Imaging Phonon Dynamics at Hetero-Interfaces by Vibrational EELS

Due to the continued miniaturization of microelectronic devices, interface thermal transport becomes increasingly imperative for facilitating heat dissipation and prolonging the lifetime of integrated circuits and multifunctional nanodevices. Thermal boundary conductance (TBC) describes the capability of allowing phonon propagation at hetero-interfaces. Their contribution is more important when the characteristic lengths are comparable to or less than the mean free paths of the heat carriers (phonon, 10–100 nm) [1]. However, experimental studies of thermal transport and local vibrational properties at individual interfaces at the atomic scale are limited due to insufficient spatial resolutions of optical spectroscopies. In contrast, the state-of-the-art monochromated electron energy-loss spectroscopy (EELS) in the aberration-corrected scanning transmission electron microscope (STEM) offers a few-meV energy resolution and down to sub-ångström spatial resolution to study nanoscale phonon properties [2]. By varying the STEM illumination conditions (e.g., convergence semi-angle, α) and projector setups, we can precisely modify the spatial and momentum resolutions for detecting local vibrational states and phonon dispersion curves [3] and even visualize the phonon flux in real space using a novel differential phonon momentum (DPM) mapping method [4]. Here, we show several cases demonstrating the mapping of local phonon spectra and phonon dynamics at hetero-interfaces in Si-SiGe quantum dots (QDs) and BiFeO3 (BFO)/TbScO3 (TSO) heterostructures. Si-SiGe QDs superlattices can efficiently reduce thermal conductivity to improve thermoelectric performance by impeding the propagation of phonons via interface scattering. In such a system, there are two types of interfaces between SiGe QDs and interlayer Si: one at the top with a gradual composition change and the other at the bottom with an abrupt composition change. We employed an α = 3 mrad off-axis condition to obtain angle-resolved phonon spectra at specific points (Δ+ and Δ−) in momentum space within the first Brillouin zone (FBZ), as shown in Figs. 1a and b. By taking the difference of forward and backward propagating modes, the net momenta of Si optical phonon modes is obtained (Fig. 1c). Mapping of the phonon flux in Fig. 1d reveals a strong reflection from the abrupt interface, while the gradual interface provides a much weaker directionality. The sharp composition change at the abrupt interface forces a sudden transition in phonon density of states (PDOS). This creates an energy barrier for optical modes that hinders their propagation across the interface leading to a strong reflection [4]. Therefore, it is optimal for nanostructures to have an abrupt change in structure and composition to achieve high phonon impedance, thus lowering thermal conductivity. Local bound charges at the interface may also alter the TBC. In the second case, we study the phonon dynamics at a ferroelectric-insulator BFO-TSO interface. The polarization termination of BFO domains is counteracted by the electrostatic potential increase and leads to the formation of two-dimensional electron or hole gases (2DE/HGs) at the interface, depending on the polarization direction. We further developed a novel intermediate convergence semi-angle condition (α = 10 mrad, Fig. 2a) to provide a unit-cell-averaged vibrational spectrum to avoid the spectral variation due to the on-column/off-column effect [5]. We applied this technique to a 100-nm-thick BFO film grown on a TSO substrate (Fig. 2b). The DPM mapping in Fig. 2d reveals anisotropic phonons whose intensities depend on their location in momentum space with respect to the first Brillouin zone (FBZ). In other words, the usual symmetry above and below the FBZ is broken due to the presence of the 2DE/HG. This flipping of the phonon momenta occurs twice: once at the BFO-2DHG interface and again at the 2DHG-TSO interface. This is due to free charge carriers near the interface may suggest preferential phonon scattering. A consequence of this is that phonon impedance culminates in the lowering of thermal conductivity at the interface. This has profound implications for nanodevice applications because it shows that not only is the TBC reduced at a heterojunction but 2D charge gases as well. By utilizing averaged and resolved momentum conditions, phonon momenta can be imaged to obtain information about phonon propagation at the nanometer scale. Both chemical composition and charge can alter the phonon transport to modify the thermal conductivity of the entire nanodevices. Beyond thermal transport, combining sub-nanometer resolution with vibrational information offers unprecedented access to nanoscale thermodynamics, such as heat capacity and entropy [6]. DPM mapping of gradual and abrupt Si-SiGe QD interfaces. (a) Schematic of the experimental setup shows an off-axis position of the EELS entrance aperture in Si's FBZ (orange hexagon). (b) Convergent beam electron diffraction pattern of Si with α = 3 mrad. The red and blue circles denote the EELS entrance aperture positions where off-axis data was acquired. (c) Mapping of net vertical momenta of Si optical modes. (d) Phonon flux vector map obtained from the product of group velocity and the quantity of phonons with a given momentum direction overlaid on a HAADF-STEM image. Dashed yellow curves indicate the gradual and abrupt interfaces. Phonon reflection and anisotropy at a ferroelectric-insulator interface. (a) Schematic of beam-detector geometry of dark-field vibrational EELS with an intermediate α of 10 mrad. (b) HAADF-STEM image of a BFO-TSO interface. The arrow indicates the polarization direction of the BFO film. (c) Convergent beam electron diffraction pattern with two labeled locations of the EELS entrance aperture (Y+ and Y-) where the off-axis vibrational spectra were acquired. (d) DPM map showing phonon reflection from the BFO-TSO and bulk-2DHG interfaces and its horizontally averaged line profile.