Supplementary Information for “Super-Joule
Heating in Graphene and Silver Nanowire Network”
Kerry Maize2, ‡, Suprem R. Das1, 2 , ‡, Sajia Sideque1, 2,Amr M. S. Mohammed1, 2, Ali Shakouri1, 2,*,
David B. Janes1, 2, Muhammad A. Alam1, 2, *
1. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN
47907, USA
2. Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA
* Author to whom correspondence should be addressed: alam@purdue.edu,
shakouri@purdue.edu
‡
Author who contributed equally to this work
I. Fabrication process of silver nanowire network and hybrid network films and devices
The fabrication of both nanowire network device and hybrid network device were started with
synthesizing controlled films consisting of silver nanowires (with similar density of wires on
similar sized quartz substrates) following a drop casting technique (from Blue Nano Inc., NC;
density 10mg/mL dispersed within an iso-propyl alcohol solution) onto 1cm x 1cm quartz
substrate (SPI Supplies, PA). The average dimension of the wires is Lav ~ 40 µm and dav ~ 90 nm
with distributions < Lav > ~ 20 - 60 µm and < dav > ~70 – 110 nm. The density of nanowires was
kept approximately 4.8x106 cm-2 that corresponds to our best TCE properties previously reported
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[1]. For hybrid network device fabrication, commercially available, chemical vapor deposited
single layer graphene grown on copper foil (ACS Materials Co., MA) was transferred onto one
of the silver nanowire network films mentioned above using standard graphene transfer
procedures [2]. The detail of the procedure is described in reference 1. The nanowire network
film was annealed in forming gas at 1500C for 1 hour with a 40 sccm flow rate and the hybrid
network film was annealed at 3000C with all other conditions similar to the nanowire network
film. For fabrication of the devices on nanowire network and hybrid network films,
photolithography was used to define circular transmission line method (CTLM) patterns using a
photo-mask with channel lengths of 100µm. For high current injection to the network structure, a
metal stack of Ti (1nm)/Pd (30nm)/Au (20nm) was e-beam evaporated using Kurt J. Lesker
electron-beam evaporator, with base pressure of ~10-7 Torr, followed by a lift-off process.
II. Nanowire-nanowire contacts
Supplementary Figure 1: A FE-SEM image of the nanowire network film showing silver
nanowire-nanowire junction (Figure a – c); and nanowire-nanowire junctions wrapped by
graphene in a hybrid network film (Figure d – f).
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Figure above shows nanowire-nanowire junctions in the nanowire network film as well as in the
hybrid network film with varied magnifications. The contrast difference between a-c and d-f is
due to the presence of graphene wrapping in the latter set of images.
III. Thermoreflectance (TR) imaging measurement technique
Thermal images were obtained using thermoreflectance imaging microscopy. [3, 4, 8] The
technique is capable of measuring device surface temperature distribution with 50 mK
temperature resolution and submicron spatial resolution. Full field thermal images are acquired
quickly with no scanning of the instrument required. Thermoreflectance imaging measures the
small change in surface optical reflectance (~10-5-10-4) as a material undergoes a change in
temperature. [4] The nanowire network sample was probed under a reflectance microscope as
illustrated in Figure 1(e) in the manuscript. Sample top surface was illuminated using a
narrowband light emitting diode (LED) centered at 530 nm wavelength. Thermoreflectance
imaging was implemented using a pulsed boxcar timing scheme [6] illustrated in Supplementary
Figure 2. The device under test is excited electrically with a continuous boxcar waveform, either
current or voltage based on the dependence to be inspected. The device is electrically active (V =
Vpk, I = Ipk) during the high part of the excitation cycle, and electrically passive (V = 0 V, I = 0
A) during the low part of the cycle. Each device pulse induces joule heating in the nanowire
network and corresponding perturbation in sample surface reflectance. A sensitive high dynamic
range CCD camera synchronized to the sample electrical repetition rate records reflected
intensity only when the illumination pulse is on. Amplitude of thermoreflectance change is
calculated from separate measurement of device reflectance during active and passive electrical
states. Acquiring thermoreflectance images for multiple values of the illumination pulse delay
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parameter (τ) measures the device thermal transient (heating and cooling) in response to boxcar
excitation. There is one illumination pulse per device excitation period. The camera records the
active and passive images during separate acquisition intervals, alternating approximately every
two seconds. Square current pulses of 1 millisecond duration at 150 Hz repetition rate were
applied across the sample inner and outer electrodes. Illumination (LED) pulse width was 100
microseconds. Thermoreflectance images of the network sample were averaged for 20 minutes,
producing temperature resolution of 0.2 K and 0.8 K for low and high magnification cases
respectively.
