Enabling low-noise null-point scanning thermal microscopy by the optimization of scanning thermal microscope probe through a rigorous theory of quantitative measurement Gwangseok Hwang, Jaehun Chung, and Ohmyoung Kwon Citation: Review of Scientific Instruments 85, 114901 (2014); doi: 10.1063/1.4901094 View online: http://dx.doi.org/10.1063/1.4901094 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hot-spot detection and calibration of a scanning thermal probe with a noise thermometry gold wire sample J. Appl. Phys. 113, 074304 (2013); 10.1063/1.4792656 Quantitative temperature measurement of an electrically heated carbon nanotube using the null-point method Rev. Sci. Instrum. 81, 114901 (2010); 10.1063/1.3499504 Electronic linearization of piezoelectric actuators and noise budget in scanning probe microscopy Rev. Sci. Instrum. 77, 073701 (2006); 10.1063/1.2213214 High-resolution scanning thermal probe with servocontrolled interface circuit for microcalorimetry and other applications Rev. Sci. Instrum. 75, 1222 (2004); 10.1063/1.1711153 Noise in scanning capacitance microscopy measurements J. Vac. Sci. Technol. B 18, 1125 (2000); 10.1116/1.591476
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 114901 (2014)
Enabling low-noise null-point scanning thermal microscopy by the optimization of scanning thermal microscope probe through a rigorous theory of quantitative measurement Gwangseok Hwang, Jaehun Chung, and Ohmyoung Kwona) Department of Mechanical Engineering, Korea University, Seoul, South Korea
(Received 23 July 2014; accepted 24 October 2014; published online 11 November 2014) The application of conventional scanning thermal microscopy (SThM) is severely limited by three major problems: (i) distortion of the measured signal due to heat transfer through the air, (ii) the unknown and variable value of the tip-sample thermal contact resistance, and (iii) perturbation of the sample temperature due to the heat flux through the tip-sample thermal contact. Recently, we proposed null-point scanning thermal microscopy (NP SThM) as a way of overcoming these problems in principle by tracking the thermal equilibrium between the end of the SThM tip and the sample surface. However, in order to obtain high spatial resolution, which is the primary motivation for SThM, NP SThM requires an extremely sensitive SThM probe that can trace the vanishingly small heat flux through the tip-sample nano-thermal contact. Herein, we derive a relation between the spatial resolution and the design parameters of a SThM probe, optimize the thermal and electrical design, and develop a batch-fabrication process. We also quantitatively demonstrate significantly improved sensitivity, lower measurement noise, and higher spatial resolution of the fabricated SThM probes. By utilizing the exceptional performance of these fabricated probes, we show that NP SThM can be used to obtain a quantitative temperature profile with nanoscale resolution independent of the changing tip-sample thermal contact resistance and without perturbation of the sample temperature or distortion due to the heat transfer through the air. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901094] I. INTRODUCTION
Since local temperature measurement with high spatial resolution is very important in both science and engineering, a lot of measurement techniques have been already developed and used. One group of these techniques are non-contact methods such as infrared or near-infrared thermography,1, 2 thermoreflectance,3–5 photoluminescence,6 Raman spectroscopy,7, 8 fluorescence thermography,9, 10 and near-field optical thermography.11, 12 However, in spite of many advantages, these techniques are not suitable for measurement that requires nanoscale resolution. Especially, in achieving sub-100 nm spatial resolution, contact techniques such as scanning thermal microscopy (SThM) is more advantageous. Due to its nanoscale spatial resolution, SThM has been utilized in many diverse fields of science and engineering, including thermal conductivity measurements of nano-materials,13–16 thermal contact resistance between dissimilar materials,17 and thermal characterization of the nanodevices.18–28 However, despite the consistent demand for broader application areas, conventional SThM, which is used to probe the local temperature or thermal conductivity by scanning a SThM probe in contact mode, mainly suffers from the following three problems: (i) distortion of the measured temperature profile due to the heat transfer through the air gap between the SThM probe and the sample surface,29 (ii) difficulty in quantitative measurements owing to the unknown and a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0034-6748/2014/85(11)/114901/10/$30.00
sometimes variable value of the tip-sample thermal contact resistance, which depends on surface properties such as wettability and hardness, and (iii) the perturbation of the sample temperature due to the heat flux through the tip-sample thermal contact. These problems have severely limited the use of SThM. Conversely, the resolution of these problems will greatly extend the applications of SThM. Lately, in order to solve the first problem mentioned above, Kim et al. rigorously established and experimentally demonstrated a new theory and measurement method, “the double scan technique.”30, 31 The double scan technique achieves a quantitative measurement of the local temperature or thermal conductivity from the difference between the thermal signal measured in contact mode and that measured in non-thermal contact mode. In non-thermal contact mode, all the parasitic heat transfer such as the one through the probe-sample air gap is identical to that in contact mode but heat conduction through the tip-sample thermal contact does not exist. Although the first problem was resolved by using double scan technique, the rest of the problems still remain unresolved. Many newly developed nanomaterials and devices are composed of heterogeneous materials, and it is critical to understand the nanoscale transport mechanism at interfaces.32–35 For example, during the thermal characterization of the nanodevices composed of carbon nanotube or graphene, the tip of the SThM probe naturally crosses the interfaces between heterogeneous materials with different surface properties. Due to a change in surface properties, the tip-sample thermal contact resistance is thus also affected. If the tip-sample thermal
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contact resistance changes during a scan, a quantitative measurement of temperature and thermal conductivity becomes very difficult. In this way, the second problem mentioned above seriously limits the applications of SThM as a thermal characterization tool at the nanoscale. In conventional SThM or double scan technique, there always exists a heat flux through the tip-sample thermal contact, which will always perturb the temperature distribution on the sample surface. If the temperature field is established by an extremely small nanoscale heat source, the perturbation due to the heat flux through the tip-sample contact grows more serious. Hence, obviously, the third problem of the conventional SThM also seriously limits the applicability of SThM as a thermal characterization tool at nanoscale. In order to resolve not only the first problem but also the rest of the problems as well, Chung et al. suggested nullpoint scanning thermal microscopy (NP SThM), verified its theory rigorously, and demonstrated its potential feasibility experimentally.36 NP SThM is based on the thermodynamic principle that when the temperatures of the probe tip and sample surface are identical, heat flux through the tip-sample thermal contact is zero. Hence, NP SThM measures the temperature that is not perturbed by the heat flux through the tip-sample thermal contact. Furthermore, even when the tipsample contact resistance is unknown or changes during a scan due to changes in surface properties, NP SThM can be used to obtain a quantitative profile of the temperature distribution of the sample surface. Therefore, NP SThM is a method that can solve all the three problems of conventional SThM mentioned above.36 However, since NP SThM traces the thermal equilibrium point at which the small heat flux through the extremely tiny tip-sample nano-contact is nullified, NP SThM is not practical without significant improvements in sensitivity of the SThM probe. In particular, as confirmed in previous experiments36 and proved theoretically in the present work later, unless the sensitivity of the SThM probe is high enough, the high spatial resolution, the most important advantage of SThM, cannot be achieved, because of the noise in the measurement. Consequently, the problem of enabling practical low-noise NP SThM that can take full advantage of the high spatial resolution of SThM boils down to how to design and fabricate the performance-optimized SThM probes. In this study, we optimize the design of SThM probes and perform batch fabrication. Although the optimal design and fabrication of SThM probes has been carried out in the past, this optimization was based on the theory of conventional SThM.37 Herein, based on a rigorous theory of quantitative measurement, we first derive the relation between the spatial resolution of the probe and the design parameters of the probe. Using the result of this analysis, we then optimize the design of the SThM probe in order to achieve maximum spatial resolution and batch-fabricate the probes. We also quantitatively estimate the performance of batch-fabricated probes. The sensitivity, measurement noise, tip radius, and spatial resolution of the probes are characterized. Finally, we demonstrate that NP SThM can profile the temperature distribution quantitatively with nanoscale spatial resolution, without perturbing the sample temperature from
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heat flux through the tip-sample contact, even if the thermal contact resistance changes during a scan.
