Mean free flight time

The mean free flight time or burst time in a many-particle system is the average time between collisions with a particle (e.g. atom , molecule , ion or electron ). ${\displaystyle \tau }$

The mean free flight time is linked to the mean free path through the mean speed : ${\displaystyle \lambda }$ ${\displaystyle {\bar {v}}}$

${\displaystyle \tau ={\frac {\lambda }{\bar {v}}}}$

The mean free time of flight is used especially in solid state physics , because when considering the Fermi sphere in momentum space, one cannot argue with the mean free path . With these two terms, free flight ends with a classic collision with another particle. They are therefore to be conceptually separated from the relaxation time at which z. B. Electrons from the electronically higher conduction band fall back into an energetically lower state.

In general, such impact processes can be viewed as a type of friction or damping . In many physical theories, a peak time is therefore introduced as a parameter for inevitable losses of the respective mechanism, see for example the harmonic oscillator or the Drude theory . ${\displaystyle \tau }$

Mean free flight time of electrons in solids

Mean free flight time , mean velocity and mean free path of conduction electrons of the Fermi surface, calculated from the conductivity and the electron density according to: ${\displaystyle \tau }$ ${\displaystyle {\bar {v}}}$ ${\displaystyle \lambda }$ ${\displaystyle \sigma }$ ${\displaystyle n_{e}}$

${\displaystyle \tau ={\frac {m_{e}}{e^{2}}}\cdot {\frac {\sigma }{n_{e}}}}$

With

• ${\displaystyle m_{e}}$ Electron mass
• ${\displaystyle e}$ Elemental charge .

element	${\displaystyle \sigma }$ ${\displaystyle 10^{5}\,\Omega ^{-1}\mathrm {cm} ^{-1}}$	${\displaystyle n_{e}}$ ${\displaystyle 10^{22}\,\mathrm {cm} ^{-3}}$	${\displaystyle \tau }$ ${\displaystyle 10^{-14}\,\mathrm {s} }$	${\displaystyle {\bar {v}}}$ ${\displaystyle 10^{8}\,\mathrm {cm/s} }$	${\displaystyle \lambda }$ ${\displaystyle 10^{-8}\,\mathrm {m} }$
Li	1.2	4.70	0.9	1.29	1.1
N / A	2.3	2.50	3.3	1.04	3.5

Individual proof

1. ↑ K. Kopitzki, P. Herzog: Introduction to solid state physics . Teubner Verlag, 2007. ISBN 3835101447 . Page 163.