Scanning thermal microscopy (SThM) is capable of collecting topography feedback and probing qualitative thermal properties simultaneously. Although topography and thermal feedback signals are obtained from two independent loops without affecting each other, thermal feedback can be distorted by topography feedback, resulting in a topography-related thermal signal, defined as the artifact phenomenon. Based on this situation, the instrument thermal response is no longer accurate, and the intrinsic generation reason and affecting factors of the artifact are still not clear. In this work, different polymeric-based materials were prepared to construct varied contact geometries at the tip/sample contact interface. Identification of the artifact was performed based on the investigation of corresponding topography and thermal feedback. Generation mechanisms of the artifact were further proposed aiming at different contact situations. This work not only clarifies the generation reason and affecting factors of the artifact but also suggests the sample preparation requirements for the eliminated artifact and accurate thermal characterization through SThM.

Thermal characterization for nanomaterials with a high spatial resolution is essential for the design, synthesis, and regulation of nanodevices.1 Based on the Atomic Force Microscopy (AFM) platform, Scanning Thermal Microscopy (SThM) is able to capture the thermal properties of different microregions.2 It can be employed in varied application fields, including determination of phase miscibility, identification of contaminant, mapping material distribution in composites, and so on.3–7 

Being recognized as a powerful tool to characterize thermal properties at the micro-/nanoscale, issues were also reported for SThM. One common phenomenon that has been frequently mentioned is the accuracy and authenticity of the testing results. Literature reported that the thermal feedback may have a certain relationship with the topography feedback signal, which, in fact, should be independent of each other.8,9 Such a “topography-related thermal signal” was defined as the artifact phenomenon, leading to the dubious thermal characterization. The artifact should not be observed since the topography and thermal feedback are obtained from two separate loops, as illustrated in Fig. 1(a). However, after realizing the core mechanism of the instrument, it is not hard to find that the total heat input from the thermal tip to sample is the summation of the tip/sample interface heat dissipation and heat transmitted to the sample. The tip/sample contact interface can be considered as a thermal resistor that bridges the tip and sample [Fig. 1(b)]. Assuming that the tip resistance (Rtip) is constant, the total energy input is related to both the interface thermal resistance (Rinterface) and sample thermal resistance (Rsample). Only if the influence of interface thermal resistance is excluded, the thermal feedback signal can represent the actual sample thermal properties. The interface thermal resistance usually consists of mechanical contact thermal resistance (Rcontact), air-conduction thermal resistance (Rair), water meniscus-conduction thermal resistance (Rwater), and thermal radiation resistance (Rradiation)10,11 [Fig. 1(b)]. It is widely accepted that, under most circumstances, water meniscus heat conduction and thermal radiation are much smaller than the other two resistances. Luo et al. first demonstrated that the contact thermal resistance is related to the real tip/sample contact area.12 They found that the topography change could directly affect the contact thermal resistance and further produce the topography-related artifact. The existence of air thermal resistance will generate the air conduction-induced artifact. Compared to the topography-related artifact, the air conduction-induced artifact can be reduced or eliminated by operating the instrument in the ultra-high vacuum atmosphere (UHV-SThM).13 The contact thermal resistance-induced heat dissipation is difficult to quantify due to the irregular surface geometries encountered by the tip during the scanning process. Researchers developed several experimental approaches to investigate and eliminate the topography-related artifact. Null-point SThM accompanied by the double scan technique was employed to investigate the influence of surface geometry on contact heat loss.14 Cross-sectional SThM was employed to perform the characterization on the flat sample surface with the eliminated influence induced by the surface geometry.15 SThM was combined with spatially resolved Raman spectroscopy to obtain accurate thermal reflection with a quantified contact heat loss.16 The topography-induced artifact can also be numerically estimated by the neighbor volume technique, neural network approach, and finite element (FEM) analysis.17 Researchers also designed a custom-fabricated probe for the simultaneous acquisition of contact thermal resistance and sample surface temperature, and the artifacts can be suppressed under this situation.18 The topography-related artifact of thin films can be avoided after going through a planar hot pressing process.19 

FIG. 1.