II. SPATIAL RESOLUTION OF A SThM PROBE BASED ON A RIGOROUS THEORY OF QUANTITATIVE MEASUREMENT
The ultimate goal of optimizing SThM probe design is to maximize the spatial resolution. In this section, we briefly derive a theory of quantitative measurement. Based on this theory, we then determine the design parameters that govern spatial resolution. After clarifying the relation between spatial resolution and the various design parameters, we optimize the design to increase spatial resolution. While deriving the theory of the double scan technique, Kim et al. rigorously proved:30, 31 Qst = C(Tc (x) − Tnc (x)),
(1)
where Qst is the heat flux from the sample surface to the tip of the probe through the tip-sample thermal contact, C is the thermal conductance of the SThM probe from the tip to the surroundings, x is the location of the tip-sample contact on the sample, Tc is the temperature measured by the temperature sensor integrated at the end of probe tip in contact mode, and Tnc is the temperature measured by the sensor in non-thermal contact mode. The non-thermal contact mode is a scanning mode, in which Qst is zero and Qair , the heat flux through the air gap, is the same as that in contact mode. Experimentally, Tnc can be obtained by linearly extrapolating the two temperature data measured at two different heights above the sample surface with respect to the height.31 Tc is induced by both Qst and Qair and Tnc is generated only by Qair . Therefore, the difference between Tc and Tnc corresponds to the effect of Qst only. In this study, we define the sensitivity of the probe (Sprobe ) as the temperature rise caused by Qst only and measured by the temperature sensor integrated at the end of the probe tip. As shown in previous measurements from conventional SThM, the temperature of the tip also rises owing to Qair . However, the temperature rise induced by Qair instead prevents the local and quantitative measurement of temperature. Only the temperature rise caused by Qst allows a local measurement. Hence, Sprobe is Sprobe ≡
Tc (x) − Tnc (x) 1 = , Qst C
(2)
which is the inverse of C defined in Eq. (1). In addition, since Qst is proportional to the difference between the temperature of sample surface (Ts ) and that of the probe tip (Tc ): Qst = Gst (Ts (x) − Tc (x)) = hst Ac (Ts (x) − Tc (x)),
(3)
where Gst is the thermal conductance of the tip-sample thermal contact and is equal to the product of hst , the interfacial heat transfer coefficient, and Ac , the area of the thermal
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contact. Combining Eqs. (2) and (3) then yields Ts (x) = Tc (x) +
equivalent spatial resolution, xn is
1 (T (x) − Tnc (x)) hst Ac Sprobe c
= Tc (x) + ϕ(Tc (x) − Tnc (x)),
xn = (4)
which is the principle equation derived for the double scan technique by Kim et al. By applying Eq. (4), Kim et al. demonstrated that the temperature profile can be obtained without distortion due to heat transfer through the air gap.31 However, the double scan technique only solves the first problem of conventional SThM, and cannot solve the remaining problems explained in the introduction. In order to solve the rest of these problems, Chung et al.36 noted that Tj (= Tc − Tnc ), the temperature jump, is proportional to Ts − Tc , as shown in Eq. (4) and that Ts becomes equal to Tc when Tj becomes zero. Hence, by properly modulating Tc so that Tj becomes zero, Ts can be obtained, irrespective of the value and change of ϕ. Furthermore, since the temperature is measured when Qst is made zero (at Tj = 0), the temperature measured in this manner is free from perturbations due to Qst . However, it is impractical to adjust Tc so that Tj becomes zero at each and every point on the sample surface with a local temperature distribution. Instead, we obtain the value of Tc when Tj becomes zero by linearly extrapolating the temperature signals measured in passive mode (Tc1 , Tnc1 ) and those measured in active mode (Tc2 , Tnc2 ). During passive mode, the thermocouple junction of the probe tip is not heated. During active mode, the thermocouple junction is locally heated. Mathematically, a linear extrapolation of the signals can be written as Tc2 (x) − Tc1 (x) Ts (x) = Tc1 (x) + (Tc1 (x) − Tnc1 (x)), Tj 1 (x) − Tj 2 (x) (5) which is the principle equation of NP SThM.36 Although Eq. (5) is derived from Eq. (4), Ts in Eq. (5) corresponds to the sample temperature when Qst is zero. Therefore, NP SThM measures the temperature that is unaffected by Qst . During the execution of the double scan technique, a calibration procedure that measures ϕ defined in Eq. (4), which is assumed to remain constant during scanning, is necessary before measurements of the surface temperature. However, as Eq. (5) shows, NP SThM does not require this separate calibration procedure. Comparing Eqs. (4) and (5), we can say that NP SThM profiles temperatures while measuring ϕ simultaneously. Now that we established a theory of quantitative measurement, we uncover the parameters that determine spatial resolution. Since the parameters relevant to the design of the probe are not shown explicitly in Eq. (5), the relation between the spatial resolution and the design parameters is derived based on Eq. (4). As explained above, Eq. (5) can be regarded as a generalized version of Eq. (4). Let Tn be the noise of the sensor integrated at the tip of the SThM probe during the measurement of Tc and Tnc . Then, while Ts is obtained by Eq. (4) from the measured Tc and Tnc , the noise is amplified to Tn /(hst Ac Sprobe ). Hence, the noise
Tn / hst Ac Sprobe (dT /dx)s
,
(6)
where (dT/dx)s is the temperature gradient of the sample. However, no matter how small xn may be, the spatial resolution of the SThM probe cannot be smaller than the diameter of the tip-sample thermal contact (dc ). When the SThM probe makes contact with the substrate under ambient conditions, a liquid meniscus forms in addition to a solidsolid contact at the tip-sample contact. Therefore, dc is determined by the diameter of the liquid meniscus and can be written as38, 39 Rtip , (7) dc = 4.16 − ln ψ where Rtip is the radius of the tip and ψ is the relative humidity of air. As a result, the spatial resolution of the probe, x, can be written as x = Max(xn , dc ),
(8)
where Max(a, b) refers to the larger of the two terms in parenthesis. As shown in Eqs. (6)–(8), the spatial resolution of the probe depends not only on the intrinsic parameters determined by the design of the SThM probe (Sprobe , Tn , Rtip ), but also on extrinsic variables irrelevant to the performance of the probe ((dT/dx)s , hst ). Hence, it is not appropriate to express the performance of the SThM probe simply by its spatial resolution. The performance of a SThM probe should be expressed by the intrinsic probe parameters such as Sprobe , Tn , and Rtip . The objective in the design of the SThM probe is to maximize its spatial resolution by optimizing each of the three intrinsic parameters. III. THE DESIGN AND FABRICATION OF A SThM PROBE WITH HIGH SPATIAL RESOLUTION AND LOW NOISE BASED ON A RIGOROUS THEORY OF QUANTITATIVE MEASUREMENT
In order to minimize x, both dc and xn should be reduced, as shown in Eq. (8). Obviously, dc can be reduced by decreasing Rtip , according to Eq. (7). However, the reduction of dc decreases Ac (= π dc2 /4), and results in an increased xn , as shown in Eq. (6). The reason for this increase can be found in Eq. (3). Because Qst is reduced due to the decrease of Ac , it becomes difficult for the temperature sensor integrated at the end of the probe tip to sense the temperature change of the sample. Hence, to reduce dc and xn simultaneously, Sprobe should be maximized and Tn should be minimized, as shown in Eq. (6). To derive a theoretical model for the maximization of Sprobe , the structure of the fabricated SThM probe in this study is depicted in Fig. 1(a), along with the coordinates used in the theoretical analysis. In a previous study, Kim et al. obtained the governing equation and boundary conditions for Tj ( = Tc − Tnc ), which is the temperature jump in the probe owing to the heat flux through the tip-sample thermal contact.
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FIG. 1. (a) A schematic of the structure of the SThM probe fabricated in this study along with the coordinates for theoretical analysis. Modeling results of the sensitivity of the probe with respect to design parameters: (b) Sprobe versus tip height, (c) the tip half angle, (d) the length of cantilever, (e) the position of the thermocouple junction, and (f) the thickness of the metal film deposited on the tip of the probe.
