Intrinsic Carrier Concentration Calculator

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Choose a preset material or enter your own semiconductor parameters below.
Absolute temperature of the semiconductor. Standard conditions are 300 K (27 degC). The Misiakos formula for silicon is valid from 78 to 340 K.
K
Enables the Misiakos-Tsamakis (1993) empirical equation for silicon, which is more accurate than the analytic model between 78 and 340 K.
Intrinsic carrier concentration (ni)
8.143 x 10^9 cm^-3cm⁻³

Number of thermally generated electron-hole pairs per cubic centimetre

ni (scientific notation)8.1434 × 10^9
Band-gap at T1.1245eV
Nc at T2.820 x 10^19 cm^-3cm⁻³
Nv at T1.830 x 10^19 cm^-3cm⁻³
log10(ni)9.911
Calculation methodAnalytic: ni = sqrt(Nc*Nv) * exp(-Eg/2kT)
9.911 log10(cm^-3)
GaAs-like (wide gap)<6Si-like (medium gap)6-10Ge-like (narrow gap)10-14Near-metallic / high T14+

ni = 8.143 x 10^9 cm^-3 at 300.0 K

  • The intrinsic carrier concentration of Silicon (Si) at 300.0 K is 8.143 x 10^9 cm^-3.
  • At 300 K the accepted silicon ni is about 9.65 x 10^9 cm^-3 (Altermatt et al. 2003). Values in the range 8e9 to 1.5e10 cm^-3 appear in older literature because of differing band-gap measurements.
  • Doubling the temperature roughly squares the exponential factor, making ni highly sensitive to temperature - a key consideration in thermal design of semiconductor devices.

Next stepFor the most accurate silicon values between 78 and 340 K, enable the Misiakos empirical formula toggle above.

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