On doping germanium metal with phosphorus we would get:-

n-type semiconductor

The correct answer is Option (3) → n-type semiconductor.

When germanium (Ge) is doped with phosphorus (P), it forms an n-type semiconductor. Let us go into the detailed explanation of how this process works and why it leads to an n-type semiconductor.

Germanium (Ge) is a group 14 element with 4 valence electrons. In its pure form, germanium is a semiconductor. Each germanium atom forms covalent bonds with four neighboring atoms, creating a lattice structure. At room temperature, some electrons gain enough energy to break free from these covalent bonds, contributing to electrical conduction. However, in pure germanium, the number of free charge carriers (electrons and holes) is quite limited, which results in moderate conductivity.

Doping is the process of intentionally adding impurities (dopants) to a pure semiconductor to modify its electrical properties. By adding a dopant with either more or fewer valence electrons than the semiconductor, we can control the type and number of charge carriers in the material.

Phosphorus (P) is a group 15 element with 5 valence electrons (one more than germanium). When phosphorus atoms are introduced into the germanium crystal lattice, each phosphorus atom bonds with four germanium atoms, just like germanium atoms would. However, since phosphorus has five valence electrons, one electron is left unbonded. This extra electron becomes a free electron, which is not bound to any atom and can move freely throughout the lattice.

The extra electron from each phosphorus atom adds to the number of free electrons available for conduction. These free electrons act as negative charge carriers, and since the majority of the charge carriers are electrons, this type of semiconductor is called an n-type semiconductor.

In an n-type semiconductor, the majority charge carriers are electrons, and the minority carriers are holes (the absence of an electron in the lattice).

The "n" in n-type stands for negative, indicating that the negatively charged electrons are the primary carriers of electrical current. Since phosphorus donates electrons to the germanium crystal, this type of doping is referred to as donor doping.

n-type semiconductors have more electrons (negative charge carriers) than holes because of the extra electrons contributed by the phosphorus dopant.

p-type semiconductors (in contrast) are created by doping germanium with a group 13 element (like boron), which has 3 valence electrons. This creates holes (positive charge carriers) due to the absence of an electron in the crystal lattice, leading to a p-type material.

n-type semiconductors are commonly used in diodes, transistors, and other semiconductor devices. When combined with a p-type semiconductor, an n-type semiconductor forms a p-n junction, which is the basic building block of many electronic devices, including diodes and solar cells.

Conclusion:

Doping germanium with phosphorus introduces free electrons into the crystal lattice, which increases the material’s conductivity. These free electrons are responsible for electrical conduction, making the material an n-type semiconductor because the majority charge carriers are negative electrons.

Thus, doping germanium with phosphorus creates an n-type semiconductor due to the presence of extra free electrons.