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in ADDITION TO LARGE OR INTERFACE AREA, ANOTHER ADVANTAGE OF SEMICONDUCTOR NANOPARTICLE IS THAT ENGERY GAP...

in ADDITION TO LARGE OR INTERFACE AREA, ANOTHER ADVANTAGE OF SEMICONDUCTOR NANOPARTICLE IS THAT ENGERY GAP CAN BE TUNED VIA PARITICAL SIZE at nm levels, use a equation to briefly explain how engery gap of an nano particle is correlated to its sizes

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Answer #1

Using effective mass approximation, we write an equation

Where E(R) is the band gap energy , is the band gap of the bulk semi-conductor, and is the effective mass of electron and hole, R is the radius of the Nano particle with dielectric constant .

Electrons in the conduction band and holes in the valence band are confined by a surface potential. Hence, electron-hole recombination energy or the lowest energy transition from valence band to conduction band increases in energy. Hence band gap increases with decrease in particle size.

h2 1 1.8e2

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