Electronic Materials and Conductivity

Electronic Materials

• Conducting materials have low resistivity, conducting heat and electricity. Electrical conduction is due to free electrons, while normal conduction involves free electrons and phonons.

Basic Terminology

• Conductors: Materials with high electrical and thermal conductivity. Measurements show metal and alloy conductivity is around 10⁸ Ω^-1 m^-1.

• Bound electrons: Valence electrons in an isolated atom, bound to their parent nucleus.

• Free electrons: Valence electrons in a solid, not bound to individual atoms due to overlapping neighboring atom boundaries. They can move easily throughout the solid.

• Difference between ordinary gas and free electron gas: Ordinary gas molecules are neutral, while a free electron gas is charged. Gas molecule density is lower than free electron density.

• Electric field (E): Potential drop (V) per unit length (l) of a conductor with uniform cross-section. E = V/l Vm^-1.

Current Density (j)

• Current per unit area of cross-section of a conductor, normal to current flow. J = I/A Am^-2 where I is current and A the area.

Conducting Materials Classification

• Zero resistive materials: Superconductors like alloys of aluminum, zinc, gallium, niobium, which exhibit zero resistance below a transition temperature. These are used in power systems, superconducting magnets, and memory storage.

• Low resistive materials: Metals like silver, aluminum, and their alloys. These have high electrical conductivity used in electrical components and power transmission.

• High resistive materials: Tungsten, platinum, and nichrome. These have high resistivity and low temperature coefficients, used in resistors and heating elements.

Electron Theory of Solids

• The outermost electrons in an atom determine electrical properties in a solid.
• The free electron theory of solids details solid structure and properties through their electron structure. The theory is applicable to all solids (metals and non-metals), explaining conductor, semiconductor and insulator behavior. It can also discuss thermal and magnetic properties.
  • Classical free electron theory, developed by Drude and Lorentz, posits that electrons in metals can be considered a free electron gas. Mutual repulsion is disregarded. Total energy is the kinetic energy.
  • Quantum free electron theory (Somerfield) incorporates quantum mechanical concepts into the model and utilizes Fermi-Dirac statistics.
  • Zone/band theory: This theory looks at electron behavior in a periodic field and the lattice. It accounts for the mechanism of superconductivity.

Classical Free Electron Theory Postulates

• Metal structure consists of a positive ion core with valence electrons freely moving among the ion cores.
• In the absence of electric field, electrons move randomly and collide elastically.
• When an electric field is applied, electrons accelerate in the opposite direction to the field.
• Free electrons follow Maxwell-Boltzmann statistics.

Drift Velocity (Vd)

• The average velocity acquired by a free electron in a particular direction due to an applied electric field. V_d = a/t; where 'a' is acceleration and t is time.

Mobility (µ)

• Drift velocity per unit electric field. µ = Vd/E m²V^-1 s^-1.

Mean Free Path (λ)

• The average distance a free electron travels between successive collisions.

Relaxation Time (τ)

• Time taken by an electron to reach equilibrium position from a disturbed position in the presence of an electric field.

Band Gap (Eg)

• Energy difference between the maximum energy of the valence band and the minimum energy of the conduction band.

Thermal Conductivity (K)

• Measure of a material’s ability to conduct heat. K = (rate of heat flow)/(temp. gradient)

Wiedemann-Franz Law

• The ratio of thermal conductivity to electrical conductivity is directly proportional to the absolute temperature (K/σ α T).

Drawbacks of Classical Free Electron Theory

• Discrepancy between theoretical and experimental values of specific heat.
• Cannot explain the conductivity of insulators or semiconductors.
• Failure to explain superconductivity and other related phenomena.

Quantum Free Electron Theory

• Assumes electrons are fully responsible for electrical conduction and have constant potential inside the metal and wave nature.
• Electrons follow Fermi-Dirac statistics and energy distributions, with interactions disregarded.

Energy Bands in Solids

• Grouping of energy levels of valence electrons forms the valence band.
• Conduction band represents levels for free electrons with higher energy.
• Forbidden band represents an energy gap separating the valence and conduction bands; it contains no energy levels.

Types of Electronic Materials

• Conductor: Materials with overlapping valence and conduction bands and low resistivity.
• Insulator: Possess a large forbidden energy gap, high resistivity and completely filled valence band.
• Semiconductors: Have a small forbidden energy gap, intermediate resistivity.

Direct and Indirect Band Gap Semiconductors

• Direct: A minimum energy of the conduction band lies directly above a maximum energy in the valence band; electrons change state directly, releasing emitted light.
• Indirect: The minimum energy of the conduction band does not lie directly above the maximum energy of the valence band, momentum changes must occur; releasing the emitted light differently (usually heat).

Fermi Levels and Fermi Functions

• The highest energy level an electron can occupy at absolute zero temperature.
• Fermi energy: the energy of electrons in the Fermi level at absolute zero.
• Fermi function (Fermi-Dirac distribution): describes the probability of an electron occupying a given energy level at a particular temperature; the highest occupied energy level.