Slide 1

  • Conductors, Semiconductors, and Insulators
  • BANDS (conduction & valence)

Slide 2

  • In solids, electrons occupy specific energy levels or bands.
  • Valence band: Highest energy band filled with electrons.
  • Conduction band: Energy band above the valence band, empty or partially filled with electrons.

Slide 3

  • Conductors have overlapping valence and conduction bands.
  • Examples: Metals like copper, silver, gold.
  • Valence electrons are loosely bound and can move freely in the conduction band.

Slide 4

  • Insulators have a significant energy gap between the valence and conduction bands.
  • Examples: Wood, glass, rubber.
  • Valence electrons are tightly bound, cannot easily move to the conduction band.

Slide 5

  • Semiconductors have a small energy gap between the valence and conduction bands.
  • Examples: Silicon (Si), Germanium (Ge).
  • At low temperatures, semiconductors behave as insulators.

Slide 6

  • Intrinsic semiconductor: Pure semiconductor with equal numbers of holes and electrons.
  • At absolute zero, valence band is fully occupied, and conduction band is empty.

Slide 7

  • Doping: Adding impurities to the intrinsic semiconductor to alter its electrical properties.
  • Types of doping:
    • N-type doping: Adding elements with more valence electrons.
    • P-type doping: Adding elements with fewer valence electrons.

Slide 8

  • N-type doping introduces extra electrons, called majority carriers.
  • Examples of N-type dopants: Phosphorus (P), Arsenic (As).
  • These extra electrons increase conductivity.

Slide 9

  • P-type doping introduces holes, which act as positive charge carriers.
  • Examples of P-type dopants: Boron (B), Gallium (Ga).
  • Holes can move in the valence band, contributing to conductivity.

Slide 10

  • The conductivity of a material depends on:
    • Number of charge carriers
    • Mobility of charge carriers
    • Temperature
  • Conductivity = Charge carrier density × Charge carrier mobility.

Slide 11

  • Band gap: Energy difference between the valence and conduction bands.
  • Larger band gap → insulator, smaller band gap → semiconductor.
  • Band gap determines the energy required for electrons to move from the valence to conduction band.

Slide 12

  • Fermi energy level: Maximum energy level in the valence band occupied at absolute zero.
  • Determines electrical conductivity and thermal properties of materials.
  • Materials with higher Fermi energy levels are better conductors.

Slide 13

  • Drift velocity: Average velocity of charge carriers in the presence of an electric field.
  • Dependent on:
    • Applied electric field strength
    • Mobility of charge carriers
  • Formula: v_d = μE, where v_d is drift velocity, μ is mobility, and E is electric field strength.

Slide 14

  • Ohm’s Law: V = IR
    • V - Voltage (volts)
    • I - Current (amperes)
    • R - Resistance (ohms)
  • Resistivity: Intrinsic property of a material, resistance per unit length and cross-sectional area.

Slide 15

  • Ohm’s Law can be written as: J = σE
    • J - Current density (A/m^2)
    • σ - Conductivity (ohm^-1 m^-1)
    • E - Electric field strength (V/m)
  • Conductivity = 1 / Resistivity
  • Conductivity depends on the number of charge carriers and their mobility.

Slide 16

  • Temperature dependence of resistivity: Resistivity increases with increasing temperature for conductors.
  • In semiconductors, resistivity decreases with increasing temperature.
  • Metals have positive temperature coefficients of resistance (TCR).
  • Semiconductors have negative TCR.

Slide 17

  • Temperature coefficient of resistance (TCR): Rate at which resistivity changes with temperature.
  • Formula: TCR = (ΔR / R_initial) / ΔT
  • Unit: 1/degrees Celsius (°C^-1) Example: If a wire’s resistance increases by 0.1 ohms for every 1-degree increase in temperature, TCR = 0.1 °C^-1.

Slide 18

  • Superconductivity: Phenomenon where certain materials exhibit zero electrical resistance below a critical temperature.
  • Allows for flow of electric current without any energy loss.
  • Examples: Mercury (Hg), Niobium (Nb), Cuprates (YBCO).

Slide 19

  • Superconducting transition temperature (Tc): Temperature below which a material becomes a superconductor.
  • Different materials have different Tc values.
  • Can range from a few Kelvin to over 100 Kelvin.

Slide 20

  • Applications of superconductors:
    • Magnetic levitation
    • High-speed trains (Maglev)
    • Magnetic resonance imaging (MRI)
    • Particle accelerators
    • Energy-efficient power transmission

Slide 21

  • Energy band diagram for conductors, semiconductors, and insulators.
  • Valence band is fully occupied in insulators.
  • Electrons in conductors can move freely between bands.
  • Semiconductors have a small energy gap between bands.

Slide 22

  • The energy gap (Eg) determines the electrical behavior of a material.
  • Eg for conductors: ~0 eV
  • Eg for insulators: >3 eV
  • Eg for semiconductors: 0.1 - 3 eV

Slide 23

  • Intrinsic semiconductors have equal numbers of electrons and holes.
  • Electrons can move to the conduction band by absorbing energy.
  • Holes can move to the valence band when electrons fill them.

Slide 24

  • Doping: Adding impurities to control electrical behavior of semiconductors.
  • N-type doping increases electron concentration.
  • P-type doping increases hole concentration.

Slide 25

  • N-type semiconductors have excess electrons as majority carriers.
  • Examples: Phosphorus (P), Arsenic (As).
  • Excess electrons increase conductivity.

Slide 26

  • P-type semiconductors have excess holes as majority carriers.
  • Examples: Boron (B), Gallium (Ga).
  • Holes can move in the valence band, contributing to conductivity.

Slide 27

  • Minority carriers: Charge carriers with lower concentration than majority carriers.
  • Example: In N-type semiconductor, holes are minority carriers.
  • Minority carriers determine recombination and conduction properties.

Slide 28

  • Extrinsic semiconductors: Doped semiconductors with excess majority carriers.
  • N-type extrinsic semiconductor is obtained by introducing N-type dopants.
  • P-type extrinsic semiconductor is obtained by introducing P-type dopants.

Slide 29

  • Electrical conductivity: Ability of a material to conduct electric current.
  • Determined by charge carrier concentration and mobility.
  • Formula: Conductivity (σ) = Charge carrier concentration (n) × Charge carrier mobility (μ)

Slide 30

  • The mobility of charge carriers depends on scattering mechanisms in the material.
  • Temperature, impurities, defects, and phonons can cause scattering.
  • High mobility results in high conductivity.