Question

Why bandgap increase as we go in nanodimensions ?

Answer 1

Usually in bulk materials, or at higher dimension, we have a bandgap equal to the separation between the ground state and the first excited state. All energy levels are broadened in bulk materials and thus the overall band gap decreases.

However, at nano-dimensions this broadining of energy levels is much lower comparatively and thus a greater bandgap. This happens because, at smaller dimensions the system behaves like a particle in a box where the energy of the levels is inversely proportional to L². Thus, small the dimension, much larger will be the corresponding energy levels for differnt value of n. Thus, there will be a larger seperation between the levels.