Schematic diagram of (a) SThM and marked two separate feedback loops (topography and thermal) and (b) heat flow and corresponding thermal resistance circuit of the SThM setup.

FIG. 1.

Schematic diagram of (a) SThM and marked two separate feedback loops (topography and thermal) and (b) heat flow and corresponding thermal resistance circuit of the SThM setup.

Close modal

Although all the above-mentioned methods provide alternative solutions to reduce or eliminate the topography-related artifact, these techniques usually have critical requirements, such as a vacuum testing environment, customized thermal probe, complex sample handling process, or other instruments that need to be employed. The most fundamental approach to solve the testing error caused by the artifact is to clarify its generation reason and affected factor, which usually require a thorough understanding of the heat conduction at the tip/sample contact interface. In this work, SThM characterization was performed based on the thermal tip operated under the contact mode. Since the testing samples are both polymeric-based materials, the height difference between the tip and the sample can be considered at the same level. Thus, the influence of the air-conduction induced artifact can be regarded as equivalent during the test. The topography-related artifact was investigated in-depth by designing varied contact surface geometries. Specifically, the uniform polymer films with different surface roughness and polymer/particle composite films with different peak height values were prepared to study the contribution and influencing factors of the artifact. Detailed line profiles for topography and thermal reflection in the localized scanning areas were collected and analyzed for the identification of the artifact. Furthermore, the generation mechanisms of the artifact were discussed based on these two systems. This work also suggested the requirements of the sample preparation for the accurate thermal characterization with the eliminated artifact phenomenon in the micro/nanoscale through SThM.

Polydimethylsiloxane (PDMS) and epoxy resin were prepared as uniformed polymer films. PDMS (sylgard-184) was provided by Dow Corning. Epoxy resin (826 RS, 178–186 g/eq) was purchased from Hexion Inc., and the curing agent (JEFFAMINE T403, max 0.25 wt.% water) was provided by Huntsman Corporation. Polyvinyl alcohol (PVA) was employed as the matrix material in the polymer composite system, and SiO2 was employed as the introduced particle. PVA powder (Mw: 14600–18600) was purchased from Sigma-Aldrich. The SiO2 solution was prepared via the following method: 30 ml NH3OH and 500 ml EtOH were first mixed with different amounts of water and stirred for 5 min, and then 20 ml Tetraethyl orthosilicate (TEOS) was added dropwise to obtain the SiO2 solution. The size of the SiO2 particles was controlled by adjusting the water amount (20, 10, and 0 ml), and the prepared solutions were named SiO2-1, SiO2-2, and SiO2-3, respectively. The average particle size for SiO2-1, SiO2-2, and SiO2-3 was 90, 250, and 350 nm, characterized by Dynamic Light Scattering (DLS).

1. Uniformed polymer film preparation

The PDMS film was prepared by mixing the base monomer with the curing agent, for which the ratio was set as 1:0.2. The epoxy film was prepared by mixing the epoxy resin with the curing agent at the ratio of 1:0.3. The well-mixed specimen was then placed in a rubber mold for curing. Samples were degassed in a vacuum oven for 30 min and then cured at 80 °C for 4 h in a convection oven to obtain films. The major difference between these two uniformed films was the surface roughness. Except for the material itself, the major difference between these two films in the surface properties is roughness. The prepared films usually have a thickness value larger than 1 mm.

2. Polymer/particle composite film preparation

PVA solution (8 wt.%) was prepared by dissolving PVA powder in deionized water at 90 °C. PVA and SiO2 solutions were then mixed with a volume ratio of 1:0.05 with a final silica concentration at around 2% in the composite. The mixed solution was stirred overnight for better dispersion. The solution was then dropped on a glass substrate and placed in a 40 °C oven for 72 h to remove water and obtain films. According to the employed SiO2 solutions, the prepared samples were marked as PVA/SiO2-1, PVA/SiO2-2, and PVA/SiO2-3 with varied particle sizes. The major difference in these films was the peak height value (decided by the SiO2 particle size), which will be discussed later in detail. The thicknesses of all the prepared samples were larger than 50 µm. It should be noticed that the soft nature of those polymer-based films makes them not the ideal candidates for the contact Atomic Force Microscopy (AFM) test.

