Question

Explain the classification of conductors, insulators and semiconductors on the basis of energy bands.

Hint:

The key distinguishing factor is the size of the forbidden energy gap (\(E_g\)): - {Conductors:} \(E_g \approx 0\) (overlapping bands). - {Semiconductors:} \(E_g\) is small (around 1 eV). - {Insulators:} \(E_g\) is large (greater than 3 eV).

Answer 1

Step 1: Understanding Energy Band Theory: 
In solids, due to the interaction between atoms, the discrete energy levels of isolated atoms broaden into continuous bands of allowed energy levels, separated by forbidden energy gaps. The highest energy band that is completely filled with electrons at absolute zero temperature (0 K) is called the Valence Band (VB). The next higher permitted energy band, which may be empty or partially filled, is called the Conduction Band (CB). The energy difference between the top of the valence band and the bottom of the conduction band is the Forbidden Energy Gap (\(E_g\)). The electrical conductivity of a solid is determined by the size of this energy gap. 
Step 2: Classification and Energy Band Diagrams: 
1. Conductors (Metals): 
In conductors, the valence band and the conduction band overlap. There is no forbidden energy gap between them (\(E_g \approx 0\)). Due to this overlap, a large number of free electrons are readily available in the conduction band to move freely throughout the material, even with a small applied electric field. This results in high electrical conductivity. 

2. Insulators: 
In insulators, the valence band is completely filled with electrons, and the conduction band is completely empty. The forbidden energy gap (\(E_g\)) between the valence and conduction bands is very large (typically \(E_g>3\) eV). A very high amount of energy is required to excite an electron from the valence band to the conduction band. Therefore, at room temperature, there are virtually no free electrons in the conduction band, and the material has very low electrical conductivity. 

3. Semiconductors: 
Semiconductors have an energy band structure similar to insulators, but with a much smaller forbidden energy gap (typically \(0.2 \, \text{eV}<E_g<3 \, \text{eV}\)). For example, \(E_g \approx 1.1\) eV for Silicon and \(E_g \approx 0.7\) eV for Germanium. At absolute zero (0 K), the valence band is full and the conduction band is empty, so they behave as insulators. However, at room temperature, some electrons gain enough thermal energy to jump across the small gap into the conduction band, leaving behind vacancies called "holes" in the valence band. Both the electrons in the CB and the holes in the VB contribute to electrical conductivity.