Electrical and Thermal Properties of Materials

Electrical and Thermal Properties of Materials

Objectives

• Classify materials based on their electrical conductivity.

• Describe a simple model explaining electrical conduction in metals and semiconductors.

• Identify the effects of processing on the conductivity of metals.

• Introduce the properties and uses of superconductors.

• Consider different applications of insulators and dielectrics.

• Introduce the thermal properties of materials.

Conductivity and Resistivity

• Conductivity: A measure of a material's ability to conduct electric current. Measured in Siemens per meter (S/m or $Ω^{-1}m^{-1}$)

• Resistivity: A measure of a material's resistance to electric current. Measured in Ohm-meters ($Ω⋅m$). It is the inverse of conductivity: $\rho = \frac{1}{\sigma}$

• Materials are classified based on their conductivity/resistivity:

  • Insulators: Very low conductivity ($10^{-18}$ to $10^{-10} S/m$) e.g., silica, alumina, ceramic insulators, polystyrene, organic polymers, polyvinylidene difluoride, lead borosilicate glass, inorganic glasses, soda-lime glass.

  • Semiconductors: Intermediate conductivity ($10^{-6}$ to $10^{4} S/m$) e.g., gallium arsenide, intrinsic silicon, extrinsic silicon (conductivity can be altered by doping).

  • Conductors: High conductivity ($10^{6}$ to $10^{8} S/m$) e.g., graphite, metals (aluminum, silver, copper, nichrome).

  • Superconductors: Exhibit almost zero resistivity at very low temperatures.

Conductors

• Resistivities less than $10^{-4} Ω⋅m$.

• Typically metallic materials.

• Some oxides and other materials can be conductors, such as Indium tin oxide (ITO), TiO, RuO2, conducting polymers, graphite, and graphene.

• Indium tin oxide (ITO): Used as a transparent conducting film in touchscreens.

Conductivity and Resistivity - Basic Equations

• Consider a rod of material with length $l$ and cross-sectional area $A$.

• A voltage $V$ is applied along the length of the rod.

• Electric field strength: $E = \frac{V}{l}$ (Electric field runs from positive to negative).

• Resistance of the object: $R = \frac{l}{\sigma A}$, where $\sigma$ is the electrical conductivity of the material ($Ω^{-1}m^{-1}$).

• Electrical Resistivity: $\rho (Ωm) = \frac{1}{\sigma}$

• Ohm’s law: $V = IR$, where $R = \frac{\rho l}{A}$.

Resistance Calculation Examples

• Example 1: Copper wire

  • Length, $l = 100 cm = 1 m$

  • Diameter = 1 mm, so radius $r = 0.5 mm = 0.0005 m$

  • Resistivity of copper, $\rho = 1.7 × 10^{-8} Ω⋅m$

  • $R = \frac{\rho l}{A} = \frac{(1.7 × 10^{-8} × 1)}{(π × 0.0005^2)} = 0.0216 Ω$

• Example 2: Piece of glass

  • Length, $l = 1 mm = 0.001 m$

  • Diameter = 1 mm, so radius $r = 0.5 mm = 0.0005 m$

  • Resistivity of glass, $\rho = 1 × 10^{12} Ω⋅m$

  • $R = \frac{\rho l}{A} = \frac{(1 × 10^{12} × 0.001)}{(π × 0.0005^2)} = 1.27 × 10^{15} Ω$

Conduction Mechanisms

• For electrical conduction to occur, there must be a net movement of charged particles.

  • In metals: electrons.

  • In liquids (and some solids): positive and negative ions.

  • In semiconductors: electrons and holes.

• The number of charged particles and their ability to travel through the material strongly influence the conductivity, $\sigma$

• $\sigma = nq\mu$

  • $n$: Number of (free) charge carriers ($m^{-3}$).

  • $q$: Charge carried by each carrier.

  • $\mu$: Mobility of those carriers.

• If there is more than one type of charge carrier in the material:

  • $\sigma<em>{total} = n</em>1q<em>1\mu</em>1 + n<em>2q</em>2\mu<em>2 + n</em>3q<em>3\mu</em>3 + …$

Free Electron Models of Conduction in Metals

• In the metallic bonding model, valence electrons are considered completely disconnected from the atoms and free to move anywhere.

• Electrons can be thought of as a