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TAM 01 aids in the easy implementation of NP SThM.

In order to make it easy to construct the NP SThM setup and minimize measurement noise, the part surrounded by the dashed line in the experimental setup is built into a PCB module, TAM01. Using TAM01, the experimental setup for NP SThM can be completed easily by just connecting the measurement instruments and AFM to the corresponding BNC terminals of TAM01 with BNC cables. Once the NP SThM setup is completed, NP SThM can be carried out by following the step-by-step instructions.Schematic diagram of an experimental setup for NP SThM

**A-1-1. Theory**

The difference between*T*and_{nc}*T*is due only to_{c}*Q*, which is the heat flux through the tip-sample thermal contact. Hence, one can predict that the difference is proportional to_{ts}*Q*, i.e.,_{ts}^{1,2}-
- (9)

- where,
*C*is a proportionality constant whose dimension is [W/K], and x is the location of the tip-sample contact. And, during the contact mode,*Q*is proportional to the difference between_{ts}*T*and_{c}*T*, i.e._{s} -
- (10)

- where
*G*is the tip-sample thermal conductance. Then, the combination of eqs 9 and 10 yields_{ts} -
- (11)

- where φ is a dimensionless constant defined as
*C/G*._{ts}

**A-1-3. Representative papers**

Quantitative Measurement with Scanning Thermal Microscope by Preventing the Distortion due to the Heat Transfer through the Air,*ACS Nano*^{2}

The double scan technqiue is experimentally verified using high-performance SThM probes. It is shown that the temperature profile measured by using double scan technique is well-matched with the modelled one at nanoscale. It makes possible new breakthroughs in quantitative measurement of temperature profile with SThM.

Moreover, 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.

Therefore, NP SThM is a method that can solve all the three problems of conventional SThM and overcome the limitation of double scan technique. Moreover, it can simultaneously measure the distribution of temperature and thermal properties.

We first explain the theory, measurement procedure, and representative papers of NP SThM with respect to profiling the temperature distribution.

However, it is quite cumbersome to adjust the temperature of the SThM tip,

- (12)

This is the principle equation of NP SThM.

As seen in eq (12) above, NP SThM utilizes the tempeature signals measured in active and passive mode (

Operation of active mode We use the active-mode operation in a dc manner, in which the thermocouple junction of the probe is heated by an ac current of high frequency through the Joule effect and the temperature of the

junction is monitored by measuring the dc thermoelectric voltage from the junction. If the frequency of the ac current is
high enough (>100 kHz) with respect to the thermal time constant of the thermocouple junction (> 1 ms), the periodic
component of the temperature variation of the junction becomes almost negligible. Even though the driving current is ac,
the thermoelectric voltage generated from the junction is dc; hence, the temperature of the junction can be monitored
without the interference of the driving ac bias.

The heating of the thermocouple junction of the SThM probe is not exactly point-heating because the junction of the probe is heated by the Joule effect. However, the current density increases approaching the junction and eventually maximizes at the junction, whose diameter is about ?? nm. Since the temperature peaks sharply at the junction (where the thermoelectric signal is measured), this technique is very close to a point-heating and point-sensing scheme, which is ideal for local measurement.

The heating of the thermocouple junction of the SThM probe is not exactly point-heating because the junction of the probe is heated by the Joule effect. However, the current density increases approaching the junction and eventually maximizes at the junction, whose diameter is about ?? nm. Since the temperature peaks sharply at the junction (where the thermoelectric signal is measured), this technique is very close to a point-heating and point-sensing scheme, which is ideal for local measurement.

Enabling low noise null-point scanning thermal microscopy by the optimization of SThM probe through a rigorous theory of quantitative measurement4

This measurement results shows that NP SThM with NP SThM 01 can measure the temperature distribution at high spatial resolution without difficulty in quantitative measurements owing to variable value of the tip-sample thermal contact resistance, which depends on surface properties such as wettability and hardness, and the perturbation of the sample temperature due to the heat flux through the tip-sample thermal contact.

