Fig. 3: Results from thermal analysis of IR thermoreflectance.
a, The thermoreflectivity response of hBN as a function of the pump–probe delay time after Au pad heating near the TO resonant frequency (black squares, 7.4 μm) of hBN alongside the analytical model fit to the on-resonance data (solid red line). The best fit for the on-resonance data shown resulted in a HPhP-mediated TBC of >500 MW m−2 K−1. The standard model (dashed blue line) shows the calculated thermoreflectance signal expected at the surface of the Au pads assuming literature thermal parameters as well as an Au–hBN phonon–phonon TBC of 12.5 MW m−2 K−1 measured with TDTR (see the Supplementary Information for details); the inset shows a comparison of the raw signal magnitude on resonance (black squares, 7.4 μm) with off resonance (red triangles, 6 μm). The inset represents the difference in magnitude and curvature between the off-resonance and on-resonance data past time zero, highlighting the strong response from the hBN when compared with the Si substrate as well as the extended duration that the hBN remains heated for. b, The current state of experimentally measured bulk TBCs across 3D/3D material interfaces (filled blue squares)2 as well as predicted 2D/3D interface conductances (open red circles region)74 and the best fit Au–hBN HPhP TBC measured in this work with error bars derived from the ±5% contour uncertainty presented in Supplementary Fig. 9, all plotted against a film to substrate ratio of Debye temperatures. c, The phonon density of states (pDOS) for hBN was reproduced from a figure in ref. 13 using density functional theory plotted with the occupied density of states the at two temperatures showing the lack of activity in the TO phonon mode 150 K above the ambient temperature, implying that the measurements in this work are due to optical phonon activity measured via IR probing, and not from thermally excited phonon modes from conduction alone. Lit. meas., literature measurements; Lit. calc., literature calculations; Dia., diamond.