SThM characterization was performed on Park System XE7 atomic force microscopy. The thermal tip was made of a silicon base and thermally grown SiO2 cantilever. The base dimension was 2 × 3 mm2, and the cantilever dimension was 150 × 60 × 1 µm3. The resistor metal was made of 5 nm NiCr and 40 nm Pd, the tip height was 12 µm, and the radius was around 100 nm. The resistance of the tip was around 200–600 Ω, and the thermal coefficient of resistivity was about 1 Ω/oC. The spring constant was 0.45 N/m, and the resonance frequency was 48 kHz. The pre-setting probe current was 1.20 mA. In this work, the conductivity contrast mode (CCM) was adopted for which the thermal tip was functioning as a resistive heater. Probe current was measured as an index of thermal conductivity. Force–displacement (F–D) characterizations were performed by the same tip via the original AFM platform. Energy-dispersive x-ray spectroscopy (EDS) characterization was performed by Hitachi TM 3000 Tabletop Scanning Electron Microscope (SEM) with a sputter-coated gold layer on the sample surface.

Sample morphology and thermal properties were simultaneously characterized by SThM. Figure 2(a) compares surface topography and thermal mapping images of the uniformed PDMS film. The line profiles show the local height and the thermal response marked with the dashed line in the corresponding mapping image. Data were collected in both the horizontal and vertical directions marked by the X-axis and Y-axis, respectively. Based on the working principle of SThM, the red part in the thermal image represents a larger probe current and higher thermal conductivity, while the blue part represents a smaller probe current and lower thermal conductivity. The surface of the PDMS film was relatively smooth with a root mean squared roughness (Rq) value of 1.101 nm. The collected data points from topography and thermal images were randomly distributed and did not show any correlation with each other, while, in the epoxy film, a much rougher surface was observed with the Rq value of 543.4 nm [Fig. 2(b)]. A certain correlation was observed between the topography and thermal mapping images: areas with high altitudes behaved with smaller probe current values. This phenomenon was further verified through the comparison of the height and probe current line profiles: peaks with values of 1.237 μm, 601 nm, and 745 nm in the topography line profiles were corresponding to the valleys with values of 4.814, 2.112, and 2.540 μA in the thermal line profiles. The current/height contrasts of the three peaks were 3.892, 3.514, and 3.409 A/m with an average value of 3.605 A/m. This inverse relationship between topography and thermal feedback was consistent with the artifact phenomenon described in earlier reports.20–23 Based on the study of these two uniformed polymer films, PDMS and epoxy, it is not hard to conclude that the surface roughness was essential in artifact generation.

FIG. 2.

AFM topography, SThM thermal mapping images, and corresponding line profiles of (a) PDMS and (b) epoxy film at different directions.

FIG. 2.

AFM topography, SThM thermal mapping images, and corresponding line profiles of (a) PDMS and (b) epoxy film at different directions.

Close modal

Polymer composite films with certain surface geometries were designed to study the generation of the artifact. Due to the disparate morphologies of different regions in the composite, it is meaningless to evaluate the artifact in terms of the surface roughness. Instead, localized profile analysis of certain selected areas with various geometries would be critical.

