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Carbon nanotube thermal probe for quantitative temperature sensing
Accepted Manuscript Title: Carbon nanotube thermal probe for quantitative temperature sensing Author: Jun Hirotani Juo Amano Tatsuya Ikuta Takashi Nishiyama Koji Takahashi PII: DOI: Reference:
S0924-4247(13)00202-1 http://dx.doi.org/doi:10.1016/j.sna.2013.04.038 SNA 8325
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
26-10-2012 16-2-2013 30-4-2013
Please cite this article as: J. Hirotani, J. Amano, T. Ikuta, T. Nishiyama, K. Takahashi, Carbon nanotube thermal probe for quantitative temperature sensing, Sensors and Actuators: A Physical (2013), http://dx.doi.org/10.1016/j.sna.2013.04.038 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Title Carbon nanotube thermal probe for quantitative temperature sensing
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Authors
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Jun Hirotania, Juo Amanoa, Tatsuya Ikutaa, Takashi Nishiyamaa and Koji Takahashia,b,c*
Department of Aeronautics and Astronautics, Graduate school of Engineering,
Kyushu University, Fukuoka 819-0395, Japan
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER),
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b
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a
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Affiliations
Kyushu University, Fukuoka 819-0395, Japan
JST, CREST, Kyushu University, Fukuoka, Japan
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* Corresponding author. Tel: +81 92 806 3016. Fax: +81 92 806 3017. E-mail address: [email protected] (K. Takahashi)
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Highlights A novel surface temperature profiler using a single carbon nanotube is developed. The quantitative temperature measurement is validated. Sensor sensitivity is analyzed and the sensor configuration is optimized. Heating technique at the nanoscale contact point is developed.
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Abstract
Quantitative temperature sensing at the nanoscale point contact is developed using a platinum
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hot film sensor with a carbon nanotube (CNT) as a thermal probe. High spatial resolution and robustness is achieved because of the small tip radius and high stiffness of the CNT. The
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quantitative local temperature at the CNT probe contact point is determined by bringing the
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probe in and out of contact and controlling the amount of heat of the Pt hot film in high vacuum
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environment. Using this method, we overcome the problems of thermal contact resistance (TCR) between the CNT and sample surface. Sensor sensitivity for TCR and thermal
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conductivity measurement of a CNT is analyzed and the sensor configuration is optimized.
Key Words
Quantitative temperature measurement; carbon nanotube; Pt hot film; MEMS
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MAIN TEXT Introduction
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With the continual miniaturization of electronic devices, understanding energy dissipation and transport in micro- and nanodevices is important for designing energy-efficient circuits for
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reliable operation [1,2]. Quantitative temperature sensing of materials are vital not only to obtain
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the material’s own thermophysical properties but also to reveal heat transport mechanisms at
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interfaces and defects. Various experimental techniques exist to obtain the temperature distribution on the micro- and nanoscale in terms of non-contact and contact-type measurements.
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In far-field optical thermal imaging techniques, such as infrared and laser reflectance techniques, the maximum spatial resolution is of the order of its wavelength. Recently, near-field optical thermometry has been proposed [3] and shows high spatial resolution (~100nm). However, the performance of non-contact type thermometry is limited to the optical characteristics of sample surfaces, thus, specific sample surface or surface coating calibrations are necessary to obtain precise signal intensities. To date, several contact-type thermal sensors such as resistance temperature detectors (RTDs) and thermocouples (TCs) have been employed. For example, a thin Wollaston wire mounted on an atomic force microscope (AFM) device [4-6] was used for thermal 3
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measurements, where the Pt-core wire operates as the hot-wire thermometer. By combining wire-type TC with AFM, thermal mapping was successfully demonstrated [7]. For all probes, the spatial resolution is dependent on the size of the contact area and wire-based sensors have
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large contact areas. To overcome this resolution problem, MicroElectro Mechanical Systems
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(MEMS) technology is useful. Recently MEMS-based scanning thermal microscopy (SThM) has been built and tested for a film-type TC consisting of Pt and Cr films deposited on an AFM
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cantilever tip [8,9]. SThM is capable of investigating nanostructures not only structurally but
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also thermally.
For quantitative temperature measurements, the thermal resistance between the SThM tip
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and sample surface needs to be known, thus, contact conditions should be constant during measurements. However, during measurements when the Si-based tip is in contact with the
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sample surface, the tip apex is damaged and the resolution deteriorates with scanning time. The
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shape changes which occur in the tip alter the amount of heat flow from the tip to the sample
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surface because the TCR between tip and sample surface changes. In addition, the local measurement of temperature fields is impeded by heat transfer between the tip and the sample via conduction through both air and the liquid meniscus that exists at the tip-sample interface [8]. Recently, Kim et al. developed an ultra-high vacuum-based SThM technique that is capable of quantitatively mapping temperature fields with ∼15 mK temperature resolution and ∼10 nm spatial resolution [10] by estimating the TCR between a tip and sample surface. However, the scanning tip is damaged and changes shape over time. As the TCR between a tip and sample surface depends on interfacial contact conditions, a systematic calibration is difficult. Therefore, there are two possible ways to improve quantitative temperature measurements in SThM systems. One way involves using a sharper and stiffer tip than the Si-based tip. The second way 4
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is to develop a measurement method which is not affected by SThM tip–sample surface TCR. Nakabeppu et al. have developed a quantitative measurement technique in which a thermocouple monitors the amount of heat and an electric heater ensures that the cantilever
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temperature is the same temperature as the sample surface [11]. Quantitative temperature
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measurement technique [12] is not affected by the TCR, but the resolution and stiffness is restricted by using a Si-based tip.
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Carbon nanotubes (CNTs) consist of honeycomb sp2 hybridized carbon networks that are
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rolled up into seamless cylinders. Because of high thermal conductivity [13,14], high Young’s modulus [15], high aspect ratio, and nanometer-radius tips, CNTs are advantageous compared
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with Si-based materials for use as AFM and SThM tips. AFM lateral resolution is governed by the shape of the tip and high spatial resolution has been achieved in AFM measurements with
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CNT tips [16]. A heated AFM tip [17] can be used for local heating, which can analyze local
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thermal effects such as phase-transitions and processing. In the past studies, a CNT thermal
[19].
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probe was also used as local heating for thermo-mechanical data storage [18] and SThM tip
In this work, we have developed a novel measurement technique which can measure the surface temperature quantitatively by using a Pt hot film sensor with a single CNT. The CNT is fixed at one end to the platinum hot film sensor and the other end can be in contact with the sample surface. The Pt hot film acts as a heater and thermometer, it controls the amount of heat and measures the temperature at the same time. The sample surface temperature is determined from the electrical resistance and pre-measured temperature-resistance coefficient of the platinum hot film [20]. TCR between the CNT and sample surface is avoided as a feedback system controls the Pt hot film heating rate, and quantitative temperature measurements are 5
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obtained. To date, the TCR of a CNT has been evaluated from estimated thermal conductivities which have error margin, thus measuring the actual thermal conductivity of a CNT leads to a more
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accurate TCR value. We have improved the measurement method of the TCR between a single
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CNT and a solid surface [21] by measuring the actual CNT thermal conductivity. However, measuring the CNT thermal conductivity reduces the TCR detection sensor sensitivity. Thus, the
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sensor sensitivity of both the thermal conductivity measurements and the TCR is analyzed to
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optimize sensor configuration and sensitivity.
Measurement methods in this work are an extension of the method of T-type nanosensors
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which measure CNT thermal conductivities [14,22]. We measure the surface temperature of a line-patterned metallic film deposited on a SiO2 substrate. In addition, we evaluate the
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sensitivity of a Pt hot film sensor depending on its configuration. We also report that heating at
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the contact point between a CNT and an arbitrary surface can be achieved once the CNT’s TCR
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and thermal conductivity is known.
