Supported by the National Natural Science Foundation of China (grant numbers: 52125307, 12004010), Prof.Peng Gao and Senior Engineer Dr.Jinlong Du from the Electron Microscopy Laboratory of Peking University and Assistant Prof.Lin Yang from the Department of Advanced Manufacturing and Robotics of the College of Engineering, Peking University and their collaborator team, discovered a new way to control the heat transfer by using inhomogeneous strain. The results were published in Nature on May 16, 2024, titled " Suppressed thermal transport in silicon nanoribbons by inhomogeneous strain". The link: https://www.nature.com/articles/s41586-024-07390-4.

As the elementary excitation of lattice vibration, phonons are the key factor determining the thermal conductivity of materials. The strain caused by the lattice change inevitably affects the local phonon modes, thereby altering the thermal transport properties. Therefore during the semiconductor device fabrication, the epitaxial growth of heterostructure (e.g., Si/SiGe) can generally introduce strain due to the lattice mismatch, affecting the local thermal conductivity. Although the influence of strain on the phonon structure and thermal conductivity has attracted extensive research attention, the reported studies mainly focus on those systems under the simplified condition of uniform strain, while the effects of inhomogeneous strain have rarely been explored. This is partly due to the difficulty in measuring local phonon modes, and on the other hand, it is very difficult to experimentally decouple the local strain gradient effect and element gradient effect. Therefore, how the inhomogeneous strain affects the thermal conductivity of nanomaterials and interface devices remains largely unknown.

To reveal the influence of inhomogeneous strain on the phonon structure and thermal conductivity of materials, the research team induces inhomogeneous strain by bending individual silicon nanoribbons (SiNRs) on a custom-fabricated microdevice to measure its effect on thermal transport, while characterizing the local vibrational spectra using electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) with sub-nanometre resolution. The results show that a strain gradient of 0.112% per nanometer could lead to a drastic thermal conductivity (k) drop of 34 ± 5%, which is over 3-fold of previously demonstrated k modulation under uniform strain. Taking advantage of recent progress in EELS equipped with a monochromator in an aberration-corrected STEM, the local phonon modes of silicon nanoribbons were measured and correlated with the nanometer-scale strain gradient. The results unambiguously show that the compressive stress in the bending silicon nanoribbons causes a blue shift while tensile stress causes a red-shift, thereby causing phonon spectrum broadening for the bent silicon nanoribbons. The ab initio theoretical modeling shows that such strain gradient caused phonon spectrum broadening effect enhances phonon scattering shortens phonon lifetimes, and ultimately suppresses the thermal conductivity.

This study indicates that inhomogeneous strain can provide a new degree of freedom for tuning the thermal properties of nanomaterials and interfaces. This discovery is of great significance for the thermal management of interface devices, as well as the design of thermoelectric materials and thermal switch devices. Atomically resolved inelastic scattering spectroscopy based on an electron microscope provides a new way for the study of thermal transport behavior at the nanometer and even angstrom scales.

Figure. Nanoscale measurement of phonon modes in inhomogeneously strained single-crystal silicon nanoribbons. (a) Schematic diagram of STEM-EELS to probe vibrational modes along the strain gradient of a bent Si nanoribbon. (b-c) HAADF images of a bent Si nanoribbon with kink (b) and zoomed-in view of the region for EELS measurements (c), where the calculated strain contour is overlaid on top. (d) Measured EELS profiles for the transverse acoustic (TA) and transverse optical (TO) phonon modes at different positions (P1 to P5) along the strain gradient, where the transverse acoustic mode exhibits a blueshift of approximately 2.2 meV, whereas the transverse optical mode shows a redshift of approximately 6.0 meV as the elastic strain varies from −3.14% to 3.26%. The peak position is extracted via Gaussian fitting. (e) A HAADF image for a bent SiNR without kink. The yellow rectangle represents the area where the EELS signals are acquired by summing each column spectra of the three-dimensional dataset along the axial direction (perpendicular to the strain gradient) to enhance the signal-to-noise ratio. (f) Vibrational spectra map for the transverse acoustic and transverse optical modes along the beam shift direction. (g) Measured EELS line profiles along the strain gradient for the region marked in (e). The top x-axis in (d) and (g) represent the phonon frequency in THz. Scale bars, 200 nm (b), 50 nm (c, e). a.u., arbitrary units.