This equation is obtained by subtracting the governing equation and boundary conditions for Tnc from those of Tc :31 dTj (ξ ) d Ai (ξ )ki dξ dξ − [p(ξ )heff (ξ ) + p∞ (ξ )h∞ (ξ )]Tj (ξ ) = 0,
Ai ki
dTj (0) dξ
= Qst , Tj (L) = 0,
(9)
(10)
where ξ represents the position on the probe (ξ = 0 at the end of the tip; ξ = L at the end of the cantilever), Ai is the crosssection of the ith composing layer, ki is the thermal conductivity of the material composing the ith layer, p is the perimeter of the probe related to the surface that exchanges heat flux with the sample surface, heff is the effective heat transfer coefficient between the probe and the sample, p∞ is the perimeter of the probe related to the surface that exchanges heat flux with the surroundings except the sample, h∞ is the effective heat transfer coefficient between the probe and the surround-
ings except the sample, and Qst is the heat flux through the tip-sample thermal contact from the sample to the tip. Hence, Sprobe defined by Eq. (2) is the same as Tj (ξ tc )/Qst , where ξ tc is the position of the thermocouple junction. Since Eq. (9) and the corresponding boundary condition in Eq. (10) are homogeneous, Tj (ξ ) is linearly proportional to Qst in the entire domain. Therefore, Sprobe is the intrinsic parameter of the probe, which is irrelevant to Qst . As shown in Eqs. (9) and (10), the sensitivity of the probe, Sprobe , is determined by Ai , ki , p, heff , p∞ , L, and ξ tc . These variables are determined by the design parameters of the probe: the height of the tip, the half angle of the tip, the length of the cantilever, the position of the thermocouple junction, and the thickness of the metal films. In this study, to maximize Sprobe , we optimize the design parameters by analyzing Eqs. (9) and (10) (see Sec. S1 of the supplementary material40 ). We uncover the influence of each design parameter of the SThM probe on Sprobe . In order to do this, we first assume a standard design of the probe for which all the design parameters are given temporarily, as shown in Table I. Then, we investigate the influence of each design parameter on Sprobe separately, while fixing the remaining design parameters at standard values. The standard design parameters are: tip height 8 μm, tip half angle 26.6◦ , cantilever length 200 μm, thermocouple junction position 100 nm, and thickness of metal films composing the thermocouple 50 nm. The tip of the probe is fabricated by anisotropically etching silicon with a high aspect ratio followed by thermal growth of SiO2 . Thus, the height of the tip can be increased as much as the following fabrication steps allow and the tip becomes a hollow cone with a small half angle. The increased height and the hollow design of the tip help improve Sprobe by increasing the thermal resistance. Based on Eqs. (9) and (10), the influence of the design parameters on Sprobe are analyzed and the results are shown in Figs. 1(b)–1(f) as a function of tip height, the half angle of the tip, the length of the cantilever, the position of the thermocouple junction, and the thickness of the metal films, respectively. In Fig. 1(b), Sprobe first increases as the tip height increases and then gradually saturates. As the tip height increases, the thermal resistance of the tip increases. At the same time, as the distance between the cantilever and substrate increases with tip height, the thermal resistance of the air gap between the cantilever and substrate also grows large. Thus, the increase of the tip height leads to better thermal insulation of the thermal sensor integrated at the end of the tip from the
TABLE I. Design parameters of the standard design and P1, P2, P3 design probes. Metal thickness (nm) Au
Cr
Probe design
Tip
Cantilever
Tip
Cantilever
Standard design P1 P2 P3
50 10 20 30
50 30 60 90
50 10 20 30
50 100 110 120
Tip height (μm)
Tip half angle (deg)
Cantilever length (μm)
Base material
8 12
26.6 26.6
200 200
Silicon dioxide Silicon dioxide
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surroundings except for the tip-sample thermal contact. As a result, Sprobe improves. However, as Fig. 1(b) shows, this effect gradually saturates as the tip height increases further. In this study, we design the tip height to be 12 μm, which is the maximum value allowed in the microfabrication steps described in this work. In Fig. 1(c), Sprobe increases with the reduction of the tip half angle. As the tip half angle decreases, the thermal resistance of the tip increases with the reduction of the heat conduction area through the tip, and the heat transfer through the air gap to the substrate decreases owing to the reduction of the surface area of the tip. Hence, the tip half angle should be minimized as much as the microfabrication process allows. We reduced the tip half angle down to 26.6◦ by taking advantage of the etch characteristics of silicon that the (411) surface of single crystal silicon etches most quickly at 60 ◦ C in an aqueous solution of KOH at 50% by weight.41 In Fig. 1(d), the dependence of Sprobe on the length of the cantilever is depicted. Because the thermal resistance increases with cantilever length, Sprobe gradually improves. However, as the cantilever length grows longer than 200 μm, the heat transferred through the tip-sample thermal contact is largely lost to the surroundings before reaching the base of the cantilever. As a result, Sprobe saturates. Therefore, we design the cantilever length of the probe to be 200 μm. In Fig. 1(e), the dependence of Sprobe on the position of the thermocouple junction is shown. Clearly, Sprobe improves as the thermocouple junction approaches the end of the tip. Therefore, to maximize Sprobe , the thermocouple junction should be integrated as close to the end of the tip as possible. As shown in the inset of Fig. 1(e), the position of the thermocouple junction is the sum of the height of the exposed part of the tip covered with the first metal film exposed by etching the insulating layer and the thickness of a second deposited metal film. During the thermocouple formation process, to maximize Sprobe , we reduce the height of the exposed part of the metal coated tip down to 100 nm and deposit a second metal film as thin as 10 nm. Finally, in Fig. 1(f), as the thickness of the metal films composing the thermocouple junction decreases, Sprobe increases sharply. As the thickness of the films decreases, the thermal resistance of the probe increases drastically, due to both the reduction of the thermal conductivity of the metal films owing to size effects and the reduction of the heat conduction area through the metal films. Compared with other design parameters, the influence of the thickness of the metal films composing the thermocouple on the improvement of Sprobe turns out to be dominant. The analysis results shown in Figs. 1(b)–1(f) suggest optimal values of the design parameters that can improve Sprobe . However, in order to reduce xn , as shown in Eq. (6), Tn should also be minimized, while Sprobe is maximized. The Tn of the thermocouple probe is determined by both Johnson noise induced by the pad-to-pad resistance of the thermocouple and the Seebeck coefficient of the thermocouple. Without affecting Tn , the tip height, the tip half angle, the length of the cantilever, and the position of thermocouple junction can be optimized to improve Sprobe . Although reducing the thickness of the metal films can improve Sprobe drastically by
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FIG. 2. The modeling result for Sprobe and the electrical resistance of the probe with respect to the thickness of metal film on the tip: (a) comparison of Sprobe of the probe with uniform metal thickness and that with relatively thicker metal lead line (∼50 nm) on the cantilever, (b) comparison of the electrical resistance for the two kinds of probes.
thermally insulating the tip, it also increases Tn significantly due to a sharp rise in pad-to-pad resistance. Since reducing the thickness of the metal films greatly improves Sprobe , we devise a design that can take advantage of the thermal insulation gained by reducing the thickness of the metal films without causing a sharp increase in pad-to-pad resistance. We note that in terms of electrical design, most of the electrical resistance occurs in the lead line on the cantilever. However, in terms of thermal design, the thermal insulation of the temperature sensor is predominantly affected by the metal films on the tip. Therefore, the optimal design for minimizing xn is that the metal films on the tip should be deposited as thin as the fabrication process allows to insulate the thermocouple integrated at the end of the tip as much as possible. In addition, the metal films composing the lead lines on the cantilever should be made thick enough so as to prevent the pad-to-pad resistance from growing excessively. In order to verify the effect of the suggested design, we compare Sprobe and the electrical resistance of the probe, which has a uniform metal thickness on the tip and cantilever, with those of the probe with a relatively thicker metal lead line (∼50 nm) on the cantilever through a theoretical analysis.37 As shown in Fig. 2(a), even though the thickness of the metal on the cantilever is kept the same, Sprobe increases sharply only if the metal film thickness on the tip is reduced. At the same time, as shown in Fig. 2(b), if only the thickness of the metal films on the tip is reduced, the pad-to-pad resistance barely increases. Based on the theoretical analysis and modeling results above, we determine the design parameters of the SThM probe, as shown in Table I. The thicknesses of gold and chromium films on the tip of the thermocouple probe for design P1, P2, and P3 are 10, 20, and 30 nm, respectively. Considering ease of fabrication, we determine the ratio between the thickness of gold films on the tip and that on the cantilever to be 1:3 and the thickness of the chromium film on the cantilever to be 90 nm thicker than that on the tip. Scanning electron micrographs of thermocouple probes fabricated according to the design parameters listed in Table I are depicted in Fig. 3. The overall fabrication steps are summarized in Sec. S2 of the supplementary material.40 In order to minimize the influence of the absorbed heat flux of the laser on the reflector, as depicted in Fig. 3(b), the reflector is located as far away from the tip as possible and the fins are attached to the reflector so that the absorbed heat flux is dissipated to the surrounding air as much as possible before the heat
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FIG. 3. Scanning electron micrographs of thermocouple SThM probes fabricated in this study: (a) the cantilever and tip of the probe (side view), (b) the reflector located far away from the tip and the fins attached to the reflector so that the absorbed heat flux from the AFM feed laser is dissipated to the surrounding air as much as possible before the heat flux reaches the tip (top view), (c) chromium film on the cantilever deposited thicker than that on the tip, (d) the end of the tip of the P1 design probe (tip radius: 26.7 nm), (e) the end of the tip of the P2 design probe (tip radius: 33.3 nm), and (f) the end of the tip of the P3 design probe (tip radius: 70.0 nm).
