Doping Concentration From Resistivity Calculator

Estimate the dopant concentration from a measured silicon resistivity via bisection on Caughey–Thomas electron or hole mobility models. Mobility models: μ_n = 92+1268/(1+(N/1.3e17)^0.91) and μ_p = 54.3+406.9/(1+(N/2.35e17)^0.88) in cm²/V·s, resistivity ρ = 1/(q·μ·N) [Ω·cm] with q=1.602176634e-19 C. Bisection searches N in [1e12, 1e21] cm⁻³ for 200 iterations (geometric mid). Inputs: carrierType 'n' or 'p', ρ>0 Ω·cm. Output: N>0 cm⁻³. Assumes 300 K, complete ionization, and low-field mobility.

Description

Estimate 300 K silicon dopant concentration from resistivity using carrier-specific Caughey–Thomas mobility and numerical inversion.

Estimate the dopant concentration from a measured silicon resistivity via bisection on Caughey–Thomas electron or hole mobility models. Mobility models: μ_n = 92+1268/(1+(N/1.3e17)^0.91) and μ_p = 54.3+406.9/(1+(N/2.35e17)^0.88) in cm²/V·s, resistivity ρ = 1/(q·μ·N) [Ω·cm] with q=1.602176634e-19 C. Bisection searches N in [1e12, 1e21] cm⁻³ for 200 iterations (geometric mid). Inputs: carrierType 'n' or 'p', ρ>0 Ω·cm. Output: N>0 cm⁻³. Assumes 300 K, complete ionization, and low-field mobility.

When to use Doping Concentration From Resistivity Calculator

  • Estimate 300 K silicon dopant concentration from resistivity using carrier-specific Caughey–Thomas mobility and numerical inversion.
  • 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

Mobility falls with concentration, so simply dividing by a constant mobility can bias the inferred doping.

ρ = 1/[q·μ(N)·N]

Interpreting the result

Mobility falls with concentration, so simply dividing by a constant mobility can bias the inferred doping.

Assumptions and limitations

  • The solver is limited to 10^12–10^21 cm⁻³ and assumes complete ionization, majority-carrier conduction, low field, uncompensated uniform silicon, and 300 K.
  • Use parameters measured for the same material, geometry, temperature, and operating regime whenever the result informs engineering work.
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