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

Interface electric field (MV/m)

Required number in MV/m. Magnitude of the vertical electric field at the silicon interface.

Zero-field splitting (ueV)

Required number in ueV. Measured zero-field intercept for this device and interface.

Electric-field slope (ueV/(MV/m))

Required number in ueV/(MV/m). Measured increase in splitting per MV/m of vertical field.

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

Estimate silicon interface valley splitting from a device-calibrated linear dependence on vertical electric field. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Valley splitting (ueV)

Returned number in ueV. Energy splitting between the lowest silicon valleys.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Interface electric field must be at least 0.
• Zero-field splitting must be at least 0.
• Electric-field slope must be at least 0.
• 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.

• 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.

• Impact Ionization Coefficient Calculator

  Compute the silicon impact ionization coefficient from the electric field using the Chynoweth law.