8th Thermal and Fluids Engineering Conference (TFEC)
May, 2023
Partially Online Virtual and at University of Maryland, MD

TFEC-2023-46023

ANALYSIS OF JOULE HEATING CHARACTERISTICS IN NANOWIRENETWORKS MEASURED BY THERMOREFLECTANCE IMAGINGMETHOD
Kanji Tamai,1,∗ Yuta Sugihara,1 Kazuya Tatsumi,1 Reiko Kuriyama,1 Kazuyoshi Nakabe1
1Kyoto University Kyodai-Katsura C-cluster-3, Nishikyo-ku, Kyoto 615-8540, JapanABSTRACT
Nanowire-network is a promising material for solar cells, touch panels, electronic devices, and neuromorphics. However, developing an evaluation method for the thermal reliability of these devices is a challenging
issue and has not been fully solved. The present study aims to develop a model which can evaluate the Joule
heating characteristics and the resulting temperature distribution of NW-networks. The NW-network consistsof NWs of diameter 120-150 nm scattered on glass substrate in the area between electrodes with a gap of 100µm. Electric current was applied periodically to the NW-network, and the temperature distribution was visualized using thermoreﬂectance imaging method 10µs after starting the heating. Overall temperature increase
was observed in the NW-networks, where high temperature regions appeared especially along the energization paths accompanied by generations of hotspots at several speciﬁc connections of NWs. The probability
density function (PDF) of the temperature was evaluated based on the Weibull plot. The distribution of thedata could be divided into two regions: a high-temperature region with small slope and a low-temperature
region with large slope. The high and low temperature regions were considered to represent the temperature
increase caused by the Joule heating and heat transfer of the wires, respectively. We could also obtain goodresults in the aggression analysis using the mixed Weibull model. Further, we evaluated the effect of thenumber density of the NWs on the PDF of the temperature, and found that the slope of the Weibull plot inboth temperature regions increased for the higher number densities.

KEY WORDS: Nanowire-network, Thermoreﬂectance imaging, Joule heating, Weibull model
1. INTRODUCTION
Nanowire(NW)-based transparent conductive electrodes are more ﬂexible than existing ITO electrodes andare known for their high transparency due to their nanoscale wire diameter. NWs are expected to be applied
to anti-fogging lenses, ﬂexible touch screens, and solar cells. Such devices function by applying an electric
current to a NW-network consisting of many interconnected NWs. However, since Joule heat is generated
during operation, functional failure or damage due to electromigration or annealing caused by temperaturerise is a problem. In this study, we measured the temperature distribution of NWs using the thermoreﬂectanceimaging (TRI) method in order to understand the characteristics of the temperature change distribution whencurrent is applied to the NW-network. The temperature change distributions were evaluated using the Weibull
distribution, and the relationship between the temperature change distribution and the number density wasquantitatively analyzed.

2. EXPERIMENTAL
The TRI method utilizes the fact that the reﬂectance of a sample surface changes with temperature to obtainthe temperature distribution from the change in intensity value of the reﬂected light captured by a sCMOS∗Corresponding Kanji Tamai: tamai.kanji.33a@st.kyoto-u.ac.jp

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camera when the surface of the sample is irradiated with light. In this measurement, the temperature wasobtained from the difference between the intensity value of the reﬂected light from the sample at the reference
temperature and the intensity value when the sample was heated to a high temperature. If the luminance valueof the sample at the reference temperature is I0 , the intensity change is ∆I, and the sample temperature change
is ∆T , the following relationship ∆I/I0 = CTR ∆T . The thermoreﬂectance coefﬁcient CTR is a coefﬁcientthat depends on the wavelength of the material and the light, and the thermoreﬂectance coefﬁcient of Ag usedin this study at the irradiation light wavelength of 530 nm was -8.96×10K−1 as a result of the pre-calibration.

Fig. 1 (a)Schematic of Ag-NW network and electrodes on the SiO2 glass substraate, (b)microscopy image ofthe Ag-NW network.
Fig. 1 shows a photograph of the sample and a schematic diagram of the temperature measurement method
using the TRI method. In this experiment, parallel Au electrodes were deposited at 100µm intervals on a glass
substrate, and Ag-NW (Sigma-Aldrich: 200-661-7) of 120-150nm in diameter and 20-50µm in length wasspread over a 100µm wide area between the electrodes. Ag-NW was applied by vaccum ﬁltration [1], and thedensity of Ag-NW was adjusted by changing the concentration of Ag-NW solution.

Fig. 2 (a)Schematic image of TRI measurement system, and(b)Time chart of the current, Thermal transient(Estimated), LED ﬂash, and camera exposure.
Fig. 2 shows a schematic diagram of the experimental apparatus. In the experiment, a square wave voltage of375 mV, application time of 10 µs, and period of 250 µs was periodically applied between both electrodes of
the Ag-NW network, and the temperature distribution of the time phase was visualized 10 µs after the start ofenergizing by the TRI method. At each time point, the sample was exposed to pulsed light with an exposure
width of 1µs, and 5000 images of the reﬂected light from the Ag-NW group were captured by an sCMOS
camera (Hamamatsu Photonics: ORCA Fusion). To reduce the inﬂuence of the Ag-NWs’ movement during
imaging, the phase-limited correlation method was used to align the images, and the temperature distribution
was calculated for each pixel. A 100x objective lens (Olympus: LMPLan FL 100X NA=0.8) was used tocapture images. The area of the image is about 100×100µm within the red frame shown in Fig. 1.

