1. Challenge question

challenge10 - wire current capacities

2. Not all are conservative

The electric field is conservative, but the force field is not!

3. Notes

Current density (a flux).

Ohm’s Law
\[J = \sigma \vec{E} \label{ohms-law}\]

Conductivity (σ) is a material property, just like εr, and thus similar to the previous constitutive equation \(D = \epsilon E\).

Electric power
\[p = \vec{J} \bullet \vec{E}\]

4. Drift in semiconductors

In ECE 340 Electronics 1, you are introduced to the concept of drift, where charge carriers (free electrons or holes) move in a semiconductor in response to an electric field.

\[\begin{align} J_n &= \mu_n \cdot q \cdot n \cdot \vec{E} \\ J_p &= \mu_p \cdot q \cdot p \cdot \vec{E} \end{align}\]
What is the conductivity of a doped semiconductor?

The total current in a semiconductor is both the electron and hole currents.

\[J_{tot} = J_n + J_p = q \left(\mu_n \cdot n + \mu_p \cdot p\right) \vec{E}\]

Matching terms with \(\eqref{ohms-law}\) means that a semiconductor’s conductivity is set by doping, the mobility material property, and temperature.

\[\sigma_{\mathrm{semi}} = q \left(\mu_n n + \mu_p p\right)\]

Remember that the relationship between free electrons and holes is fixed by:

\[n \cdot p = n_i^2\]

The current mentioned in the book is DRIFT current, and there are other ways for charges to move, i.e. create a current. One other method is diffusion current, which is a major player in semiconductors. Or movement of ions in an electrolyte.
Diffusion is microscopic drift??

Consider what diffusion is about: movement of charges from high concentration to low concentration.

In the high concentration area it stands to reason that the forces between the charges is greater because the average spacing is smaller. If there is a region of lower concentration, the forces between the charges will be lower.

You can think of diffusion like opening a door between a crowded room and an empty room. People will move through the doorway (“people flux”) because the net forces on the people near the door are not zero, but facing in the direction of lower concentration.

Thus, the diffusion is compelled by Coulomb’s law at the microscopic level.