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Microscopic Evaluation of Electrical and Thermal Conduction in Random Metal Wire Networks RITU GUPTA, Ankush Kumar, Sridhar Sadasivam, Sunil Walia, Giridhar U. Kulkarni, Timothy S. Fisher, and Amy M. Marconnet ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b00342 • Publication Date (Web): 22 Mar 2017 Downloaded from http://pubs.acs.org on March 26, 2017

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ACS Applied Materials & Interfaces

Microscopic Evaluation of Electrical and Thermal Conduction in Random Metal Wire Networks Ritu Gupta,1,2#* Ankush Kumar,3# Sridhar Sadasivam,1 Sunil Walia,4 Giridhar U. Kulkarni, 4,5 Timothy S. Fisher1,6 and Amy Marconnet1,6*

1

Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana, USA- 47907. 2

Department of Chemistry, Indian Institute of Technology, Jodhpur, Rajasthan, India342011.

3

Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore, India-560064. 4

Centre for Nano and Soft Matter Sciences (CeNS), Jalahalli, Bangalore, India-560013. 5

6

On Lien from JNCASR, Bangalore

School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA-47907. # Ritu Gupta and Ankush Kumar share equal first authorship.

* Address correspondence to [email protected] , [email protected]

KEYWORDS: Metal network, IR microscopy, Joule heating, Transparent thin film heater, Heat conduction.

1 ACS Paragon Plus Environment


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ABSTRACT Ideally, transparent heaters exhibit uniform temperature, fast response time, high achievable temperatures, low operating voltage, stability across a range of temperatures, and high optical transmittance. For metal network heaters, unlike for uniform thin film heaters, all of these parameters are directly or indirectly related to the network geometry. In the past, at equilibrium, the temperature distributions within metal networks have primarily been studied using either a physical temperature probe or direct infrared thermography, but there are limits to the spatial resolution of these cameras and probes and thus only average regional temperatures have typically been measured. But knowledge of local temperatures within the network with very high spatial resolution is required for ensuring safe and stable operation. Here, we examine the thermal properties of random metal network thin film heaters fabricated from crack templates using high resolution infrared (IR) microscopy. Importantly, the heaters achieve predominantly uniform temperatures throughout the substrate despite of the random crack network structure (e.g., unequal sized polygons created by metal wires), but the temperatures of wires in the network are observed to be significantly higher than the substrate due to significant thermal contact resistance at the interface between the metal and the substrate. Lastly, the electrical breakdown mechanisms within the network are examined through transient IR imaging. In addition to experimental measurements of temperatures, an analytical model of the thermal properties of the network is developed in terms of geometrical parameters and material properties providing insight into key design rules for such transparent heaters. Beyond this work, the methods and understanding developed here extends to other network-based heaters and conducting films including those that are not transparent.


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Introduction Transparent and flexible conducting films are essential for modern devices such as touch screens, solar cells, organic light emitting diodes, and transparent heaters.1 In particular, transparent heaters2-3 play an important role in defogging and defrosting of display panels, windows of automobiles, and lenses of optical instruments. Further, the combination of optical transparency and controlled application of heat are essential for devices requiring uniform operating temperature such as transparent heated stages, transparent sensors, and LCD displays.2 Transparent heaters use Joule heating to control temperature; thus, the films should have high optical transmittance and low sheet resistance simultaneously. Several types of transparent heaters have been recently developed including periodic metal meshes,4-7 CNTs,8 graphene,9 metal nanowires,10 and hybrid networks6,

11-13

deposited on

transparent and flexible substrates. In such systems, the open space between the conductive network is transparent, while the network itself, which facilitates the Joule heating, may be opaque. For those heaters fabricated from deposited nanowires (NWs), high junction (or contact) resistances, as well as non-uniform density or distribution of the NWs, results in non-uniform temperatures (i.e., hot spots) that are detrimental to performance. Templatebased metallic wire networks have been developed using techniques such as electro-spinning, leaf venation architectures, and nano-trough or crackle templates.14-17 The excellent electrical and thermal conductivities of these continuous metal wire networks with negligible junction effects, complete connectivity, and tuneable metal thickness make them particularly suitable for transparent heater applications. Thus, it is unlike conventional nanowire-based network, and ultimately demonstrates lower sheet resistance and high transmittance. Furthermore, the fabrication methods for these networks are highly scalable using industrial techniques such as roll coating,18 rod coating,19 and spray coating20 and result in highly robust, flexible, transparent heaters that are stable under harsh oxidation conditions.



