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Formula Free Electron Gas in 3d Fermi temperature    Charge carrier density   

Formula
Formula: Free Electron Gas in 3d
Banddiagramm: Metall, Halbleiter, Isolator

Fermi temperature

Unit
Fermi temperature is used to compare Fermi energy with thermal energy. Typical value is \( 50 \, 000 \, \text{K} \), which is well above the melting temperature of most elements. The Fermi temperature is related to the Fermi energy via the Boltzmann constant: \( T_{\text F} = \frac{E_{\text F}}{k_{\text B}}\).

Charge carrier density

Unit
Charge carrier density is the number \(N\) of charges per volume \(V\): \( n = N/V \). Since the free Fermi gas is mostly used to describe the free electrons, \(n\) gives the electron density.

Mass

Unit
Mass of a particle of the Fermi gas. This can be for example the (effective) mass of the electron.

Reduced Planck's constant

Unit
Action quantum is a physical constant (of quantum mechanics) and has the value: \( \hbar ~=~ \frac{h}{2\pi} ~=~ 1.054 \, 571 \, 817 \,\cdot\, 10^{-34} \, \text{Js} \).

Boltzmann Constant

Unit
This physical constant is often used in statistical physics and thermodynamics. It has the value: \( k_{\text B} ~\approx~ 1.380 \,\cdot\, 10^{-23} \, \frac{\text J}{\text K} \).