2 Temperature measurement 2.1 Measurement principle
The heat transfer model of the sensor is shown in Fig. 1, where k is the thermal conductivity, A is the cross-sectional area, L is the length of Pt film, xi (i=1-3) define the distances along the Pt film (in relation to the CNT), and T0 is the heat sink temperature. The subscripts h and f refer to the Pt hot film and the CNT, respectively. The Joule heating induced by a direct current is uniform in the suspended film with a constant cross-sectional area. We assume one-dimensional (1D) heat flow along the hot-film because of the high aspect ratio of the film. As the 6
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experiments are conducted under high vacuum conditions (10-3 Pa), heat convection is negligible. Thermal radiation is also negligible because the Pt hot film average temperature increase is less than 10 K. Here we note that the Pt hot film is fully suspended between two heat
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sinks (does not rest on the substrate), thus the heat conduction in this film is analyzed using
2Ti ( xi ) qh 0 xi 2
for i 1, 2
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kh
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simple 1D heat conduction equation, as shown in Eq. (1),
The Joule heating per unit volume and time, qh is Qh Ah ( L1 L2 )
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qh
(1)
(2)
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and the heat generation of Pt hot film, Qh is given by Qh=IV. I is the electrical current and V is the voltage. When no heat is generated in the CNT, the equation is
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2T3 ( x3 ) 0 x3 2
(3)
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kf
By solving Eqs. (1) and (3), the temperature at points x1, x2, and x3 can be obtained: Qh x12 C1 x1 C2 2kh Ah ( L1 L2 )
(4)
T2 ( x2 )
Qh x22 C3 x2 C4 2kh Ah ( L1 L2 )
(5)
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T1 ( x1 )
T3 ( x3 ) C5 x3 C6
(6)
where C1 - C6 are integration constants. When the CNT probe is not in contact with the surface, C1 - C4 are determined by applying the boundary condition that the surface film temperature is equal to that of the SiO2/Si wafer, T0. Ti (0) Ti ( L1 L2 ) T0
for i 1, 2
(7)
Therefore, the temperature distribution in the Pt film is given by 7
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T1 ( x1 )
Qh Qh x12 x1 T0 2kh Ah ( L1 L2 ) 2kh Ah
(8)
T2(x2) is expressed the same way, and the hot-film temperature at the CNT-Pt junction, Tj is
Qh L1 L2 T0 2kh Ah L1 L2
(9)
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T j T1 ( L1 ) T2 ( L2 )
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obtained by substituting L1 (or L2) for x1 (or x2)
When the CNT is in contact with the sample surface, the boundary conditions are for i 1, 2
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Ti ( xi 0) T0 T1 ( L1 ) T2 ( L2 )
T3 ( x3 ) T ( L ) T3 (0) 1 1 x3 x 0 Rj
k f Af
T ( L ) Ts T3 ( x3 ) 3 f x3 x L Re f
(12)
(13)
(14)
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3
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3
(11)
x3 0
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k f Af
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T ( x ) T ( x ) T ( x ) k f Af 3 3 kh Ah 1 1 2 2 x2 x L x3 x1 x1 L1 2 2
(10)
where Ts is the sample surface temperature, R is the TCR, and subscripts j and e denote the
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Pt-CNT and CNT-sample interfaces, respectively. By solving Eqs. (4)-(6) (for details see Ref. [21]) the temperature profiles are obtained. The temperature of the Pt hot film is affected by the thermal resistances of a CNT, and by two TCRs, Rj and Re. If the Pt/CNT junction temperature, Tj is higher than that of the sample surface, Ts, (Tj > Ts), a portion of heat in the hot film goes to the target on the surface and the temperature profile changes (see dotted line in Fig. 1). In contrast, if the junction temperature, Tj is lower than the sample surface temperature, Ts, (Tj < Ts), heat comes from the sample surface through the CNT to the Pt film. Hence, the Pt film gets additional heat and the temperature distribution in the film follows the dashed line shown in Fig 1. However, when the CNT-junction temperature is the 8
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same as the target surface temperature, (Tj = Ts), heat flow through the CNT does not occur and the temperature of the target surface and the hot-film at the CNT-Pt junction is the same. We control the hot-film temperature by changing the heat generation in the Pt hot film; this ensures
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that the temperature at the CNT-Pt junction and the target surface are the same. Therefore, the
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sample surface temperature can be quantitatively estimated when the temperature of the Pt hot-film in the non-contact case and in the contact case, are the same.
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The sample surface temperature is estimated using Eq. (9). The average thermal conductivity
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of the Pt hot film is estimated from the average temperature, Tave and the premeasured relationship between the thermal conductivity and temperature in the hot film. Because the
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relationship between the temperature and resistance of platinum is linear over a wide temperature range, Tave is associated with the electrical resistance of the hot film, Rh as ave
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Rh – Rref)ref Here is the pre-measured temperature coefficient of resistance of the Pt
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hot film, and Rref is the electrical resistance at the reference temperature Tref. In this study, Tref is
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300 K and Tave is estimated from Rref at 300 K.
2.2 Experiments
The SEM image of the fabricated sensor and the TEM image of a multi-walled CNT whose diameter is 70 nm are shown in Fig. 2. The CNT protrudes from the edge of the SiO2/Si substrate, and can be in contact with the sample surface. The experimental procedure is outlined in the flowchart in Fig. 3. First, an electrical current is applied to a Pt hot film, and the voltage of the Joule-heated hot film, Vbefore is measured. Then, if the voltage after contact, Vafter is not the same with Vbefore when the CNT contacts with the sample surface, the CNT is detached from sample surface and an increase/decrease applied electrical current to meet Vbefore with Vafter. By 9
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repeating this process, the difference between Vbefore and Vafter becomes less than the voltage fluctuation caused by the controlled-temperature instability; and the condition Vbefore=Vafter is met. Finally, we calculate the electrical resistance of the hot film, Rave from Vbefore (Vafter) and the
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applied electrical current I, and estimate the sample temperature, Ts. The temperature of the
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CNT probe sensor is controlled and monitored by a peltier device and thermometer, respectively. We checked the validity of our thermal sensor by contacting a CNT probe with the reference
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sample whose temperature is monitored by a thermocouple. As shown in Table 1, there is good
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agreement (within 1 K) between the estimated temperature from our method and the measured temperature of a sample surface. Hence, the validity of our temperature measurement technique
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is confirmed.
A patterned platinum/titanium film is prepared, and the line-patterned heater is connected
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with two electrodes (Fig. 4A). The length and width of the heater is 9.73 m and 604 nm,
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respectively. The 50-nm-thick heater consists of Pt (42 nm) and Ti (8 nm) layers, and the film is
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deposited on a 200 nm-thick SiO2 layer. The longitudinal direction is defined as the direction along the line heater, and the transverse direction is perpendicular to the longitudinal direction. The fabricated heater has a high aspect ratio so one dimensional heat flow along the longitudinal direction is plausible. We applied electrical currents of 1.5 mA and 3.0 mA and measured the temperature in two directions for each electrical current. Fig. 4B shows the SEM image of the CNT in contact with the target surface. In our experiment, the moment of probe contact with a sample surface is identified by electrical resistance signal of the Pt hot film, which changes due to the temperature gap. However, we will combine atomic force microscopy (AFM) with our method for greater spatial and temperature resolution. The measured temperature profile in the longitudinal direction is shown in Fig. 5A. The 10
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temperature at both ends of the heater at 3.0 mA is higher than that obtained under 1.5 mA because of high heat generation, however at the extreme ends of the heat sink (on which the heater is placed) the temperature is considered to be almost the same as the ambient temperature
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The temperature profile along the transverse directions is shown in Fig. 5B. The measured
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temperature at 1.5 m from the edge of the heater is almost the same as the room temperature at
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1.5 and 3.0mA.
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3. CNT thermal contact resistance and thermal conductivity measurements As shown in Fig. 6A, the thermal conductivity of a single CNT can be measured by a T-type
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nanosensor [14]. Fig. 6B shows the heat transfer model of the measurement method of the TCR between a CNT end and solid surface [21]. Our developed system is shown in Fig. 6C, which
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can measure both the thermal conductivity of a single CNT and the TCR between a CNT and solid surface. This new system is beneficial as both the thermal conductivity and the TCR of a
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CNT are measured. However, the electrical resistance change decreases when the CNT contacts the solid surface compared with the case of Fig.6B. Therefore, we have employed the sensor sensitivity analysis proposed by Dames et al [23] to confirm the detectable electrical resistance change.
First, the temperature distribution of a Pt hot film without a CNT, Tbefore is same with Eq. (8), and we assume that a CNT is set on the middle of the Pt hot film (L1=L2=L/2). Thus, the temperature increase per unit volume of a Pt hot film, T1,vol, is calculated as L
T1,vol
1 QL 1 Tbefore ( x) T0 dx QRPt L0 12kh Ah 12
(15) 11
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Here, Q is the heat generation, RPt is the thermal resistance of a Pt hot film, and x is the coordinate along the Pt hot film.
