Nanoscale Thermoelasticity in Silicon Nitride Membranes: Implications for Thermal Management

Abstract

The characterization of thermal and elastic properties at the nanometer length scale is fundamental for the implementation of materials in nanotechnology. Here, we show how four-wave mixing of extreme ultraviolet ultrashort pulses allows for high-precision measurements of nanoscale elasticity in thin suspended silicon nitride membranes through the generation and detection of Lamb waves at 10's of nm wavelengths. Our approach is contact-free and nondestructive, and it provides an estimate of both shear and longitudinal elastic moduli, without the need of nanopatterning. The data provide important information on nanoscale thermal transport and reveal a heat carrier behavior compatible with the diffusive regime. By controlling the fluence of the free-electron laser excitation pulses, we study the dependence of elastic moduli and the thermal relaxation rate on the sample temperature, which increases by hundreds of kelvins due to radiation absorption. At the same time, the experimental data allow us to estimate the characteristic time of phonon attenuation. The capability of determining this parameter, as well as the elastic moduli, at nanoscale wavelengths is a key aspect for the fundamental understanding of solids without translational invariance.

Extreme ultraviolet transient gratings: A tool for nanoscale photoacoustics

“…Fig. 7 displays representative EUV TG data collected in the forward diffraction geometry from different samples, namely: amorphous Si 3 N 4 (panels (a) and (b) [4] , [14] ), amorphous metallic alloy Zr 65 Cu 27.5 Al 7.5 (panels (c) and (d)) and crystalline atomic metal Co (panel (e)); the last two samples were grown on a thin Si 3 N 4 membrane. The total thickness of all samples was sufficiently small (< 150 nm) to permit transmission of the signal beam.…”

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Fig. 7 Circles connected by lines are the EUV TG signal in forward diffraction as a function of Δt for amorphous Si 3 N 4 at 28 nm (panel (a)) and at 84 nm (panel (b)) [4] , [14] , Zr 65 Cu 27.5 Al 7.5 at 24 nm (panel (c)) and at 84 nm (panel (d)), and Co at 44 (panel (e)). The inset in the latter panel shows, in a semi logarithmic scale, the signal waveform on a longer range in Δt; we vertically offset by a factor 10 −9 to fit in the logarithmic vertical scale.

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“…For panels (a)-(d) it consists of a slow decay of , which can be ascribed to thermal transport over a characteristic distance [60] , modulated by oscillations due to propagation of acoustic phonons, i.e. : where is the thermal decay constant, while and are, respectively, the phonon frequency and lifetime of the i th phonon mode in the waveform [4] , [14] , [34] . Data in Figs.…”

“…The measurement, and thus the understanding, of the thermoelastic response of matter at the nanoscale is paramount for technological applications exploiting either heat or vibrations, such as phonon engineering in hetero- [12] , [13] and confined [14] structures, thermal barrier coatings [15] , heat assisted magnetic recording [16] , nano-enhanced photovoltaics, thermoelectric energy conversion, high power optoelectronics, etc.…”

“…The EUV TG approach has been pioneered at the FERMI FEL (Trieste, Italy) with the dedicated endstation TIMER [32] . First results beyond the proof of principle [33] reveal that EUV TG is capable of incisively and selectively studying bulk and surface phonons [4] , [34] , thermal transport kinetics [14] , [35] and magnetic dynamics [36] , [37] . The recent development of the technique has revealed specific peculiarities with respect to the well-established optical TG spectroscopy that need to be considered both when predicting as well as when interpreting experimental EUV TG results.…”