Forbidden Energy Gap and Temperature Relationship

  Problem : Forbidden Energy Gap of Semiconductor:

1. Increases with temperature

2. Decreases with temperature

3. Slightly increase ,then decrease with temperature

4. Does not change with temperature

Solution : B.  Decreases with Temperature.

Explanation :

We shall be first discussing what actually is a “Forbidden Energy Gap” and then be discussing its variation with change in temperature.

As we know, the Energy band is a concept derived from the Bohr Model of an atom where the energy of an electron is dependent on the orbit in which it is revolving. Since solids have atoms closely packed, so the orbits of any two neighbouring atoms in a crystal may be overlapping and the entire energy model of atoms will be entirely different from those as isolated atoms. 

Every different atom in the crystal has a different energy band and no two electrons will have the same set of surrounding charges or electrons. These different energy levels with continuous energy variation form what are called energy bands. The energy band associated with the energy level of valence electrons of atoms is known as valence band and the energy band above the level of valence band is known as conduction band.

The energy gap or difference in level of energy between conduction band and valence band is known as energy band gap or forbidden energy gap. 

If the electrons in the highest level of valence band are completely bound and there is a sufficient amount of band gap ,the material will act as an insulator.

In the other case, when the lowest level of conduction band lies below the highest level of valence band, means that the forbidden energy gap is zero or electrons may travel freely between the two bands, the material will act as a conductor.

Whenever the electrons in valence band get excitation energy ( maybe thermal ) from an external source ,the electrons jump from valence band to conduction band ,the crystal may act as a semiconductor. Or, it can be said that the energy required for a valence electron to jump to conduction band in  case of semiconductor is forbidden energy gap.

Having clarified the concept of  forbidden energy gap along with its relationship with conductivity of a material, we shall be discussing the temperature variation of Forbidden energy  gap in a much better way.

Forbidden energy gap is the difference between energy of valence electrons and conduction band. If the valence electrons receive some energy from an external source ultimately increasing its energy means the electron’s energy is much nearer to the conduction band.

When the temperature of a semiconductor is increased, the electrons vibrate from their bounded position resulting in electron-hole pairs and mobility. Also ,the energy of the electrons rises in valence band to a much higher orbit or ionize itself if the thermal energy matches ionization energy setting the electron free. So, the electron will require much less energy to jump into the conduction band which means the forbidden energy gap has been reduced upon increasing the temperature.

So the correct option is:

B.  Decreases with Temperature.

Note : It is very important to note here that the valence band energy of an electron will match the Bohr energy of that orbit only at absolute zero temperature. At a temperature higher than absolute zero , the electrons will have some thermal energy which means valence electrons will have higher energy than that of Bohr energy. At absolute zero, the conduction band remains totally empty.