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Next, we consider the case of the thermal conductivity measurement of a CNT in Fig.6A. In the thermal conductivity measurement [14], a portion of the Joule heat in a Pt hot film goes
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through the CNT into heat sink, which depends on the thermal resistance ratio between a Pt hot
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film, RPt and the thermal resistance of a CNT, RCNT,f =Lf /(kf Af). Therefore, we define the thermal resistance ratio, as
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RPt 4 RCNT , f
(16)
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1
The temperature distribution of a Pt hot film in Fig.6A, Tafter is expressed as
L1 ( L1 L2 ) RCNT , f L2 Ah Q Q x12 x1 T0 2kh Ah ( L1 L2 ) 2 Ah ( L1 L2 ) kh L1 L2 ( L1 L2 ) RCNT , f kh Ah
(17)
T2, after ( x2 )
L2 ( L1 L2 ) RCNT , f L1 Ah Q Q x22 x2 T0 2kh Ah ( L1 L2 ) 2 Ah ( L1 L2 ) kh L1L2 ( L1 L2 ) RCNT , f kh Ah
(18)
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T1, after ( x1 )
The temperature increase per unit volume for thermal conductivity measurement of a CNT, T2,vol, is calculated by
T2,vol
L L/ 2 L /2 1 1 T x T dx T x T dx T2,after ( x2 ) T0 dx2 ( ) ( ) 1,after 1 0 0 1 after L0 L 0 0
1 3 RPt 3 1 1 QRPt 1 1 1 T1,vol 1 1 4 4R 12 4 CNT , f
1
1
(19)
Here we define the dimensionless sensor sensitivity of the Pt hot film for thermal conductivity measurement of a CNT, S1 as 12
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S1
T2,vol T1,vol RCNT , f RCNT , f
(20)
By combining Eqs. (19) and (20), S1 can be re-written as Eq. (21) as previously shown [23]
3 1/ 2 1 / 2 1 1 4
2
(21)
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S1
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Finally, we consider the case of the thermal contact resistance measurement of a CNT. The temperature distribution of the Pt hot film in Fig.6C, Tfinal is obtained by solving Eqs. (4)-(6),
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and Eq. (22) under the boundary conditions from Eqs. (23)-(27). T4 ( x 4 ) C 7 x 4 C 8
for i 1, 2
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Ti ( xi 0) T0
(23) (24)
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T4 ( x4 L f ) T0
T1 ( x1 L1 ) T2 ( x 2 L2 ) T3 ( x3 0) T4 ( x 4 0) kh Ah x1 L1
T3 ( x3 L p ) T0
k f Af
k f Af x2 L2
T3 x3
T3 x3
k f Af
x3 0
T4 x4
(26) x4 0
(27)
x3 L p
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Re
T2 x2
d
T1 x1
(25)
te
kh Ah
(22)
Temperature distributions of the Pt hot film in Fig.6C are determined as follows.
T1, final ( x1 )
Q x12 C1x1 T0 2kh Ah ( L1 L2 )
(28)
Q x22 C3 x2 T0 2kh Ah ( L1 L2 )
(29)
T2, final ( x2 )
Here, C1 and C3 are constants of integration expressed by C1
1 L1
QL12 T0 2 k h Ah ( L1 L2 )
( L L2 ) k h Ah L f T0 Q ( L p k f A f Re ) T0 1 T0 L f k f Af L1 L2 2 k h Ah ( L1 L2 ) ( L L2 ) k h Ah L f ( L p k f A f Re ) 1 1 Lf L1 L2 k f A f
(30)
13
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QL2 2 T0 2 k h Ah ( L1 L2 )
( L L2 ) k h Ah L f T0 Q ( L p k f A f Re ) T0 1 T0 L f k f Af L1 L2 2 k h Ah ( L1 L2 ) ( L L2 ) k h Ah L f ( L p k f A f Re ) 1 1 Lf L1 L2 k f A f
(31)
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1 L2
C3
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We analyze the sensor sensitivity of the TCR measurements. Here, we define the dimensionless thermal resistance ratio, as
Lp k f Af
Re RCNT , p Re
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R3,total
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RPt 4 R3,total
2
(32)
(33)
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Here, R3,total is total of thermal resistances of a CNT probe and thermal contact resistance between a CNT end and sample surface. Then, the temperature increase per unit volume, T3,vol is
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expressed as L L /2 L /2 1 1 T x T dx T x T dx T2, final ( x2 ) T0 dx2 ( ) ( ) 1, final 1 final 0 0 1 L0 L 0 0 3 1 1 16 RCNT , f R3,total T1,vol 1 1 1 1 1 4 RCNT , f R3,total RPt
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te
T3,vol
(34)
and the sensor sensitivity S2 is defined and derived as S2
S2
T3,vol T1,vol R3,total R3,total
3 1/ 2 1 / 2 2 1 1 2 4
(35)
2
(36)
Fig. 7 shows the sensitivity S2 as a function of As seen in the range of 10-1< < 100 and when is 100, good sensitivity for both thermal conductivity and TCR measurements are obtained. 14
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4. Control of heat transport at the CNT point contact Nano probe sensors are applicable for controlling local heating at the nanoscale. We consider
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the situation that the temperature of the Pt hot film–CNT junction, Tj is higher than the
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temperature of the sample surface, Ts. (Tj > Ts). Here Ts is assumed to be equal to the heat sink temperature, T0 (Ts =T0). Under these conditions, the heat transfer rate depends on the thermal
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resistances, Rj, RCNT and Re, which can be determined by the TCR measurements method of a
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CNT, as described in Ref. 21. In the supplementary information of the Ref. 21, the CNT temperature distribution, T3 is described as
L1 L2Q x3 2k f Af L1 L2 ( L1 L2 )( R j RCNT Re )kh Ah
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T3 ( x3 )
(37)
d
L1 L2 ( RCNT Re )Q T0 2 L1 L2 ( L1 L2 )( R j RCNT Re ) kh Ah
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Then, the heat-transfer rate through a CNT ,QCNT, is obtained by Fourier’s law as QCNT =-kf Af
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dT3/dx3. Hence, the heating rate through a CNT at the contact point is expressed as
QCNT
L1 L2Q 2 L1 L2 ( L1 L2 )( R j RCNT Re )kh Ah
(38)
As previously reported, the change in the measured electrical resistance is 0.415 ohms (on average) for a CNT when it comes in contact with the target surface during DC heating [21]. From this electrical resistance change R, (Rj+RCNT+Re) is estimated as 1.70×107 K/W. The heat transfer rate in this experiment is estimated from Eq. (38) as 0.784 [W]. Here, we note that the TCR and thermal conductivity of the CNT does not vary with temperature for small temperature changes (~10K) around room temperature conditions. The heat transfer rate applied at the CNT contact point can be controlled by changing the heat generation of the Pt hot film, Q. In this 15
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section, we assume that surface temperature and thermal contact resistance are constant, but heating depends on complicated interfacial phenomena such as contact conditions, which should
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be investigated in the future.
5. Summary
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Novel surface temperature profiler using a single CNT is developed, which enable us to
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quantitatively measure the surface temperature. In this measurement, the problem of the thermal contact resistance between a CNT end and sample surface is avoided and high spatial resolution
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is achieved because of the small CNT tip radius. In additional application of a Pt hot film sensor, thermal contact resistance measurement of a carbon nanotube and local heating at the point
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contact place of a carbon nanotube end are introduced. We envisage that these measurement
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methods are applicable for different fiber materials. Our new proposed method has great
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potential to reveal nanoscale heat transport phenomena and in the future we will measure the thermal profile of nanomaterials.
ACKNOWLEDGEMENTS
This work was partially supported by Grants-in-Aid for Scientific Research (23360101, 23656153, 23760191, 24560237) and a Grant-in-Aid for JSPS Fellows (231457). Sensor fabrication was partially conducted at the Collabo-Station II of Kyushu University. The HRTEM and AFM observations were conducted in the Research Laboratory for High Voltage Electron Microscopy and in the Center of Advanced Instrumental Analysis, Kyushu University, respectively. 16
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Biographies
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J. Hirotani is currently a PhD candidate in Kyushu University. He has been a research fellow of
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the Japan Society for the Promotion of Science (JSPS) since 2011. His current research interests include thermal transport at interfaces, thermophysical properties of nanomaterials, scanning
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thermal microscopy and MEMS.
