Materials Science and Engineering/Equations/Electronic Materials

Electrons

Conductivity and Ohm's Law

 $E={\frac {U}{L}}$

$U$: applied potential difference

$L$: length

$E$: electric field

 $a={\frac {e}{m}}E$

 $v_{\mbox{average}}=a\tau \;$

$\tau$: average time between collisions (mean free time, relaxation time, collision time)

 $v_{D}=\left({\frac {e}{m}}\tau \right)E$

$v_{D}$: drift velocity

 $J=N_{e}ev_{D}\;$
 $J={\frac {N_{e}e^{2}\tau }{m}}E$
 $J=\sigma E\;$

$J$: electric current density

$N_{e}$: multiply the drift velocity by the density of electrons

$\sigma$: electrical conductivity

 $\sigma =\left({\frac {e}{m}}\tau \right)(N_{e}e)$
 $\sigma =\mu _{e}(N_{e}e)\;$