The thermal conductivity of graphene, which attracts much attention as thermal management and electronic materials, is measured by using NP SThM

We explain the theory and representitative papers of NP SThM with respect to measure the thermal resistances. Since NP SThM simultaneously measure the temperature distribution and thermal resistances, the measurement procedure is same as that explained in A-2-1-2

- It is already proved that the differenc between
*T*and_{c}*T*is proportional to_{nc}*Q*_{st}^{.3, 4} -
- (13)

- where,
*C*is the thermal conductance of the SThM probe from the tip to the surroundings. Obviously, the inverse of*C*can be written as*R*, which is the thermal resistance of the SThM probe from the tip to the surroundings._{p}

Since*Q*is proportional to the difference between the disturbed temperature of sample surface (_{st}*T*) owing to_{s}’*Q*and that of the probe tip (_{st}*T*):_{c} -
- (14)

- where, Gst is the thermal conductance at the tip-sample contact point and proportional to the product of the heat transfer
coefficient,
*hst*, and thermal contact area,*A*._{c}

Then, the combination of eqs (13) and (14) yields -
- (15)

- Using eq (15), Kim
*et al*. experimentally proved that the temperature distribution can be measured quantitatively without the distortion of heat transfer through the air gap.^{2}

However, as seen in eqs (14) and (15),*T*’, which is measured using double scan technique, is the temperature disturbed by_{s}*Q*. In order to measure the undisturbed temperature, the disturbance owing to_{st}*Q*should be considered.If_{st}*Q*occurs,_{st}*T*changes into_{s}*T*, and it is determined by local spreading thermal resistance,_{s}’*R*._{s}

According to the definition o f*R*, one can obtain the relation below._{s} -
- (16)

*T*in eq (14) is eliminated by using eq (16)._{s}’-
- (17)

- The physical meaning of eq (17) is similar with that of eq (14). Eq (17) means that (
*R*+_{c}*R*) should be used instead of_{s}*R*if_{c}*T*is used instead of_{s}*T*._{s}’

The combination of eqs (13) and (17) yields -
- (18)

- Since the undisturbed temperature,
*T*can be obtained through eq (18), it is more advanced than eq (15). However, for experimentally obtaining Ts through eq (18), the ratio of the sum of the contact and spreading thermal resistances to thermal resistance of the probe,_{s},*φ*, should be measured first.

In order to experiementally measure*φ*, as seen in eqs (13) and (17), we utilize that both*(T*and_{s}- T_{c})*T*_{j}*(≡T*is proportional to_{c}- T_{nc})*Q*, and then the ratio between them,_{st}*φ*, remains constant irrespective of*Q*. In other words,_{st}*φ*measured in passive mode is same as that in active mode: subscript 1 denotes the signals measured in passive mode; subscript 2 denotes the signals measured in active mode. Therefore, -
- (19)

- In eq (19), the third term is derived from the first and second terms through basic algebra. The third term of eq (19) is
composed of values which can be obtained by experiment, and then undisturbed temperature,
*T*can be experimentally measured through eq (18)._{s},

The combination of eqs (18) and (19) yields the principle equation of NP SThM, which is same as that derived in terms of profiling the temperature distribution in NP SThM. -
- (20)

The derivation procedure clearly shows the physical meaning of *φ*, the ratio of the sum of the contact and spreading
thermal resistances to thermal resistance of the probe.

Measuring the size dependence of the thermal conductivity of suspended graphene disks.

1. Quantitative scanning thermal microscopy using double scan technique,

2. Quantitative measurement with scanning thermal microscope by preventing the distortion due to the heat transfer through the air,

3. Quantitative temperature profiling through null-point scanning thermal microscopy,

4. Enabling low-noise null-point scanning thermal microscopy by the optimization of SThM probe through a rigorous theory of quantitative measurement,

5. Measuring the thermal conductivity of residue-free suspended CVD graphene using null point scanning thermal microscopy,

6. Measuring the size dependence of the thermal conductivity of suspended graphene disks

- Based on the preceding description
^{1}, we suggest that the phase lag measured by SThM probe is composed of the following four components: -
- (21)