J. Amano received his Bachelor degree from the Department of Aeronautics and Astronautics,
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Kyushu University, Fukuoka, Japan, in 2012. His research during that period was on plasma
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radiation, rarefied gas dynamics, and thermal protection systems (TPS) for reentry vehicles. He
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is currently enrolled as a master student at Kyushu University. His research interests are in near-field radiation, nano probe sensors, and MEMS. T. Ikuta is currently the Chief Technical Official of the Department of Aeronautics and Astronautics, Graduate school of Engineering, Kyushu University. His research interests include investigating micro/nano thermo-fluid systems using MEMS. T. Nishiyama received his B.E. (1998), M.E. (2000), D.E. (2010) from Kyushu University. He is currently the Assistant Professor of the Department of Aeronautics and Astronautics, Faculty of Engineering, Kyushu University. His research interests include fabrication and characterization of functional thin films. K. Takahashi received his PhD in engineering from the University of Tokyo in 1992 and is a 17
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Professor at the Department of Aeronautics and Astronautics, Kyushu University. His current research interests are thermophysical properties of nanomaterials, nanoscale heat and mass
cr
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transfer and MEMS.
References
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[1] D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin,
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thermal microscopy of graphite, Langmuir, 13, (1997) 4493-4497 [5] S. Volz, X. Feng, C. Fuentes, P. Guérin and M. Jaouen, Thermal conductivity measurements of thin amorphous silicon films by scanning thermal microscopy, International Journal of Thermophysics, 23 (2002) 1645–1657 [6] S. Lefe`vre, S. Volz and P. Chapuis, Nanoscale heat transfer at contact between a hot tip and a substrate, International Journal of Heat and Mass Transfer, 49 (2006) 251–258. [7] A. Majumdar, J. P. Carrejo and J. Lai, Thermal imaging using the atomic force microscope, Applied Physics Letters, 62 (1993) 2501 –2503 [8] L. Shi, S. Plyasunov, A. Bachtold, P. L. McEuen and A. Majumdar, Scanning thermal microscopy of carbon nanotubes using batch-fabricated probes, Applied Physics Letters, 77 18
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[10] K. Kim, W. Jeong, W. Lee and P. Reddy, Ultra-high vacuum scanning thermal microscopy
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for nanometer resolution quantitative thermometry, ACS Nano, 6 (2012) 4248–4257
[11] O. Nakabeppu and T. Suzuki, Microscale temperature measurement by scanning thermal
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microscopy, Journal of Thermal Analysis and Calorimetry, 69 (2002) 727-737
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[12] J. Chung, K. Kim, G. Hwang, O. Kwon, S. Jung, J. Lee, J. W. Lee, and G. T. Kim, Quantitative temperature measurement of an electrically heated carbon nanotube using the
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null-point method, Review of Scientific Instruments, 81, (2010), 114901 [13] P. Kim, L. Shi, A. Majumdar, and P. L. McEuen, Thermal Transport Measurements of
d
Individual Multiwalled Nanotubes, Physical Review Letters, 87, (2001), 215502
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[14] M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, and T. Shimizu,
Ac ce p
Measuring the thermal conductivity of a single carbon nanotube, Physical Review Letter, 95 (2005) 065502
[15] M. M. J. Treacy, T. W. Ebbesen, and J. M. Gibson, Exceptionally high Young's modulus observed for individual carbon nanotubes, Nature, 381, (1996), 678-680 [16] N. R. Wilson and J. V. Macpherson, carbon nanotube tips for atomic force microscopy, Nature nanotechnology, 4 (2009) 483-491 [17] B. A. Nelson and W.P. King, Temperature caribration of heated silicon atomic force microscope cantilevers, Sensors and Actuators A, 140 (2007) 51-59 [18] M. A. Lantz, B. Gotsmann, U. T. Durig, P. Vettiger, Y. Nakayama, T. Shimizu, and H. Tokumoto, Carbon nanotube tips for thermomechanical data storage, Applied Physics Letter, 19
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83 (2003) 1266-1268 [19] P. Tovee, M. Pumarol, D. Zeze, K. Kjoller, and O. Kolosov, Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials, Journal of Applied Physics, 112, (2012) 114317
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[20] X. Zhang, H. Xie, M. Fujii, H. Ago, K. Takahashi, and T. Ikuta, H. Abe, and T. Shimizu,
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thermal and electrical conductivity of a suspended platinum nanofilm, Applied Physics Letter, 86 (2005) 171912
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[21] J. Hirotani, T. Ikuta, T. Nishiyama and K. Takahashi, Thermal boundary resistance
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between the end of an individual carbon nanotube and a Au surface, Nanotechnology 22 (2011) 315702
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[22] M. F. P. Bifano, J. Park, P. B. Kaul, A. K. Roy, and V. Prakash, Effects of heat treatment and contact resistance on the thermal conductivity of individual multiwalled carbon
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054321
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nanotubes using a Wollaston wire thermal probe, Journal of Applied Physics, 111, (2012)
Ac ce p
[23] C. Dames S. Chen C. T. Harris J. Y. Huang Z. F. Ren M. S. Dresselhaus G. Chen, A hot-wire probe for thermal measurements of nanowires and nanotubes inside a transmission electron microscope, Review of Scientific Instruments, 78 (2007) 104903
20
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Figures and figure captions
Fig.1 Heat transfer model of a suspended platinum hot film with a single carbon nanotube probe.
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Tj and Ts are the hot-film temperatures at the CNT-Pt junction and sample surface temperature,
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respectively. The temperature distribution along the Pt film for three cases are shown: CNT-Pt
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Ts.
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junction temperature, Tj, is same as the sample surface temperature, Ts, or higher, or lower than
Page 21 of 28
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Fig. 2 SEM image of the fabricated sensor. The CNT is fixed on the Pt hot film and protrudes
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from the silicon substrate. Two Pt electrodes work as heat sinks. Inset: HRTEM image of the
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d
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multi-walled CNT tip.
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Fig. 3 Flow chart of the experimental procedure. Vbefore and Vafter represent the voltage of the Pt hot film in CNT non-contact and contact modes, respectively. Electrical current I changes the heat generation to meet the Vbefore =Vafter. When Vbefore = Vafter, Ts, =Tj.
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Table 1 Comparison of temperatures obtained from the thermometer and from our measured
Ac ce p
te
d
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an
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cr
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data at the sample surface.
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Fig. 4 (A) Schematic diagram of a temperature measurement using a carbon nanotube probe.
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The sample is a line-patterned Pt/Ti film, and line patterned heater is connected to electrodes. The coordinates are defined as along the line heater (longitudinal direction) and perpendicular to the line heater (transverse direction). The contact point of the carbon nanotube probe on the sample surface is arbitrary. (B) SEM images of the CNT in contact with (top image) the line patterned Pt/Ti heater and (bottom image) the substrate, during temperature measurements along the transverse direction.
Page 25 of 28
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Fig. 5 (A) Temperature measurements along the Pt heater (longitudinal direction) for the 3.0 mA
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and 1.5 mA heating cases. Dashed line is room temperature in the experiment as 302 K. (B) Sample surface temperature distributions perpendicular to the Pt heater (transverse direction).
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The origin is the edge of the Pt/Ti heater. Measured temperatures are the same as the the room
Ac ce p
te
d
temperature at about 1.5 m distance away from the heater.
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Fig. 6 Heat transfer model for (A) single CNT thermal conductivity measurements, (B) single CNT TCR measurements , (C) combined A and B systems. The generated heat in the Pt hot film dissipates in three (before contact) or four directions (after contact) in the TCR measurements. (D) SEM image of a fabricated sensor. The CNT is fixed on the heat sink (CNT end) and Pt hot film (CNT middle), and protrudes from the SiO2/Si edge.
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Fig. 7 Sensor sensitivity vs. thermal resistance ratio. Inset: Relationship between 1 and S1. Area
Ac ce p
te
d
of good sensitivity is indicated where 10-1< < 100 and is 100.