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3. RESULTS AND DISCUSS
Fig. 3 shows the temperature distribution of Ag-NWs. The temperature distribution of the Ag-NW network
can be considered as the spatial distribution of the energization paths, if we consider that the Ag-NW network
is composed of energization paths and heat transfer paths by connecting NWs. The temperature distribution of
the Ag-NW network can be considered as the spatial distribution of these paths. The Weibull distribution has
been proposed as a method for evaluating the temperature distribution, and the Weibull distribution, which isusually used for lifetime prediction as a distribution with respect to time, is used for the evaluation of spatialcharacteristics.

Fig. 3 The experiment result of TRI method,(a)temperature change distribution after heating 10µs
Ltotal =67000µm,(b)Ltotal =77000µm,(c)Ltotal =100000µm,.
Fig. 4 plots the temperature distribution on the Ag-NW center line on Weibull probability paper. The results
show that the temperature distribution can be divided into two regions: a high-temperature region with a small
slope and a low-temperature region with a large slope. The high-temperature and low-temperature regions are
considered to be caused by two phenomena, heat generation on the energization path and heat transfer fromthe heat generation line, respectively, and a mixture model that expresses them as superpositions is consideredappropriate. Therefore, in this study, the mixture weibull distribution model with a mixture number of 2
shown in Eq. 1 was applied as the ﬁtting function to the data in Fig. 3. The parameters ai and mi in theWeibull distribution are the Scale parameter and Weibull parameter. The parameters ai and mi are the scaling
parameter and Weibull coefﬁcient, respectively. i=1 and i=2 represent the low and high temperature regions,respectively. The Scale parameter ai represents the degree of similarity of the temperature increase in the entire
system, and the Weibull parameter mi represents the degree of uniformity of the temperature distribution inthe entire system. w is a weight parameter.
[( ()m1 )][( ()m2 )]∆T∆TF (∆T ) = w 1 − exp −+ (1 − w) 1 − exp −a1a2(1)

Fig. 5 shows the relationship between the nanowire number density and the mixture weibull distribution
model parameters. In Fig. 5(a), the Scale parameter a1 in the low temperature region shows almost no changewith number density, while the Scale parameter a2 in the high temperature region shows a sharp downward
trend. There are two possible reasons for this. One is the difference in the number of energization paths. The
second reason is the heat transfer to the non energized Ag-NWs connected to the heat-generating part. Weibull
parameter m in Fig. 5 (b) increases with number density for both m1 and m2 , which is thought to be related
to the fact that the temperature dispersion in the heated area becomes smaller and the temperature distribution
approaches uniformity due to the increase in the energization path, and at the same time, the heat dissipation
path increases. The increase in energization paths is also reﬂected in the change in the weight parameter inFig. 5 (c), which decreases with respect to the number density, indicating a decrease in the number of nonenergized nanowires. The weight parameter is around w=0.75-0.95, indicating the approximate percentage ofnanowires in the energization path.

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TFEC-2023-46023(a)Ltotal =67000µm(b)Ltotal =77000µm(c)Ltotal =100000µm

Fig. 4 Example of ﬁtting results for each NW-network. The red lines are the curves of the mixture weibull
distribution model used in the ﬁtting.

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a14000

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2w

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Weight parameter

25m

1.4m

a30

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a [-]

40

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1.00.8m

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20.4

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Nanowire total length

6000

L

total

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[µm]

7000

0.8

0.6

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Nanowire total length

6000

L

total

7000

[µm](b)Weibull parameter

3000

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Nanowire total length

6000

L

total

7000

[µm](c)Weight parameter

Fig. 5 Relationship between the parameters of the mixture weibull distribution model and the nanowire-totallength Ltotal in the region.

4. CONCLUSIONSThe temperature distribution of joule-heated Ag-NWs was measured using the TRI method, and it was foundthat this was caused by two phenomena: heat generation on the energization path and heat transfer fromthe energization path to the non-energized wires. The results of experiments with samples of different wire
number densities showed changes in each parameter, especially the Scale parameter a2 in the high temperature
region, which rapidly decreases with increasing wire number density and approaches the value of a2 . This isdue to the increase in energization paths (dispersion) caused by the increase in the number of wires and theincrease in heat transfer paths caused by the contact of non-energized nanowires with the heat-generating area.
Since the effect of the increase in heat transfer (dissipation) paths due to the increase in energization paths oneach mixture weibull distribution model parameter has not been separated, it will be necessary to combine theresults with the numerical current distribution analysis results in the future.

REFERENCES[1] Lee, P., Lee, J., Lee, H., Yeo, J., Hong, S., Nam, K. H., Lee, D., Lee, S. S., Highly Stretchable and HighlyConductive Metal Electrode by Very Long Metal Nanowire Percolation Network , Adv. Mater., 24, pp.25262562, (2012).
[2] Suprem R. D., Amr M. S. M., Kerry M., Sajia S., Ali, S., David, B. J., and Muhammad A. A., Evidence ofUniversal Temperature Scaling in Self-Heated Percolating Networks , Nano. Lett., 16, pp.3130-3136, (2016).

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