The continued downscaling of integrated circuit, optoelectronic, and data storage devices inevitably leads to smaller hotspots and sharper temperature gradients. As a result, thermometers with increasingly fine spatial resolution are required in order to capture the true peak temperature rise. While it has been recognized previously that a coarse thermometer will underestimate the peak temperature in a comparatively small hotspot, this type of measurement error has not been systematically quantified using either modeling or experiments. Here, we present analytical expressions for the true and measured temperature rises as a function of thermometer size for Gaussian, disk-shaped, and rectangular surface heat sources. We find that even a thermometer the same size as the hotspot can underestimate the true peak temperature rise by more than 15%. Furthermore, this error frequently exceeds 75% and can approach 90% for certain geometries when the thermometer is ten times larger than the measured hotspot. We also find that a thermometer with resolution approximately two times smaller than the hotspot size is required in order to measure the peak temperature rise with less than 5% error for the three common hotspot geometries that we consider.   

 

While these conclusions hold true for heat sources and thermometers of any size, the strongest practical implications are for micro- and nanoscale heat sources where satisfying this constraint is typically challenging due to the scarcity of thermometers with nanoscale spatial resolution. Therefore, we also experimentally demonstrate that a 50 x 50 x 50 nm^3^ individual upconverting NaYF~4~:Yb^3+^,Er^3+^ nanoparticle thermometer captures the peak temperature rise due to laser heating more accurately than conventional diffraction limited optical techniques that our modeling results show would underestimate this value. To study laser heating, we designed samples consisting of a 50 nm platinum (Pt) film evaporated on a borosilicate glass substrate. We use a single 980 nm laser to both heat the Pt-coated glass and excite the upconverting nanoparticle luminescence. We measure a peak temperature rise of 167 K, which is consistent with the range of modeled values for the true peak temperature rise. We also confirm that, in contrast to apparent self-heating effects that spuriously increase the nanoparticle thermometry signal at high laser excitation intensities, we measure true laser heating. We show that this laser heating can be effectively eliminated by replacing the glass with a higher thermal conductivity diamond substrate. Single nanoparticle thermometry therefore provides a practical, minimally invasive approach to accurately characterizing hotspots at the nanoscale. 


Size and Shape Effects on the Measured Peak Temperatures of Nanoscale Hotspots

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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