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S0924-4247(13)00202-1 http://dx.doi.org/doi:10.1016/j.sna.2013.04.038 SNA 8325
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
26-10-2012 16-2-2013 30-4-2013
Please cite this article as: J. Hirotani, J. Amano, T. Ikuta, T. Nishiyama, K. Takahashi, Carbon nanotube thermal probe for quantitative temperature sensing, Sensors and Actuators: A Physical (2013), http://dx.doi.org/10.1016/j.sna.2013.04.038 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Title Carbon nanotube thermal probe for quantitative temperature sensing
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Authors
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Jun Hirotania, Juo Amanoa, Tatsuya Ikutaa, Takashi Nishiyamaa and Koji Takahashia,b,c*
Department of Aeronautics and Astronautics, Graduate school of Engineering,
Kyushu University, Fukuoka 819-0395, Japan
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER),
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b
an
a
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Affiliations
Kyushu University, Fukuoka 819-0395, Japan
JST, CREST, Kyushu University, Fukuoka, Japan
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c
* Corresponding author. Tel: +81 92 806 3016. Fax: +81 92 806 3017. E-mail address: [email protected] (K. Takahashi)
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Highlights A novel surface temperature profiler using a single carbon nanotube is developed. The quantitative temperature measurement is validated. Sensor sensitivity is analyzed and the sensor configuration is optimized. Heating technique at the nanoscale contact point is developed.
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Abstract
Quantitative temperature sensing at the nanoscale point contact is developed using a platinum
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hot film sensor with a carbon nanotube (CNT) as a thermal probe. High spatial resolution and robustness is achieved because of the small tip radius and high stiffness of the CNT. The
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quantitative local temperature at the CNT probe contact point is determined by bringing the
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probe in and out of contact and controlling the amount of heat of the Pt hot film in high vacuum
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environment. Using this method, we overcome the problems of thermal contact resistance (TCR) between the CNT and sample surface. Sensor sensitivity for TCR and thermal
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conductivity measurement of a CNT is analyzed and the sensor configuration is optimized.
Key Words
Quantitative temperature measurement; carbon nanotube; Pt hot film; MEMS
2
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MAIN TEXT Introduction
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With the continual miniaturization of electronic devices, understanding energy dissipation and transport in micro- and nanodevices is important for designing energy-efficient circuits for
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reliable operation [1,2]. Quantitative temperature sensing of materials are vital not only to obtain
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the material’s own thermophysical properties but also to reveal heat transport mechanisms at
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interfaces and defects. Various experimental techniques exist to obtain the temperature distribution on the micro- and nanoscale in terms of non-contact and contact-type measurements.
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In far-field optical thermal imaging techniques, such as infrared and laser reflectance techniques, the maximum spatial resolution is of the order of its wavelength. Recently, near-field optical thermometry has been proposed [3] and shows high spatial resolution (~100nm). However, the performance of non-contact type thermometry is limited to the optical characteristics of sample surfaces, thus, specific sample surface or surface coating calibrations are necessary to obtain precise signal intensities. To date, several contact-type thermal sensors such as resistance temperature detectors (RTDs) and thermocouples (TCs) have been employed. For example, a thin Wollaston wire mounted on an atomic force microscope (AFM) device [4-6] was used for thermal 3
Page 3 of 28
measurements, where the Pt-core wire operates as the hot-wire thermometer. By combining wire-type TC with AFM, thermal mapping was successfully demonstrated [7]. For all probes, the spatial resolution is dependent on the size of the contact area and wire-based sensors have
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large contact areas. To overcome this resolution problem, MicroElectro Mechanical Systems
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(MEMS) technology is useful. Recently MEMS-based scanning thermal microscopy (SThM) has been built and tested for a film-type TC consisting of Pt and Cr films deposited on an AFM
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cantilever tip [8,9]. SThM is capable of investigating nanostructures not only structurally but
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also thermally.
For quantitative temperature measurements, the thermal resistance between the SThM tip
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and sample surface needs to be known, thus, contact conditions should be constant during measurements. However, during measurements when the Si-based tip is in contact with the
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sample surface, the tip apex is damaged and the resolution deteriorates with scanning time. The
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shape changes which occur in the tip alter the amount of heat flow from the tip to the sample
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surface because the TCR between tip and sample surface changes. In addition, the local measurement of temperature fields is impeded by heat transfer between the tip and the sample via conduction through both air and the liquid meniscus that exists at the tip-sample interface [8]. Recently, Kim et al. developed an ultra-high vacuum-based SThM technique that is capable of quantitatively mapping temperature fields with ∼15 mK temperature resolution and ∼10 nm spatial resolution [10] by estimating the TCR between a tip and sample surface. However, the scanning tip is damaged and changes shape over time. As the TCR between a tip and sample surface depends on interfacial contact conditions, a systematic calibration is difficult. Therefore, there are two possible ways to improve quantitative temperature measurements in SThM systems. One way involves using a sharper and stiffer tip than the Si-based tip. The second way 4
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is to develop a measurement method which is not affected by SThM tip–sample surface TCR. Nakabeppu et al. have developed a quantitative measurement technique in which a thermocouple monitors the amount of heat and an electric heater ensures that the cantilever
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temperature is the same temperature as the sample surface [11]. Quantitative temperature
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measurement technique [12] is not affected by the TCR, but the resolution and stiffness is restricted by using a Si-based tip.
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Carbon nanotubes (CNTs) consist of honeycomb sp2 hybridized carbon networks that are
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rolled up into seamless cylinders. Because of high thermal conductivity [13,14], high Young’s modulus [15], high aspect ratio, and nanometer-radius tips, CNTs are advantageous compared
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with Si-based materials for use as AFM and SThM tips. AFM lateral resolution is governed by the shape of the tip and high spatial resolution has been achieved in AFM measurements with
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CNT tips [16]. A heated AFM tip [17] can be used for local heating, which can analyze local
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thermal effects such as phase-transitions and processing. In the past studies, a CNT thermal
[19].
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probe was also used as local heating for thermo-mechanical data storage [18] and SThM tip
In this work, we have developed a novel measurement technique which can measure the surface temperature quantitatively by using a Pt hot film sensor with a single CNT. The CNT is fixed at one end to the platinum hot film sensor and the other end can be in contact with the sample surface. The Pt hot film acts as a heater and thermometer, it controls the amount of heat and measures the temperature at the same time. The sample surface temperature is determined from the electrical resistance and pre-measured temperature-resistance coefficient of the platinum hot film [20]. TCR between the CNT and sample surface is avoided as a feedback system controls the Pt hot film heating rate, and quantitative temperature measurements are 5
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obtained. To date, the TCR of a CNT has been evaluated from estimated thermal conductivities which have error margin, thus measuring the actual thermal conductivity of a CNT leads to a more
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accurate TCR value. We have improved the measurement method of the TCR between a single
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CNT and a solid surface [21] by measuring the actual CNT thermal conductivity. However, measuring the CNT thermal conductivity reduces the TCR detection sensor sensitivity. Thus, the
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sensor sensitivity of both the thermal conductivity measurements and the TCR is analyzed to
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optimize sensor configuration and sensitivity.
Measurement methods in this work are an extension of the method of T-type nanosensors
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which measure CNT thermal conductivities [14,22]. We measure the surface temperature of a line-patterned metallic film deposited on a SiO2 substrate. In addition, we evaluate the
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sensitivity of a Pt hot film sensor depending on its configuration. We also report that heating at
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the contact point between a CNT and an arbitrary surface can be achieved once the CNT’s TCR
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and thermal conductivity is known.
