DopingMVP
Carrier concentration
Find majority and minority carrier concentrations from the dopant level and the intrinsic carrier concentration.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
Choose a dopant type and enter the dopant and intrinsic concentrations.
Formula
n·p = nᵢ² , majority ≈ Nd/2 + √((Nd/2)² + nᵢ²)
Charge neutrality combined with mass action.
Variables
| Symbol | Variable | Unit |
|---|---|---|
| n | Electron concentration | m⁻³ (shown as cm⁻³) |
| p | Hole concentration | m⁻³ (shown as cm⁻³) |
| Nd / Na | Donor / acceptor concentration | m⁻³ |
| nᵢ | Intrinsic carrier concentration | m⁻³ |
Assumptions & validity
This tool assumes:
- Complete dopant ionization; non-degenerate (Boltzmann) statistics.
- Single dopant type, no compensation.
- Equilibrium (no applied bias or illumination).
Worked example
n-type, Nd = 1×10¹⁶ cm⁻³, nᵢ = 1×10¹⁰ cm⁻³.
n ≈ 1×10¹⁶ cm⁻³; p = nᵢ²/n ≈ 1×10⁴ cm⁻³