Quantum shape oscillations in the thermodynamic properties of confined electrons in core–shell nanostructures

Abstract

Quantum shape effect appears under the size-invariant shape transformations of strongly confined structures. Such a transformation distinctively influences the thermodynamic properties of confined particles. Due to their characteristic geometry, core-shell nanostructures are good candidates for quantum shape effects to be observed. Here we investigate the thermodynamic properties of non-interacting degenerate electrons confined in core-shell nanowires consisting of an insulating core and a GaAs semiconducting shell. We derive the expressions of shape-dependent thermodynamic quantities and show the existence of a new type of quantum oscillations due to shape dependence, in chemical potential, internal energy, entropy and specific heat of confined electrons. We provide physical understanding of our results by invoking the quantum boundary layer concept and evaluating the distributions of quantized energy levels on Fermi function and in state space. Besides the density, temperature and size, the shape per se also becomes a control parameter on the Fermi energy of confined electrons, which provides a new mechanism for fine tuning the Fermi level and changing the polarity of semiconductors.