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An efficient wire network should achieve a uniform operating temperature with a fast response time, low operating voltage, and sufficiently high operating temperature for the desired application. Such networks find great use as heaters in small-sized microelectromechanical systems (MEMS), lab on chip (LoC), heatable textiles,21 smart sensors, and bio-medical devices.22 Microheaters are also utilized in microfluidic channels for chemical reactions as well as localized heating applications.23-24 Usually, the device size is of the order of few hundred microns for heating in multiple temperature zones. For example, DNA amplification in microscale polymerase chain reaction (PCR) devices can be performed on a single chip with different temperatures by Joule heating of such networks.25 The thermal response of transparent heater networks has predominantly been studied by non-contact methods such as infrared (IR) thermography.2,

26-27

The spatial and temporal

resolutions of such cameras limit the measurement to local average temperatures. However, many projected applications of transparent heaters such as temperature-dependent spectroscopy and studies of reactions on heater stages require knowledge of the local temperature profile with precise spatial and temporal resolution.2 For accurate local temperatures, the wire width must be larger than the spatial resolution of the imaging system. The performance of transparent heaters is usually measured using IR camera which enable local variations of temperatures at a nominal resolution of ∼1 mm, much longer than the wire width.2, 26, 28 In this context, infrared thermal microscopy is a powerful tool for studying local temperatures with high spatial resolution. Using a typical liquid nitrogen cooled MidWavelength IR (MWIR) microscope, a spatial resolution of 1.6 µm is achievable at the diffraction limit. Such a tool has been deployed in a variety of applications including measuring the thermal conductivity of vertically aligned CNTs,29 Joule heating effects on solder joints,30 and the heat produced due to chemical reactions within liquids.31 Here, we


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demonstrate the first measurements of local, transient temperature profiles in a flexible, transparent conducting heater. Specifically, this work focuses on the thermal response of metallic wire networks formed by a crack template method with wire widths ranging from 2 to 100 µm. First, the thermal, electrical, and optical properties are analyzed theoretically in terms of measurable and controllable geometrical and material priorities to provide insight into the design of the transparent heater network. Then, the spatially and temporally resolved temperature distributions in the metal and the substrate are measured experimentally using an infrared microscope. Finally, a theoretical model of the thermal response is developed and agrees well with experimental results.

Results and Discussion Characteristics of metal network heaters A transparent heater is characterized by its maximum allowable temperature, dissipation losses, response time for temperature saturation, and power density. The steady state temperature of a heater is achieved when its collective dissipation losses (convection and radiation to surrounding) equals its input Joule heating energy. The steady state rise in the temperature based on an energy balance can be written as32

∆ =

2

ℎ

=

2

.

ℎ

2

(1)

Here, V is the applied voltage, and are the resistance and sheet resistance of network of size a × b (with a in the direction of the field and b along perpendicular direction of the field as shown in Figure 1d), and ℎ is the effective heat transfer coefficient considering



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convection and radiation losses to the surroundings that can be written approximately for low temperature rise as31: ℎ

= ( ℎ + ℎ ) + 4 ( ε + ε ) σ30.

(2)

Here, ℎ and ℎ represent the convection heat transfer coefficients and ε and ε are the emissivities of the top and bottom surfaces of substrate, respectively. On the top surface, the convection heat transfer coefficient and emissivity can also be written in terms of a twodimensional metal fill factor, f, and the substrate and metal properties as ℎ = (1 − )ℎ + ℎ

!

and ε = (1 − )ε + ε ! , where ℎ and ℎ

transfer coefficients and ε and ε

!

