Electrical Properties of Solids
Band Theory, Semiconductors, and the Science of Doping.
Solids exhibit an astounding range of electrical conductivities, extending over 27 orders of magnitude (from $10^{-20}$ to $10^7 \text{ ohm}^{-1} \text{m}^{-1}$). Based on their ability to conduct electricity, solids are classified into three distinct categories: Conductors, Insulators, and Semiconductors. To understand why a metal conducts but a piece of plastic does not, we use Band Theory.
1. Band Theory
According to molecular orbital theory, when atomic orbitals of millions of metal atoms interact, they form an equal number of molecular orbitals. Because these orbitals are so close in energy, they merge to form continuous bands.
- Valence Band: The energy band containing the valence electrons. It is either partially or fully occupied.
- Conduction Band: The empty energy band immediately above the valence band. For electricity to flow, electrons must be able to jump into this band.
- Forbidden Gap (Band Gap): The energy gap separating the valence band and the conduction band where no electron can exist.
2. Classification Based on Band Gap
The valence band is either partially filled, or it overlaps with the conduction band. Because there is no energy gap, electrons can easily flow under an applied electric field. (e.g., Metals).
The forbidden energy gap between the filled valence band and the empty conduction band is very large. Electrons cannot jump the gap. (e.g., Wood, Plastics, Sulfur).
The energy gap is small. At absolute zero (0 K), they act as perfect insulators. But at room temperature, some electrons acquire enough thermal energy to jump the gap into the conduction band, allowing weak conduction. (e.g., Silicon, Germanium).
3. Semiconductors and Doping
The intrinsic conductivity of pure Silicon or Germanium is too low to be practically useful in electronics. To increase their conductivity, we intentionally add specific impurities in a process called Doping.
A. n-type Semiconductors (Electron Rich)
Formed when a Group 14 element (like Si or Ge) is doped with a Group 15 element (like P or As).
- Silicon has 4 valence electrons; Phosphorus has 5.
- Four electrons of Phosphorus form normal covalent bonds with the surrounding Silicon atoms.
- The fifth extra electron is free/delocalized and becomes responsible for conducting electricity.
- Since conduction is due to negative electrons, it is called n-type.
B. p-type Semiconductors (Electron Deficient)
Formed when a Group 14 element (like Si or Ge) is doped with a Group 13 element (like B, Al, or Ga).
- Silicon has 4 valence electrons; Boron has only 3.
- Boron can only form 3 covalent bonds with the surrounding Silicon atoms. The fourth bond is missing an electron, creating an empty space called an electron hole (or simply a hole).
- Under an electric field, neighboring electrons jump to fill the hole, creating a new hole behind them. The hole effectively moves through the crystal like a positive charge.
- Since conduction appears to be due to positive holes, it is called p-type.
For Metals (Conductors), as temperature increases, the positive metal kernels vibrate more vigorously, obstructing electron flow. Thus, conductivity decreases with an increase in temperature.
For Semiconductors, as temperature increases, more electrons gain enough thermal energy to jump the band gap into the conduction band. Thus, conductivity increases with an increase in temperature.
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