Surface Phonon-Polariton Heat Capacity of Polar Nanofilms
José Ordoñez-Miranda, Sébastian Volz, Masahiro Nomura
Abstract
The surface phonon-polariton heat capacity of polar nanofilms is analytically determined and analyzed as a function of their thickness and temperature. It is shown that the polariton heat capacity increases with the square of the nanofilm thickness, such that for thin enough nanofilms at sufficient low temperature $T$, its value becomes independent of the material properties and is given by $C=1.15{\ensuremath{\epsilon}}_{0}{k}_{B}{({k}_{B}T/\ensuremath{\hbar}c)}^{2}$, where ${\ensuremath{\epsilon}}_{0}$ and $c$ are the respective relative permittivity of the surrounding medium and light speed in vaccum, while ${k}_{B}$ and $2\ensuremath{\pi}\ensuremath{\hbar}$ are the Boltzmann and Planck constants, respectively. The photonlike nature of surface phonon polaritons is found to be responsible for their main contribution to the material heat capacity. As a result of the polariton speed close to $c$ and hence much higher than that of phonons, the polariton heat capacity of ${\mathrm{Si}\mathrm{O}}_{2}$, SiC, and $\mathrm{SiN}$ is found to be several orders of magnitude smaller than its corresponding phonon counterpart. Surface phonon polaritons are thus not expected to increase the expansion coefficient of polar nanofilms, which favors their utilization as effective heat dissipators.