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 equilibrium electron and hole concentrations for compensated material from donor, acceptor, and intrinsic concentrations.
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.
When to use Charge Neutrality Carrier Solver
- Solve equilibrium electron and hole concentrations for compensated material from donor, acceptor, 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 stable solver computes the majority carrier first, avoiding cancellation when acceptors exceed donors by many orders of magnitude.
n−p = ND−NA; n·p = ni² Interpreting the result
The stable solver computes the majority carrier first, avoiding cancellation when acceptors exceed donors by many orders of magnitude.
Assumptions and limitations
- Ionized dopant concentrations are required; freeze-out, degeneracy, nonequilibrium quasi-Fermi levels, and multiple charge states are omitted.
- Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.