Convection Current (I or J): is due to charge movement with no external $\vec E$, wind driven cloud for instance
Charged particles moving due to electric field $\vec E$
Conductivity $(\sigma)$: When electrons can travel
Resistivity $(\Omega)$: Opposite of conductivity
Conductor: Have an abundance of free electrons
Insulator: Does not have free electrons
Superconductor: Mostly operate around absolute zero
Semiconductors: Pure silicon, can add impurities to increase free electrons or holes by doping
Drift velocity $\vec u$: no electric field, free electrons are drifting around. In a conductor:
When i = 0, $\vec E = 0$, free electrons move randomly at speed of $10^6$ m/s
When i≠0, $\vec E ≠0$, then free electrons still move randomly but at the same time drift opposite to $\vec E$ direction at drift velocity of $10^{-5}$ m
Electron mobility: In presence of $\vec E$, given for electrons by $\vec U_e = - \mu _e \vec E$ \
Measure of how quickly an electron moves through a solid material
Hole mobility: $\vec U _h = \mu _h \vec E$
Semi conductor current flows due to electrons and holes
Electrons going in the direction of $\vec E$
Holes going in the opposite of $\vec E$
Total current density: $\vec J = \rho _v \vec u$
$$\vec J = \vec J_l + \vec
$\rho _{v,e} = -N _e |e|$ where $N_e$ is the number of electrons
$\rho _{v,e} = -N _h |e|$ where $N_h$ is the number of holes
Good conductor: $N_n \mu_n << N_e \mu _e$
$\sigma =-\rho _{v,e} \mu _e = N_e \mu _e e$
Perfect conductor: $\sigma → \infty$
$\vec E =\frac{\vec J}{\sigma} → 0$
Perfect insulator: $\sigma = 0→ \vec J = 0$
Resistance
Measure of opposition to flow of current
Joule’s Law: When charges move through a material then some of their energy is given up in collisions with atoms of material