Shape and size effects on electronic thermodynamics in nanoscopic quantum dots

The thermodynamic properties of strongly confined semiconductor nanostructures are significantly influenced by their geometry because the thermal de Broglie wavelength of the particles is comparable to the size of the structure. GaAs quantum dots (QDs) are nanostructures that can be configured in various geometrical forms, which makes them excellent candidates for studying how geometrical variations affect their thermodynamic properties. In this work, we present the study of the thermodynamic properties of a GaAs QD in spherical, cylindrical, cubic, and pyramidal shapes, through the finite element method (FEM) considering external infinite confinement and the effective mass approximation. The design of QDs guarantees the same volume (V) and cross-sectional area (A) for each case, providing structures with similar size characteristics. We observe stepwise behaviors in the particle number and entropy as a function of chemical potential due to shape dependence for the highest confinement configuration, which agrees with the nature of the Fermi–Dirac distribution function. Finally, we present the effect of geometrical shape for all geometrical configurations of the QD. We compare the thermodynamic properties of each arrangement and investigate the heat capacity response for different temperatures.