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.
- Bring differently doped p-type and n-type regions into contact.
- Let carriers redistribute until fixed dopant charge creates an opposing electric field.
- At equilibrium, balance carrier diffusion with field-driven drift; applied bias shifts that balance.
Science and assumptions
Built-in junction potential
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. and are acceptor and donor densities, while 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 increases the logarithm in 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?
- It grows without external energy
- Drift and diffusion contributions balance
- 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.