Yes, it is indeed possible for the band gap of a semiconductor material to change under the influence of external pressure. This phenomenon is known as the pressure-induced band gap tuning or pressure-induced band gap shift. The behavior of the band gap under pressure can vary depending on the specific semiconductor material and its crystal structure.

Yes, it is indeed possible for the band gap of a semiconductor to change under the influence of applied pressure, and this phenomenon is known as "pressure-induced band gap tuning." The behavior of the band gap under pressure can be quite complex and depends on the specific material's properties, its crystal structure, and the nature of its electronic states.

In some cases, increasing pressure can cause the band gap of a semiconductor to increase. This can occur due to changes in the electronic structure as the interatomic distances are altered under pressure. As atoms are brought closer together, the energy levels of electrons in the material's energy bands can shift, leading to changes in the band gap.

However, your question suggests an interesting scenario where the band gap increases up to a certain pressure and then starts to decrease again. This behavior could potentially be observed under specific circumstances, such as:

It's important to note that predicting the exact behavior of the band gap under pressure is challenging and often requires detailed computational simulations or experimental measurements. The interplay of various factors, such as the material's composition, crystal structure, electronic properties, and the specific pressure conditions, can lead to unique and sometimes unexpected behavior.

In summary, while it is possible for a semiconductor's band gap to increase under pressure and then decrease again at certain pressure ranges, the specific behavior will depend on the material's characteristics and the underlying physical mechanisms governing its electronic properties.

When you apply pressure to a crystal along one direction you modify the distances between the atoms. On that direction the energy becomes higher because the atoms are closer to each other. Indeed the band gap is modified when applying pressure (because the potential of the lattice is changed).