Specifically, PVA/SiO2 composites with varied particle sizes were designed for which the embedded SiO2 will generate the different topography features. EDS was first used to study the existence formation of the SiO2 particles in the composite system. It proves that the surface layer belongs to the polymer and the detection signal of SThM was the changes in thermal feedback caused by the localized topographic factors. Figures 3(a) and 3(b) provide the element analysis images of the particles and polymer matrix areas. The clear response of the C atom in the particle area demonstrated that the particles were embedded inside the matrix. The general morphology was investigated by AFM 3D images [Fig. 3(c)] that confirmed the particle size variations in the composite films. The images went through a flatting process to clearly show the differences in various regions. The dark parts in the topography images were the PVA matrix, and the white parts were the raised polymer surface with aggregated SiO2 particles underneath. The maximum peak height value observed in these three samples were around 400, 200, and 120 nm, respectively. The corresponding SThM 3D images are shown in Fig. 3(d). At a holistic level, all the raised parts behave with lower thermal conductivity values, which is exactly the manifestation of the artifact. Thus, to have a deeper and better understanding of the artifact as well as investigate its generation mechanism, certain special areas of each sample need to be selected to perform further detailed analysis on the correspondence of topography and thermal responses.

FIG. 3.

SEM image and EDS elemental spectrum of (a) particle area and (b) polymer matrix area; AFM (c) and SThM (d) 3D images of the polymer composite films.

FIG. 3.

SEM image and EDS elemental spectrum of (a) particle area and (b) polymer matrix area; AFM (c) and SThM (d) 3D images of the polymer composite films.

Close modal

Three typical cases were selected to perform the studies based on the characterization and analysis of the height and probe current feedback, including the line profiles along with a certain direction for varied peak height values, line profiles of a certain peak along with different directions, and line profiles of the polymer matrix in different areas.

Figure 4 shows the mapping images and corresponding line profiles of varied peaks along the horizontal direction. Figures 4(a)4(c) show the characterization results of the larger peaks in PVA/SiO2-1, PVA/SiO2-2, and PVA/SiO2-3, respectively. Figure 4(d) shows the characterization result of the smaller peaks in PVA/SiO2-3. Obvious inverse correlations between the height and probe current feedback were observed in the first three images, indicating the existence of the artifact. Specifically, the largest peak height value was 358 nm with a probe current difference of 437 nA. With the peak height values decreased to 233 and 122 nm, the probe current difference decreased to 248 and 134 nA. The calculated current/height contrasts of the three above peaks was 1.221, 1.064, and 1.098 A/m with an average value of 1.128 A/m. The decreased current/height contrast values compared to the uniformed polymer films indicate the weakening of the artifact to a certain extent. The impairment was caused by the high intrinsic thermal conductivity of SiO2 (∼1.5 W/mK). The underneath SiO2 particles provide a more preferable heat conduction pathway, leading to an increased probe current of the raised area and decreased current/height contrast value. However, this inverse correlation disappeared when the peak height value further decreased to 27, 19, and 17 nm [as shown in Fig. 4(d)]. The line profile of the probe current was randomly distributed without observing the corresponding peaks or valleys. Based on the above observations, for the localized area, the peak height value has significant influences on the generation of the artifact.

FIG. 4.

AFM topography, SThM thermal mapping images, and corresponding line profiles of the peaks along the horizontal direction for (a) PVA/SiO2-1, (b) PVA/SiO2-2, and (c) and (d) PVA/SiO2-3, respectively.

FIG. 4.

AFM topography, SThM thermal mapping images, and corresponding line profiles of the peaks along the horizontal direction for (a) PVA/SiO2-1, (b) PVA/SiO2-2, and (c) and (d) PVA/SiO2-3, respectively.

Close modal

Since the transverse scanning direction is consistent with the direction of the former horizontal line profile analysis, characterization of a certain peak along other directions was performed to confirm that the scanning direction did not affect the generation of the artifact. Figure 5 shows the mapping images and corresponding line profiles of certain peaks along the vertical direction. The same inverse correlation between topography and thermal feedback was observed in most circumstances except the peak height value of 32 nm. The probe current difference was decreased with the reduced peak height values. Although a smaller probe current difference with the value of 21 nA was observed of line 2 in Fig. 5(c), the correspondence was not clear compared to the previous ones, indicating a reduced artifact phenomenon. Except for the last case, the above samples show the current/height contrast values of 1.142, 1.151, 1.094, 1.292, 1.126, and 1.095 A/m. The perfect agreement with the horizontal analysis data confirmed that introduced SiO2 particles play an essential role in increasing heat conduction and final acquisition of the thermal feedback signal.

