Fermi speed

The Fermi speed (according to Enrico Fermi ) is the speed of an electron whose kinetic energy is equal to the Fermi energy : ${\displaystyle u_{\mathrm {F} }}$ ${\displaystyle E_{\mathrm {kin} }}$ ${\displaystyle E_{\mathrm {F} }}$

${\displaystyle E_{\mathrm {F} }=E_{\mathrm {kin} }={\frac {1}{2}}m_{\mathrm {e} }\cdot u_{\mathrm {F} }^{2}}$

Then:

${\displaystyle \Leftrightarrow u_{\mathrm {F} }={\sqrt {\frac {2\cdot E_{\mathrm {F} }}{m_{\mathrm {e} }}}}}$

in which

• ${\displaystyle m_{\mathrm {e} }}$is the electron mass .

Like the Fermi energy, the Fermi velocity is independent of the temperature.

The Fermi speed is particularly important in the quantum mechanical analysis of conductivity , since it is assumed here that only electrons close to the Fermi speed participate in conducting the electric current .

literature

• Neil W. Ashcroft, N. David Mermin: Solid State Physics . 2nd Edition. Oldenbourg, Munich 2005, ISBN 3-486-57720-4 .
• Rudolf E. Hummel: Electronic Properties of Materials . 4th edition. Springer, New York 2011, ISBN 978-1-4419-8164-6 .