!

are the convection heat

are the emissivity of the substrate and the metal,

respectively.On the bottom surface, ℎ = ℎ andε = ε . Combining the top and bottom heat loss coefficients, the net heat transfer coefficient can also be written as32: ℎ

= 2(ℎ " + 4 ε " σ30 ) − (ℎ " − ℎ# $ ) − 4 σ30 (ε " − ε# $ ).

(3)

The sheet resistance of this type of network was recently evaluated using a statistical approach33 and can be estimated from %

= 2 '

&

()*

.

(4)

Here & is the resistivity of the metal, w is the wire width, t is film thickness, and )+ is the edge density of the network (i.e., the number of wire segments per unit area). Note that sheet ,

resistance of a continuous film is = . Thus, in other words, the effective thickness of a -

network, , is reduced from t to = . '()+ for a network with =

,

/00

. The

sheet resistance can also be evaluated as a function of metal fill factor and other geometric parameters as: %& 1

32

= 2 1 2254 $$

1

4 $$ (

,

(5)

where 1 is the fraction of wires in the current carrying backbone (removing isolated and dangling edges), 36!! is the mean perimeter of cell, 56!! is the mean area of each polygonal 6 ACS Paragon Plus Environment

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cell, and is average number of sides of the polygonal cells. Combining Equation (1) and (4), the estimated average temperature rise of the heater (considering both the wire network and the substrate), ∆ is ∆ =

2 2 '()* . ℎ

2 % &

(6)

Equation (6) can be further modified so that the average temperature rise of the heater is expressed completely in terms of measurable parameters. Thus, by combining Equation (1) and (5), the estimated temperature rise is ∆ =

2 2 254 $$ 2 2 1 ( . ℎ

2 % & 34 $$

(7)

These relationships illustrate that the maximum temperature rise is obtained at high voltages, wide wire widths, thick metal film, and for an edge density with minimum material resistivity at constant voltage. Importantly, these equations enable estimation of sheet resistance, temperature and thermal properties of a sample using only its template image before metallization, electrical measurement, and IR imaging assuming that the processing is performed free of defects. However, in addition to the thermal performance, a transparent heater also requires high optical transmittance, 7 , which is achieved by minimizing the fill factor, f, since34 = 1 − η ,

(8)

where η is a parameter that depends mostly on metal film thickness and the wavelength of light. Thus, a trade-off exists between optical transmittance and thermal characteristics. An increase in the metal fill factor raises the maximum achievable temperature range but decreases the transmittance concomitantly. The fill factor needs to be optimized in order to achieve an ideal balance for a given application. A heater network must possess low wire widths and wire spacings, high interconnectivity, and large film thicknesses. For meeting such requirements, crack templates with small crack widths, narrow spacing, and high



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interconnectivity are used in this study. However, the network geometry can be further tuned by optimizing conditions for crack formation.35-37

Structural and Electrical Characterization of the Micro-heater The Ag wire network is fabricated on various substrates with the crackle lithography technique shown in Figure 1a. The crackle precursor film forms a network of well-connected channels upon drying. The process of formation can be tuned to produce desired crack network geometry (see Experimental for details). An optimized Au metal network (shown in Figure 1b) with wire of widths 2-10 µm and wire spacings of 50 -100 µm on glass was chosen for characterizing the transient heating response. The wires have a metal 2D fill factor, f, of approximately 15% and nearly complete connectivity (Figure 1c).The network produces a sheet resistance Rsn=1.5 Ω/sq, which is significantly lower than networks obtained from CNTs (~130-190 Ω/sq)38 and Ag NWs (~6 Ω/sq).39 Optical profilometry shows an average wire thickness of approximately 80 nm (Figure S1). The model discussed above is verified with experimental data collected from six different thin film network-based heaters (labeled as A-F) of varying wire width, spacing, and thickness (see Table S1 in Supporting Information). Initial examination of the fabricated thin film heaters is performed by operating at low bias with IR imaging (Figure S3).

