Materials Science and Engineering/Equations/Electronic Materials

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

$$J = N_e e v_D\;$$ $$J = \frac{N_e e^2 \tau}{m} E$$ $$J = \sigma E\;$$


 * $$J$$: electric current density
 * $$N_e$$: multiply the drift velocity by the density of electrons
 * $$\sigma$$: electrical conductivity

$$\sigma = \left ( \frac{e}{m} \tau \right ) (N_e e)$$ $$\sigma = \mu_e (N_e e)\;$$