The p-n Junction at Equilibrium
Built-in Fields and Depletion Regions
Formation of the junction
When p-type and n-type regions are brought together, electrons and holes diffuse across the interface and recombine near the junction. This leaves behind fixed ionized dopants, producing a depletion region and an internal electric field.
Built-in potential
The junction reaches equilibrium when drift current exactly balances diffusion current, creating a built-in potential barrier.
Equilibrium band bending
Band bending reflects the electrostatic potential across the depletion region. At equilibrium, the Fermi level is flat across the junction, even though the bands curve.
p-n junction concepts
| Concept | Meaning | Why it matters |
|---|---|---|
| Depletion region | Area depleted of mobile carriers | Creates rectification |
| Built-in potential | Barrier at equilibrium | Controls current flow |
| Band bending | Energy shift across space | Visualizes electrostatics |
| Charge neutrality | Balanced fixed charge | Determines depletion width |
What is the depletion region primarily composed of?
Mobile carriers are swept out near the junction, leaving fixed ionized dopants.
Correct answer: Fixed ionized donor and acceptor ions
What balances diffusion current at equilibrium in a p-n junction?
The internal electric field drives drift current that opposes diffusion.
Correct answer: Drift current
How to analyze an equilibrium p-n junction
-
1
Identify the dopings on both sides.
-
2
Determine which carriers diffuse across the junction.
-
3
Infer the sign of the space charge in the depletion region.
-
4
Use equilibrium conditions to conclude that the Fermi level is constant.
Before and after junction formation
Separate p and n regions
- No built-in field at the interface
- Carrier distributions are uniform in each region
Joined p-n junction
- Depletion region forms
- Band bending and barrier potential appear
At equilibrium across a p-n junction, what must be flat?
Equilibrium requires a constant Fermi level throughout the structure.
Correct answer: The Fermi level
What physical process creates the depletion region?
Carrier motion near the interface leaves behind uncovered dopant ions.
Correct answer: Diffusion and recombination of carriers near the interface