Conductors, Semiconductors & Insulators

Key Terminology & Overview

• Electric Conduction
  • Transfer of electrical charge through the movement of electrons.
  • Governing equation: $I = \frac{Q}{t}$ (current $I$, charge $Q$, time $t$).
  • Relation between conductivity $\sigma$ and resistivity $\rho$: $\sigma = \frac{1}{\rho}$.
• Three Main Classes of Solids
  • Conductors – high electrical conductivity.
  • Semiconductors – intermediate electrical conductivity.
  • Insulators – negligible electrical conductivity.

Electron-Level Explanation

• All solids contain electrons, but their ability to move differs.
• Metals (Conductors)
  • Outer (valence) electrons are delocalised and form an “electron sea”.
  • These free electrons drift when an external electric field is applied, producing current.
• Insulators
  • Electrons are tightly bound to atoms; no free carriers at ordinary temperatures.
  • Cannot sustain a macroscopic current.
• Semiconductors
  • At 0 K act like insulators, but at ordinary / elevated temperatures some electrons gain enough energy to cross a modest energy gap, providing limited carriers.
  • Electrical properties are tunable by doping, temperature, light, or electric fields.

Band-Theory Picture

• Energy bands dictate carrier availability.
• Conductor
  • No forbidden gap; conduction and valence bands overlap.
• Semiconductor
  • Small forbidden gap $\left( E_g \approx 0.1 \text{–} 3\;\text{eV} \right)$.
  • Thermal energy can excite electrons from valence to conduction band.
• Insulator
  • Large forbidden gap \left( E_g > 3\;\text{eV} \right).
  • Practically impossible for electrons to cross at room temperature.
• Diagrammatic summary (qualitative):
  • a) Insulator – large gap between valence & conduction.
  • b) Semiconductor – small gap.
  • c) Conductor – bands overlap.

Comparative Table (Extracted Values)

• Conductivity $\sigma$
  • Conductors: High.
  • Semiconductors: Moderate.
  • Insulators: Low.
• Resistivity $\rho$
  • Conductors: Very Low.
  • Semiconductors: Moderate.
  • Insulators: Very High.
• Temperature Coefficient of Resistance (TCR)
  • Conductors: Positive (resistance increases with $T$).
  • Semiconductors: Negative (resistance decreases with $T$).
  • Insulators: Negative / negligible (already very high resistance).
• Valence Electrons (outer-shell count)
  • Conductors: 1 (e.g.
    $\text{Na: }3s^1$).
  • Semiconductors: 4 (e.g.
    $\text{Si: }3s^2 3p^2$).
  • Insulators: ≈8 (stable octet).
• Bond Type
  • Conductors: Metallic bonding.
  • Semiconductors: Covalent bonding (crystal lattice).
  • Insulators: Ionic or strongly covalent with full valence shells.

Examples & Case Studies

• Typical Conductors
  • Solid metals: Gold, Aluminium, Copper, Steel, Brass.
  • Non-metal conductor: Graphite (delocalised $\pi$-electrons).
  • Metal alloys.
  • Liquid metal: Mercury.
  • Certain ionised gases (plasmas).
  • Electrolytes: Ionic solutions that conduct via ions rather than electrons.
• Typical Insulators
  • Glass, Rubber, Quartz, Wood, Wool, Plastics, Pure (distilled) water.
• Typical Semiconductors (examples mentioned + common context)
  • Tellurium, Tin (grey allotrope behaves semiconductingly).
  • Common technological semiconductors (not explicitly in transcript but foundational): Silicon, Germanium, GaAs.

Classroom Demonstration

• Steel Paperclip Circuit
  • Steel (an alloy) connected in series with a bulb, battery and wires.
  • Bulb glows ⇒ steel is a conductor; electrons move through paperclip.
• Prediction Activity – Will the bulb glow?
  • Aluminium – Yes (metal conductor).
  • Wood – No (insulator).
  • Plastic – No (insulator).
  • Copper – Yes (excellent conductor).
• Key Takeaway: Metals allow current flow; non-metals generally do not, with graphite being an important exception.

Practical & Real-World Relevance

• Electrical Wiring: Copper/aluminium used for low resistive losses.
• Safety: Insulators (e.g.
  rubber handles, plastic coatings) protect users from electric shock.
• Electronics Industry: Semiconductors form the basis of diodes, transistors, integrated circuits.
• Environmental / Ethical Considerations
  • Mining of conductive and semiconductor materials (Cu, Au, Si, Te) has ecological impacts.
  • Proper disposal/recycling of electronic waste reduces heavy-metal contamination.

Concept Links to Earlier / Future Lectures

• Electrostatics – charge, electric fields, potential difference introduce the “driving force” for electron motion.
• Ohm’s Law – $V = IR$ relates material property (R) to observed current/voltage.
• Thermal Physics – carrier mobility and bandgap depend on temperature.
• Quantum Mechanics – origin of energy bands (Bloch theorem).

Numerical & Formula Highlights

• Conductivity range (orders of magnitude illustrative):
  • Metals: $\sigma \sim 10^7\;\text{S/m}$.
  • Semiconductors (intrinsic): $\sigma \sim 10^{-5} \text{–} 10^2\;\text{S/m}$.
  • Insulators: $\sigma \lesssim 10^{-10}\;\text{S/m}$.
• Example bandgap magnitudes:
  • Si: $E_g \approx 1.1\;\text{eV}$.
  • Ge: $E_g \approx 0.66\;\text{eV}$.
  • Quartz (SiO$2$): $E</em>g \approx 9\;\text{eV}$.

Summary Checklist

• [ ] Define conductors, semiconductors, insulators.
• [ ] Explain electron mobility and band theory.
• [ ] Memorise key examples of each category.
• [ ] Understand temperature effects on resistivity.
• [ ] Apply concept to predict conduction in everyday items.