flux can reach the tip. As shown in Fig. 3(c), the chromium film deposited on the cantilever is thicker than that on the tip. Scanning electron micrographs of the tips of thermocouple probes fabricated according to probe designs P1, P2, and P3 are shown in Figs. 3(d)–3(f). These figures show that the radius of each tip, Rtip , is about 26.7, 33.3, and 70.0 nm, for probe designs P1, P2, and P3, respectively. IV. EVALUATION OF PERFORMANCE OF THE FABRICATED PROBE
As explained above, the spatial resolution is determined not only by the intrinsic parameters (Sprobe , Tn , Rtip ) determined by the design of the SThM probe but also by extrinsic variables ((dT/dx)s , hst ) irrelevant to the probe. Hence, SThM probe performance must not only be judged simply by the spatial resolution. The performance of a SThM probe should be represented by the intrinsic parameters of the probe such as Sprobe , Tn , and Rtip . First, we experimentally estimate Sprobe of the fabricated probe. According to Eq. (4), Sprobe can be written as Sprobe =
1 . hst Ac ϕ
(11)
The Ac in Eq. (11) can be obtained from Eq. (7) using the values of Rtip evaluated from Figs. 3(d)–3(f). Thus, once ϕ is measured experimentally, Sprobe of a certain probe can be compared with those of others using Eq. (11). hst is the interfacial heat transfer coefficient between the probe tip and the sample surface, and so is assumed to be constant for a particular sample. The experimental setup for measuring ϕ is illustrated in Fig. 4(a). The setup is composed of a preamplifier, a notch-filter, a signal access module, a SThM probe, and an atomic force microscope (AFM). To determine ϕ, as shown in Figure 4(b), the temperature measured by the thermocouple of the probe is monitored, while the tip of the probe approaches an aluminum line heater, whose temperature is measured from
its temperature coefficient of resistance. Until the tip touches the heater, the temperature of the tip rises gradually due to the increasing heat transfer through the air. At the moment the tip touches the sample, the temperature of the tip jumps from Tnc to Tc due to Qst . The temperature jumps are measured at several different temperatures of the sample. Once, Ts , Tnc , and Tc are obtained in this manner, ϕ can be evaluated from Eq. (4). The ϕ for this particular probe (P1) is 4.92 K/K. Repeating the same procedure, we measure ϕ values in order to evaluate Sprobe for the standard and P1, P2, P3 design probes. In Fig. 4(c), Sprobe for the standard and P1, P2, P3 design probes are compared with the analysis in Fig. 2(a). The value of hst that minimizes the mean square of the difference between the analysis result and experimental data is 5.3 × 108 W/m2 K. As predicted from the modeling, Sprobe increases sharply with decreasing metal film thickness on the tip. Sprobe of the P1 design probe is about 4.7 times higher than that of the standard design probe. In addition, we compare Sprobe for the probe fabricated in this study with that in a previous work. In this previous work,29 the temperature response of the probe with respect to the vertical position is monitored, while the probe approaches an electrically heated 350 nm wide gold heater; and this temperature response is represented by a dimensionless temperature φ. We obtain Tc and Tnc from the monitored dimensionless temperature; and, by substituting thus obtained Tc , Tnc and Rtip into Eq. (4), evaluate ϕ of the thermocouple probe developed in the previous work. As shown in Fig. 4(c), Sprobe of the standard design probe and that of the P1 design probe are about 18 times and about 85 times higher than Sprobe of the probe developed in the previous work, respectively. With the estimation of Sprobe completed, Tn must now be estimated. For a thermocouple probe, Tn is given by 4kB T Rf , (12) Tn = S where kB is the Boltzmann constant, T is the absolute temperature, R is electrical resistance of the SThM probe, f is the
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FIG. 4. (a) The experimental setup for the measurement of ϕ of the probe. (b) The temperature measured by the thermocouple of the probe as the tip approaches the sample. The measured temperature rises gradually due to the heat transfer through the air. When the tip makes contact with the sample, the temperature of the tip jumps from Tnc to Tc due to the heat flux through the tip-sample contact. (c) Comparison of Sprobe of the standard and P1, P2, P3 design probes evaluated with the measured ϕ (symbols) and Sprobe obtained from 1D modeling (solid line). (d) Comparison of the measured electrical resistances of SThM probes (symbols) with the modeled electrical resistances as a function of the thickness of the metal film on the tip (solid line: thick metal lead line, dashed line: uniform metal thickness).
frequency bandwidth, and S is the Seebeck coefficient of the thermocouple. To obtain Tn , we measure the electrical resistance of the fabricated probes and compare the measured data with the modeling results in Fig. 4(d). For probes with a uniform metal thickness, the measured resistance is approximately two times larger than that estimated by the modeling, which takes into account the dependence of the electrical resistivity on thickness. Nevertheless, the trend in measured resistance with respect to thickness is very similar to the modeling result.29 For the probe with a thick lead metal film, the measured resistance (for P1, P2, and P3 design SThM probes) does not decrease as sharply as that estimated by the modeling. Nevertheless, the measured electrical resistance is smaller than that of the probe with uniform metal thickness over the entire range of metal thickness. For the P1 design SThM probe in particular, the reduction in resistance (∼30%) is most evident. Now that the electrical resistances of the probes are measured (1906.4 ± 113.6 , 914.6 ± 121.0 , and 877.0 ± 36.7 for P1, P2, and P3 design SThM probes, respectively), we calculate Tn for each probe using Eq. (12), along with T, f, and S, set to be 300 K, 1 kHz, and 20.5 μV/K, respectively. For each of the P1, P2, and P3 design SThM probes, Tn is found to be 8.7 mK, 6.0 mK, 5.9 mK, respectively. The last intrinsic parameter that represents the performance of the SThM probe is Rtip . If the tip is fabricated exactly as intended, Rtip should be equal to the summation of the tip radius of the bare silicon oxide tip and the thicknesses of the metal films composing the thermocouple junction. However, due to the uncertainties that always accompany the actual fabrication process, Rtip for probes fabricated according
to the probe designs P1, P2, and P3 are about 26.7, 33.3, 70.0 nm, respectively, as shown in Figs. 3(d)–3(f).
V. ENABLING LOW-NOISE, HIGH-RESOLUTION NP SThM USING FABRICATED PROBES
We demonstrate here that because of the significant improvement in intrinsic parameters (Sprobe , Tn , Rtip ) of the probes fabricated in this study, the NP SThM method can be used to quantitatively measure the temperature profile without perturbations in sample temperature from the heat flux through the tip-sample contact point, even if the heat transfer coefficient at the tip-sample thermal contact changes due to a variation in surface properties such as wettability and hardness. Furthermore, by analyzing the measured signals, we demonstrate that the spatial resolution of NP SThM implemented using the probe fabricated in this study is high enough for experimental analysis of recently developed nano-devices and materials. An overall schematic of the sample used for the demonstration is depicted in Fig. 5(a). The platinum heater is patterned into a 4-probe configuration on a 300 nm thick SiO2 layer thermally grown on a silicon wafer. In order to change only the surface properties without affecting the temperature distribution, half of the sample surface is coated with a very thin (∼50 nm) Teflon layer, which is intended to change both the wettability and hardness of the surface. As shown in the micrograph in the inset of Fig. 5(a), the contact angle of water on the Teflon-coated surface is much larger than that on the SiO2 surface.
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FIG. 5. (a) An overall schematic of the sample used for the demonstration of NP SThM. A platinum heater is patterned into a 4-probe configuration on a 300 nm thick SiO2 layer thermally grown on a silicon wafer. Half of the platinum heater is coated with a very thin (∼50 nm) Teflon layer. The contact angle of water on the Teflon-coated surface is much larger than that on the SiO2 surface (inset). (b) Comparison of the temperature distribution across the heater (a–a ) obtained by NP SThM and that by finite element modeling.
