

Internal field Output

Electrostatic barrier and junction capacitance

## Check your understanding

### What happens to net current at thermal equilibrium?

1.  It grows without external energy
2.  Drift and diffusion contributions balance
3.  The depletion region becomes a metallic short

Answer and reasoning

Drift and diffusion contributions balance

Internal carrier motion and opposing contributions can exist while the equilibrium net current is zero.

## Evidence and scope

The equation assumes an abrupt equilibrium junction and ideal statistics.

Use the switching investigation to connect physical charge, circuit load and arithmetic; the numerical library has no standalone model of this lesson’s full mechanism.

## Sources

-   [MIT 6.012 — PN Junction Electrostatics](https://ocw.mit.edu/courses/6-012-microelectronic-devices-and-circuits-fall-2005/188f6340d4d10b0e923d1c0166c8fba1_lec5.pdf)

[Published lesson data](https://semiaifoundry.com/ai-atlas/lesson-data/pn-junction-6a1fb41fe7e4475e.json) · [Atlas releases and licensing](https://semiaifoundry.com/ai-atlas/licenses.html)

## Continue exploring

### Foundations

-   [Donor and acceptor doping](https://semiaifoundry.com/learn/atlas/doping/)

### Related lessons

-   [Metal–oxide–semiconductor field-effect transistor](https://semiaifoundry.com/learn/atlas/mosfet/)
-   [Source and drain regions](https://semiaifoundry.com/learn/atlas/source-drain/)