2 Temperature measurement 2.1 Measurement principle
The heat transfer model of the sensor is shown in Fig. 1, where k is the thermal conductivity, A is the cross-sectional area, L is the length of Pt film, xi (i=1-3) define the distances along the Pt film (in relation to the CNT), and T0 is the heat sink temperature. The subscripts h and f refer to the Pt hot film and the CNT, respectively. The Joule heating induced by a direct current is uniform in the suspended film with a constant cross-sectional area. We assume one-dimensional (1D) heat flow along the hot-film because of the high aspect ratio of the film. As the 6
Page 6 of 28
experiments are conducted under high vacuum conditions (10-3 Pa), heat convection is negligible. Thermal radiation is also negligible because the Pt hot film average temperature increase is less than 10 K. Here we note that the Pt hot film is fully suspended between two heat
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sinks (does not rest on the substrate), thus the heat conduction in this film is analyzed using
2Ti ( xi ) qh 0 xi 2
for i 1, 2
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kh
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simple 1D heat conduction equation, as shown in Eq. (1),
The Joule heating per unit volume and time, qh is Qh Ah ( L1 L2 )
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qh
(1)
(2)
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and the heat generation of Pt hot film, Qh is given by Qh=IV. I is the electrical current and V is the voltage. When no heat is generated in the CNT, the equation is
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2T3 ( x3 ) 0 x3 2
(3)
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kf
By solving Eqs. (1) and (3), the temperature at points x1, x2, and x3 can be obtained: Qh x12 C1 x1 C2 2kh Ah ( L1 L2 )
(4)
T2 ( x2 )
Qh x22 C3 x2 C4 2kh Ah ( L1 L2 )
(5)
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T1 ( x1 )
T3 ( x3 ) C5 x3 C6
(6)
where C1 - C6 are integration constants. When the CNT probe is not in contact with the surface, C1 - C4 are determined by applying the boundary condition that the surface film temperature is equal to that of the SiO2/Si wafer, T0. Ti (0) Ti ( L1 L2 ) T0
for i 1, 2
(7)
Therefore, the temperature distribution in the Pt film is given by 7
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T1 ( x1 )
Qh Qh x12 x1 T0 2kh Ah ( L1 L2 ) 2kh Ah
(8)
T2(x2) is expressed the same way, and the hot-film temperature at the CNT-Pt junction, Tj is
Qh L1 L2 T0 2kh Ah L1 L2
(9)
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T j T1 ( L1 ) T2 ( L2 )
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obtained by substituting L1 (or L2) for x1 (or x2)
When the CNT is in contact with the sample surface, the boundary conditions are for i 1, 2
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Ti ( xi 0) T0 T1 ( L1 ) T2 ( L2 )
T3 ( x3 ) T ( L ) T3 (0) 1 1 x3 x 0 Rj
k f Af
T ( L ) Ts T3 ( x3 ) 3 f x3 x L Re f
(12)
(13)
(14)
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3
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3
(11)
x3 0
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k f Af
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T ( x ) T ( x ) T ( x ) k f Af 3 3 kh Ah 1 1 2 2 x2 x L x3 x1 x1 L1 2 2
(10)
where Ts is the sample surface temperature, R is the TCR, and subscripts j and e denote the
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Pt-CNT and CNT-sample interfaces, respectively. By solving Eqs. (4)-(6) (for details see Ref. [21]) the temperature profiles are obtained. The temperature of the Pt hot film is affected by the thermal resistances of a CNT, and by two TCRs, Rj and Re. If the Pt/CNT junction temperature, Tj is higher than that of the sample surface, Ts, (Tj > Ts), a portion of heat in the hot film goes to the target on the surface and the temperature profile changes (see dotted line in Fig. 1). In contrast, if the junction temperature, Tj is lower than the sample surface temperature, Ts, (Tj < Ts), heat comes from the sample surface through the CNT to the Pt film. Hence, the Pt film gets additional heat and the temperature distribution in the film follows the dashed line shown in Fig 1. However, when the CNT-junction temperature is the 8
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same as the target surface temperature, (Tj = Ts), heat flow through the CNT does not occur and the temperature of the target surface and the hot-film at the CNT-Pt junction is the same. We control the hot-film temperature by changing the heat generation in the Pt hot film; this ensures
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that the temperature at the CNT-Pt junction and the target surface are the same. Therefore, the
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sample surface temperature can be quantitatively estimated when the temperature of the Pt hot-film in the non-contact case and in the contact case, are the same.
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The sample surface temperature is estimated using Eq. (9). The average thermal conductivity
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of the Pt hot film is estimated from the average temperature, Tave and the premeasured relationship between the thermal conductivity and temperature in the hot film. Because the
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relationship between the temperature and resistance of platinum is linear over a wide temperature range, Tave is associated with the electrical resistance of the hot film, Rh as ave
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Rh – Rref)ref Here is the pre-measured temperature coefficient of resistance of the Pt
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hot film, and Rref is the electrical resistance at the reference temperature Tref. In this study, Tref is
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300 K and Tave is estimated from Rref at 300 K.
2.2 Experiments
The SEM image of the fabricated sensor and the TEM image of a multi-walled CNT whose diameter is 70 nm are shown in Fig. 2. The CNT protrudes from the edge of the SiO2/Si substrate, and can be in contact with the sample surface. The experimental procedure is outlined in the flowchart in Fig. 3. First, an electrical current is applied to a Pt hot film, and the voltage of the Joule-heated hot film, Vbefore is measured. Then, if the voltage after contact, Vafter is not the same with Vbefore when the CNT contacts with the sample surface, the CNT is detached from sample surface and an increase/decrease applied electrical current to meet Vbefore with Vafter. By 9
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repeating this process, the difference between Vbefore and Vafter becomes less than the voltage fluctuation caused by the controlled-temperature instability; and the condition Vbefore=Vafter is met. Finally, we calculate the electrical resistance of the hot film, Rave from Vbefore (Vafter) and the
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applied electrical current I, and estimate the sample temperature, Ts. The temperature of the
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CNT probe sensor is controlled and monitored by a peltier device and thermometer, respectively. We checked the validity of our thermal sensor by contacting a CNT probe with the reference
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sample whose temperature is monitored by a thermocouple. As shown in Table 1, there is good
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agreement (within 1 K) between the estimated temperature from our method and the measured temperature of a sample surface. Hence, the validity of our temperature measurement technique
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is confirmed.
A patterned platinum/titanium film is prepared, and the line-patterned heater is connected
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with two electrodes (Fig. 4A). The length and width of the heater is 9.73 m and 604 nm,
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respectively. The 50-nm-thick heater consists of Pt (42 nm) and Ti (8 nm) layers, and the film is
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deposited on a 200 nm-thick SiO2 layer. The longitudinal direction is defined as the direction along the line heater, and the transverse direction is perpendicular to the longitudinal direction. The fabricated heater has a high aspect ratio so one dimensional heat flow along the longitudinal direction is plausible. We applied electrical currents of 1.5 mA and 3.0 mA and measured the temperature in two directions for each electrical current. Fig. 4B shows the SEM image of the CNT in contact with the target surface. In our experiment, the moment of probe contact with a sample surface is identified by electrical resistance signal of the Pt hot film, which changes due to the temperature gap. However, we will combine atomic force microscopy (AFM) with our method for greater spatial and temperature resolution. The measured temperature profile in the longitudinal direction is shown in Fig. 5A. The 10
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temperature at both ends of the heater at 3.0 mA is higher than that obtained under 1.5 mA because of high heat generation, however at the extreme ends of the heat sink (on which the heater is placed) the temperature is considered to be almost the same as the ambient temperature
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The temperature profile along the transverse directions is shown in Fig. 5B. The measured
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temperature at 1.5 m from the edge of the heater is almost the same as the room temperature at
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1.5 and 3.0mA.
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3. CNT thermal contact resistance and thermal conductivity measurements As shown in Fig. 6A, the thermal conductivity of a single CNT can be measured by a T-type
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nanosensor [14]. Fig. 6B shows the heat transfer model of the measurement method of the TCR between a CNT end and solid surface [21]. Our developed system is shown in Fig. 6C, which
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can measure both the thermal conductivity of a single CNT and the TCR between a CNT and solid surface. This new system is beneficial as both the thermal conductivity and the TCR of a
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CNT are measured. However, the electrical resistance change decreases when the CNT contacts the solid surface compared with the case of Fig.6B. Therefore, we have employed the sensor sensitivity analysis proposed by Dames et al [23] to confirm the detectable electrical resistance change.
First, the temperature distribution of a Pt hot film without a CNT, Tbefore is same with Eq. (8), and we assume that a CNT is set on the middle of the Pt hot film (L1=L2=L/2). Thus, the temperature increase per unit volume of a Pt hot film, T1,vol, is calculated as L
T1,vol
1 QL 1 Tbefore ( x) T0 dx QRPt L0 12kh Ah 12
(15) 11
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Here, Q is the heat generation, RPt is the thermal resistance of a Pt hot film, and x is the coordinate along the Pt hot film.
