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.
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