- where,
*ϕ*is the absolute phase lag measured by the STWM setup shown in Fig. 15. The explanation for each component is as follows. First,_{t}*ϕ*is the phase lag due to the thermal insulation surrounding the heater. It is the phase lag of the oscillating temperature of the heater with respect to the phase of the periodic heat generation in the heater. Second,_{i}*ϕ*is the phase lag due to the distance traveled by the wave in the medium and is directly related to the position of the heater. For a one-dimensional plane thermal wave,_{d}*ϕ*is given by_{d} -
- (22)

where, *∆f, α*, and *d* are the frequency, thermal diffusivity, and the distance in the medium traveled by the thermal wave,
respectively. Thermal diffusivity *α* is defined as *k/ρcp*, where *k, ρ*, and *c*_{p} are thermal conductivity, density and the specific
heat. Third, *ϕ*_{r} is the phase lag due to the thermal contact resistance between the probe tip and the surface of the sample.
Finally, *ϕ*_{p} is the phase lag determined by the thermal time constant of the SThM probe, which is subject to several factors
such as tip radius, size of the thermocouple junction, and the materials of the probe.^{1}

Among the four components comprising*ϕ*_{t}, only *ϕ*_{d} is directly related to the position and structure of the heater.
Therefore, isolating and using *ϕ*_{d} by measuring the other components composing *ϕ*_{t}, subsurface heaters are exactly located.^{2}

Among the four components comprising

In Fig. 1, the conventional SThM and quantitative measurement techniques(double scan technique, NP SThM) are compared. Double scan technique and NP SThM can quantitatively profile the temperature distribution and thermal resistances by solving the main problems of conventional SThM. The main problems of conventional SThM and the distinguishable features of quantitative measurement technique are explained below.

The 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

**i) distortion of the measured temperature profile due to the heat transfer through the air gap**Conventional SThM measures the temperature distribution or thermal properties simply using single scanning of a SThM probe, which has a temperature sensor at the end of a sharp tip, on a sample surface. At an early stage of developement of conventional SThM, in order to estimate the temperature distribution from the measured signals, researchers assumed that the heat conduction through the air gap can be ignored and the heat is successively transferred from a sample, an end of a tip, a tip, a cantilever, and a probe body. Therefore, they thought that the temperature signals measured in the contact mode,*T*is proportional to the temperature of the sample surface,_{t},*T*so that only proportional constant,_{s},*ϕ*, which is determined by the ratio between the tip-sample thermal contact resisitance and thermal resistance of the cantilever, is needed for quatitatively obtaining the*T*(Fig. 2)_{s}^{1}.-
- (1)

- However, it is experimentally confirmed that the temperature profile, which is measured by the conventional SThM and
multiplied by
*ϕ*, is totally not matched with the exact temperature profile of the sample surface.^{2}This is caused by the distortion of the thermal signal measured by SThM probe owing to the large heat transfer through the air gap between the probe and sample surface.(Fig. 3)**ii) difficulty in quantitative measurements owing to the unknown and sometimes variable value of the tip-sample thermal contact resistance**Many newly developed nanomaterials and devices are composed of heterogeneous materials, and it is critical to understand the nanoscale transport mechanism at interfaces. For example, during the thermal characterization of the nano-devices 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.(Fig. 4) Since the heat flux at the tip-sample contact is changed by not only the temperature of the sample surface but the tip-sample thermal contact resistance, if the tip-sample thermal contact resistance changes during a scan, a quantitative measurement of temperature and thermal conductivity becomes very difficult.^{3} -
**Figure 3.**The heat flux between the probe and the sample in contact (left) and the previous measurement result of temperature distribution disturbed by heat transfer through the air gap by using the conventional SThM (right).

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, this problem also seriously limits the applicability of SThM as a thermal characterization tool at nanoscale.

1. Sensor nanofabrication, performance, and conduction mechanisms in scanning thermal microscopy.

2. Thermal transport mechanisms at nanoscale point contacts.

3. Quantitative temperature profiling through null-point scanning thermal microscopy,

4. Quantitative scanning thermal microscopy using double scan technique,

5. Quantitative measurement with scanning thermal microscope by preventing the distortion due to the heat transfer through the air,

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E-mail: tspnano@gmail.com Copyrights (C) TSP Nanoscopy. All rights reserved.

E-mail: tspnano@gmail.com Copyrights (C) TSP Nanoscopy. All rights reserved.