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Near-field radiative nano-thermal imaging of nonuniform Joule heating in narrow metal wires Qianchun Weng, Kuanting Lin, Kenji Yoshida, Hirofumi Nema, S* Komiyama, Sunmi Kim, Kazuhiko Hirakawa, and Yusuke Kajihara Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01178 • Publication Date (Web): 07 Jun 2018 Downloaded from http://pubs.acs.org on June 7, 2018

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Near-field radiative nano-thermal imaging of nonuniform Joule heating in narrow metal wires Qianchun Weng,†,* Kuan-Ting Lin, † Kenji Yoshida, †Hirofumi Nema, † Susumu Komiyama,‡,* Sunmi Kim, † Kazuhiko Hirakawa, † and Yusuke Kajihara† †

Institute of Industrial Science, the University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo,

153-8505, Japan ‡

Department of Basic Science, the University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-

8902, Japan KEYWORDS: Near-field radiation, thermal imaging, nanothermometry, Joule heating, hot spots

ABSTRACT: Probing spatial variation of temperature at the nanoscale provides key information for exploring diverse areas of modern science and technology. Despite significant progress in the development of contact thermometers with high spatial resolution, one inherent disadvantage is that the quantitative analysis of temperature can be complicated by the direct thermal contact. On the other hand, noncontact infrared radiation thermometer is free from such contact-induced disturbance, but suffers from insufficient spatial resolution stemming from diffraction-limit in the micrometer range. Combining a home-built sensitive infrared microscope with a noncontact scattering probe, we detected fluctuating electromagnetic evanescent fields on locally heated material surface, and thereby mapped temperature distribution in subwavelength scales. We visualize nanoscale Joule heating on current-carrying metal wires and find localized “hot-spots” developing along sharp corners of bended wires in the temperature mapping. Simulation calculations give quantitative account of the nanoscale temperature distribution, definitely indicating that the observed effect is caused by the non-uniform energy dissipation due to the current-crowding effect. The equipment in this work is a near-field version of infrared radiation thermometer with a spatial resolution far below the detection wavelength (< 100 nm, or λ/140), in which local temperature distribution of operating nanoscale devices can be noninvasively mapped with a temperature resolution ~ 2 K at room-temperature.

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Heat managements for designing modern microelectronic devices become increasingly more important as the device size is reduced down to nanoscales. Local Joule heating causes large thermal gradients on small length scales in microelectronics devices, resulting in serious problems of device performance and reliability.1, 2 Thermometric techniques with high spatial resolution on submicron scales have attracted strong interest in recent years, being motivated by applications in a variety of areas such as microelectronic devices,3 dissipative quantum systems, 4, 5

and even living cells.6 Nanoscale temperature mapping is, however, not an easy task to

realize. In contact thermometers, like scanning thermal microscopes (SThMs), a thermocouple or a thermistor7, 8 is incorporated in an atomic force microscope (AFM) tip, which requires direct thermal contact to the target system of study. Noncontact infrared thermometers that probe temperature via photons spontaneously emitted by the target system are appealing because the sensitivity of detecting photons is much higher than that of probing heat, so that the measurements can be done in a non-invasive manner7. The drawback of existing infrared radiation thermometers, however, is its diffraction-limited spatial resolution, which restricts its application to structures larger than micrometers.9, 10 The diffraction-limited spatial resolution can be overcome by introducing near-field (NF) technique, which probes fluctuating electromagnetic (EM) evanescent fields11. Scattering-type scanning near-field optical microscope (s-SNOM) has been demonstrated to achieve subwavelength spatial resolution in the infrared wavelength12, 13. In those microscopes, the nearfield signal is excited by external illuminations and the light-matter interactions are studied in the nano-scale.14-17 The detection of fluctuating EM evanescent fields is more challenging because external optical excitation should be avoided. Intrinsic near-field radiation power, which can be extracted from a sub-micrometer region of the targeted material, is extremely low, typically in a


