  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.
