(a) Explain why no hole is generated by the electron excitation involving a donor impurity atom. (b) Explain why no free electron is generated by the electron excitation involving an acceptor impurity atom.

Donor impurity atoms have extra valence electrons that can be easily given to the conduction band of a semiconductor. When an electron is excited from the donor impurity atom to the conduction band, it becomes a free electron, increasing the electrical conductivity of the material. However, unlike intrinsic semiconductors, the donor atom does not leave behind a hole in the valence band in this process. This is because the electron was originally in the extra orbit of the donor atom, not in the semiconductor's valence band. On the other hand, acceptor impurity atoms have fewer valence electrons compared to the atoms surrounding it in the semiconductor. They can accept an electron from the valence band of the semiconductor, which eventually fills the space in the valence band, and simultaneously creates a hole. This process does not result in the generation of a free electron in the conduction band, as the electron is just moving from the valence band to an acceptor atom's electron shell instead of moving to the conduction band of the semiconductor.

When an electron is excited in a donor impurity atom, it moves to the conduction band of the semiconductor. This excitation leaves a positively charged ion on the donor impurity atom, but no hole in the valence band is created. The reason for this is that the electron that has been excited to the conduction band initially belonged to the donor atom, and it was not part of the valence band of the semiconductor. As a result, no hole is generated in the valence band during this process.

In the case of acceptor impurity atoms, an electron from the valence band of the semiconductor is excited and moves to fill the vacant space in the acceptor atom's electron shell. This creates a hole in the valence band since the electron has left its original position. However, no free electron is generated in the conduction band, because the excited electron is now part of the acceptor atom's electron shell rather than moving into the conduction band of the semiconductor. Consequently, the only change is the creation of a hole in the valence band, and no free electron is generated in the conduction band during electron excitation involving an acceptor impurity atom. In summary, donor and acceptor impurities in semiconductors exhibit different behaviors during electron excitations. While donor impurity atoms give away their extra valence electron, creating a free electron in the conduction band but leaving behind no hole in the valence band. Acceptor impurity atoms, however, take an electron from the valence band to fill their electron shell, creating a hole in the valence band but not generating any free electron in the conduction band.