Characterizing Highly-Confined Heat Flow, Elastic Properties and Porosity in a Semiconductor Metalattice

Nanostructured semiconductors can exhibit thermal properties unachievable in bulk systems due to the increased influence of surfaces and interfaces. The ability to understand and fully characterize the thermal, elastic, and structural properties of these nanostructured semiconductor materials is important for developing new materials with tunable properties for applications in next-generation nanoelectronics and energy efficient devices. Managing thermal transport in nanoscale materials is critical for optimizing the performance of computer chips—however, when the critical dimensions have the same length scales as the average phonon mean free paths, traditional theories of heat flow break down. Moreover, first principles models of nanoscale thermal transport are too computationally challenging for 3D nanostructured geometries, while mechanistic approaches make overly simplistic assumptions about the nature of phonon-boundary interactions.<br/><br/>Here, we probe the elastic and thermal properties of a 3D nanostructured silicon metalattice, which consists of an interconnected network of nanoscale pores that dramatically alter the material properties compared to bulk crystalline silicon. We impulsively heat nickel grating transducers that are fabricated on the 3D silicon metalattice sample using an infrared pump laser pulse. This launches acoustic waves and heat into the metalattice, which we probe using diffraction from an extreme ultraviolet (EUV) probe pulse. This technique has high spatial and temporal resolution, since the ~30nm EUV light has a wavelength much shorter than that of visible light, with a pulse duration of ~10fs.<br/><br/>By using metallic gratings of varying linewidths and periodicities, we launch surface acoustic waves in the metalattice with wavelengths equal to the grating periodicity. These surface acoustic waves are detected by the probe as changes in the reflectivity and the surface displacement of the sample. We compare the experimental data to finite element models of the 3D silicon metalattice to nondestructively extract porosity and Young’s modulus. Also, by varying the period of the metallic grating we can vary the acoustic wave penetration depth, allowing us to characterize the 3D silicon metalattice film thickness and substrate elastic properties. To validate our extracted porosity value and the metalattice geometry models, we compare to 3D electron tomography reconstructions of the sample geometry [1].<br/><br/>Using the extracted porosity and elastic properties, we model heat flow in the metalattice using finite element methods and fit an apparent thermal conductivity two orders of magnitude below bulk silicon. We model the heat flow dynamics using a Fourier-like relation with an apparent conductivity indicating two key conclusions: the size of the heat source does not significantly affect the heat flow as the metalattice geometry dominates, and the transport is diffusive-like in highly-confined situations where ballistic transport is traditionally expected. We compare our results to other highly-confined nanostructured systems by separating the thermal conduction into a permeability component, which captures the geometry of the system, and a viscosity component related to the intrinsic phonon properties. This treatment reveals a universal trend in the permeability which can be used to predict the thermal conductivity in general nanostructured silicon systems—from nanomeshes, to metalattices, to porous nanowires and nanowire networks.<br/><br/>[1] <i>ACS AMI </i><b>14</b>, 41316 (2022). [2] arXiv:2209.11743