To demonstrate quantitative temperature profile measurements, we measure the temperature distribution across the heater (a–a ) as illustrated in Fig. 5(a). The experimental setup for NP SThM is the same with that in Fig. 4(a). During an active mode scan, the thermocouple junction of the probe is heated by an AFM feedback laser. The temperature profile from NP SThM matches quite well with that obtained by finite element modeling. We now check whether the surface properties of the sample affect the quantitative temperature profile during the mea-
Rev. Sci. Instrum. 85, 114901 (2014)
surement using NP SThM. To check this influence rigorously, we carry out NP SThM along a line, where only the surface properties change and the temperature is kept constant. As shown in Fig. 5(a), the temperature is measured through NP SThM along a scan line (b–b ) about 250 nm away from, and parallel to the platinum heater, crossing the hydrophilic (silicon oxide) and the hydrophobic (Teflon-coated) surfaces. Since the aspect ratio of the heater (250 μm long and 3.2 μm wide) is quite large, we assume that the temperature is kept constant along a line parallel with and close to the heater (
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 114901 (2014)
Enabling low-noise null-point scanning thermal microscopy by the optimization of scanning thermal microscope probe through a rigorous theory of quantitative measurement Gwangseok Hwang, Jaehun Chung, and Ohmyoung Kwona) Department of Mechanical Engineering, Korea University, Seoul, South Korea
(Received 23 July 2014; accepted 24 October 2014; published online 11 November 2014) The application of conventional scanning thermal microscopy (SThM) is severely limited by three major problems: (i) distortion of the measured signal due to heat transfer through the air, (ii) the unknown and variable value of the tip-sample thermal contact resistance, and (iii) perturbation of the sample temperature due to the heat flux through the tip-sample thermal contact. Recently, we proposed null-point scanning thermal microscopy (NP SThM) as a way of overcoming these problems in principle by tracking the thermal equilibrium between the end of the SThM tip and the sample surface. However, in order to obtain high spatial resolution, which is the primary motivation for SThM, NP SThM requires an extremely sensitive SThM probe that can trace the vanishingly small heat flux through the tip-sample nano-thermal contact. Herein, we derive a relation between the spatial resolution and the design parameters of a SThM probe, optimize the thermal and electrical design, and develop a batch-fabrication process. We also quantitatively demonstrate significantly improved sensitivity, lower measurement noise, and higher spatial resolution of the fabricated SThM probes. By utilizing the exceptional performance of these fabricated probes, we show that NP SThM can be used to obtain a quantitative temperature profile with nanoscale resolution independent of the changing tip-sample thermal contact resistance and without perturbation of the sample temperature or distortion due to the heat transfer through the air. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901094] I. INTRODUCTION
Since local temperature measurement with high spatial resolution is very important in both science and engineering, a lot of measurement techniques have been already developed and used. One group of these techniques are non-contact methods such as infrared or near-infrared thermography,1, 2 thermoreflectance,3–5 photoluminescence,6 Raman spectroscopy,7, 8 fluorescence thermography,9, 10 and near-field optical thermography.11, 12 However, in spite of many advantages, these techniques are not suitable for measurement that requires nanoscale resolution. Especially, in achieving sub-100 nm spatial resolution, contact techniques such as scanning thermal microscopy (SThM) is more advantageous. Due to its nanoscale spatial resolution, SThM has been utilized in many diverse fields of science and engineering, including thermal conductivity measurements of nano-materials,13–16 thermal contact resistance between dissimilar materials,17 and thermal characterization of the nanodevices.18–28 However, despite the consistent demand for broader application areas, conventional SThM, which is used to probe the local temperature or thermal conductivity by scanning a SThM probe in contact mode, mainly suffers from the following three problems: (i) distortion of the measured temperature profile due to the heat transfer through the air gap between the SThM probe and the sample surface,29 (ii) difficulty in quantitative measurements owing to the unknown and a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0034-6748/2014/85(11)/114901/10/$30.00
sometimes variable value of the tip-sample thermal contact resistance, which depends on surface properties such as wettability and hardness, and (iii) the perturbation of the sample temperature due to the heat flux through the tip-sample thermal contact. These problems have severely limited the use of SThM. Conversely, the resolution of these problems will greatly extend the applications of SThM. Lately, in order to solve the first problem mentioned above, Kim et al. rigorously established and experimentally demonstrated a new theory and measurement method, “the double scan technique.”30, 31 The double scan technique achieves a quantitative measurement of the local temperature or thermal conductivity from the difference between the thermal signal measured in contact mode and that measured in non-thermal contact mode. In non-thermal contact mode, all the parasitic heat transfer such as the one through the probe-sample air gap is identical to that in contact mode but heat conduction through the tip-sample thermal contact does not exist. Although the first problem was resolved by using double scan technique, the rest of the problems still remain unresolved. Many newly developed nanomaterials and devices are composed of heterogeneous materials, and it is critical to understand the nanoscale transport mechanism at interfaces.32–35 For example, during the thermal characterization of the nanodevices composed of carbon nanotube or graphene, the tip of the SThM probe naturally crosses the interfaces between heterogeneous materials with different surface properties. Due to a change in surface properties, the tip-sample thermal contact resistance is thus also affected. If the tip-sample thermal
85, 114901-1
© 2014 AIP Publishing LLC
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contact resistance changes during a scan, a quantitative measurement of temperature and thermal conductivity becomes very difficult. In this way, the second problem mentioned above seriously limits the applications of SThM as a thermal characterization tool at the nanoscale. In conventional SThM or double scan technique, there always exists a heat flux through the tip-sample thermal contact, which will always perturb the temperature distribution on the sample surface. If the temperature field is established by an extremely small nanoscale heat source, the perturbation due to the heat flux through the tip-sample contact grows more serious. Hence, obviously, the third problem of the conventional SThM also seriously limits the applicability of SThM as a thermal characterization tool at nanoscale. In order to resolve not only the first problem but also the rest of the problems as well, Chung et al. suggested nullpoint scanning thermal microscopy (NP SThM), verified its theory rigorously, and demonstrated its potential feasibility experimentally.36 NP SThM is based on the thermodynamic principle that when the temperatures of the probe tip and sample surface are identical, heat flux through the tip-sample thermal contact is zero. Hence, NP SThM measures the temperature that is not perturbed by the heat flux through the tip-sample thermal contact. Furthermore, even when the tipsample contact resistance is unknown or changes during a scan due to changes in surface properties, NP SThM can be used to obtain a quantitative profile of the temperature distribution of the sample surface. Therefore, NP SThM is a method that can solve all the three problems of conventional SThM mentioned above.36 However, since NP SThM traces the thermal equilibrium point at which the small heat flux through the extremely tiny tip-sample nano-contact is nullified, NP SThM is not practical without significant improvements in sensitivity of the SThM probe. In particular, as confirmed in previous experiments36 and proved theoretically in the present work later, unless the sensitivity of the SThM probe is high enough, the high spatial resolution, the most important advantage of SThM, cannot be achieved, because of the noise in the measurement. Consequently, the problem of enabling practical low-noise NP SThM that can take full advantage of the high spatial resolution of SThM boils down to how to design and fabricate the performance-optimized SThM probes. In this study, we optimize the design of SThM probes and perform batch fabrication. Although the optimal design and fabrication of SThM probes has been carried out in the past, this optimization was based on the theory of conventional SThM.37 Herein, based on a rigorous theory of quantitative measurement, we first derive the relation between the spatial resolution of the probe and the design parameters of the probe. Using the result of this analysis, we then optimize the design of the SThM probe in order to achieve maximum spatial resolution and batch-fabricate the probes. We also quantitatively estimate the performance of batch-fabricated probes. The sensitivity, measurement noise, tip radius, and spatial resolution of the probes are characterized. Finally, we demonstrate that NP SThM can profile the temperature distribution quantitatively with nanoscale spatial resolution, without perturbing the sample temperature from
Rev. Sci. Instrum. 85, 114901 (2014)
heat flux through the tip-sample contact, even if the thermal contact resistance changes during a scan.
