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 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.
Doping Concentration From Resistivity Calculator is a focused tool for the following task. 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. It reports Doping from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Doping Concentration From Resistivity
Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.
- Carrier type
- Required string. Majority carrier type.
- Resistivity (Ω·cm)
- Required number in Ω·cm. Measured resistivity of the material. Must be greater than 0 Ω·cm.
The cited overview of Electron mobility supplies background for the terminology and domain context used by this tool.1
How Doping Concentration From Resistivity works
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. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Doping (cm^-3)
- Returned number in cm^-3. Estimated dopant concentration. Greater than 0 cm⁻³.
Limitations and assumptions
- Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
- Resistivity 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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Electron mobility — Wikipedia contributors
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