Heat capacity of suspended phonon cavities

Details Heat capacity of suspended phonon cavities Heat capacity of suspended phonon cavities

2006-12-18

arxiv.org/abs/cond-mat/0612463v2

Phys. Rev. B 75, 045320 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, double column, 3 figures. To appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.75.045320

We present a detailed analysis of the vibrational spectrum and heat capacity of suspended mesoscopic dielectric plates, for various thickness-to-side ratios at sub-Kelvin temperatures. The vibrational modes of the suspended cavity are accurately obtained from the three-dimensional (3D) elastic equations in the small strain limit and their frequencies assigned to the cavity phonon modes. The calculations demonstrate that the heat capacity of realistic quasi-2D phonon cavities approach the linear dependence on T at sub-Kelvin temperatures. The behavior is more pronounced for the thinnest cavities, but takes place also for moderately thick structures, with thickness-to-side ratios $\gamma$=0.1 to 0.2. It is also demonstrated that the heat capacity of the suspended phonon cavities is invariant under the product of the temperature (T) with a characteristic lateral dimension (L) of the sample. The present results establish a lower bound for the heat capacity of suspended mesoscopic structures and indicate the emergence of the quantum mechanical regime in the dynamics of bounded phonon cavities.

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