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

Doping concentration (cm^-3)

Required number in cm^-3. Substrate doping concentration.

Temperature (K)

Optional number in K. Absolute device temperature.

Intrinsic concentration (cm^-3)

Required number in cm^-3. Intrinsic carrier concentration.

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

Compute the magnitude of the strong-inversion MOS surface potential, 2 phi-F, from substrate doping, intrinsic carrier concentration, and temperature. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Surface potential (V)

Returned number in V. Strong-inversion surface potential psi_s.

• Material composition, geometry, process history, temperature, electric field, bias, interfaces, parasitics, and fitted parameter ranges can invalidate a compact semiconductor model.
• Doping concentration must be at least 0.
• Intrinsic concentration 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.

• Built-In Potential Calculator

  Compute the pn-junction built-in potential at 300 K as Vbi = (kT/q)·ln(NA·ND/ni²) where kT/q = 0.02585 V, NA and ND are acceptor and donor concentrations and ni is intrinsic concentration in cm⁻³.

• Intrinsic Carrier Concentration Calculator

  Compute the intrinsic carrier concentration from the band gap and effective densities of states. Uses ni = sqrt(Nc·Nv)·exp(-Eg/(2·kB·T)).

• APD Multiplication Factor Calculator

  Compute the avalanche photodiode multiplication factor from the Miller model M=1/[1-(V/Vb)^N]. Inputs are magnitudes: reverse-bias magnitude V≥0 V must remain below breakdown magnitude Vb>0 V (numerator V, denominator Vb; V=0 gives M=1, V→Vb- diverges). Exponent N in [1, 6] (default 2) captures the ionization coefficients. Signed voltages are not supported (use magnitudes). Result M≥1 is a dimensionless factor (per-carrier gain, not total current).