Precise nanoscale temperature mapping in operational microelectronic devices by use of a phase change material

The microelectronics industry is pushing the fundamental limit on the physical size of individual elements to produce faster and more powerful integrated chips. These chips have nanoscale features that dissipate power resulting in nanoscale hotspots leading to device failures. To understand the reliability impact of the hotspots, the device needs to be tested under the actual operating conditions. Therefore, the development of high-resolution thermometry techniques is required to understand the heat dissipation processes during the device operation. Recently, several thermometry techniques have been proposed, such as radiation thermometry, thermocouple based contact thermometry, scanning thermal microscopy, scanning transmission electron microscopy and transition based threshold thermometers. However, most of these techniques have limitations including the need for extensive calibration, perturbation of the actual device temperature, low throughput, and the use of ultra-high vacuum. Here, we present a facile technique, which uses a thin film contact thermometer based on the phase change material \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ge_2 Sb_2 Te_5$$\end{document}Ge2Sb2Te5, to precisely map thermal contours from the nanoscale to the microscale. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Ge_2 Sb_2 Te_5$$\end{document}Ge2Sb2Te5 undergoes a crystalline transition at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {T}_{{g}}$$\end{document}Tg with large changes in its electric conductivity, optical reflectivity and density. Using this approach, we map the surface temperature of a nanowire and an embedded micro-heater on the same chip where the scales of the temperature contours differ by three orders of magnitude. The spatial resolution can be as high as 20 nanometers thanks to the continuous nature of the thin film.


TCR measurement for the nanowire
To measure the TCR of the nanowire (acting as thermometer), we put the nanowires in an isothermal Cascade Tek Oven with temperature control. Four-probe measurement scheme is used to determine the resistance of the nanowire and a K-type thermocouple is used to monitor the temperture inside the oven as shown in Figure S1. In the TCR measurement, the current source is at low bias of 0.1 mA such that the self-heating of the nanowire can be ignored (about 0.1 • C increase). The oven temperature rises from room temperature to around 115 • C in steps. For each temperature, the resistance and the reading of the thermocouple are recorded when steady. The slope in Figure S2 is exactly TCR α and all three samples show the same TCR 0.003/ • C. Therefore, the nanowire, with known TCR, can be used as a measure of the temperature. Figure S2. The ∆R/R 0 as a function of ∆T for three samples.

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2 Effect of Ge 2 Sb 2 Te 5 thin film on the heat transport in our system In this section, we show that the effect of Ge 2 Sb 2 Te 5 thin film on the heat transport in our system is negligible. Figure S3 shows the measured average temperature of the nanowire as a function of its power before and after Ge 2 Sb 2 Te 5 coating. Both two samples show that the Ge 2 Sb 2 Te 5 coating has almost no effect on the thermal transport (∼ 0.2 • C difference, which is negligible). Figure S4 shows the temperature profile across the nanowire (along the minor axis of the transition contour) from the simulations. In the center of the nanowire, the simulations show a 0.2 • C difference, which matches well with results shown in Figure S3. Considering that the dimension of the transition area due to nanowire self-heating (< 0.5 µm), the temperature difference caused by Ge 2 Sb 2 Te 5 thin film is ∼ 0.2 • C, which is small and acceptable. It is worthwhile noting that an interface conductance of 100 MW/(m 2 K) is considered between the device surface and Ge 2 Sb 2 Te 5 film in the simulations. Figure S3. The average temperature as a function of the nano-heater power. Figure S4. The simulated temperature profile across the nanowire with/without presence of Ge 2 Sb 2 Te 5 film 3/7

Time dependent PCTC
In our phase change temperature contour (PCTC) technique, the phase change material (PCM) Ge 2 Sb 2 Te 5 undergoes a phase change along with changes in electric conductivity, optical reflectivity and density. But the transition takes time to fulfill. In this section, we design a time dependent PCTC experiment to study the time it takes to complete transition.
In the time dependent PCTC experiment, the nano-heater is biased at a constant nano-heater power of 0.68 mW. Ge 2 Sb 2 Te 5 senses the self-heating of the nanowire and begins to transit from amorphous to FCC state. After a certain heating time, the nano-heater is turned off and the surface topography of the nanowire is characterized by AFM. Then repeat the step until the transition is complete. The attached video "Time_Dependence.mp4" shows a video of phase change area at the center of the nanowire from 0 to 300 s. The contour has a shape of perfect ellipse. The long and short axes are measured to calculate the area of the transition. Figure S5 shows the result of transition area with the accumulative time and the corresponding curve fitting using an exponential function. It is revealed that the time constant for such a nanowire self-heating scheme is 37.6 s and it takes 3.1 minutes for the transition to fulfill.
Obviously, 3.1 minutes is also sufficient for micro-heating scheme to attain the equilibrium because the heating has a broader area which is three orders of magnitude larger than the nanowire self-heating scheme. Subsequently, the dwell time for each heating experiment is always kept as 5 minutes such that the phase change of Ge 2 Sb 2 Te 5 is totally completed, namely the contour is in steady state. In this section, the kinetics of the phase change from the amorphous state to crystalline is further studied using transmission electron microscopy (TEM). A 22 nm film of Ge 2 Sb 2 Te 5 is deposited on a SiC substrate. The sample is heated in-situ such that the electron diffraction analysis and TEM imaging are performed in real time. Figure S6 shows the result of the electron diffraction patterns and TEM images. Before the critical temperature T g = 149 • C, (a) shows that the material is amorphous. Then the sample is soaked at T g = 149 • C for 1 min as (b), some diffraction spots appear indicating that the phase change begins. After soaking for 5 mins, several orientations of the crystalline form clearly. Meanwhile, (d) and (e) are the TEM images before/after the phase change. It is obvious that Ge 2 Sb 2 Te 5 undergoes the phase change from amorphous to crystalline. Figure S6. (a)-(c) Show the electron diffraction pattern of Ge 2 Sb 2 Te 5 before the critical temperature and soak at the critical temperature (1 min/5 mins). (d)(e) Show the TEM of Ge 2 Sb 2 Te 5 before and after the phase change.

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5 Accumulation behavior of the PCM Ge 2 Sb 2 Te 5 The activation energy E a to undergo a structural change from an amorphous to rock salt FCC structure is around 2.6 eV. When temperature T is below the glass transition temperature T g , there is still a small proportion of the material that transits to FCC. The proportion can be expressed as where P i refers to the proportion of transition at the temperature T i and k B is Boltzmann constant. Therefore, when we heat the same material in multiple heating cycles (N cycles), the total proportion of transition is the summation of all the previous heating cycles: Figure S7 plots the modelling result of the transition proportion of Ge 2 Sb 2 Te 5 with temperature for single heating and accumulating heating. In the single heating, 100% of the material transits at 149 • C. However, as for accumulating heating, all the heating cycles have contribution to the phase change although below the critical temperature T g , so finally the measured critical temperature corresponded to 100% transition is about 2 • C below the real value, which is acceptable. Figure S7. The transition proportion of the PCM with temperature for single heating and accumulating heating In the following experiments of the nano-heater self-heating or micro-heater heating schemes, the temperature step is maintained above 10 • C such that the accumulation behavior of the phase change becomes negligible. 6/7 6 The transition area of Ge 2 Sb 2 Te 5 phase change vs. the accumulated heating time Figure S8 shows the bigger sized version of Fig. 3(a) inset. The AFM images of the transition area vs. the accumulated heating time are shown. Figure S8. The transition area of Ge 2 Sb 2 Te 5 phase change vs. the accumulated heating time at a constant nano-heater power of 0.68 mW