N-Type Carrier Concentration Calculator
Solve the n-type charge-neutrality relation n = (ND + sqrt(ND² + 4·ni²))/2 for equilibrium electron concentration. ND is ionized donor concentration in cm⁻³ and ni is intrinsic concentration in cm⁻³, both per volume.
Description
Solve equilibrium electron concentration for uncompensated n-type material from ionized donor and intrinsic concentrations.
Solve the n-type charge-neutrality relation n = (ND + sqrt(ND² + 4·ni²))/2 for equilibrium electron concentration. ND is ionized donor concentration in cm⁻³ and ni is intrinsic concentration in cm⁻³, both per volume.
When to use N-Type Carrier Concentration Calculator
- Solve equilibrium electron concentration for uncompensated n-type material from ionized donor and intrinsic concentrations.
- Compare fabrication or device scenarios while holding coefficients and unit conventions constant.
- Check a hand calculation before moving to a higher-fidelity process, circuit, or TCAD model.
How the calculation works
The exact quadratic approaches ni at zero donor concentration and ND when donors dominate.
n = ND/2 + √[(ND/2)² + ni²] Interpreting the result
The exact quadratic approaches ni at zero donor concentration and ND when donors dominate.
Assumptions and limitations
- The result assumes equilibrium mass action, one donor species, complete ionization, and no acceptor compensation.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.