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 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.
N-Type Carrier Concentration Calculator is a focused tool for the following task. 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. It reports Electron concentration from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use N-Type Carrier Concentration
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- Donor concentration (cm^-3)
- Required number in cm^-3. Ionized donor concentration. Must be at least 0 cm⁻³; 0 yields n = ni.
- Intrinsic concentration (cm^-3)
- Required number in cm^-3. Intrinsic carrier concentration. Must be greater than 0 cm⁻³.
The cited overview of Semiconductor device supplies background for the terminology and domain context used by this tool.1
How N-Type Carrier Concentration works
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. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Electron concentration (cm^-3)
- Returned number in cm^-3. Equilibrium electron concentration. At least ni, approaches ND when ND >> ni.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- Donor concentration must be at least 0.
- Intrinsic concentration must be at least 5e-324.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
Compare the estimate with measured process data, current device documentation, and a higher-fidelity circuit, field, thermal, quantum, or TCAD model when the decision requires it.
References
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Semiconductor device — Wikipedia contributors
Similar or alternative tools
- P-Type Carrier Concentration Calculator
Solve the p-type charge-neutrality relation p = (NA + sqrt(NA² + 4·ni²))/2 for equilibrium hole concentration. NA is ionized acceptor concentration and ni is intrinsic concentration in cm⁻³.
- Charge Neutrality Carrier Solver
Solve the exact charge-neutrality relations n = (Nd-Na+√((Nd-Na)²+4ni²))/2 and p = ni²/n for equilibrium electron and hole concentrations. Nd, Na, ni in cm⁻³.
- Intrinsic Carrier Concentration Calculator
Compute the intrinsic carrier concentration from the band gap and effective densities of states. Uses ni = sqrt(Nc·Nv)·exp(-Eg/(2·kB·T)).