Introduction:
To understand why germanium needs to be doped with indium to obtain a p-type semiconductor, we need to first understand the concept of doping and the difference between p-type and n-type semiconductors.

Doping:
Doping is the process of adding impurities to a semiconductor material to alter its electrical properties. These impurities are called dopants and they can either introduce extra electrons (n-type doping) or create holes (p-type doping) in the semiconductor lattice.

P-type and N-type Semiconductors:
P-type semiconductors are created by doping a pure semiconductor material with impurities that have fewer valence electrons than the host material. This creates "holes" in the valence band, which act as positive charge carriers.

N-type semiconductors, on the other hand, are created by doping a pure semiconductor material with impurities that have more valence electrons than the host material. This introduces "extra" electrons into the conduction band, which act as negative charge carriers.

Doping Germanium with Indium:
In the case of germanium, which is a group IV element with four valence electrons, we need to introduce impurities that have fewer valence electrons to create holes and form a p-type semiconductor.

Indium, which is a group III element with three valence electrons, is suitable for p-type doping of germanium. When indium atoms are added to the germanium lattice, they replace some of the germanium atoms. Due to the difference in the number of valence electrons, the indium atoms create "holes" in the valence band of germanium.

These holes act as positive charge carriers and contribute to the conductivity of the semiconductor. The indium atoms effectively accept electrons from neighboring germanium atoms, creating a surplus of positive charge carriers.

Conclusion:
In conclusion, to obtain a p-type germanium semiconductor, it must be doped with indium. Indium, being a group III element with fewer valence electrons than germanium, introduces "holes" in the valence band of germanium, creating positive charge carriers and enabling conductivity in the material.