Fermi Level Calculator

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Intrinsic uses the pure semiconductor. N-type adds donor atoms; p-type adds acceptor atoms.
Presets fill in the standard bandgap and effective masses. Choose Custom to enter your own values.
Absolute temperature in Kelvin. Room temperature is 300 K.
K
Energy gap between the valence band maximum and conduction band minimum. Set automatically by the material preset.
eV
Effective mass of electrons in the conduction band relative to the free-electron mass. Used to compute the density of states Nc.
Effective mass of holes in the valence band relative to the free-electron mass. Used to compute the density of states Nv.
Intrinsic carrier concentration (ni)Intrinsic
8.863 x 10^9cm⁻³

Thermally generated electron-hole pairs per cubic centimetre

Intrinsic Fermi level (EFi - Ev)0.5544eV
Fermi level shift (EF - EFi)0eV
Fermi level above valence band (EF - Ev)0.5544eV
Electron concentration (n)8.863 x 10^9cm⁻³
Hole concentration (p)8.863 x 10^9cm⁻³
Thermal voltage (kT/q)0.0259eV
Effective density of states - conduction band (Nc)2.811 x 10^19cm⁻³
Effective density of states - valence band (Nv)1.826 x 10^19cm⁻³
Semiconductor classificationIntrinsic
0.5544 eV
Near valence band<0.5Near midgap0.5-1.25Upper half1.25-1.75Near conduction band1.75+

Intrinsic Fermi level sits 0.554 eV above the valence band in silicon at 300 K.

  • Thermal voltage (kT/q) at 300 K is 0.0259 eV. This sets the scale for Fermi-Dirac carrier statistics and junction built-in potentials.
  • The intrinsic Fermi level deviates from the exact midgap by -0.0056 eV because Nv and Nc differ (effective masses are not equal).
  • At higher temperatures ni grows exponentially, making the material more conductive. At low T, ni collapses and the semiconductor becomes essentially an insulator.

Next stepTry switching to n-type or p-type and entering a doping concentration to see how the Fermi level shifts relative to the band edges.

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