MP Board · Class 12 · Physics · Semiconductor ElectronicsWhat is energy band formation in solids? Differentiate between conductors, insulators, and semiconductors on the basis of energy bands with the help of suitable energy band diagrams.

Introduction to Energy Band Formation\nIn an isolated atom, electrons occupy well-defined, discrete energy levels. However, when a large number of atoms (of the order of $10^{23}$ atoms/cm³) are brought together to form a solid crystal, the outermost electrons interact strongly with neighboring atoms. According to Pauli's exclusion principle, no two electrons can have the same set of all four quantum numbers. Due to this mutual interaction, each discrete atomic energy level splits into a large number of closely spaced, continuous energy levels known as an energy band.

Important Energy Bands

• Valence Band (VB): The energy band containing valence electrons is called the valence band. It is normally filled with electrons at absolute zero temperature and may be partially or completely filled at higher temperatures. Electrons in this band cannot contribute to electric conduction.
• Conduction Band (CB): The energy band above the valence band is called the conduction band. It may be empty or partially filled with electrons. Electrons in this band are free to move through the crystal and are responsible for electrical conduction.
• Forbidden Energy Gap ($E_g$): The energy gap between the top of the valence band and the bottom of the conduction band is called the forbidden energy gap. No electrons can stay in this region.

Classification of Solids Based on Energy Bands

1. Conductors (Metals):

   • In conductors, the valence band and conduction band overlap each other, or the forbidden gap is extremely small ($E_g = 0$).
   • A large number of free electrons are available for conduction even at low temperatures.
   • Example: Copper, Aluminium.

2. Insulators:

   • In insulators, the forbidden energy gap is very large ($E_g > 3 \text{ eV}$).
   • The valence band is completely filled, and the conduction band is completely empty.
   • At room temperature, thermal energy is insufficient to promote electrons from the valence band to the conduction band, hence they do not conduct electricity.
   • Example: Diamond, Glass.

3. Semiconductors:

   • In semiconductors, the forbidden energy gap is small ($E_g \approx 1 \text{ eV}$, e.g., $1.1 \text{ eV}$ for silicon and $0.7 \text{ eV}$ for germanium).
   • At absolute zero temperature, the valence band is completely filled and the conduction band is completely empty, acting as an insulator.
   • At room temperature, thermal agitation provides enough energy for some valence electrons to cross the small forbidden gap into the conduction band, imparting moderate conductivity.
   • Example: Silicon, Germanium.