FIG. 5.

AFM topography, SThM thermal mapping images, and corresponding line profiles of the peaks along the vertical direction for (a) PVA/SiO2-1, (b) PVA/SiO2-2, and (c) PVA/SiO2-3.

FIG. 5.

AFM topography, SThM thermal mapping images, and corresponding line profiles of the peaks along the vertical direction for (a) PVA/SiO2-1, (b) PVA/SiO2-2, and (c) PVA/SiO2-3.

Close modal

Figure 6(a) shows the mapping images and corresponding line profiles of the PVA matrix at different locations. Two different cases were selected to perform the analysis: polymer matrix near and far away from the SiO2 particle. A peak with the height value of 37 nm was observed for the matrix area close to the particle, which was caused by the local changes in the topography applied by the induced particle. Surprisingly, an obvious peak with the value of 128 nA was also observed in the thermal profile. This positive relationship between the topography and thermal profile went against the formerly mentioned artifact phenomenon. To the best of our knowledge, this phenomenon was caused by the “long-range confinement” of the introduced particle applied to the adjacent polymer matrix, rather than another expression of the artifact.3 This long-range confinement would rearrange the polymer chains to a more oriented state. Under this situation, there will decrease the phonon scattering between the polymer chains, and an improved heat conduction process with increased thermal conductivity is expected. The orientation degree of the polymer chain could be evaluated by the micro-mechanical properties characterized by the Force–Distance (F–D) spectroscopy.24 Specifically, the stiffness values calculated from the curve slope of the interaction areas were used to represent the micro-mechanical properties. Based on the same equipment platform, it is not only convenient but also accurate to characterize the micro-mechanical properties of the local scanning area. Figure 6(b) shows the F–D curve comparison of the polymer matrix near and far from the particle. The stiffness of the polymer matrix far from the particle was much larger than that near the particle, indicating the higher orientation degree of the polymer chains in the polymer matrix near the particle. For the line 2 in Fig. 6(a), the analyzed area was far from the induced particle with polymer chains hardly affected, confirmed by the similar stiffness value of pure PVA. There was no positive correlation between topography and thermal signal observed. Instead, with a littlish peak height value of 17 nm, the probe current line profile was randomly distributed, indicating that the artifacts are not dominant here, which was in good consistency with the former horizontal analysis results.

FIG. 6.

(a) AFM topography, SThM thermal mapping images, and corresponding line profiles of the polymer matrix at different distances from the particle and (b) F–D curves and corresponding stiffness value of the PVA matrix near, far from the particle and pure PVA.

FIG. 6.

(a) AFM topography, SThM thermal mapping images, and corresponding line profiles of the polymer matrix at different distances from the particle and (b) F–D curves and corresponding stiffness value of the PVA matrix near, far from the particle and pure PVA.

Close modal

Synthesizing above all kinds of cases discussed, it is not hard to conclude that roughness was the direct reason for the generation of the artifact in the uniformed polymer films. For the polymer composite films, situations are more complicated. Not only the local topography influences the thermal feedback signal but also the high intrinsic thermal conductivity of the introduced particle. The still observed artifact phenomenon in the composite with larger-sized particles implies the high thermal conductivity of SiO2 cannot eliminate the artifacts caused by the topographic factors. The peak height value should be responsible for the artifact generation in the composite films. According to the image-producing mechanism of the AFM, the overall image was pieced together by the feedback signals of each point. The line profile analysis for the uniformed polymer films with different roughness was focused on the whole scanning image that was more likely at the macroscopic level, while the line profile analysis of a single peak in the composite films was more likely at the microscopic level. Based on this understanding, the following discussion for the formation mechanism of the artifact will be expanded in the macro-view and micro-view, aiming at uniformed polymer film and polymer composite film, respectively.

