A Sandia-led research team has, for the first time, observed the coherent propagation of thermal phonons in silicon at room temperature—in two-dimensional phononic crystals formed by introducing air holes in a silicon matrix with minimum feature sizes ~250 nm. To separate incoherent from coherent boundary scattering, the team fabricated phononic crystals with a fixed minimum feature size—differing only in unit cell geometry (see Figure 1). This research was presented in a paper in Nature Communications.

Scanning electron microscope (SEM) image of the fabricated phononic crystal structures. All samples were fabricated to have a periodicity a = 1100 nm, thickness t = 366 nm and a chosen critical dimension Lc = 250 nm. Highlighted in white is the unit cell of each supercell lattice: (a) simple cubic, SC, (b) 1 × 1, (c) 2 × 2, (d) 3 × 3 and (e) 4 × 4.

Figure 1.  Scanning electron microscope image of the fabricated phononic crystal structures. All samples were fabricated to have a periodicity a = 1100 nm, thickness t = 366 nm and a chosen critical dimension Lc = 250 nm. Highlighted in white is the unit cell of each supercell lattice: (a) simple cubic, SC, (b) 1 × 1, (c) 2 × 2, (d) 3 × 3 and (e) 4 × 4.

Almost all physical processes produce heat as a byproduct, making heat one of the most abundant forms of energy. In semiconductors, this thermal energy is carried by quasiparticles called phonons, which are quantized molecular vibrations. Thermoelectric systems are among the few technologies that can convert heat directly into electricity, using the Peltier effect. While silicon-based semiconductors typically have very favorable power factors, making them attractive for chip cooling and ‘heat scavenging’ applications, their large phonon-dominated thermal conductivity has prevented their use in thermoelectric systems. At low temperatures (70 K and below), phonons behave like waves, undergoing constructive and destructive interference (and allowing one to develop methods of harnessing this behavior to harvest energy). However, around room temperature and higher, phonons were believed to always behave more like particles, undergoing purely incoherent scattering. This means that they would propagate from hot to cold randomly, with no hope of controlling their flow.

   Ihab El-Kady, Charles Reinke, and Zayd C. Leseman (in Sandia’s Applied Photonic Microsystems Dept. and at the University of New Mexico) and Seyedhamidreza Alaie, Drew Goettler, and Mehmet Su (all at UNM).

   A phonon is a quantum-mechanical description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency. Due to the bonds between atoms, the displacement of one or more atoms from their equilibrium positions give rise to a set of vibration waves propagating through the lattice. Long-wavelength phonons give rise to sound; shorter-wavelength higher-frequency phonons give rise to heat. Phonons play a major role in many of the physical properties of condensed (solid) matter, like thermal conductivity and electrical conductivity.

In previous journal articles, this research group has proposed that coherent boundary scattering in phononic crystals with relatively large feature sizes (≥100 nm) may hold the key to solving this problem by scattering phonons with minimal influence on electrons. As phonons traverse such a lattice, they can undergo two types of scattering processes:

  1. simple particle-like incoherent scattering as a result of encountering a boundary, and
  2. wave-like coherent scattering due to the periodic geometry of the artificial lattice of air holes.
Normalized thermal conductivities of phononic crystal samples. The measured thermal conductivity of the SC and the 1 × 1, 2 × 2, 3 × 3 and 4 × 4 supercell phononic crystal samples, along with the predicted values using various models described in the text.

Figure 2.  Normalized thermal conductivities of phononic crystal samples. The measured thermal conductivity of the SC and the 1 × 1, 2 × 2, 3 × 3, and 4 × 4 supercell phononic crystal samples, along with the predicted values using various models described in the text.

Here, coherence implies that the phonon phase is preserved and that scattering from material boundaries exhibits at least some measure of specularity (angle of reflection is equal to the angle of incidence, past a perpendicular). Practically, this can have profound implications because, while incoherent boundary scattering depends only on the shape, size, and separation of the holes, coherent boundary scattering additionally depends on the symmetry and geometry with which these holes are distributed.

In a novel experiment that uses microscale phononic crystals, i.e., periodic arrangements of different materials, our research team was able, for the first time, to distinguish coherent phonon events from incoherent phonon scattering. In addition, our team developed a hybrid thermal conductivity model that accounts for partially coherent and partially incoherent phonon boundary scattering: the concept of a threshold mean-free path in conjunction with a hybrid theoretical model—where the incoherent and coherent contributions to thermal conductivity are weighted according to the fractional portion of the phonon population mean-free paths relative to that threshold. We observe excellent agreement between this model and experimental data (see Figure 2), and the results suggest that significant room-temperature coherent phonon boundary scattering occurs.

Although the periodicity of the phononic crystal samples is large compared to the average phonon wavelength, our results indicate that a significant portion of the phonon population remains coherent even after undergoing several scattering events. From a different perspective, because there is no direct way to measure the coherence length, our approach has enabled us to use the thermal conductivity as a macroscopic metric for inferring the average phonon coherence length in our phononic crystal samples.

This work could profoundly impact thermoelectrics by allowing for an additional mechanism for reducing the thermal conductivity of a material without affecting its electrical conductivity—by simply arranging the pores in an optimal phononic crystal geometry. Coherent phonon effects can be amplified and engineered for applications such as thermal management, heat scavenging, and energy harvesting, opening the door for guiding heat on-chip and thermal isolation of sensitive microelectronics. While the coherent phononic crystal effects seen here represent a small yet significant fraction of the overall thermal conductivity reduction, their presence at room temperature is extremely encouraging. Given that a more pronounced effect is expected at lower temperatures, the impact on thermoelectric cooling could be profound.