Nanoscale Temperature Mapping for Operating Devices with Reflection Electron Elastic Energy Thermometry (REEET)

Experimental characterization of nanoscopic temperature distribution and heat transfer in devices with ever-decreasing feature size is fundamental to realizing next-generation chip-level thermal management and validating and unifying fundamental non-diffusive thermal models. However, existing scannable thermal metrologies have their limitations. For instance, scannable far-field optical methods suffer from diffraction-limited spatial resolution; scanning probe techniques are complex due to the tip-sample thermal contact and sometimes perturb the sample thermal field, despite offering nanoscale resolution; TEM-based thermometries require impractically thin, electron-transmissible samples. A flexible metrology that can directly map temperature fields with 10s of nanometer spatial resolution for practical working devices is still lacking.<br/><br/>In this work, we develop a novel nanoscale thermal imaging methodology built upon Reflection Electron Energy Loss Spectroscopy (REELS) in SEM. This method, termed Reflection Electron Elastic Energy Thermometry (REEET), directly measures the mean kinetic energy of thermally-vibrating atoms in materials leveraging the quasi-elastic peak of electrons in the spectrum. Our calibration experiments and first-principles-based calculation of kinetic energy confirmed the physical model for REEET based on simple individual electron-nucleus scattering constrained by conservation laws under the Born approximation. The relative temperature sensitivity of the technique is estimated as ~0.09%/K for light elements such as C and Si at 300-600 K, which compares favorably with other electron-beam-based thermometry.<br/><br/>We used REEET to demonstrate far-field temperature mapping of nanostructured graphitic thin film devices with 300-400 nm feature size, as well as a 250-nm diameter multiwalled carbon nanotube, both under Joule heating. Local hotspots with peak temperature rise of 500-800 K in these nanodevices can be visualized with a spatial resolution estimated as 30-50 nm. The temperature profiles can be well described by our analytical and finite element modeling based on modified Fourier’s law using suppressed thermal conductivity of ~480 and ~360 W m^-1 K^-1 for graphite and MWCNT, respectively. These results are consistent with prior reports on such carbon materials on substrates due to the Casimir size effect and interface scattering. Additionally, the 2-kV 3-nA electron beam is found to have negligible impact on the lattice temperature rise (&lt;0.1 K) in such devices based on our Monte Carlo simulations (CASINO) and a multi-temperature model.