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Next, we consider the case of the thermal conductivity measurement of a CNT in Fig.6A. In the thermal conductivity measurement [14], a portion of the Joule heat in a Pt hot film goes
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through the CNT into heat sink, which depends on the thermal resistance ratio between a Pt hot
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film, RPt and the thermal resistance of a CNT, RCNT,f =Lf /(kf Af). Therefore, we define the thermal resistance ratio, as
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RPt 4 RCNT , f
(16)
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1
The temperature distribution of a Pt hot film in Fig.6A, Tafter is expressed as
L1 ( L1 L2 ) RCNT , f L2 Ah Q Q x12 x1 T0 2kh Ah ( L1 L2 ) 2 Ah ( L1 L2 ) kh L1 L2 ( L1 L2 ) RCNT , f kh Ah
(17)
T2, after ( x2 )
L2 ( L1 L2 ) RCNT , f L1 Ah Q Q x22 x2 T0 2kh Ah ( L1 L2 ) 2 Ah ( L1 L2 ) kh L1L2 ( L1 L2 ) RCNT , f kh Ah
(18)
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T1, after ( x1 )
The temperature increase per unit volume for thermal conductivity measurement of a CNT, T2,vol, is calculated by
T2,vol
L L/ 2 L /2 1 1 T x T dx T x T dx T2,after ( x2 ) T0 dx2 ( ) ( ) 1,after 1 0 0 1 after L0 L 0 0
1 3 RPt 3 1 1 QRPt 1 1 1 T1,vol 1 1 4 4R 12 4 CNT , f
1
1
(19)
Here we define the dimensionless sensor sensitivity of the Pt hot film for thermal conductivity measurement of a CNT, S1 as 12
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S1
T2,vol T1,vol RCNT , f RCNT , f
(20)
By combining Eqs. (19) and (20), S1 can be re-written as Eq. (21) as previously shown [23]
3 1/ 2 1 / 2 1 1 4
2
(21)
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S1
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Finally, we consider the case of the thermal contact resistance measurement of a CNT. The temperature distribution of the Pt hot film in Fig.6C, Tfinal is obtained by solving Eqs. (4)-(6),
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and Eq. (22) under the boundary conditions from Eqs. (23)-(27). T4 ( x 4 ) C 7 x 4 C 8
for i 1, 2
an
Ti ( xi 0) T0
(23) (24)
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T4 ( x4 L f ) T0
T1 ( x1 L1 ) T2 ( x 2 L2 ) T3 ( x3 0) T4 ( x 4 0) kh Ah x1 L1
T3 ( x3 L p ) T0
k f Af
k f Af x2 L2
T3 x3
T3 x3
k f Af
x3 0
T4 x4
(26) x4 0
(27)
x3 L p
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Re
T2 x2
d
T1 x1
(25)
te
kh Ah
(22)
Temperature distributions of the Pt hot film in Fig.6C are determined as follows.
T1, final ( x1 )
Q x12 C1x1 T0 2kh Ah ( L1 L2 )
(28)
Q x22 C3 x2 T0 2kh Ah ( L1 L2 )
(29)
T2, final ( x2 )
Here, C1 and C3 are constants of integration expressed by C1
1 L1
QL12 T0 2 k h Ah ( L1 L2 )
( L L2 ) k h Ah L f T0 Q ( L p k f A f Re ) T0 1 T0 L f k f Af L1 L2 2 k h Ah ( L1 L2 ) ( L L2 ) k h Ah L f ( L p k f A f Re ) 1 1 Lf L1 L2 k f A f
(30)
13
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QL2 2 T0 2 k h Ah ( L1 L2 )
( L L2 ) k h Ah L f T0 Q ( L p k f A f Re ) T0 1 T0 L f k f Af L1 L2 2 k h Ah ( L1 L2 ) ( L L2 ) k h Ah L f ( L p k f A f Re ) 1 1 Lf L1 L2 k f A f
(31)
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1 L2
C3
cr
We analyze the sensor sensitivity of the TCR measurements. Here, we define the dimensionless thermal resistance ratio, as
Lp k f Af
Re RCNT , p Re
an
R3,total
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RPt 4 R3,total
2
(32)
(33)
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Here, R3,total is total of thermal resistances of a CNT probe and thermal contact resistance between a CNT end and sample surface. Then, the temperature increase per unit volume, T3,vol is
d
expressed as L L /2 L /2 1 1 T x T dx T x T dx T2, final ( x2 ) T0 dx2 ( ) ( ) 1, final 1 final 0 0 1 L0 L 0 0 3 1 1 16 RCNT , f R3,total T1,vol 1 1 1 1 1 4 RCNT , f R3,total RPt
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te
T3,vol
(34)
and the sensor sensitivity S2 is defined and derived as S2
S2
T3,vol T1,vol R3,total R3,total
3 1/ 2 1 / 2 2 1 1 2 4
(35)
2
(36)
Fig. 7 shows the sensitivity S2 as a function of As seen in the range of 10-1< < 100 and when is 100, good sensitivity for both thermal conductivity and TCR measurements are obtained. 14
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4. Control of heat transport at the CNT point contact Nano probe sensors are applicable for controlling local heating at the nanoscale. We consider
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the situation that the temperature of the Pt hot film–CNT junction, Tj is higher than the
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temperature of the sample surface, Ts. (Tj > Ts). Here Ts is assumed to be equal to the heat sink temperature, T0 (Ts =T0). Under these conditions, the heat transfer rate depends on the thermal
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resistances, Rj, RCNT and Re, which can be determined by the TCR measurements method of a
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CNT, as described in Ref. 21. In the supplementary information of the Ref. 21, the CNT temperature distribution, T3 is described as
L1 L2Q x3 2k f Af L1 L2 ( L1 L2 )( R j RCNT Re )kh Ah
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T3 ( x3 )
(37)
d
L1 L2 ( RCNT Re )Q T0 2 L1 L2 ( L1 L2 )( R j RCNT Re ) kh Ah
te
Then, the heat-transfer rate through a CNT ,QCNT, is obtained by Fourier’s law as QCNT =-kf Af
Ac ce p
dT3/dx3. Hence, the heating rate through a CNT at the contact point is expressed as
QCNT
L1 L2Q 2 L1 L2 ( L1 L2 )( R j RCNT Re )kh Ah
(38)
As previously reported, the change in the measured electrical resistance is 0.415 ohms (on average) for a CNT when it comes in contact with the target surface during DC heating [21]. From this electrical resistance change R, (Rj+RCNT+Re) is estimated as 1.70×107 K/W. The heat transfer rate in this experiment is estimated from Eq. (38) as 0.784 [W]. Here, we note that the TCR and thermal conductivity of the CNT does not vary with temperature for small temperature changes (~10K) around room temperature conditions. The heat transfer rate applied at the CNT contact point can be controlled by changing the heat generation of the Pt hot film, Q. In this 15
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section, we assume that surface temperature and thermal contact resistance are constant, but heating depends on complicated interfacial phenomena such as contact conditions, which should
cr
ip t
be investigated in the future.
5. Summary
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Novel surface temperature profiler using a single CNT is developed, which enable us to
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quantitatively measure the surface temperature. In this measurement, the problem of the thermal contact resistance between a CNT end and sample surface is avoided and high spatial resolution
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is achieved because of the small CNT tip radius. In additional application of a Pt hot film sensor, thermal contact resistance measurement of a carbon nanotube and local heating at the point
d
contact place of a carbon nanotube end are introduced. We envisage that these measurement
te
methods are applicable for different fiber materials. Our new proposed method has great
Ac ce p
potential to reveal nanoscale heat transport phenomena and in the future we will measure the thermal profile of nanomaterials.
ACKNOWLEDGEMENTS
This work was partially supported by Grants-in-Aid for Scientific Research (23360101, 23656153, 23760191, 24560237) and a Grant-in-Aid for JSPS Fellows (231457). Sensor fabrication was partially conducted at the Collabo-Station II of Kyushu University. The HRTEM and AFM observations were conducted in the Research Laboratory for High Voltage Electron Microscopy and in the Center of Advanced Instrumental Analysis, Kyushu University, respectively. 16
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Biographies
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J. Hirotani is currently a PhD candidate in Kyushu University. He has been a research fellow of
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the Japan Society for the Promotion of Science (JSPS) since 2011. His current research interests include thermal transport at interfaces, thermophysical properties of nanomaterials, scanning
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thermal microscopy and MEMS.