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sub-picowatt level, and one has to extract the small NF component out of much stronger far-field background radiation arising from the environment. Due to the experimental difficulties, only a few groups attempted to detect thermally fluctuating near-field signal18-20. NF signals correspond to the energy density of fluctuating evanescent waves21, which potentially serves as a local probe of temperature. The study of such thermal near-field microscopy, however, has so far been seriously hampered by the stringent requirement of sensitivity.19, 20 In some of existing studies, the lack of sensitivity was circumvented by heating up the sample20, 22 or the probe tip19, 23, 24, which makes it difficult to probe local temperature. In addition, resonant spectral regions should be avoided for the targeted wavelength range. This is because the electromagnetic local density of states (EM-LDOS) of evanescent waves are featured by sharp resonance peaks (like those of surface phonon polaritons19, 20 or surface plasmon polaritons22), which make it difficult to deduce temperature values via quantitative analysis. Thus, highly demanded for the nanoscale temperature mapping is an ultra-highly sensitive s-SNOM, in which neither external optical excitation nor external heating is employed and NF signals are probed in spectral regions away from resonant structures.11 Prior to this work, thermally excited evanescent waves on the samples in thermal equilibrium at room temperature have been successfully studied with such sensitive sSNOMs, assuming the uniform temperature distribution on sample.18, 25-27 Physically, the NF signals detected in thermal equilibrium are thermal noise (Johnson-Nyquist noise).28 Currentinduced evanescent waves in non-equilibrium condition have also been detected with a similar sSNOM,29 where detected NF signals are excess noise.30 We term the equipment “scanning noise microscope (SNoiM)”

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to specifically notify that the detected signal is thermal noise and/or

excess noise.


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In this work, the sample is driven out of equilibrium by applied electric field and no longer featured with a uniform temperature distribution as in the previous works. We directly visualize non-uniform local Joule-heating in micro current leads, by detecting real-space distribution of fluctuating evanescent fields with SNoiM. The equipment (Fig. 1(a)) is described in Ref. 27: Fluctuating EM evanescent waves on the sample surface are scattered by a near-field tip, collected by a home-made infrared confocal microscope,31 and detected with a sensor, called charge-sensitive infrared phototransistor (CSIP)32-34. The CSIP is by two orders of magnitude more sensitive34 than commercially available HgCdTe detectors, with the detection wavelength of ~ 14.1 µm. It should be noted that the electromagnetic energy of the fluctuating fields in a nano-scale region probed by the tip (< 100 nm) is extremely small in amplitude. The ultra-high sensitivity of CSIP makes the near-field detection possible without relying on the external heating.18, 26 In addition, the small NF signal component has to be extracted from much stronger far-field (FF) background radiation components, which arise from the emission/reflection in a much larger area of the sample (focal spot size ~ 25 µm) of the confocal microscope (Fig. 1(b)). For this sake, we modulate the tip height with an amplitude of 100 nm at a frequency of 27 Hz, and demodulate the CSIP output at the fundamental frequency (27 Hz) with a lock-in amplifier (see detailed discussion in Supporting Information, Figure S1; The near-field decay curve is shown in Figure S3). The tip is operated in a noncontact mode, with the shortest distance to the sample surface kept at 10 nm during the scan. An example of the samples studied is shown in Figs. 2. The devices are fabricated by depositing 50 nm-thick NiCr layers (80% Ni and 20% Cr) on top of 90 nm-thick SiO2 layer covering the Si substrate. As shown in the center of the inset of Fig. 2(a), the metal layers are patterned with electron-beam lithography (EBL) to 3.3 µm-wide “U-shape” wires of a total


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length of 60 µm. The narrow “U-shape” wire extends to 40 µm-wide NiCr leads, and eventually connected to 20 µm-wide 100 nm-thick Au leads (Fig. 3(a)). Five NiCr wires are fabricated on a single chip with a common electrode C (Fig. 2(a)), where 50 µmφ-Au wires are bonded to the patches of electrodes 1-5 and C. In this work, we apply bias voltage Vb to electrodes 1 and C, and the current-voltage characteristic of the device is linear throughout the experiments. With this structure, the resistance, R= 1.3 kΩ, between electrodes 1 and C (Fig. 2a) is substantially determined by the narrow “U-shape” NiCr region. Figures 2(b)-(d) display far-field (FF) thermal image of the sample chip obtained with our infrared confocal microscope without using the probe tip, where different bias voltages (0 V, 10 V, 18 V) are applied in (b) through (d). The detected FF signal is determined by the emissivity and the temperature. In the non-biased condition (Fig. 2(b)), the temperature is uniform, 27℃ (T0 ≈ 300 K), but finite contrast of the image is visible between metal leads (Au, NiCr) and substrate (SiO2) due to the difference in the emissivity.31 When bias voltage is applied to the device, electrical energy fed to the metal wire causes Joule heating and is, in turn, released to the lattice, elevating lattice temperature of the substrate on macroscopic length scales. The images of Figs. 2(c) and (d) are taken in a steady state condition, reached about several minutes after applying the bias voltage. The thermal emission of the substrate (SiO2) is noted to be more or less uniformly intensified by the heating. By fitting the intensification to the theoretically predicted temperature dependence, P ∝ 1/{exp(ħω/kBT) − 1} (Plank’s radiation formula), the temperature of the SiO2 substrate is estimated to be ~ 34℃ (T~ T0+ 7 K) at 10 V or 7.7 mA (Fig. 2(c)) and ~ 53℃ (T~ T0+ 26 K) at 18 V or 13.8 mA (Fig. 2(d)). The temperature of Au leads is not uniform


