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

Band gap (eV)

Required number in eV. Band gap energy. Must be greater than 0 eV.

Nc (cm^-3)

Optional number in cm^-3. Effective conduction-band density of states at the selected temperature. The default is a common 300 K silicon value and is not temperature-scaled automatically.

Nv (cm^-3)

Optional number in cm^-3. Effective valence-band density of states at the selected temperature. The default is a common 300 K silicon value and is not temperature-scaled automatically.

Temperature (K)

Optional number in K. Lattice temperature. Must be greater than 0 K.

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

Compute the intrinsic carrier concentration from the band gap and effective densities of states. Uses ni = sqrt(Nc·Nv)·exp(-Eg/(2·kB·T)). Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

ni (cm^-3)

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

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

• N-Type Carrier Concentration Calculator

  Solve the n-type charge-neutrality relation n = (ND + sqrt(ND² + 4·ni²))/2 for equilibrium electron concentration. ND is ionized donor concentration in cm⁻³ and ni is intrinsic concentration in cm⁻³, both per volume.

• P-Type Carrier Concentration Calculator

  Solve the p-type charge-neutrality relation p = (NA + sqrt(NA² + 4·ni²))/2 for equilibrium hole concentration. NA is ionized acceptor concentration and ni is intrinsic concentration in cm⁻³.

• Semiconductor Effective Density Conduction Band Calculator

  Compute the conduction-band effective density of states from a density-of-states effective mass and temperature. Formula: Nc(T) = 2.51e19·(m*_dos/m0)^{3/2}·(T/300)^{3/2} [cm⁻³], where 2.51e19 cm⁻³ is the 300 K value for m*=m0, m*_dos>0 is the DOS effective mass ratio, T>0 K is lattice temperature (default 300 K). Inputs: m*_dos>0 (default 1), T>0 K (default 300 K). Output: Nc>0 cm⁻³. Assumes parabolic band, Boltzmann statistics, and isotropic effective mass.