For lithium niobate, as I increase the pressure as a result the bandgap also increases but lattice parameters decreases. I am applying equal pressure in all directions (x, y, z). anyone can explain it with references. In advance thanks a lot.
You know, generally, Pressure's influence on band gap might indeed be described as easy as pie. Pressure modifies the lattice characteristics, leading to changes in the mean distance between electrons/holes and ions. As a consequence, the amplitude of the electron/hole - ion potential changes. Such a potential is pivotal in establishing the band gap at the Brillouin zone. Furthermore, the mean distance between electrons/holes varies significantly. This affects the overlap integral. Changes in the overlap integral affect the band width and, as a function, the band gap.
Shakeel Ahmad Hi Friend based on your explanation,
I don't have any idea about the computational chemistry aspects. However, when it comes to the theoretical approach there are some factors that affect the band alignment. In your case, I may suggest a change in the crystal structure.
If pressure is applied on a closed system, according to the thermodynamic principles it resulted to an increase in temperature. Ultimately this yields to changes in the crystal structure of your material.
In the case of indirect excitation, if your material doesn't have a new dopant CB vertical energy alignment should be in the same position. However, with the change of the crystal structure, there should be an additional requirement for "Proton assigned energy" of the horizontal direction. That could be the season for the increment of the bandgap.
I don't know to what extent my statement is valid. If you can check the crystalline structure data before and after the treatment, you can make a good conclusion based on my hypothesis.
Interesting topic, I work with LiNbO3 every day, it's a perovskite material with optimal properties for optics and photonics. For your question, I quote:
""The compressibility of LN is thought to be related to the compressibility of the bond. Therefore, we have investigated the charge and chemical bonding of Pnma phase using a detailed Mulliken population analysis. The bond populations indicate the overlap degree of the electron cloud of two bonding atoms and can be used to access the covalent or ionic nature of a chemical bond. For the bond populations, the lowest and highest values imply that the chemical bond exhibits strong iconicity and covalency, respectively. The changes in the average Nb– O bond length and the bond population is shown in Fig. 7. As pressure increases, the average Nb– O bond length decreases while the Nb– O bond population increases as the pressure increases, indicating the increased covalent character between Nb and O atoms under high pressure at the Pnma phase. The increase of the Nb– O interactions under high pressure leads to the increase of hybridization between O 2p and Nb 4d orbitals at the Pnma phase.""