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because the electrode patches, 1-5 and C, are efficiently cooled down due to thermal anchoring with 50 µmφ-Au wires. Figure 3(a) is a replot of the upper inset of Fig. 2(a), which shows an optical microscope image of a 190×190 µm2 region centered around the U-shape NiCr wire. A FF thermal image (Vb= 18 V) of the same region as Fig. 3(a) is shown in Fig. 3(b). The central region is found to be hotter, ~ 60℃ (T~ T0+ 33 K), due to heating of the U-shape NiCr wire. Detailed subwavelength structure of the temperature distribution, however, cannot be resolved due to the diffraction limited FF spatial resolution (∼ 30×30 µm2).

The corner region of the U-shape NiCr wire is shown via SEM image in Fig. 3(c). Figure 3(d) is a NF image disclosing submicron structure of the temperature distribution in the region shown in Fig. 3(c). Remarkable feature is that a submicron “hot-spot” emerges along the inner corner of the wire. This effect is interpreted below as a consequence of local Joule heating, which results from the concentration of current along the inner corner, known as current crowding effect.35, 36 The detected NF signal is supposed theoretically to be proportional to the electromagnetic energy density, u(z, ω), of the fluctuating evanescent waves at the location of the tip apex, written as 21

,

(1)

where z is the distance from the sample surface, ω is the angular frequency of the EM wave, ħ is the reduced Planck constant, kB is the Boltzmann constant. Here, ρ(z, ω) is the EM local density


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of states (EM-LDOS), which is material-specific function of z and ω.37 In our previous work,18,25-27 samples were in thermal equilibrium at room temperature, so that the spatial profile of the EM-LDOS, ρ(z, ω), has been studied in the condition of uniform distribution of temperature T. In the present measurements, we study the spatial profile of temperature T given by the second term in Eq. (1),

, in the condition of uniform distribution of the EM-

LDOS, ρ(z, ω). (Note that ρ(z, ω) is a material specific parameter, and z= 10 nm and ω= 2πc/λ = 1.34x1014 Hz (λ= 14.1 µm, c: the light velocity) are fixed in the measurements. Hence ρ(z, ω) is a constant in the region of a given material.) By carrying out additional measurements in the equilibrium condition at room temperature T0= 300 K, absolute T-values can be derived without knowing ρ(z, ω) from VNF(T)/VNF (T0) = {exp(ħω/kBT0) − 1}/{exp(ħω/kBT)−1} ,

(2)

where VNF(T) is the near-field signal intensity in the biased condition and VNF (T0) is the one for the thermal equilibrium state at T0= 300 K, obtained in the non-biased condition. The temperature values estimated in this method are shown by the color bar scale in Fig. 3(d). Large temperature difference is created between the inner corner (~ 420℃) and the outer corners (~ 50℃) in the 3.3 µm-wide NiCr wire. This remarkably large temperature gradient in the metal wire is interpreted to be caused by strong concentration of current in the inner corner of the wire, called the current crowding effect.35,

36

The current crowding effect has been well

known through the study of local current distribution via various scanning probe microscopes (e.g., magnetic force microscope for current density mapping36). This work is the first report of this phenomenon in terms of the energy dissipation (or temperature), which has been technically challenging because dissipation was not easily accessible on nano-scale.


