Heat conduction engineering in pillar-based phononic crystals

Pillar-based phononic crystals belong to a class of acoustic metamaterials that can control heat conduction based on the design of the structure. In this work, we systematically investigate how various parameters of pillar-based phononic crystals affect thermal conductance at low temperatures. We find that the lowest thermal conductance is achieved when the pillars are short, have a large radius, a long period, and are made of materials with few local resonances, whereas pillars with many local resonances can, on the contrary, increase thermal conductance. We argue that properly designed pillar-based phononic crystals can serve as an alternative to conventional hole-based phononic crystals because local resonances in pillars introduce additional degrees of freedom, which allows not only suppressing but also enhancing heat conduction. Moreover, we propose hybrid hole/pillar-based phononic crystals that can further reduce thermal conductance.

Figure 1

(a) Schematic of a pillar-based PnC consisting of a silicon membrane and an array of pillars. (b) The hexagonal lattice of pillars and (c) a simulated unit cell.

Figure 2

Phonon dispersion of a pillar-based PnC ($a=160\mathrm{nm}, r/a=0.4$, and $h_{\mathrm{Membrane}}=h_{\mathrm{Pillar}}=80\mathrm{nm}$), shown by solid lines, plotted together with the dispersion of a silicon membrane without pillars $(h_{\mathrm{Membrane}}=80\mathrm{nm})$, shown by green dashed lines, and eigenfrequencies of a single aluminum pillar, shown by black horizontal dash-dotted lines. Color indicates relative height (ξ) of the physical location of the modes.

Figure 3

(a) DOS spectra of a silicon membrane and PnCs with aluminum phosphide and diamond pillars ($a=160\mathrm{nm}, r/a=0.4$, and $h_{\mathrm{Pillar}}=h_{\mathrm{Membrane}}=80\mathrm{nm}$). Eigenfrequencies of such pillars without an underlying membrane are plotted in the top panel. (b) Relative thermal conductance of pillar-based PnCs ($a=160\mathrm{nm}, r/a=0.4$, and $h=80\mathrm{nm}$) with pillars made of different materials vs number of LRs in the phonon spectrum at 0.5 K. The membrane is made of silicon in all the PnCs.

Figure 4

Relative thermal conductance and number of LRs in the phonon spectrum at 0.5 K as a function of pillar height ($a=160\mathrm{nm}, r/a=0.4$, and $h_{\mathrm{Membrane}}=80\mathrm{nm}$).

Figure 5

Relative thermal conductance and number of LRs in phonon spectrum at 0.5 K as a function of pillar radius ($a=160\mathrm{nm}$ and $h_{\mathrm{Membrane}}=h_{\mathrm{Pillar}}=80\mathrm{nm}$).

Figure 6

Relative thermal conductance of hole- and pillar-based PnCs ($r/a=0.4$ and $h_{\mathrm{Membrane}}=h_{\mathrm{Pillar}}=80\mathrm{nm}$) as a function of (a) the period at 0.5 K and (b) temperature for the period of 160 nm.

Figure 7

Relative thermal conductance of PnCs ($a=160\mathrm{nm}, r/a=0.4$, and $h_{\mathrm{Pillar}}=80\mathrm{nm}$) and thermal conductance of membranes as a function of membrane thickness.

Figure 8

(a) Relative thermal conductance of PnCs of different types and lattices ($a=160\mathrm{nm}, r/a=0.4$, and $h_{\mathrm{Membrane}}=h_{\mathrm{Pillar}}=80\mathrm{nm}$) and (b) schematic of hybrid hole/pillar lattices with indicated unit cell.

Figure 9

Normalized thermal conductance as a function of (a) number of finite elements in the unit cell and (b) number of the wave vectors on each side of the irreducible triangle.