II. SPATIAL RESOLUTION OF A SThM PROBE BASED ON A RIGOROUS THEORY OF QUANTITATIVE MEASUREMENT
The ultimate goal of optimizing SThM probe design is to maximize the spatial resolution. In this section, we briefly derive a theory of quantitative measurement. Based on this theory, we then determine the design parameters that govern spatial resolution. After clarifying the relation between spatial resolution and the various design parameters, we optimize the design to increase spatial resolution. While deriving the theory of the double scan technique, Kim et al. rigorously proved:30, 31 Qst = C(Tc (x) − Tnc (x)),
(1)
where Qst is the heat flux from the sample surface to the tip of the probe through the tip-sample thermal contact, C is the thermal conductance of the SThM probe from the tip to the surroundings, x is the location of the tip-sample contact on the sample, Tc is the temperature measured by the temperature sensor integrated at the end of probe tip in contact mode, and Tnc is the temperature measured by the sensor in non-thermal contact mode. The non-thermal contact mode is a scanning mode, in which Qst is zero and Qair , the heat flux through the air gap, is the same as that in contact mode. Experimentally, Tnc can be obtained by linearly extrapolating the two temperature data measured at two different heights above the sample surface with respect to the height.31 Tc is induced by both Qst and Qair and Tnc is generated only by Qair . Therefore, the difference between Tc and Tnc corresponds to the effect of Qst only. In this study, we define the sensitivity of the probe (Sprobe ) as the temperature rise caused by Qst only and measured by the temperature sensor integrated at the end of the probe tip. As shown in previous measurements from conventional SThM, the temperature of the tip also rises owing to Qair . However, the temperature rise induced by Qair instead prevents the local and quantitative measurement of temperature. Only the temperature rise caused by Qst allows a local measurement. Hence, Sprobe is Sprobe ≡
Tc (x) − Tnc (x) 1 = , Qst C
(2)
which is the inverse of C defined in Eq. (1). In addition, since Qst is proportional to the difference between the temperature of sample surface (Ts ) and that of the probe tip (Tc ): Qst = Gst (Ts (x) − Tc (x)) = hst Ac (Ts (x) − Tc (x)),
(3)
where Gst is the thermal conductance of the tip-sample thermal contact and is equal to the product of hst , the interfacial heat transfer coefficient, and Ac , the area of the thermal
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contact. Combining Eqs. (2) and (3) then yields Ts (x) = Tc (x) +
equivalent spatial resolution, xn is
1 (T (x) − Tnc (x)) hst Ac Sprobe c
= Tc (x) + ϕ(Tc (x) − Tnc (x)),
xn = (4)
which is the principle equation derived for the double scan technique by Kim et al. By applying Eq. (4), Kim et al. demonstrated that the temperature profile can be obtained without distortion due to heat transfer through the air gap.31 However, the double scan technique only solves the first problem of conventional SThM, and cannot solve the remaining problems explained in the introduction. In order to solve the rest of these problems, Chung et al.36 noted that Tj (= Tc − Tnc ), the temperature jump, is proportional to Ts − Tc , as shown in Eq. (4) and that Ts becomes equal to Tc when Tj becomes zero. Hence, by properly modulating Tc so that Tj becomes zero, Ts can be obtained, irrespective of the value and change of ϕ. Furthermore, since the temperature is measured when Qst is made zero (at Tj = 0), the temperature measured in this manner is free from perturbations due to Qst . However, it is impractical to adjust Tc so that Tj becomes zero at each and every point on the sample surface with a local temperature distribution. Instead, we obtain the value of Tc when Tj becomes zero by linearly extrapolating the temperature signals measured in passive mode (Tc1 , Tnc1 ) and those measured in active mode (Tc2 , Tnc2 ). During passive mode, the thermocouple junction of the probe tip is not heated. During active mode, the thermocouple junction is locally heated. Mathematically, a linear extrapolation of the signals can be written as Tc2 (x) − Tc1 (x) Ts (x) = Tc1 (x) + (Tc1 (x) − Tnc1 (x)), Tj 1 (x) − Tj 2 (x) (5) which is the principle equation of NP SThM.36 Although Eq. (5) is derived from Eq. (4), Ts in Eq. (5) corresponds to the sample temperature when Qst is zero. Therefore, NP SThM measures the temperature that is unaffected by Qst . During the execution of the double scan technique, a calibration procedure that measures ϕ defined in Eq. (4), which is assumed to remain constant during scanning, is necessary before measurements of the surface temperature. However, as Eq. (5) shows, NP SThM does not require this separate calibration procedure. Comparing Eqs. (4) and (5), we can say that NP SThM profiles temperatures while measuring ϕ simultaneously. Now that we established a theory of quantitative measurement, we uncover the parameters that determine spatial resolution. Since the parameters relevant to the design of the probe are not shown explicitly in Eq. (5), the relation between the spatial resolution and the design parameters is derived based on Eq. (4). As explained above, Eq. (5) can be regarded as a generalized version of Eq. (4). Let Tn be the noise of the sensor integrated at the tip of the SThM probe during the measurement of Tc and Tnc . Then, while Ts is obtained by Eq. (4) from the measured Tc and Tnc , the noise is amplified to Tn /(hst Ac Sprobe ). Hence, the noise
Tn / hst Ac Sprobe (dT /dx)s
,
(6)
where (dT/dx)s is the temperature gradient of the sample. However, no matter how small xn may be, the spatial resolution of the SThM probe cannot be smaller than the diameter of the tip-sample thermal contact (dc ). When the SThM probe makes contact with the substrate under ambient conditions, a liquid meniscus forms in addition to a solidsolid contact at the tip-sample contact. Therefore, dc is determined by the diameter of the liquid meniscus and can be written as38, 39 Rtip , (7) dc = 4.16 − ln ψ where Rtip is the radius of the tip and ψ is the relative humidity of air. As a result, the spatial resolution of the probe, x, can be written as x = Max(xn , dc ),
(8)
where Max(a, b) refers to the larger of the two terms in parenthesis. As shown in Eqs. (6)–(8), the spatial resolution of the probe depends not only on the intrinsic parameters determined by the design of the SThM probe (Sprobe , Tn , Rtip ), but also on extrinsic variables irrelevant to the performance of the probe ((dT/dx)s , hst ). Hence, it is not appropriate to express the performance of the SThM probe simply by its spatial resolution. The performance of a SThM probe should be expressed by the intrinsic probe parameters such as Sprobe , Tn , and Rtip . The objective in the design of the SThM probe is to maximize its spatial resolution by optimizing each of the three intrinsic parameters. III. THE DESIGN AND FABRICATION OF A SThM PROBE WITH HIGH SPATIAL RESOLUTION AND LOW NOISE BASED ON A RIGOROUS THEORY OF QUANTITATIVE MEASUREMENT
In order to minimize x, both dc and xn should be reduced, as shown in Eq. (8). Obviously, dc can be reduced by decreasing Rtip , according to Eq. (7). However, the reduction of dc decreases Ac (= π dc2 /4), and results in an increased xn , as shown in Eq. (6). The reason for this increase can be found in Eq. (3). Because Qst is reduced due to the decrease of Ac , it becomes difficult for the temperature sensor integrated at the end of the probe tip to sense the temperature change of the sample. Hence, to reduce dc and xn simultaneously, Sprobe should be maximized and Tn should be minimized, as shown in Eq. (6). To derive a theoretical model for the maximization of Sprobe , the structure of the fabricated SThM probe in this study is depicted in Fig. 1(a), along with the coordinates used in the theoretical analysis. In a previous study, Kim et al. obtained the governing equation and boundary conditions for Tj ( = Tc − Tnc ), which is the temperature jump in the probe owing to the heat flux through the tip-sample thermal contact.
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FIG. 1. (a) A schematic of the structure of the SThM probe fabricated in this study along with the coordinates for theoretical analysis. Modeling results of the sensitivity of the probe with respect to design parameters: (b) Sprobe versus tip height, (c) the tip half angle, (d) the length of cantilever, (e) the position of the thermocouple junction, and (f) the thickness of the metal film deposited on the tip of the probe.
