Semiconductor physicsMVP
Built-in potential
Equilibrium junction potential of an abrupt silicon PN junction from its doping.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
Enter the two doping levels and the temperature. This uses silicon (n_i ≈ 1×10¹⁰ cm⁻³ at 300 K).
Formula
V_bi = (kT/q) · ln(N_a · N_d / n_i²)
k = Boltzmann constant, q = elementary charge, n_i = intrinsic concentration.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| V_bi | Built-in potential | V |
| k | Boltzmann constant | J/K |
| T | Temperature | K |
| q | Elementary charge | C |
| N_a | Acceptor concentration | m⁻³ |
| N_d | Donor concentration | m⁻³ |
| n_i | Intrinsic concentration | m⁻³ |
Assumptions & validity
This tool assumes:
- Abrupt (step) PN junction in thermal equilibrium.
- Non-degenerate doping: Boltzmann statistics apply.
- Complete ionization of dopants.
- Silicon at ~300 K: n_i ≈ 1×10¹⁰ cm⁻³ (sources vary ~0.9–1.5×10¹⁰).
Worked example
N_a = 1×10¹⁷ cm⁻³, N_d = 1×10¹⁵ cm⁻³, T = 300 K.
V_bi = 0.02585 V × ln(10¹⁷·10¹⁵ / (10¹⁰)²) ≈ 0.71 V