J. Amano received his Bachelor degree from the Department of Aeronautics and Astronautics,
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Kyushu University, Fukuoka, Japan, in 2012. His research during that period was on plasma
te
radiation, rarefied gas dynamics, and thermal protection systems (TPS) for reentry vehicles. He
Ac ce p
is currently enrolled as a master student at Kyushu University. His research interests are in near-field radiation, nano probe sensors, and MEMS. T. Ikuta is currently the Chief Technical Official of the Department of Aeronautics and Astronautics, Graduate school of Engineering, Kyushu University. His research interests include investigating micro/nano thermo-fluid systems using MEMS. T. Nishiyama received his B.E. (1998), M.E. (2000), D.E. (2010) from Kyushu University. He is currently the Assistant Professor of the Department of Aeronautics and Astronautics, Faculty of Engineering, Kyushu University. His research interests include fabrication and characterization of functional thin films. K. Takahashi received his PhD in engineering from the University of Tokyo in 1992 and is a 17
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Professor at the Department of Aeronautics and Astronautics, Kyushu University. His current research interests are thermophysical properties of nanomaterials, nanoscale heat and mass
cr
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transfer and MEMS.
References
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[1] D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin,
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thermal microscopy of graphite, Langmuir, 13, (1997) 4493-4497 [5] S. Volz, X. Feng, C. Fuentes, P. Guérin and M. Jaouen, Thermal conductivity measurements of thin amorphous silicon films by scanning thermal microscopy, International Journal of Thermophysics, 23 (2002) 1645–1657 [6] S. Lefe`vre, S. Volz and P. Chapuis, Nanoscale heat transfer at contact between a hot tip and a substrate, International Journal of Heat and Mass Transfer, 49 (2006) 251–258. [7] A. Majumdar, J. P. Carrejo and J. Lai, Thermal imaging using the atomic force microscope, Applied Physics Letters, 62 (1993) 2501 –2503 [8] L. Shi, S. Plyasunov, A. Bachtold, P. L. McEuen and A. Majumdar, Scanning thermal microscopy of carbon nanotubes using batch-fabricated probes, Applied Physics Letters, 77 18
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(2000), 4295–4297 [9] L. Shi and A. Majumdar, Thermal transport mechanisms at nanoscale point contacts, Journal of Heat Transfer, 124 (2002) 329–337
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[10] K. Kim, W. Jeong, W. Lee and P. Reddy, Ultra-high vacuum scanning thermal microscopy
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for nanometer resolution quantitative thermometry, ACS Nano, 6 (2012) 4248–4257
[11] O. Nakabeppu and T. Suzuki, Microscale temperature measurement by scanning thermal
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microscopy, Journal of Thermal Analysis and Calorimetry, 69 (2002) 727-737
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[12] J. Chung, K. Kim, G. Hwang, O. Kwon, S. Jung, J. Lee, J. W. Lee, and G. T. Kim, Quantitative temperature measurement of an electrically heated carbon nanotube using the
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null-point method, Review of Scientific Instruments, 81, (2010), 114901 [13] P. Kim, L. Shi, A. Majumdar, and P. L. McEuen, Thermal Transport Measurements of
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Individual Multiwalled Nanotubes, Physical Review Letters, 87, (2001), 215502
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[14] M. Fujii, X. Zhang, H. Xie, H. Ago, K. Takahashi, T. Ikuta, H. Abe, and T. Shimizu,
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Measuring the thermal conductivity of a single carbon nanotube, Physical Review Letter, 95 (2005) 065502
[15] M. M. J. Treacy, T. W. Ebbesen, and J. M. Gibson, Exceptionally high Young's modulus observed for individual carbon nanotubes, Nature, 381, (1996), 678-680 [16] N. R. Wilson and J. V. Macpherson, carbon nanotube tips for atomic force microscopy, Nature nanotechnology, 4 (2009) 483-491 [17] B. A. Nelson and W.P. King, Temperature caribration of heated silicon atomic force microscope cantilevers, Sensors and Actuators A, 140 (2007) 51-59 [18] M. A. Lantz, B. Gotsmann, U. T. Durig, P. Vettiger, Y. Nakayama, T. Shimizu, and H. Tokumoto, Carbon nanotube tips for thermomechanical data storage, Applied Physics Letter, 19
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83 (2003) 1266-1268 [19] P. Tovee, M. Pumarol, D. Zeze, K. Kjoller, and O. Kolosov, Nanoscale spatial resolution probes for scanning thermal microscopy of solid state materials, Journal of Applied Physics, 112, (2012) 114317
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[20] X. Zhang, H. Xie, M. Fujii, H. Ago, K. Takahashi, and T. Ikuta, H. Abe, and T. Shimizu,
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thermal and electrical conductivity of a suspended platinum nanofilm, Applied Physics Letter, 86 (2005) 171912
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[21] J. Hirotani, T. Ikuta, T. Nishiyama and K. Takahashi, Thermal boundary resistance
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between the end of an individual carbon nanotube and a Au surface, Nanotechnology 22 (2011) 315702
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[22] M. F. P. Bifano, J. Park, P. B. Kaul, A. K. Roy, and V. Prakash, Effects of heat treatment and contact resistance on the thermal conductivity of individual multiwalled carbon
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nanotubes using a Wollaston wire thermal probe, Journal of Applied Physics, 111, (2012)
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[23] C. Dames S. Chen C. T. Harris J. Y. Huang Z. F. Ren M. S. Dresselhaus G. Chen, A hot-wire probe for thermal measurements of nanowires and nanotubes inside a transmission electron microscope, Review of Scientific Instruments, 78 (2007) 104903
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Figures and figure captions
Fig.1 Heat transfer model of a suspended platinum hot film with a single carbon nanotube probe.
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Tj and Ts are the hot-film temperatures at the CNT-Pt junction and sample surface temperature,
d
respectively. The temperature distribution along the Pt film for three cases are shown: CNT-Pt
Ac ce p
Ts.
te
junction temperature, Tj, is same as the sample surface temperature, Ts, or higher, or lower than
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Fig. 2 SEM image of the fabricated sensor. The CNT is fixed on the Pt hot film and protrudes
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from the silicon substrate. Two Pt electrodes work as heat sinks. Inset: HRTEM image of the
Ac ce p
te
d
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multi-walled CNT tip.
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Fig. 3 Flow chart of the experimental procedure. Vbefore and Vafter represent the voltage of the Pt hot film in CNT non-contact and contact modes, respectively. Electrical current I changes the heat generation to meet the Vbefore =Vafter. When Vbefore = Vafter, Ts, =Tj.
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Table 1 Comparison of temperatures obtained from the thermometer and from our measured
Ac ce p
te
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M
an
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data at the sample surface.
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Fig. 4 (A) Schematic diagram of a temperature measurement using a carbon nanotube probe.
Ac ce p
The sample is a line-patterned Pt/Ti film, and line patterned heater is connected to electrodes. The coordinates are defined as along the line heater (longitudinal direction) and perpendicular to the line heater (transverse direction). The contact point of the carbon nanotube probe on the sample surface is arbitrary. (B) SEM images of the CNT in contact with (top image) the line patterned Pt/Ti heater and (bottom image) the substrate, during temperature measurements along the transverse direction.
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Fig. 5 (A) Temperature measurements along the Pt heater (longitudinal direction) for the 3.0 mA
an
and 1.5 mA heating cases. Dashed line is room temperature in the experiment as 302 K. (B) Sample surface temperature distributions perpendicular to the Pt heater (transverse direction).
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The origin is the edge of the Pt/Ti heater. Measured temperatures are the same as the the room
Ac ce p
te
d
temperature at about 1.5 m distance away from the heater.
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Fig. 6 Heat transfer model for (A) single CNT thermal conductivity measurements, (B) single CNT TCR measurements , (C) combined A and B systems. The generated heat in the Pt hot film dissipates in three (before contact) or four directions (after contact) in the TCR measurements. (D) SEM image of a fabricated sensor. The CNT is fixed on the heat sink (CNT end) and Pt hot film (CNT middle), and protrudes from the SiO2/Si edge.
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Fig. 7 Sensor sensitivity vs. thermal resistance ratio. Inset: Relationship between 1 and S1. Area
Ac ce p
te
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of good sensitivity is indicated where 10-1< < 100 and is 100.
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