This equation is obtained by subtracting the governing equation and boundary conditions for Tnc from those of Tc :31 dTj (ξ ) d Ai (ξ )ki dξ dξ − [p(ξ )heff (ξ ) + p∞ (ξ )h∞ (ξ )]Tj (ξ ) = 0,
Ai ki
dTj (0) dξ
= Qst , Tj (L) = 0,
(9)
(10)
where ξ represents the position on the probe (ξ = 0 at the end of the tip; ξ = L at the end of the cantilever), Ai is the crosssection of the ith composing layer, ki is the thermal conductivity of the material composing the ith layer, p is the perimeter of the probe related to the surface that exchanges heat flux with the sample surface, heff is the effective heat transfer coefficient between the probe and the sample, p∞ is the perimeter of the probe related to the surface that exchanges heat flux with the surroundings except the sample, h∞ is the effective heat transfer coefficient between the probe and the surround-
ings except the sample, and Qst is the heat flux through the tip-sample thermal contact from the sample to the tip. Hence, Sprobe defined by Eq. (2) is the same as Tj (ξ tc )/Qst , where ξ tc is the position of the thermocouple junction. Since Eq. (9) and the corresponding boundary condition in Eq. (10) are homogeneous, Tj (ξ ) is linearly proportional to Qst in the entire domain. Therefore, Sprobe is the intrinsic parameter of the probe, which is irrelevant to Qst . As shown in Eqs. (9) and (10), the sensitivity of the probe, Sprobe , is determined by Ai , ki , p, heff , p∞ , L, and ξ tc . These variables are determined by the design parameters of the probe: the height of the tip, the half angle of the tip, the length of the cantilever, the position of the thermocouple junction, and the thickness of the metal films. In this study, to maximize Sprobe , we optimize the design parameters by analyzing Eqs. (9) and (10) (see Sec. S1 of the supplementary material40 ). We uncover the influence of each design parameter of the SThM probe on Sprobe . In order to do this, we first assume a standard design of the probe for which all the design parameters are given temporarily, as shown in Table I. Then, we investigate the influence of each design parameter on Sprobe separately, while fixing the remaining design parameters at standard values. The standard design parameters are: tip height 8 μm, tip half angle 26.6◦ , cantilever length 200 μm, thermocouple junction position 100 nm, and thickness of metal films composing the thermocouple 50 nm. The tip of the probe is fabricated by anisotropically etching silicon with a high aspect ratio followed by thermal growth of SiO2 . Thus, the height of the tip can be increased as much as the following fabrication steps allow and the tip becomes a hollow cone with a small half angle. The increased height and the hollow design of the tip help improve Sprobe by increasing the thermal resistance. Based on Eqs. (9) and (10), the influence of the design parameters on Sprobe are analyzed and the results are shown in Figs. 1(b)–1(f) as a function of tip height, the half angle of the tip, the length of the cantilever, the position of the thermocouple junction, and the thickness of the metal films, respectively. In Fig. 1(b), Sprobe first increases as the tip height increases and then gradually saturates. As the tip height increases, the thermal resistance of the tip increases. At the same time, as the distance between the cantilever and substrate increases with tip height, the thermal resistance of the air gap between the cantilever and substrate also grows large. Thus, the increase of the tip height leads to better thermal insulation of the thermal sensor integrated at the end of the tip from the
TABLE I. Design parameters of the standard design and P1, P2, P3 design probes. Metal thickness (nm) Au
Cr
Probe design
Tip
Cantilever
Tip
Cantilever
Standard design P1 P2 P3
50 10 20 30
50 30 60 90
50 10 20 30
50 100 110 120
Tip height (μm)
Tip half angle (deg)
Cantilever length (μm)
Base material
8 12
26.6 26.6
200 200
Silicon dioxide Silicon dioxide
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surroundings except for the tip-sample thermal contact. As a result, Sprobe improves. However, as Fig. 1(b) shows, this effect gradually saturates as the tip height increases further. In this study, we design the tip height to be 12 μm, which is the maximum value allowed in the microfabrication steps described in this work. In Fig. 1(c), Sprobe increases with the reduction of the tip half angle. As the tip half angle decreases, the thermal resistance of the tip increases with the reduction of the heat conduction area through the tip, and the heat transfer through the air gap to the substrate decreases owing to the reduction of the surface area of the tip. Hence, the tip half angle should be minimized as much as the microfabrication process allows. We reduced the tip half angle down to 26.6◦ by taking advantage of the etch characteristics of silicon that the (411) surface of single crystal silicon etches most quickly at 60 ◦ C in an aqueous solution of KOH at 50% by weight.41 In Fig. 1(d), the dependence of Sprobe on the length of the cantilever is depicted. Because the thermal resistance increases with cantilever length, Sprobe gradually improves. However, as the cantilever length grows longer than 200 μm, the heat transferred through the tip-sample thermal contact is largely lost to the surroundings before reaching the base of the cantilever. As a result, Sprobe saturates. Therefore, we design the cantilever length of the probe to be 200 μm. In Fig. 1(e), the dependence of Sprobe on the position of the thermocouple junction is shown. Clearly, Sprobe improves as the thermocouple junction approaches the end of the tip. Therefore, to maximize Sprobe , the thermocouple junction should be integrated as close to the end of the tip as possible. As shown in the inset of Fig. 1(e), the position of the thermocouple junction is the sum of the height of the exposed part of the tip covered with the first metal film exposed by etching the insulating layer and the thickness of a second deposited metal film. During the thermocouple formation process, to maximize Sprobe , we reduce the height of the exposed part of the metal coated tip down to 100 nm and deposit a second metal film as thin as 10 nm. Finally, in Fig. 1(f), as the thickness of the metal films composing the thermocouple junction decreases, Sprobe increases sharply. As the thickness of the films decreases, the thermal resistance of the probe increases drastically, due to both the reduction of the thermal conductivity of the metal films owing to size effects and the reduction of the heat conduction area through the metal films. Compared with other design parameters, the influence of the thickness of the metal films composing the thermocouple on the improvement of Sprobe turns out to be dominant. The analysis results shown in Figs. 1(b)–1(f) suggest optimal values of the design parameters that can improve Sprobe . However, in order to reduce xn , as shown in Eq. (6), Tn should also be minimized, while Sprobe is maximized. The Tn of the thermocouple probe is determined by both Johnson noise induced by the pad-to-pad resistance of the thermocouple and the Seebeck coefficient of the thermocouple. Without affecting Tn , the tip height, the tip half angle, the length of the cantilever, and the position of thermocouple junction can be optimized to improve Sprobe . Although reducing the thickness of the metal films can improve Sprobe drastically by
Rev. Sci. Instrum. 85, 114901 (2014)
FIG. 2. The modeling result for Sprobe and the electrical resistance of the probe with respect to the thickness of metal film on the tip: (a) comparison of Sprobe of the probe with uniform metal thickness and that with relatively thicker metal lead line (∼50 nm) on the cantilever, (b) comparison of the electrical resistance for the two kinds of probes.
thermally insulating the tip, it also increases Tn significantly due to a sharp rise in pad-to-pad resistance. Since reducing the thickness of the metal films greatly improves Sprobe , we devise a design that can take advantage of the thermal insulation gained by reducing the thickness of the metal films without causing a sharp increase in pad-to-pad resistance. We note that in terms of electrical design, most of the electrical resistance occurs in the lead line on the cantilever. However, in terms of thermal design, the thermal insulation of the temperature sensor is predominantly affected by the metal films on the tip. Therefore, the optimal design for minimizing xn is that the metal films on the tip should be deposited as thin as the fabrication process allows to insulate the thermocouple integrated at the end of the tip as much as possible. In addition, the metal films composing the lead lines on the cantilever should be made thick enough so as to prevent the pad-to-pad resistance from growing excessively. In order to verify the effect of the suggested design, we compare Sprobe and the electrical resistance of the probe, which has a uniform metal thickness on the tip and cantilever, with those of the probe with a relatively thicker metal lead line (∼50 nm) on the cantilever through a theoretical analysis.37 As shown in Fig. 2(a), even though the thickness of the metal on the cantilever is kept the same, Sprobe increases sharply only if the metal film thickness on the tip is reduced. At the same time, as shown in Fig. 2(b), if only the thickness of the metal films on the tip is reduced, the pad-to-pad resistance barely increases. Based on the theoretical analysis and modeling results above, we determine the design parameters of the SThM probe, as shown in Table I. The thicknesses of gold and chromium films on the tip of the thermocouple probe for design P1, P2, and P3 are 10, 20, and 30 nm, respectively. Considering ease of fabrication, we determine the ratio between the thickness of gold films on the tip and that on the cantilever to be 1:3 and the thickness of the chromium film on the cantilever to be 90 nm thicker than that on the tip. Scanning electron micrographs of thermocouple probes fabricated according to the design parameters listed in Table I are depicted in Fig. 3. The overall fabrication steps are summarized in Sec. S2 of the supplementary material.40 In order to minimize the influence of the absorbed heat flux of the laser on the reflector, as depicted in Fig. 3(b), the reflector is located as far away from the tip as possible and the fins are attached to the reflector so that the absorbed heat flux is dissipated to the surrounding air as much as possible before the heat
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Hwang, Chung, and Kwon
Rev. Sci. Instrum. 85, 114901 (2014)
FIG. 3. Scanning electron micrographs of thermocouple SThM probes fabricated in this study: (a) the cantilever and tip of the probe (side view), (b) the reflector located far away from the tip and the fins attached to the reflector so that the absorbed heat flux from the AFM feed laser is dissipated to the surrounding air as much as possible before the heat flux reaches the tip (top view), (c) chromium film on the cantilever deposited thicker than that on the tip, (d) the end of the tip of the P1 design probe (tip radius: 26.7 nm), (e) the end of the tip of the P2 design probe (tip radius: 33.3 nm), and (f) the end of the tip of the P3 design probe (tip radius: 70.0 nm).
