Universal Behavior of Highly Confined Heat Flow in Semiconductor Nanosystems: From Nanomeshes to Metalattices

Nanostructuring on length scales corresponding to phonon mean free paths provides control over heat flow in semiconductors and makes it possible to engineer their thermal properties. However, the influence of boundaries limits the validity of bulk models, while first-principles calculations are too computationally expensive to model real devices. Here we use extreme ultraviolet beams to study phonon transport dynamics in a 3D nanostructured silicon metalattice with deep nanoscale feature size and observe dramatically reduced thermal conductivity relative to bulk. To explain this behavior, we develop a predictive theory wherein thermal conduction separates into a geometric permeability component and an intrinsic viscous contribution, arising from a new and universal effect of nanoscale confinement on phonon flow. Using experiments and atomistic simulations, we show that our theory applies to a general set of highly confined silicon nanosystems, from metalattices, nanomeshes, porous nanowires, to nanowire networks, of great interest for next-generation energy-efficient devices.

Structural and Elastic Properties of Empty-Pore Metalattices Extracted via Nondestructive Coherent Extreme UV Scatterometry and Electron Tomography

Semiconductor metalattices consisting of a linked network of three-dimensional nanostructures with periodicities on a length scale <100 nm can enable tailored functional properties due to their complex nanostructuring. For example, by controlling both the porosity and pore size, thermal transport in these phononic metalattices can be tuned, making them promising candidates for efficient thermoelectrics or thermal rectifiers. Thus, the ability to characterize the porosity, and other physical properties, of metalattices is critical but challenging, due to their nanoscale structure and thickness. To date, only metalattices with high porosities, close to the close-packing fraction of hard spheres, have been studied experimentally. Here, we characterize the porosity, thickness, and elastic properties of a low-porosity, empty-pore silicon metalattice film (∼500 nm thickness) with periodic spherical pores (∼tens of nanometers), for the first time. We use laser-driven nanoscale surface acoustic waves probed by extreme ultraviolet scatterometry to nondestructively measure the acoustic dispersion in these thin silicon metalattice layers. By comparing the data to finite element models of the metalattice sample, we can extract Young's modulus and porosity. Moreover, by controlling the acoustic wave penetration depth, we can also determine the metalattice layer thickness and verify the substrate properties. Additionally, we utilize electron tomography images of the metalattice to verify the geometry and validate the porosity extracted from scatterometry. These advanced characterization techniques are critical for informed and iterative fabrication of energy-efficient devices based on nanostructured metamaterials.

Optical transient grating pumped X-ray diffraction microscopy for studying mesoscale structural dynamics

A fundamental understanding of materials’ structural dynamics, with fine spatial and temporal control, underpins future developments in electronic and quantum materials. Here, we introduce an optical transient grating pump and focused X-ray diffraction probe technique (TGXD) to examine the structural evolution of materials excited by modulated light with a precisely controlled spatial profile. This method adds spatial resolution and direct structural sensitivity to the established utility of a sinusoidal transient-grating excitation. We demonstrate TGXD using two thin-film samples: epitaxial BiFeO₃, which exhibits a photoinduced strain (structural grating) with an amplitude proportional to the optical fluence, and FeRh, which undergoes a magnetostructural phase transformation. In BiFeO₃, structural relaxation is location independent, and the strain persists on the order of microseconds, consistent with the optical excitation of long-lived charge carriers. The strain profile of the structural grating in FeRh, in comparison, deviates from the sinusoidal excitation and exhibits both higher-order spatial frequencies and a location-dependent relaxation. The focused X-ray probe provides spatial resolution within the engineered optical excitation profile, resolving the spatiotemporal flow of heat through FeRh locally heated above the phase transition temperature. TGXD successfully characterizes mesoscopic energy transport in functional materials without relying on a specific transport model.

A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures: Theory and Experiment

Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier's law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation.

Nondestructive Measurements of the Mechanical and Structural Properties of Nanostructured Metalattices

Metalattices are artificial 3D solids, periodic on sub-100 nm length scales, that enable the functional properties of materials to be tuned. However, because of their complex structure, predicting and characterizing their properties is challenging. Here we demonstrate the first nondestructive measurements of the mechanical and structural properties of metalattices with feature sizes down to 14 nm. By monitoring the time-dependent diffraction of short wavelength light from laser-excited acoustic waves in the metalattices, we extract their acoustic dispersion, Young's modulus, filling fraction, and thicknesses. Our measurements are in excellent agreement with macroscopic predictions and potentially destructive techniques such as nanoindentation and scanning electron microscopy, with increased accuracy over larger areas. This is interesting because the transport properties of these metalattices do not obey bulk predictions. Finally, this approach is the only way to validate the filling fraction of metalattices over macroscopic areas. These combined capabilities can enable accurate synthesis of nanoenhanced materials.

Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams

Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved-sub-100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution-represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.

Full Characterization of the Mechanical Properties of 11-50 nm Ultrathin Films: Influence of Network Connectivity on the Poisson's Ratio

Precise characterization of the mechanical properties of ultrathin films is of paramount importance for both a fundamental understanding of nanoscale materials and for continued scaling and improvement of nanotechnology. In this work, we use coherent extreme ultraviolet beams to characterize the full elastic tensor of isotropic ultrathin films down to 11 nm in thickness. We simultaneously extract the Young's modulus and Poisson's ratio of low-k a-SiC:H films with varying degrees of hardness and average network connectivity in a single measurement. Contrary to past assumptions, we find that the Poisson's ratio of such films is not constant but rather can significantly increase from 0.25 to >0.4 for a network connectivity below a critical value of ∼2.5. Physically, the strong hydrogenation required to decrease the dielectric constant k results in bond breaking, lowering the network connectivity, and Young's modulus of the material but also decreases the compressibility of the film. This new understanding of ultrathin films demonstrates that coherent EUV beams present a new nanometrology capability that can probe a wide range of novel complex materials not accessible using traditional approaches.