As fractal dimension of a thin film surface implies the irregularity in the surface. Is it possible that the energy states of the electrons are also affected by the fractal dimension?
It is definitely a possibility. In general, the electronic states and optoelectronic properties vary in surfaces, compared to that of the bulk. To investigate such differences, very scrupulous experiments are necessary; as most experiments result an average effect of the bulk and surface.
Thank you @ Souvik Bhattacharjee for your kind reply. But, I was thinking that if I could show that through equation that fractal dimension is affected by, suppose thickness of the film and then if it can be shown that energy states are also affected by thickness. Then, could we discuss that energy states are affected by fractal dimension?
Typically dimensions affect energy states in such systems. The simplest example is nanoparticles, 0D, 1D, and 2D materials. All they have different energy landscape.
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