As stated in the Introduction, the total heat input from the instrument (Qinput) is equal to the summation of the heat flux of the sample (Qinput) and heat flux at the tip/sample interface area (Qinterface),

Qinput=Qsample+Qinterface.
(1)

Thermal feedback signals were obtained by subsequent data processing of the heat transmitted to the sample. When the Qinterface dominated the overall conduction path, the feedback signal was more representative of the interface heat flux, leading to the unreal thermal reflection captured and artifact phenomenon. Investigations of the interface heat flux will be carried out from macroscopic and microscopic aspects, respectively.

1. Interface heat dissipation investigation from the macro-view

The study of interface heat flux at the macroscopic scale is more suitable for the conduction analysis of uniform contact surfaces. Under this situation, multi-point contact was considered between the tip and sample. A reliable empirical model was proposed to correlate the probe current with the contact surface characteristics in our previous work based on isothermal flux tube mode,25 

I=ARsample+Rcontact+B=A1πka+14ka+HπkFσm+B.
(2)

I is the average probe current of the whole scanning image, Rsample is the sample thermal resistance, and Rcontact is the contact resistance at the tip/sample interface. Rsample was calculated by the moving heat source method:26 Rsample=1πka. Rcontact can be described in terms of 14ka+HπkFσm, a is the tip radius, k is the sample thermal conductivity, H is the sample micro-hardness, σ is the sample roughness, F is the contact force applied by the tip, and m is the sample surface slope. A and B are constant parameters related to the instrument. It is not hard to conclude that the effect of surface roughness on probe current was decided by the magnitude between the three terms in the denominator. These three items were systematically compared through a splitting method. Specifically, HπkFσm was thermal resistance contributed by surface contact with the abbreviation of Rsc, 1πr0k+14ka was thermal resistance only related to the sample thermal conductivity with the abbreviation of Rconst. The variation trends of Rsc and Rtotal with surface roughness are described in Fig. 7. Suppose the interaction error between Rsc and Rconst was 5%. When σ was smaller than 13.51 nm, Rconst was 20 times larger than Rsc, the contribution of the interface thermal resistance caused by roughness to the overall thermal resistance of the system was negligible, and the instrument thermal feedback was able to represent the real thermal conductivity without affected by the topography variation, leading to the elimination of the artifact. When σ fell between 13.51 and 27.02 nm, Rsc increased to between 120Rconst and 110Rconst and the artifact phenomenon was gradually emerging. With a continuous increase in σ value (27.02–270.2 nm), Rsc increased further accompanied by the generation of obvious artifact. When σ was larger than 270.2 nm, Rsc was much larger than Rconst and the interface heat dissipation dominated the overall heat conduction. Under this situation, the thermal feedback signal was completely a false reflection that cannot represent the local thermal properties at all. This analysis quantifies the effect of the surface roughness on the generation of the artifact in the uniformed system. It also verifies the observations in the previous experimental section: no artifact was observed for the PDMS film with the surface roughness of 1.101 nm, while an obvious artifact was observed for the epoxy film with the surface roughness of 543.4 nm. Macroscale analysis confirmed that the surface roughness played an essential role in the artifact generation in the uniformed system.

FIG. 7.

Rsc, Rconst, and Rtotal change with the surface roughness.

FIG. 7.

Rsc, Rconst, and Rtotal change with the surface roughness.

Close modal

2. Interface heat dissipation investigation from the micro-view

Micro-view investigation was more suitable for the heat dissipation analysis of the composite system, in which a single-point contact was considered. Different from multi-point contact investigation that focuses on the whole scanning plane, the study at the micro-level place more emphasis on the analysis of the local area. The overarching assumption of microanalysis was that the tip and sample were rigorously contacted at each moment and the cantilever will generate deformations when the tip encounters different geometries. Under this situation, the determining factor for mechanical contact heat conduction is the real contact area between the tip and sample.