Supplementary Figure 2: Signal timing for thermoreflectance imaging using pulsed boxcar
averaging.
Pulsed boxcar averaging is a complementary variation on the established lock-in homodyne [9]
and lock-in heterodyne [10] thermoreflectance imaging algorithms. For the purposes of this
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study both heterodyne and boxcar averaging provide similar efficacy. We have focused on the
latter method because it offers a combination of good temperature resolution, transient capability
(the subject of a future study for the same network structures), and relatively simple experiment
configuration. Homodyne, heterodyne and boxcar averaging offer similar temperature resolution
(signal to noise ratio.) Extensive comparison of the homodyne and boxcar methods by analyzing
thermal images of microrefrigerators on a chip are presented in [12, 13]. Both heterodyne and
boxcar averaging are capable of high speed transient characterization. The former is
implemented using stroboscopic illumination and analyzed in the frequency domain [14] and the
latter by time-gating the illumination pulse with respect to the boxcar waveform. [11]
The resulting thermoreflectance image is a pixel for pixel map of temperature induced
reflectance change amplitude (ΔR/R) for the sample surface material in response to the applied
bias pulse. This raw thermoreflectance image is converted to a map of sample surface
temperature change by scaling with appropriate thermoreflectance coefficient (CTH).
Thermoreflectance coefficients are material specific parameters that describe optical reflectance
dependence on temperature. Because the amplitude of the thermoreflectance change (for most
metals and semiconductors) is small, typically on the order of 10-4-10-5 K-1, acquisition of
thermoreflectance images with good signal to noise ratio requires averaging over many device
excitation cycles. This method of extracting small signals from background noise by use of an
external reference excitation is commonly called ‘lock-in’ amplification. [10]
Thermoreflectance coefficient, CTH, varies with both illumination wavelength [4, 16] and as a
function of objective magnification (numerical aperture). All measurements were obtained with a
monochromatic LED source centered at 530 nm wavelength. However, unique thermoreflectance
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coefficients had to be estimated for the silver nanowires at the two different numerical apertures
used: 20 X with NA = 0.22, and 100 X with NA = 0.75. In both cases, CTH for the silver
nanowires was estimated indirectly from the measured temperature change on the gold electrode
visible in each thermoreflectance image. For low magnification (20 X) the value of C TH used for
the gold electrode was 2.34 x 10-4/K. This value for CTH_Au was obtained using the experiment
calibration method described in [15] with a gold calibration sample. Our experimentally
calibrated CTH_Au is similar to values reported in other thermoreflectance studies. [4] The
calibrated thermoreflectance coefficient for gold was used to estimate temperature change on the
gold inner electrode for thermoreflectance images acquired at 20 X magnification. Because of
the high thermal conductivity of silver, temperature at the interface of the gold electrode and
adjoining silver nanowires is assumed to be very similar over very short distances (less than 100
nanometers) at thermal steady state. Using this assumption, we estimated temperature change for
the silver nanowires in close proximity to the gold electrode, which was then used to estimate
CTH for the silver nanowires based on the measured thermoreflectance amplitude in those
regions. At 20 X and 530 nm illumination, CTH_Ag was estimated to be 1.7 ± 0.3 x 10-4/K. The
same method was used to estimate CTH_Ag at 100 X, assuming temperature change on the gold
electrode is identical at both magnifications for identical applied bias. At 100 X, CTH_Ag was 1.1
± 0.5 x 10-4/K.
