Dimensional transitions of density of states and heat capacity in spherical quantum dots

We evaluate analytically and numerically the density of states (DOS) and the heat capacity in a spherical quantum dot formed by a spherical thin barrier. The control of the spherical barrier thickness or the potential barrier height is found to cause the dimensional transition from the three-dimensional (3D) behavior to the quasi-zero dimensional (Q0D) behavior in the DOS and the heat capacity. When the barrier is thick enough, the DOS shows the Q0D-like behavior but when the barrier is thin enough to allow electrons to tunnel through it, the temperature dependence of the heat capacity exhibits quite a distinct behavior depending on the electron density. Explicit numerical plots are given in the low density regime.