Fig. 4: Momentum-resolved DPM map of phonon momentum normal to gradual and abrupt QD interfaces.
From: Nanoscale imaging of phonon dynamics by electron microscopy
a, Schematic of the experimental beam geometry showing an off-axis position of the EELS aperture in the first Brillion Zone (FBZ) of Si, achieved via post-specimen tilting of the scattered electron beam. The crystal axes are superimposed on the Si–QD crystal structure, and the momentum conservation vectors of the electron–phonon energy exchange process are superimposed on the momentum space portion of the diagram. The electron scattering wavevector diagram illustrates the fast electron–phonon momentum transfer. Under these momentum-resolved experimental conditions, q ≈ qr and since the generated phonons have an opposite sign to the momentum change of the electron beam, the momentum of generated phonons is predominantly in the in-plane direction (perpendicular to the interface). b, The 3 mrad convergence semi-angle convergent beam electron diffraction pattern where the 002 and 00\(\bar{2}\) spots are labelled. The slightly transparent orange hexagonal shape in the centre denotes the FBZ of Si with the Γ–X distance labelled as 8.96 mrad. The red and blue circles near the centre denote the EELS entrance aperture positions where off-axis data were acquired. c, Mapping of net vertical momenta of Si optical phonons. 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 3 mrad HAADF image. Panels c and d are accompanied by their respective horizontally averaged line profiles. Error bars in c and d represent standard deviation.