The

geometric parameters of the six different network heaters and their experimentally obtained sheet resistances and temperature values at an applied voltage of 1.5 V are given in Table S1. The measured resistance of these samples increases approximately linearly with the inverse of the effective thickness8

9

/00

:, as shown in Figure 1e, with an extracted resistivity value of

17 ×10-8 Ω-m. This estimated resistivity is 8 times the bulk resistivity of Au (2.2 ×10-8Ω-m),40 thus supporting Equation (4). Since the Au in wire network is physically evaporated, it is usually polycrystalline with grain boundaries and defects as the dominant scattering sources 8 ACS Paragon Plus Environment

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leading to high sheet resistance.27 As shown in Figure 1f, the corresponding temperatures of the network heaters increase approximately linearly with in agreement with Equation (6). Thus, these results illustrate that the approximate model developed above can be used to estimate sheet resistance and the temperature profile for a given network with known geometric parameters that contribute to the effective thickness, . The heaters are further examined in detail using IR microscopy (Figure 2a-b) at increased magnifications. Prior to the thermal measurements, a calibration procedure accounts for the spatial variation of emissivity in the sample. Before applying the bias voltage, the radiance emitted from the heater surface at room temperature is measured (see Figure S2 and Figure 2c) and compared to that of a blackbody at the same temperature in order to obtain an emissivity map (Figure 2c). The metal wires have a lower infrared emissivity compared to the glass substrate, as expected. With 4X magnification (~5 µm resolution), the wire network is clearly distinguishable, with the substrate having higher emissivity than the wire. The average emissivity of the Au wire observed by the microscope is 0.42, which is lower than that of the glass substrate (0.65). Within the Au wire network, the emissivity is observed to vary, as a secondary wire network of thinner wires seems to have higher emissivity than the primary network of thicker wires, likely due to the resolution limits (1.6 µm). Further, the measured emissivity of Au is higher than the expected value (> 0.1), likely due to contributions from the substrate, residual crackle precursor on Au during lift-off, and/or the surface roughness of the Au layer. After emissivity calibration, thermal images are obtained during Joule heating. The 4X magnification thermal image in Figure 2d shows the temperature distribution with a maximum temperature of 60 ± 0.5 °C at the middle of the network and a minimum temperature (25± 0.5 °C) at the contacts under an applied voltage of 1.5 V. Thermal maps at other applied voltages and their corresponding transient temperature profiles are shown in 9 ACS Paragon Plus Environment


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Figure S4. Note that from these large-area images, the temperatures in the middle region of the heater and some thicker wires are higher than those at the periphery. Clearly, the microscopic details of heat transport can be observed by thermal imaging only at higher resolution.

The wire-substrate thermal profile is probed by measuring the emissivity and temperature distributions via imaging at 20X magnification (Figure 3a). The emissivity map in Figure 3b displays regions of high and low emissivities corresponding to PET and Ag respectively. At higher magnification of 20X, metals display lower emissivity (< 0.1) than that observed at 4X as evident from the blue color of the emissivity map (Figure 3b). The applied voltage is ramped up gradually through the Au wire network until the current increased linearly without significant change in resistance. Thermal maps are acquired at 0.5 s intervals until the steady state temperature is obtained at the final applied voltage (see supporting video SV1). Figure 3c-f shows a steady state temperature map of the Au wire network/PET at different applied voltages. Note that the wire temperatures are slightly higher than of the substrate, even at steady state. Given that the time gap between the two frames is 0.5 s and that the temperature equilibrates at a much faster rate, the transient information related to local heat diffusion could not be obtained. Steady state is achieved at the time when conductive, convective, and radiative heat losses from the sample are balanced by the Joule heating (Figure 3g). The dynamics of temperature change in the heater (average of wire and substrate temperature) are studied with a lumped capacitance model: (## $ ;# $ +# " ; " )

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