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.
Description
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.
Charge Neutrality Carrier Solver is a focused tool for the following task. 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. It reports Electron concentration, Hole concentration from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Charge Neutrality Carrier Solver
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.
- Acceptor concentration (cm^-3)
- Required number in cm^-3. Ionized acceptor concentration. Must be at least 0 cm⁻³.
- 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 Charge Neutrality Carrier Solver works
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. 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. Satisfies n·p = ni².
- Hole concentration (cm^-3)
- Returned number in cm^-3. Equilibrium hole concentration. Satisfies n·p = ni².
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.
- Acceptor 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
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