Conductors, Semiconductors, and Insulators: Essential Facts and Shortcuts

1. Conductivity Values:

• Conductors (Low Resistivity):

  • Metals: (10^{-8}) to (10^{-6}) (\Omega\cdot\text{m})
  • Examples: Silver (Ag), copper (Cu), gold (Au)

• Semiconductors:

  • Conductivity range: (10^{-4}) to (10^{4}) (\Omega\cdot\text{m})
  • Examples: Silicon (Si), germanium (Ge)

• Insulators (High Resistivity):

  • Resistivity: Usually > (10^{12}) (\Omega\cdot\text{m})
  • Examples: Rubber, glass, plastics

2. Mobility of Charge Carriers:

• Metals (High Mobility):

  • Carrier mobilities: (10^{-3}) to (10^{-2}) (\text{m}^{2}/\text{Vs})

• Semiconductors:

  • Variable carrier mobility
  • Typical range: (10^{-1}) to (10^{3}) (\text{m}^{2}/\text{Vs})

• Insulators (Low Mobility):

• Carrier mobilities: Usually below (10^{-8}) (\text{m}^{2}/\text{Vs})

3. Bandgaps:

• Conductors:

• Overlapping conduction and valence bands

• Bandgap energy (Eg) = 0 eV

• Semiconductors:

• Bandgap energy range: 0.1 to 3.0 eV

• Examples: Silicon (1.1 eV), gallium arsenide (1.42 eV)

• Insulators:

  • Large bandgap energy (> 3.0 eV)
  • Examples: diamond (5.47 eV), glass ((E_g \approx 9) eV)

4. Resistivity Temperature Coefficient:

• Metals:

• Positive temperature coefficient of resistivity

• Typical range: (3\times10^{-3}) to (6\times10^{-3}) (\text{K}^{-1})

• Semiconductors:

• Negative temperature coefficient of resistivity

• Range: (-2\times10^{-3}) to (-8\times10^{-3}) (\text{K}^{-1})

• Insulators:

• Slightly positive temperature coefficient

• Indicates a slight increase in resistivity with rising temperature.

5. Applications:

• Conductors:

  • Electrical wiring, electronics, and electrical components.

• Semiconductors:

  • Transistors, ICs, solar cells, LEDs, various electronic devices.

• Insulators:

  • Electrical insulation, heat insulation, substrates for electronic components.

Remember:

• These values are approximate ranges, actual properties may vary.
• Understanding these concepts and their significance is essential for JEE and CBSE board exams.