Question

If the lattice constant of this semiconductor is decreased, then which of the following is correct? (Where ${{\text{E}}_{\text{c}}}$ is conduction bandwidth,${{\text{E}}_{\text{g}}}$ Is Band gap and ${{\text{E}}_{\text{v}}}$ is valence bandwidth)
$\text{(A) All }{{\text{E}}_{\text{c}}}\text{, }{{\text{E}}_{\text{g}}}\text{, }{{\text{E}}_{\text{v}}}\text{ decrease}$
$\text{(B) All }{{\text{E}}_{\text{c}}}\text{, }{{\text{E}}_{\text{g}}}\text{, }{{\text{E}}_{\text{v}}}\text{ increase}$
$\text{(C) }{{\text{E}}_{\text{c}}}\text{ and }{{\text{E}}_{\text{v}}}\text{ increase but }{{\text{E}}_{\text{g}}}\text{ decreases}$
$\text{(D) }{{\text{E}}_{\text{c}}}\text{ and }{{\text{E}}_{\text{v}}}\text{, decrease }{{\text{E}}_{\text{g}}}\text{ increases}$

Answer 1

We can solve this question with the concept of lattice constant. We can define lattice constant as the physical dimension of unit cells within a crystal lattice simply, it is the side length of the cube. If the lattice constant of a semiconductor is decreased, that means electrons are more tightly bonded towards the atom and if lattice constant is increased, electrons are loosely bound to the atom.

Complete answer:
Energy gap between the valence band and the conduction band is less than 3eV as we have learned in semiconductors where,
1. $\Delta {{\text{E}}_{\text{g}}}$ lies between the conductor and the insulator.
2. Both the electrons and the holes are responsible for conductivity.
3. At 0K, elements like Si and Ge behave like insulators.
Hence, we know that when we decrease the lattice parameter of a semiconductor, the electrons are more tightly bound to the atom, and hence need more energy to excite or remove one atom. That is, the width of energy bands of both valence and conduction bands decreases. This sums up in the increase in energy gaps between conduction and valence band and the increment of band gap.

So, the correct answer is “Option D”.

Note:
In solid state Physics we should know that a band gap is also known as an energy gap. It is an energy range in a solid where no electronic state of the solid can exist.
The valence band is known as the band of electron orbitals from where the electrons can jump out of, or move into the conduction band when they are in the excited state. The valence bond is simply the outermost electron orbital of an atom or of any specific material that electrons actually can occupy.
In the question we can see that there is the mentioning of the concept of lattice constant. By lattice constant we mean any lattice parameter which will refer to the physical dimension of any unit cell of the crystal lattice taken into consideration.