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

Black prefactor

Required number. Empirical prefactor A calibrated with current density expressed numerically in A/cm^2. Its dimensions depend on exponent n, so it must come from a compatible fit.

Current density (A/cm^2)

Required number in A/cm^2. Conductor current density in amperes per square centimeter.

Current-density exponent

Optional number. Empirical current-density exponent n for the fitted failure mode.

Activation energy (eV)

Optional number in eV. Activation energy Ea for the fitted electromigration mechanism.

Temperature (K)

Required number in K. Absolute conductor temperature.

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

Estimate electromigration median time to failure with Black's equation, MTTF = A J^-n exp(Ea/kBT). Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Median time to failure (h)

Returned number in h. Predicted median time to failure under the fitted conditions.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Black prefactor must be at least 5e-324.
• Current density must be at least 5e-324.
• Current-density exponent must be at least 5e-324.
• Activation energy must be at least 5e-324.
• 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.

• Black Exponent Extraction Calculator

  Extract Black's-law current-density exponent n from two electromigration median-time-to-failure measurements taken under otherwise matching conditions.

• BTI Threshold Shift Calculator

  Estimate bias temperature instability threshold shift as prefactor·t^{0.25}·exp((Ea/kB)·(1/300-1/T)). t is stress time in hours, T is temperature in K, Ea activation energy in eV, prefactor in mV.

• MRAM Retention Time

  Néel–Arrhenius MRAM retention estimate τ=τ₀ exp(Δ) from attempt time and dimensionless thermal-stability factor.