The percolation network structures (nanowire network and the hybrid network) were probed on
the quartz substrates on which the devices were fabricated. An SRS DS345 function generator
supplied a voltage waveform to the pulsing circuit. Amplitude of current across the sample was
monitored precisely on an oscilloscope by measuring the voltage drop across a sense resistor
connected in series with the sample. Quartz substrate was thermally bonded to a large copper
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heat sink maintained at room temperature. System timing, CCD acquisition, sample bias
waveforms, and custom hardware triggers are controlled by a LabVIEW program.
IV. Self-heating model in resistor networks
With a simple resistor network model, this section qualitatively describes that the hot spots are
formed at high resistance points in the hybrid network. We show that the maximum heating
occurs at the weak links in the most conductive paths. This implies that a low-resistance junction
would actually be a cold spot.
Case 1: 1-D networks in parallel
Consider the case shown in figure S4.1. Here, ‘W’ implies ‘Wire’ and ‘J’ implies ‘Junction’. We
wish to compare two pathways, 1 and 2. In path 1, two crossed NWs form a junction, with
resistance RJ1. In path 2, the junction resistance is RJ2.
Supplementary Figure 3: Resistor network model for 1-D networks in parallel
Path 1 has total resistance of
R1 = RW1 + RJ1 +RW1 and a total current of I1 = V/R1
Path 2 has a total resistance of
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R2 = RW2 + RJ2 +RW2 and a total current of I2 = V/R2
If we assume that R1 > R2, then we have I1 < I2. Power (P) = I2 R, so P2 > P1, i.e. the power is
largest within the most conductive path.
Within path 2, I2 is constant. If RJ2 > (RW2+RW2), PRJ2 > PRW2.
Therefore, power (and therefore T) is largest in the weakest links within the most conductive
paths.
Case 2: 2-D network
Next, consider the simple 2-D network shown in figure S4.2. In this case, the resistors represent
junctions, rather than wires; i.e.,
R1 = RW1 + RJ1 + RW1  RJ1
If we assume that R1<< R2 and R3 << R2, R4, and R5 << R4, then the dominant pathway is R1 –
R3 – R5. The current flowing through R3 as a function of R3 is then
I3 = V/ (R1+R3+R5)
P3 = I32 R3= V2 R3 / (R1+R3+R5)2
Supplementary Figure 4: Resistor network model for 2-D networks
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P3 is maximized when R3 = (R1+R5), obtained by setting (dP3/dR3) = 0 (see figure S4.2). In
contrast, the total power in R1 and R5 (denoted “P1_5” in the figure S4.3), the maximum occurs at
R3=0; Indeed P1_5 > P3 until R3 > (R1+R5). As in the 1-D case, we can conclude that the
maximum power (and therefore maximum T) occurs in the weakest link(s) within the most
conductive pathway. We will explore the generality of the conclusion within the framework of
percolation theory in a future publication [9].
Supplementary Figure 5: Plot of power in R3 (i.e., P3) and combined power in R1 and R5 (i.e.,
P1_5) vs R3 for R1+R5=1 k
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V. Microscopic self-heating and coupled electrothermal super-Joule model fitting
Supplementary Figure 6 (a): Microscopic network self-heating and fits for hybrid network
device # 1.
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Full data range
Data range well above noise floor,
Temperature change > 1 K.
Supplementary Figure 6 (b): Microscopic network self-heating and fits for hybrid network
device # 2.
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Full data range
Data range well above noise floor,
Temperature change > 1 K.
Supplementary Figure 6 (c): Microscopic network self-heating and fits for hybrid network
device # 3.
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Full data range
Data range well above noise floor,
Temperature change > 1 K.
Supplementary Figure 6 (d): Microscopic network self-heating and fits for nanowire network
device # 1.
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Full data range
Data range well above noise floor,
Temperature change > 1 K.
Supplementary Figure 6 (e): Microscopic network self-heating and fits for nanowire network
device # 2.
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