Use this semiconductor calculation for first-order device, material, fabrication, interconnect, packaging, or reliability estimates when every coefficient and unit convention is known.

Saturation velocity (cm/s)

Required number in cm/s. Carrier saturation drift velocity.

Mobility (cm^2/Vs)

Required number in cm^2/Vs. Low-field carrier mobility.

The cited overview of Electron mobility supplies background for the terminology and domain context used by this tool.^[1]

Derive the critical electric field where drift velocity saturates from the saturation velocity and low-field mobility. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Critical field (kV/cm)

Returned number in kV/cm. Critical field for velocity saturation.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

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.

• Ballistic Mean Free Path Calculator

  Estimate the ballistic mean free path from low-field mobility using λ = (μ·Vt/vsat)·1e7 with thermal voltage Vt=0.02585 V (300 K) and saturation velocity vsat=1e7 cm/s (λ[nm]=μ·0.02585). Input mobility μ>0 cm²/V·s must be the low-field, non-degenerate value; rpm vs linear-velocity and per-area vs total distinctions do not apply. Model assumes Maxwell-Boltzmann statistics and constant vsat, valid only near 300 K as a quasi-ballistic estimate.

• Conductivity From Doping Calculator

  Compute the silicon conductivity of uniformly doped material from majority-carrier mobility at 300 K. Assumes low-field Caughey-Thomas mobility and complete ionization.

• 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.