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To have firm interpretation, we have carried out simulation calculation using a commercial software, COMSOL, where heat generation due to electrical current and cooling process due to heat flow are consistently treated in the experimental configuration of the metal wire and the substrate: Parameters used are the electrical conductivity of NiCr (2.86×105 S/m), the thermal conductivities of NiCr (15 W/(m·K)) , SiO2 (1.4 W/(m·K)), and Si (150 W/(m·K)), and the thermal resistances across the interfaces of NiCr-SiO2 (3×10-8 K·m2/W)38 and SiO2-Si (3×10-9 K·m2/W)39. (Boundary conditions and parameters used in the simulation are described in more detail in section 2 of Supporting Information, Figure S6.) The simulated current density distribution, shown in Fig. 3(e), demonstrates the current crowding effect in the inner corner of the NiCr wire. The derived profile of temperature distribution, displayed in Fig. 3(f), well reproduces not only the overall feature of the experimentally obtained near-field image in Fig. 3(d) but also the experimentally derived amplitude of temperature rise. The distinct agreement between the calculation and the experiment ensures our interpretation and successful temperature mapping, validating our equipment to be a nanothermometric near-field microscope. We have studied a number of different U-shape NiCr wires with differing widths/shapes, and confirmed that the experimental results are well reproduced by simulation calculation. Figures 4 display an example obtained on 2.2 µm-wide NiCr wire with a rounded corner with a radius of curvature ~ 1.9 µm (Fig. 4(a)). Distinct hot spot is not recognized to develop along the inner corner in the experimental near-field image (Fig. 4(b)). This is consistent with the simulation calculation, which shows that the concentration of local Joule heating, or the current crowding effect, is less remarkable in the rounded corner (Fig. 4(c)), yielding more uniform temperature distribution (Fig. 4(d)). The spatial resolution of temperature mapping is evaluated to be ~ 100 nm in this work (Figure S5). Since the spatial resolution of our equipment is known


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to be determined by the tip-size,40 the improvement to a value less than 50 nm may be readily achieved by using sharper tips.29, 40 The SNoiM is a near-field analog of the infrared radiation thermometer, with a spatial resolution well beyond the diffraction-limit and a temperature sensitivity ~ 2 K (Figure S4). The scheme of measurements is of two distinguished features when compared to existing scanning nano-thermal microscopes (SThMs)3-5. First it provides potential to realize smallest perturbation to the local temperature probing. In the present work, the measurements are carried out in air, yielding an air-mediated sample-to-tip thermal conductance of a comparable amplitude to the one of contact-type SThMs 3. It is not difficult, however, to carry out measurements in vacuum, where the sample-to-tip thermal conductance is dramatically reduced to a level mediated only via near-field radiative heat transfer41, which is by orders of magnitude smaller than the one of contact-type SThMs 3. (See Supporting Information and Figure S2 for more detailed discussion.) Secondly, the measurement is made via monochromatic radiation, not via integrated spectra (heat). Owing to this characteristic, conduction- electron temperature, not the lattice temperature, is selectively probed in this work: Conduction electrons, not phonons, give largest contribution to the EM-LDOS for the fluctuating evanescent waves at the detected frequency, ω ~ 1.34x1014 Hz (λ ~ 14.1 µm). In dielectrics and /or semiconductors, electron temperature or lattice temperature would be selectively probed by choosing appropriate frequencies: The lattice temperature would be probed when the target frequency is chosen to be that of the surface phonon polariton (SPhP) resonance, while the electron temperature would be studied when the frequency is well away from the resonance, as demonstrated in Ref. 29. All the existing SThMs so far developed3-5, 7, 8 probe substantially the lattice temperature only, because the heat capacity is dominated by the lattice in most materials. The spectroscopic measurements with our


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equipment will thus provide a unique and powerful method for investigating non-equilibrium systems on nanoscales29. In summary, we demonstrated a novel radiative nanothermometric technique using a highlysensitive infrared s-SNOM, called SNoiM. Localized Joule heating at the corner of narrow NiCr wires has been directly imaged, revealing that the electron energy dissipation is strongly concentrated in sharp corners of the current pass. This work will pave the way for noncontact mapping of nanoscale energy dissipation and heat transfer in a variety of modern nanomaterials and microelectronic devices.

Figure 1. (a) Diagram of the SNoiM equipped with an ultra-highly sensitive infrared detector (CSIP), with a peak detection wavelength at ~ 14.1 µm. (b) A close-up diagram of the far-field (FF) focal spot region and the nanoscale tip for near-field (NF) optics. The focal spot size of the objective is ~ (25 µm)2. The tip is positioned at the center of the focal spot region, and scatters fluctuating EM evanescent fields. The tip-scattered NF evanescent fields together with the FF


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background radiation are collected and led to the detector, where only the NF components are extracted via tip-height modulation technique.

