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

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

 $v_{\text{average}}=a\tau$

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

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

$v_D$: drift velocity

 $J=N_{e}e{v}_D$
 $J=\frac{N_e{e}^2\tau }{m}E$
 $J=\sigma E$

$J$: electric current density

$N_e$: multiply the drift velocity by the density of electrons

$\sigma$: electrical conductivity

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