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.

Note

In a conductor, such as a wire, the charge carriers are typically electrons. Due to thermal motion, electrons in a conductor have random velocities in all different directions.

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:

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

Carrier Mobility

Denoted by $\mu$. $$

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