Since the small particle has low band gap energy and thus shift the absorption profile to the lower wavelength, somehow, a higher particle size behaves contrarily. Is there any formula to illustrate this phenomenon in the semiconductor-based materials?
Band gap energy of any semiconductor always depends upon the particle size and shape. Whenever band gap energy increases as the particle size of the semiconductor nanomaterials decreases
This question was asked here before. Check this link: https://www.researchgate.net/post/Energy_Band_Gap_Versus_Nanoparticle_Size
Kind Regards,
L.A. Majewski
You may find useful answers here
https://www.researchgate.net/post/Why_does_the_band_gap_increase_when_decreasing_the_size_of_nanostructures
This article may help you as well
Relationship between Band Gap and Particle Size of Cadmium Sulfide Quantum Dots, Chemistry Research Journal, 2017, 2(5):15-21
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Article CODEN(USA): CRJHA5 Relationship between Band gap and particl...
Particle size affects the band gap value of the material only if the particle size is in the quantum confinement regime. This means that if the size of the particle is comparable, equal or smaller than the bohr exciton radius of the material (whose particle size is under consideration), the band gap value gets affected.
When the size is small, due to quantum confinement there occurs discretization of energy levels. the valance band levels move downwards while as the conduction band levels move upwards and hence result in increase of the bandgap.
There occurs decrease in band gap value as the particle size increases, till it reaches its bulk value.
Due to the spatial confinement of the charge carriers, the edge of the valance and conduction bands split into discrete, quantized, electronic levels. These electronic levels are similar to those in atoms and molecules. The spacing of the electronic levels and the band gap increases with decreasing particle size. This is because the electron hole pairs are now much closer together and the Coulombic interaction between them can no longer be neglected giving an overall higher kinetic energy.
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