Size or shape - What matters most at the nanoscale?

Bidimensional quantum dots with different shapes and areas are considered and the Schrodinger equation is used within a finite element method to calculate electron energies and localization probabilities. At the nanoscale, shape may not be as important as the size is. Our work proves that studying quantum effects in some particularly symmetrical structures may be very conclusive for other symmetries as well. Quantities relevant for intraband optics may be further obtained by using the electric-dipole matrix formalism. The dots area is proposed as a quantitative criterion to compare the results obtained for different and regular shapes. It is found that the majority of differently-shaped quantum dots behave electronically and optically in a remarkably similar manner. No matter the shape, any regular polygonal quantum dot with more than four sides and a given area has just the same quantitative optoelectronic properties.