The most commonly used model was the spherical contact mechanics model in which continuum mechanics was applied to model contact between the tip and sample surface. The real contact area A can be calculated via the Hertz equation27,28

AHertz=π3FR4E2/3.
(3)

In this equation, F is the loading force of the tip, R is the effective radius of the contacting bodies, calculated by R=(1R1+1R2)1 (R1 and R2 are the curvatures of the tip and sample, respectively), and E is the effective elastic modulus. The contact situation changes when the tip encounters varied surface geometries, as illustrated in Fig. 8(a). At the initial contact, the flat sample surface can be regarded as a long flat plate with an infinite radius of curvature. Under this situation, the effective radius was R1 with the real contact area of AHertz=π(3FR14E)2/3. When the tip was meeting a raised part, a contact surface with the radius of curvature (R2) was produced. The real contact area became smaller since R2 was involved in the formula. There would be insufficient heat conduction through the mechanic contact due to the reduced contact area, in other words, more heat transmitted to the air.

FIG. 8.

(a) Contact situation change as the tip encounters with varied surface geometries; (b) geometric schematic of the tip/sample contact surface via thermal wave theory; and (c) tip and cantilever change at different heights, accompanied by the characterizations of the corresponding selected composite films.

FIG. 8.

(a) Contact situation change as the tip encounters with varied surface geometries; (b) geometric schematic of the tip/sample contact surface via thermal wave theory; and (c) tip and cantilever change at different heights, accompanied by the characterizations of the corresponding selected composite films.

Close modal

In addition to using the real contact area to evaluate mechanical heat conduction, heat transfer at the interface was analogous to the wave transfer, inspired by the thermal wave theory. Although the interfacial heat transfer was fundamentally different from the essence of the thermal wave theory, its description of the energy transport process of specific geometry can still be used for reference. Thermal wave theory considers the reflection and refraction of heat at the interface, which was more applicable for the single point contact heat transfer analysis.29–31 The schematic diagram of the thermal wave theory is shown in the inset of Fig. 8(b), including the incident, reflection, and refraction waves. The angles between the waves and the normal vector were the incident angle (α), reflection angle (θ), and refraction angle (β), respectively. Cao et al. proposed a theoretical equation to calculate the thermal energy transmittance ratio (r) based on the Cattaneo–Vernotte model,29 shown as follows:

r=2(ρCV)2v2cosθ(ρCV)2v2cosβ+(ρCV)1v1cosθ=QTransmittedQInput.
(4)

r is the thermal energy transmittance ratio (TETR) representing the portion of heat transferred from media I to II. ρ is the material density, CV is the material-specific heat, and v is the speed of the thermal wave in the media. Material speed ratio (m) was employed to correlate the incident and refraction angles,

m=v2v1=sinβsinθ.
(5)

The boundary condition was considered as the tip scanning on the horizontal surface, for which the incident angle was zero. Under this situation, r was calculated as 2(ρCV)2v2(ρCV)2v2+(ρCV)1v1, marked as r0. rθ is the thermal energy transmittance ratio at the reflection angle θ. According to the thermal wave theory, the incident angle α equals to the reflection angle θ. A smaller rθ value indicated more heat reflection at the interface, and rθ decreased with the increase of α. A certain incident angle will produce when the tip encounters the highland areas, as shown in the geometric schematic of the contact surface [inset of Fig. 8(b)]. With the increased incident angle α, more interface heat reflection will be generated. Once it reaches a certain level, the interface heat reflection will be dominated in the overall heat conduction, leading to the inauthentic thermal feedback. The incident angle at this time was marked as αcritical, which was decided by the material physical properties and contact geometries, i.e., CV and m. Since CV and m remained constant during the scanning, whether this inauthentic thermal feedback is generated or not is decided by the tip/sample contact angle, one step further, the particle height the tip encountered.

