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

Doping (cm^-3)

Required number in cm^-3. Dopant concentration.

Ionization energy (eV)

Required number in eV. Ionization energy of the dopant level.

Temperature (K)

Required number in K. Lattice temperature.

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

Compute the fraction of dopants thermally ionized at a given temperature using the charge-neutrality approximation. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Ionized fraction

Returned number. Fraction of dopants ionized, between zero and one.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Doping must be at least 5e-324.
• Ionization energy must be at least 5e-324.
• Temperature 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.

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