flux can reach the tip. As shown in Fig. 3(c), the chromium film deposited on the cantilever is thicker than that on the tip. Scanning electron micrographs of the tips of thermocouple probes fabricated according to probe designs P1, P2, and P3 are shown in Figs. 3(d)–3(f). These figures show that the radius of each tip, Rtip , is about 26.7, 33.3, and 70.0 nm, for probe designs P1, P2, and P3, respectively. IV. EVALUATION OF PERFORMANCE OF THE FABRICATED PROBE
As explained above, the spatial resolution is determined not only by the intrinsic parameters (Sprobe , Tn , Rtip ) determined by the design of the SThM probe but also by extrinsic variables ((dT/dx)s , hst ) irrelevant to the probe. Hence, SThM probe performance must not only be judged simply by the spatial resolution. The performance of a SThM probe should be represented by the intrinsic parameters of the probe such as Sprobe , Tn , and Rtip . First, we experimentally estimate Sprobe of the fabricated probe. According to Eq. (4), Sprobe can be written as Sprobe =
1 . hst Ac ϕ
(11)
The Ac in Eq. (11) can be obtained from Eq. (7) using the values of Rtip evaluated from Figs. 3(d)–3(f). Thus, once ϕ is measured experimentally, Sprobe of a certain probe can be compared with those of others using Eq. (11). hst is the interfacial heat transfer coefficient between the probe tip and the sample surface, and so is assumed to be constant for a particular sample. The experimental setup for measuring ϕ is illustrated in Fig. 4(a). The setup is composed of a preamplifier, a notch-filter, a signal access module, a SThM probe, and an atomic force microscope (AFM). To determine ϕ, as shown in Figure 4(b), the temperature measured by the thermocouple of the probe is monitored, while the tip of the probe approaches an aluminum line heater, whose temperature is measured from
its temperature coefficient of resistance. Until the tip touches the heater, the temperature of the tip rises gradually due to the increasing heat transfer through the air. At the moment the tip touches the sample, the temperature of the tip jumps from Tnc to Tc due to Qst . The temperature jumps are measured at several different temperatures of the sample. Once, Ts , Tnc , and Tc are obtained in this manner, ϕ can be evaluated from Eq. (4). The ϕ for this particular probe (P1) is 4.92 K/K. Repeating the same procedure, we measure ϕ values in order to evaluate Sprobe for the standard and P1, P2, P3 design probes. In Fig. 4(c), Sprobe for the standard and P1, P2, P3 design probes are compared with the analysis in Fig. 2(a). The value of hst that minimizes the mean square of the difference between the analysis result and experimental data is 5.3 × 108 W/m2 K. As predicted from the modeling, Sprobe increases sharply with decreasing metal film thickness on the tip. Sprobe of the P1 design probe is about 4.7 times higher than that of the standard design probe. In addition, we compare Sprobe for the probe fabricated in this study with that in a previous work. In this previous work,29 the temperature response of the probe with respect to the vertical position is monitored, while the probe approaches an electrically heated 350 nm wide gold heater; and this temperature response is represented by a dimensionless temperature φ. We obtain Tc and Tnc from the monitored dimensionless temperature; and, by substituting thus obtained Tc , Tnc and Rtip into Eq. (4), evaluate ϕ of the thermocouple probe developed in the previous work. As shown in Fig. 4(c), Sprobe of the standard design probe and that of the P1 design probe are about 18 times and about 85 times higher than Sprobe of the probe developed in the previous work, respectively. With the estimation of Sprobe completed, Tn must now be estimated. For a thermocouple probe, Tn is given by 4kB T Rf , (12) Tn = S where kB is the Boltzmann constant, T is the absolute temperature, R is electrical resistance of the SThM probe, f is the
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114901-7
Hwang, Chung, and Kwon
Rev. Sci. Instrum. 85, 114901 (2014)
FIG. 4. (a) The experimental setup for the measurement of ϕ of the probe. (b) The temperature measured by the thermocouple of the probe as the tip approaches the sample. The measured temperature rises gradually due to the heat transfer through the air. When the tip makes contact with the sample, the temperature of the tip jumps from Tnc to Tc due to the heat flux through the tip-sample contact. (c) Comparison of Sprobe of the standard and P1, P2, P3 design probes evaluated with the measured ϕ (symbols) and Sprobe obtained from 1D modeling (solid line). (d) Comparison of the measured electrical resistances of SThM probes (symbols) with the modeled electrical resistances as a function of the thickness of the metal film on the tip (solid line: thick metal lead line, dashed line: uniform metal thickness).
frequency bandwidth, and S is the Seebeck coefficient of the thermocouple. To obtain Tn , we measure the electrical resistance of the fabricated probes and compare the measured data with the modeling results in Fig. 4(d). For probes with a uniform metal thickness, the measured resistance is approximately two times larger than that estimated by the modeling, which takes into account the dependence of the electrical resistivity on thickness. Nevertheless, the trend in measured resistance with respect to thickness is very similar to the modeling result.29 For the probe with a thick lead metal film, the measured resistance (for P1, P2, and P3 design SThM probes) does not decrease as sharply as that estimated by the modeling. Nevertheless, the measured electrical resistance is smaller than that of the probe with uniform metal thickness over the entire range of metal thickness. For the P1 design SThM probe in particular, the reduction in resistance (∼30%) is most evident. Now that the electrical resistances of the probes are measured (1906.4 ± 113.6 , 914.6 ± 121.0 , and 877.0 ± 36.7 for P1, P2, and P3 design SThM probes, respectively), we calculate Tn for each probe using Eq. (12), along with T, f, and S, set to be 300 K, 1 kHz, and 20.5 μV/K, respectively. For each of the P1, P2, and P3 design SThM probes, Tn is found to be 8.7 mK, 6.0 mK, 5.9 mK, respectively. The last intrinsic parameter that represents the performance of the SThM probe is Rtip . If the tip is fabricated exactly as intended, Rtip should be equal to the summation of the tip radius of the bare silicon oxide tip and the thicknesses of the metal films composing the thermocouple junction. However, due to the uncertainties that always accompany the actual fabrication process, Rtip for probes fabricated according
to the probe designs P1, P2, and P3 are about 26.7, 33.3, 70.0 nm, respectively, as shown in Figs. 3(d)–3(f).
V. ENABLING LOW-NOISE, HIGH-RESOLUTION NP SThM USING FABRICATED PROBES
We demonstrate here that because of the significant improvement in intrinsic parameters (Sprobe , Tn , Rtip ) of the probes fabricated in this study, the NP SThM method can be used to quantitatively measure the temperature profile without perturbations in sample temperature from the heat flux through the tip-sample contact point, even if the heat transfer coefficient at the tip-sample thermal contact changes due to a variation in surface properties such as wettability and hardness. Furthermore, by analyzing the measured signals, we demonstrate that the spatial resolution of NP SThM implemented using the probe fabricated in this study is high enough for experimental analysis of recently developed nano-devices and materials. An overall schematic of the sample used for the demonstration is depicted in Fig. 5(a). The platinum heater is patterned into a 4-probe configuration on a 300 nm thick SiO2 layer thermally grown on a silicon wafer. In order to change only the surface properties without affecting the temperature distribution, half of the sample surface is coated with a very thin (∼50 nm) Teflon layer, which is intended to change both the wettability and hardness of the surface. As shown in the micrograph in the inset of Fig. 5(a), the contact angle of water on the Teflon-coated surface is much larger than that on the SiO2 surface.
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Hwang, Chung, and Kwon
FIG. 5. (a) An overall schematic of the sample used for the demonstration of NP SThM. A platinum heater is patterned into a 4-probe configuration on a 300 nm thick SiO2 layer thermally grown on a silicon wafer. Half of the platinum heater is coated with a very thin (∼50 nm) Teflon layer. The contact angle of water on the Teflon-coated surface is much larger than that on the SiO2 surface (inset). (b) Comparison of the temperature distribution across the heater (a–a ) obtained by NP SThM and that by finite element modeling.
To demonstrate quantitative temperature profile measurements, we measure the temperature distribution across the heater (a–a ) as illustrated in Fig. 5(a). The experimental setup for NP SThM is the same with that in Fig. 4(a). During an active mode scan, the thermocouple junction of the probe is heated by an AFM feedback laser. The temperature profile from NP SThM matches quite well with that obtained by finite element modeling. We now check whether the surface properties of the sample affect the quantitative temperature profile during the mea-
Rev. Sci. Instrum. 85, 114901 (2014)
surement using NP SThM. To check this influence rigorously, we carry out NP SThM along a line, where only the surface properties change and the temperature is kept constant. As shown in Fig. 5(a), the temperature is measured through NP SThM along a scan line (b–b ) about 250 nm away from, and parallel to the platinum heater, crossing the hydrophilic (silicon oxide) and the hydrophobic (Teflon-coated) surfaces. Since the aspect ratio of the heater (250 μm long and 3.2 μm wide) is quite large, we assume that the temperature is kept constant along a line parallel with and close to the heater (
