Germanium crystal, the crystal becomes n- type semiconductor because antimony is a pentavalent substrate. that's why there will be more free electrons than holes in the semiconductor

Introduction:
When a small amount of antimony is added to germanium crystals, it has several effects on the properties of the semiconductor. One of the significant impacts is an increase in the number of free electrons compared to the number of holes in the material. This can be explained by understanding the behavior of antimony as a dopant in germanium.

Explanation:
1. Doping: Doping is the process of intentionally introducing impurities into a semiconductor to alter its electrical properties. In this case, antimony is added as a dopant to germanium crystals.

2. Antimony as a donor impurity: Antimony belongs to the group of elements known as pentavalent impurities, which means it has five valence electrons. Germanium, on the other hand, is a tetravalent element with four valence electrons.

3. Substitutional doping: Antimony atoms replace some of the germanium atoms in the crystal lattice. This is known as substitutional doping.

4. Extra electron: When antimony substitutes germanium, it introduces an extra valence electron into the crystal structure. This extra electron is not tightly bound to any atom and is relatively free to move within the crystal.

5. Creation of free electrons: The extra electron from the antimony atom can easily break free from its parent atom and become a free electron in the crystal lattice. These free electrons contribute to the electrical conductivity of the material.

6. Formation of holes: When the antimony atom donates its extra electron, it leaves behind an unfilled electron "hole" in its parent atom. These holes can move through the crystal lattice and behave as positively charged carriers.

7. More free electrons than holes: Since antimony is a pentavalent impurity, each antimony atom contributes one extra electron to the crystal. Therefore, the number of free electrons introduced by antimony doping exceeds the number of holes created by the absence of electrons in the germanium lattice.

8. P-type semiconductor: Although antimony is a donor impurity, the overall effect of adding it to germanium is to create an excess of free electrons. This results in an excess of negative charge carriers, making the material behave as a p-type semiconductor.

9. Increased conductivity: The presence of more free electrons than holes in the semiconductor leads to a higher conductivity as the free electrons are the majority carriers and contribute to the flow of electric current.

In conclusion, when a small amount of antimony is added to germanium crystals, it increases the number of free electrons compared to the number of holes in the material, leading to a higher conductivity and making it behave as a p-type semiconductor.