Native surface oxide turns alloyed silicon membranes into nanophononic metamaterials with ultralow thermal conductivity

A detailed understanding of the relation between microscopic structure and phonon propagation at the nanoscale is essential to design materials with desired phononic and thermal properties. Here we uncover a new mechanism of phonon interaction in surface oxidized membranes, i.e., native oxide layers interact with phonons in ultrathin silicon membranes through local resonances. The local resonances reduce the low frequency phonon group velocities and shorten their mean free path. This effect opens up a new strategy for ultralow thermal conductivity design as it complements the scattering mechanism which scatters higher frequency modes effectively. The combination of native oxide layer and alloying with germanium in concentration as small as 5% reduces the thermal conductivity of silicon membranes to 100 times lower than the bulk. In addition, the resonance mechanism produced by native oxide surface layers is particularly effective for thermal conductivity reduction even at very low temperatures, at which only low frequency modes are populated.

Figure 1

Thermal conductivities of silicon membranes as functions of thickness and Ge concentration at 300 K. ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ membranes with ordered $2\times 1$ surface reconstruction (labeled as SiGe) are compared to those covered by native oxide layers (labeled as SiGeO). The error bars are calculated as the standard deviation.

Figure 2

Phonon mean free paths evaluated from the length dependent transmission functions for the following membranes of 3.2 nm in thickness: pristine Si membrane, ${\mathrm{SiGe}}_{0.1}$ membrane, amorphous ${\mathrm{SiO}}_2$ covered Si membrane, and amorphous ${\mathrm{SiO}}_2$ covered ${\mathrm{SiGe}}_{0.1}$ membrane.

Figure 3

Schematic of a surface oxidized Si membrane and the definition of regions for DSF calculations (top). Dispersion of acoustic phonons as calculated from DSF (down): (a) pristine Si membrane; surface oxidized Si membrane calculated from (b) the whole sample, (c) region II (the region next to the interface), and (d) region III (middle Si region away from interfaces); (e) partial DSF of region II with 10 holes introduced in the interface region I.

Figure 4

Visualization of three selected modes on the same branch by VMD software [58]. (a) A transverse acoustic mode at wave vector $q=0.2$; (b) a hybridized mode at $q=0.6$ resulting from the hybridization between a transverse acoustic mode and a surface resonant mode; (c) $q=0.95$, a resonant mode localized in the native oxide layers. The wave vector is perpendicular to the $y\text{−}z$ plane.