Dynamic EUV scatterometry measurements of nanoscale heat flow in 3D geometries and next-generation semiconductors

At sub-micron length scales, boundaries and highly nonequilibrium conditions cause phonon thermal transport in semiconductors to deviate from classical diffusive predictions, creating inefficient hot spots and bottlenecks which limit the performance of nanoelectronic devices. While visible laser-based metrologies have successfully mapped the onset of this non-diffusive transport regime, they are diffraction-limited to near-micron length scales and are primarily sensitive to the nonequilibrium electron distribution at short time scales. A coherent extreme ultraviolet (EUV) probe can overcome these limitations; derived via high harmonic generation from an infrared Ti:Sapphire driving laser and tuned off-resonance with core shell electronic transitions, the ~30nm wavelength provides picometer vertical and <100nm lateral sensitivity when diffracting from periodic surface profiles. Past EUV scatterometry experiments used the infrared driving laser to excite arrays of metallic nanoscale gratings on various semiconductor substrates, and monitored their thermal expansion by capturing the diffraction pattern of the time-delayed EUV probe. These experiments revealed the onset of inefficient quasi-ballistic phonon transport for nanoheater gratings of small linewidth and large period, along with a surprising behavior, where reducing the nanoheater period below a characteristic length scale related to the average phonon mean free path actually increases the rate of thermal dissipation¹. Atomistic simulations² and a mesoscopic phonon hydrodynamic treatment³ suggest that this close-packing effect may arise from the modification of anharmonic phonon properties, such as mean free path and lifetime, in nonequilibrium, nanoscale environments beyond a first-order truncation due to boundary scattering. Ongoing EUV scatterometry experiments seek to spatially resolve the surface temperature evolution through more advanced analysis of the diffraction profiles, and to extend the technique to 3D geometries⁴ and nontraditional semiconductors, including ultrawide bandgap⁵ and phase change materials. For example, in VO₂ thin films, the large surface roughness complicates the metallic nanograting fabrication and instead motivates a spectral analysis of the EUV harmonics, which provides insight into heat flow across grain boundaries and between metallic and insulating domains. The resolution and versatility of the EUV scatterometry technique makes it a promising tool for the development of advanced phonon transport models and strategies for enhanced thermal management and energy efficiency in nanoscale devices.

¹Frazer et al., Phys. Rev. Appl. 11, 024042 (2019)
²Honarvar et al. PNAS 118 e2109056118 (2021)
³Beardo, Knobloch et al. ACS Nano 15 13019 (2021)
⁴McBennett et al. Nano Letters 23 2129 (2023)
⁵McBennett, Esashi et al. Phys. Rev. Mat. 8 096001 (2024)