Basic operation possibilities

As all the following work has been performed using resistive probes, we explain here the methodology commonly used in SThM setups. Traditionally, the resistive probe is part of a resistor bridge, e.g. a Wheatstone bridge (see figure 2.7). This configuration allows the detection of small resistance variation. Different bridge balance conditions are possible through a parallel variable resistor (Re on the fig- ure). The bridge can be balanced when power is applied to the probe or the bridge is balanced at low power. Both DC and AC operations are possible. However, AC setups are believed to be more sensitive, have lower drift and smaller uncertain- ties[60]. AC measurements can be performed with the 3-ω method[61, 62] where

the third harmonic of the bridge output can be shown to directly relate to the probe self-heating and therefore the heat losses[63].

Figure 2.7: Typical Wheatstone bridge for a SThM probe. Ra and Rb are fixed resistors and Re is variable to balance the probe resistance. The bridge is biased byVin and the bridge output is the difference between A and B.

Three typical applications can be highlighted: thermometry, thermal conduc- tivity/conductance characterization and for local heating purposes[8]. In all these applications and for most SThM setups, the probe-sample system is similar (see figure 2.8). In a common situation the microscope temperatureTm and the sample temperature Tsample are equal. Therefore, when some heat Q is provided at the sensor, two heat channels are possible: through the cantilever thermal resistance

Rp and through the tip to the sample via the tip-sample resistance Rts. We de- velop further the different physical mechanisms for heat transfer between the tip and the sample (see section 2.3.3).

Figure 2.8: Schematic of the probe-sample system. Some heat Q is supplied

at the sensor which is at Tsensor. Sample and microscope are at Tsample and Tm, respectively. Heat can flow through the cantilever thermal resistancce Rp and through the tip-sample thermal resistance Rts.

Thermometry

For thermometry application,Rts is a significant unknown as it can be difficult to estimate and measure. It also suffers from artefacts such as topography-related contrast[64] which arise due to modulation of the effective probe-sample contact area. In most cases, Rts needs to be calibrated and a calibration factor is applied to extract the sample temperatureTsample such as in Kimet al.[65] even when the sensor is in direct contact with the sample.

To overcome this limitation, different methods were developed: the null-point method[66] and the dual-sensing technique of Menges et al.[67]. The null-point method, which has the advantage of being applicable in air, is based on a double scan approach [68, 69]. The first scan is performed out of contact immediately before the contact and the second scan is in contact with the sample (see figure 2.9).

Figure 2.9: Null-point method principles[68]. Two measurements are performed

one just before contact and one in contact. This allows to eliminate the parasitic air heat transfer, Qair, contribution and measure sample-tip heat transfer, Qts.

Similar to the null-point method, Menges et al.[70] have mapped the temper- ature of a silicon nanowire by a double scan technique with a first scan at room temperature and a second one with the nanowire heating the sample. Modulating the temperature of the sample enables the determination of both the thermal resis- tance and the temperature of the sample. They further improved their technique by applying an AC bias creating an oscillating temperature distribution and using lock-in detection at the bias frequency, they achieved 7 mK resolution [67, 71]. Thermal conductance measurements

When the sensor is heated, the heat flux to the sample can be measured. However, the sample temperature is often assumed to be equal to the heat sink temperature. It was shown that this assumption holds for high thermally conductive materi- als[50] but, for lower ones, it might not be the case, especially when measuring in ambient conditions. For example, polymers get heated by the probe before it enters into contact.

SThM can be a powerful tool to investigate heat transfer in nanostructures. Thin films on substrate [72–74] or even 2D materials[68, 75, 76] have been inves- tigated. Complex structures can also be scanned as long as the surface is smooth enough to avoid dominance of topography-related artefacts[77–79].

Local heating element

A third application uses SThM in active mode to create a local temperature varia- tion. Most uses reported are for phase change temperature such as glass transition temperature or melting temperature of polymers[41, 80]. Lee et al.[81] used a thermocouple probe to induce local heating in a Si p-n junction and map with nanoscale resolution the Seebeck coefficient. We will show in chapter 7 similar measurements using the SThM as a local heating element allowing to measure thermoelectric effect in graphene constrictions.

Environments

These modes of operations have been reported in various environmental conditions. Aside from ambient air conditions, pressure dependence has been investigated[82] as well as the impact of humidity[83] and pressure[84]. Vacuum and high vacuum SThM have also been developed. Vacuum operations are usually more quantifiable as both liquid meniscus and air conduction are removed therefore increasing the thermal and spatial resolutions. Kimet al. used an ultra-high vacuum technique and obtained 15 mK temperature resolution and 10 nm spatial resolution.

Under liquid immersion, SThM has also been demonstrated. A liquid environ- ment provides very gentle scanning and is therefore suitable for soft materials such as biological samples[85]. Forces between the probe and the sample are about 10 times smaller than in air[86]. Aigouy et al.[87] developed a setup working in liquid (70% water and 30% glycerol) using a fluorescence probe to monitor self-heating of a nickel microheater. This technique thus requires an active sample which limits its uses. More recently, Tovee et al.[88] designed an immersion SThM (iSThM) working with a resistive probe. The design is shown on figure 2.10. In order to avoid corrosion of the probe, they used dodecane as surrounding liquid. In their experiments, they achieved 30 nm spatial resolution.

Figure 2.10: Immersion SThM setup design[88]. The liquid forms a meniscus

between the liuquid holder and a glass slide above the SThM tip.