Fermi Level Calculator, Formula, Calculation

Fermi Level Calculator :

Enter the Fermi wave number in nm⁻¹, Fermi energy in eV, Fermi temperature in K, Fermi velocity in m/s, Fermi-Dirac distribution Energy in eV,  and you get the Fermi-Dirac distribution temperature in Kelvin (K).

Fermi Level Calculator

Fermi Level Formula:

Fermi level formula wavenumber kf(nm) in nanometer is equal to the square of the  3π2 and multiply the  number density n(em) in electron meter.Hence the Fermi level formula can be written as

Fermi wavenumber or Fermi wave vector kf(nm) =(3π2 * n(em) )(1/3)

Fermi velocity Vf = h* kF/m

Fermi energy Ef = h2 * KF2 / (2m)

Fermi temperature Tf = Ef /K

Where,

N = Number density

H = planck constant

M = 9.109 *10-31 kg mass of the electron

K = 1.38 *10-23 m2-Kg /(s2K) Boltzmann constant

The Fermi dirac distribution is the probability that na electron is in a special energy state. The Fermi function formula is

F(E) = 1/ (e[(E-Ef)/ (k*T)] +1)

here,

E=energy of a particle in eV

T= temperature in K

Example:1

Calculate the gold metal  Fermi energy, Fermi velocity, Fermi temperature and Fermi wave number?

Answer:

Given material  is gold

Number density n =5.90*1028 electrons /m3

Fermi wav vector kf =(3π2 * n )(1/3)

Kf = (3π2 * 5.90*1028 ) (1/3)

=12.043 1/nm

Fermi velocity vf =h* kF /m

Vf =6.626 *10-34 *12.043 /9.109 *10-31

Vf = 8.76022 m/s

Fermi energy Ef =h2 *kf2 /(2 *m)

Ef =(6.626 *10-34)2 *12.043 1 2 / (2* 9.109 *10-31)

Ef =2.89913 ev

Fermi temperature Tf =Ef /K

Tf =2.899 /1.38 *10-23

=2.10072K

Therefore, the copper metal Fermi temperature is 2.10072K , Fermi energy 2.89913 ev,Fermi velocity is 8.76022 m/s and Fermi wave vector is 12.043 1/nm

Example:2

Calculate the Fermi wave number of magnesium?

Answer:

kf =(3π2 * n )(1/3)

n= 8.61 *1028electrons /m3

kf =(3π2 * n )(1/3)

kf =(3* π2 *8.61 *1028)(1/3)

kf= 136607477m-1

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