Introduction to Electrical Properties

Electrical properties include the response of a material for an applied electric field.

Resistivity

Measure of how strongly a material opposes the flow of electric current.

Resistance

$R=\rho\frac{l}{A}$

Not a property of a material.

Temperature Coefficient of Resistivity

\rho=\rho_0\Big[1 + \alpha(T-T_0)\Big]

Here:

$\rho$: resistivity at temperature $T$
$\rho_0$: resistivity at temperature $T_0$
$\alpha$: temperature coefficient of resistivity

Conductivity

Reciprocal of the electrical resistivity.

$\sigma=\frac{1}{\rho}$

Depends on:

Number of available charge carriers
Material’s composition
Material’s structure
Temperature
Impurities

Electron Mobility

When an electrical field is applied, the free electron in a solid can be accelerated under force applied by electric field.

Force acting on a single electron is $–eE$ . Here:

$e$ - charge of electron
$E$ - electric field strength

In a solid, the electrons are scattered by obstacles such as atom cores/imperfections etc. The electrons have a net drift at the direction opposite to the electric field

Drift Velocity

Average velocity attained by charge carriers accelerated in an electric field.

Carrier Concentration

Number of charge carriers per unit volume. Usually denoted by $n$ .

Current Density

Amount of electric current flowing through a unit area.

$J=nq\overline{\nu}=\sigma E$

Here:

J=nq\overline{\nu}=\sigma E

Here:

$n$: carrier concentration
$q$: charge on a single charge carrier
$\overline{\nu}$: drift velocity
$\sigma$: conductivity
$E$: applied electric field

Carrier Mobility

Denoted by $\mu$ .

\mu=\frac{\overline{\nu}}{E} \;\; \text{and} \;\; \sigma=nq\mu