Figure 2. (a) Optical microscope image of the NiCr sample under study. Five independent devices are fabricated with their electrodes marked from “1” through “5”, where “C” denotes the common electrode. As shown in the upper margin for Device “1”, each device consists of a “Ushape” narrow (3.3 µm) NiCr wire extended by a much wider (40 µm) region, which is connected further to a 20-µm wide Au leads reaching to the electrode. (b), (c), (d): FF infrared thermal images of the sample with different voltages applied between “C” and “1”: Device “1” (R= 1.3 kΩ) is heated. Small area around the “U-shape” narrow wire is hotter: This is apparently not very clear in Fig. 2(d) but will be made clearer in Fig. 3(b) with more sensitive color representation.


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Figure 3. (a) Optical microscope image of the device studied. (b) FF thermal image in the same area as (a). Bias voltage of Vb= 18 V is applied. (c) SEM image (false color) of an end region of the “U-shape” narrow NiCr wire. (d) Near-field (NF) image in the same area as (c), with Vb= 18 V. The scale of NF signal is given by temperature values in the color bar. (e) Simulated current density distribution in the same area as (c). The current density is indicated by the areal density of arrows. (f) Simulated temperature distribution in the same area as (c).

Figure 4. (a) SEM image (false color) of a “U-shape” narrow NiCr wire (width= 2.2 µm), with a rounded inner corner (radius ~ 1.9 µm). (b) NF image in the same area as (a) with a temperature


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scale. (c) Simulated current density distribution in the same area as (a). The current density is indicated by the areal density of arrows. (d) Simulated temperature distribution in the same area as (a).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Q. W.) *E-mail: [email protected] (S. K.) Author Contributions Q. W. and S. K. co-wrote the manuscript. Q. W., K. -T. L. and H. N. performed the experiments. K. Y. fabricated the samples. S. K. designed and fabricated the CSIP detector. All authors discussed the results and commented on the manuscript. Notes The authors declare no competing financial interest. ASSOCIATED CONTENT Supporting Information Tip-height modulation for near-field detection; The feature of radiative temperature detection; near-field decay with increasing the tip height; temperature sensitivity; spatial resolution; FEM simulation for temperature distribution.

ACKNOWLEDGMENT


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We thank R. Yanagisawa and M. Nomura for helpful discussions in simulation calculations with the software (Comsol). Q. Weng is an Overseas researcher under Postdoctoral Fellowship of Japan Society for the Promotion of Science (JSPS). This work was supported by Grant-in-aid for JSPS Fellows, and Collaborative Research Based on Industrial Demand by Japan Society and Technology Agency (JST). REFERENCES (1) Pop, E. Nano Res. 2010, 3, 147-169. (2) Brites, C. D. S.; Lima, P. P.; Silva, N. J. O.; Millan, A.; Amaral, V. S.; Palacio, F.; Carlos, L. D. Nanoscale. 2012, 4, 4799. (3) Menges, F.; Mensch, P.; Schmid, H.; Riel, H.; Stemmer, A.; Gotsmann, B. Nat. Commun. 2016, 7, 10874. (4) Halbertal, D.; Cuppens, J.; Ben Shalom, M.; Embon, L.; Shadmi, N.; Anahory, Y.; Naren, H. R.; Sarkar, J.; Uri, A.; Ronen, Y.; Myasoedov, Y.; Levitov, L. S.; Joselevich, E.; Geim, A. K.; Zeldov, E. Nature 2016, 539, 407-410. (5) Halbertal, D.; Ben Shalom, M.; Uri, A.; Bagani, K.; Meltzer, A.; Marcus, I.; Myasoedov, Y.; Birkbeck, J.; Levitov, L.; Geim, A.; Zeldov, E. Science 2017, 358, 1303-1306. (6) Kucsko, G.; Maurer, P. C.; Yao, N. Y.; Kubo, M.; Noh, H. J.; Lo, P. K.; Park, H.; Lukin, M. D. Nature 2013, 500, 54-58. (7) Nonnenmacher, M.; Wickramasinghe, H. K. Appl. Phys. Lett. 1992, 61, 168. (8) Shi, L.; Plyasunov, S.; Bachtold, A.; McEuen, P. L.; Majumdar, A. Appl. Phys. Lett. 2000, 77, 4295. (9) Cahill, D.; Goodson, K.; Majumdar, A. J. Heat Transfer 2002, 124, 223-241. (10) Christofferson, J.; Maize, K.; Ezzahri, Y.; Shabani, J.; Wang, X.; Shakouri, A. J. Electron. Packag. 2008, 130, 041101. (11)

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