Specifically, cases with varied valley height values discussed in Sec. III B were employed here to determine the generation of the artifact. Based on the laser reflection mechanism of the AFM platform, the incident angle α was proportional to the cantilever bending angle γ, as illustrated in Fig. 8(b). The cantilever bending angle was related to its deflection, characterized by the AB voltage in the PSPD panel. The PSPD was a position-sensitive photodiode that was used to track the surface geometry change. The AB voltage value was the voltage in the vertical direction of the scanner, which was used to identify the laser movement along the vertical direction and cantilever bending. A higher AB voltage value was corresponding to a higher cantilever bending angle and larger incident angle.32Figure 8(c) illustrates the changes of the tip and cantilever at different heights, accompanied by the characterizations of the corresponding selected composite films. When the height value was 17 nm, the tip was in almost vertical contact with the sample, identified by the laser reflection focused on the PSPD panel center and A–B voltage of 0.0059 V.

When the tip encountered such a smaller height change, there is very little movement of the laser on the PSPD panel and A–B voltage did not change much, indicating a small vertical movement of the tip. Simultaneously, there is no relationship between the scanned topography and thermal image, indicating that sufficient heat flux will be transmitted from the tip to the sample with rarely any heat reflection at the tip/sample interface. By this approach, one may identify the local topographic factors causing the correlation between topography and thermal signal. When the height value increased to 32 nm, the cantilever will be bent, and an obvious angle will be generated between the tip and contact surface, identified by an increased A–B voltage value of 0.2424 V and upward movement of the laser reflection point in the PSPD panel. Due to the increase of larger incident angle caused by the enhanced height (32 nm), the heat transmittance is significantly reduced compared with that by the 17 nm height value [as shown in Fig. 8(c)]. The heat reflection was starting to dominate in the overall conduction, resulting in the emerging artifact. When the peak height was large enough (i.e., 233 nm), the heat reflection will be dominated, and the heat transmitted to the material was much less than the input heat, leading to the inauthentic thermal feedback and artifact phenomenon. Microscopic analysis based on thermal wave theory confirmed that the height difference played an essential role in the artifact generation of the composite system.

To conclude, we studied the topography-related artifact of SThM micro/nanoscale thermal characterization based on polymeric materials. Specifically, the uniformed polymer and composite polymer/particle films were prepared for the investigation. Detailed data analysis was performed, and rational understanding for the artifact generation was provided and verified. For the uniformed polymer films, the surface roughness was the direct factor leading to the observation of the artifact in the thermal feedback. No artifact was observed for the PDMS film with a smooth surface, while an obvious artifact was observed for the epoxy film with a rough surface. Subsequent calculations from the macro-view revealed the relationship between surface roughness and the generation of the artifact, which also supported the experimental observations. When the surface roughness of the material is less than 13.51 nm, accurate characterization can be expected with the eliminated topography-related artifact. For the composite films, the peak height value was the direct cause for the artifact generation. No obvious artifact was observed for a smaller peak height value (<30 nm), while the artifact started to emerge at the peak height value of 32 nm. Therefore, preparing composites with a local height value of less than 30 nm can effectively reduce the generation of the artifact. Obvious artifacts were observed for the larger peak height values, irrespective of the scanning direction. The correlation between the peak heights and artifact generation was analyzed in-depth based on the spherical contact mechanics model and thermal wave theory. This work not only clarifies the generation and affecting factors of the artifact for varied specimens in SThM characterization but also suggests the sample preparation requirements for the eliminated artifact and accurate thermal characterization in micro-/nanoscale, i.e., decrease the surface roughness in the uniformed samples or reduce the particle size in the composite samples.

The authors acknowledge the funding support from the National Natural Science Foundation of China (Grant No. 12004242), the Shanghai Rising-Star Program (Grant No. 21QA1403300), the Shanghai Sailing Program (Grant No. 21YF1414200), Shanghai Polytechnic University (Grant No. EGD21QD22), and the Shanghai Engineering Research Center of Advanced Thermal Functional Materials.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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