Scanning Thermal Microscope (SThM)

1. Theory

• Definition: A scanning thermal microscope is an AFM with a probe whose apex is a temperature sensor and often a heater, mapping local temperature or thermal conductance with sub-micrometre resolution (Tovee et al.; Munde et al.).
• Thermometry: A thermoresistive element changes resistance as $\Omega ={\Omega }_0[1+\alpha (\tilde{T}-T_0)]$ (Munde et al.).
• Thermal network: A heated probe loses power through the cantilever, air, radiation, a water meniscus and the solid contact; the contact path adds interface and spreading resistances in the sample (Munde et al.; Tovee et al.).
• Contrast: Higher sample conductivity lowers the spreading resistance and cools the tip, but the tip-sample interface limits sensitivity for good conductors (Tovee et al.; Munde et al.).

2. Working Principle

• Probes: Wollaston Pt wire, doped-silicon, or Pd thin-film resistors on silicon nitride cantilevers (Tovee et al.).
• Electronics: The probe forms one arm of a bridge; the bridge voltage tracks resistance and hence tip temperature (Munde et al.; background knowledge, Gomes et al.).
• Active mode: The probe is Joule-heated and the drop in its temperature on contact gives thermal conductance contrast (Ge; Munde et al.).
• Passive mode: A small sensing current reads the temperature of a self-heated sample, such as a powered device (Ge; background knowledge).

3. Applications

• Thin-film thermal conductivity: Metal and dielectric films where size effects lower conductivity (Munde et al.).
• Device hotspots: Temperature mapping of transistors, interconnects and failure sites (background knowledge, Gomes et al.).
• Polymers and composites: Low-conductivity materials such as PMMA (Tovee et al.).
• Probe development: Sharper doped-Si and carbon-nanotube probes for higher resolution (Tovee et al.).

Probe Thermometry and Heat Balance

Name	Formula	Related Formulae	Variables/Constants
Thermoresistive probe	$\Omega ={\Omega }_0\left[1+\alpha \left(\tilde{T}-T_0\right)\right]$	$\frac{\Delta \Omega }{{\Omega }_0}=\alpha \Delta T$	$\Omega :probeelectricalresistance$ ${\Omega }_0:resistanceat{T}_0$ $\alpha :temperaturecoefficientofresistance$ $\begin{array}{r}\tilde{T}:meanprobetemperature;Mundeetal.:\\ Pd-on-Si3N4probe,3800ppm/K\\ (manufacturer),177\Omega at294\mathrm{K},tipheight\\ about10\mu \mathrm{m},temperatureresolutionabout\\ 0.1\mathrm{K};Toveeetal.:5\mu \mathrm{m}PtWollaston\\ wire,doped-Siprobeabout3\mathrm{k\Omega }to500{}^{\circ }C,\\ Pdprobe300\Omega to150{}^{\circ }C\end{array}$ $\begin{array}{r}(computed:0.1\mathrm{K}changes177\Omega by0.067\Omega ,\\ afractionof3.8\times 10^{-4};50\mathrm{K}heatingraises\\ itto211\Omega )\end{array}$
Probe heat balance	$Q_h=\frac{{\tilde{T}}_h^{nc}-T_0}{R_{nc}},Q_h=\frac{{\tilde{T}}_h^c-T_0}{R_{nc}}+\frac{{\tilde{T}}_h^c-T_s}{R_c}$	$P_{tip}=\frac{V_{tip}^2}{\Omega },R_{nc}=\frac{\Delta T}{P_{tip}}$	$Q_h:heaterpower$ $R_{nc}:non-contactprobethermalresistance$ $R_c:contact-paththermalresistance$ $T_s:sampletemperature$ $\begin{array}{r}ncandc:outofandincontact;Mundeet\\ al.:theseequations,R_{n}c=(5.97+/-\\ 0.40)e4K/Wfromregression;Toveeetal.:\\ non-contact4.16\times 10^{4}K/W(dopedSi)and\\ 5.06\times 10^{4}K/W(Pd)measured\end{array}$ $\begin{array}{r}(assumed:50\mathrm{K}rise;computed:0.84\mathrm{mW}\\ heaterpowerat{R}_{n}c=5.97\times 10^{4}K/W)\end{array}$
Contact signal	$\frac{V^{nc}-V^c}{V^{nc}}=\frac{R_{nc}}{R_{nc}+R_c}$	$\frac{1}{R_c}=\frac{1}{R_{rad}}+\frac{1}{R_{air}}+\frac{1}{R_{ss}}+\frac{1}{R_{water}}$	$V:bridgeoutput$ $\begin{array}{r}{R}_{rad},R_{air},R_{ss},R_{water}:radiation,air,\\ solid-solidandwater-meniscuspaths;\\ Mundeetal.:theserelations,contact\\ setpointbelow10\mathrm{nN},watermeniscus\\ treatedas6percentuncertainty;Tovee\\ etal.:airconductiongivesalarge-scale\\ background,meniscusnotmodelled\end{array}$ $\begin{array}{r}(computed:R_{c}of5.47MK/WonSiO2gives\\ 1.08percentand2.66MK/WonAlgives\\ 2.2percent)\end{array}$

Contact and Sample Resistance

Name	Formula	Related Formulae	Variables/Constants
Solid-solid resistance decomposition	${\left(R_c-R_{nc}\right)}_{meas}\approx R_{ss}=R_{int}+R_{spr}+f{R}_{BD}$	$R_{spr}\approx \frac{1}{4k_{s}b}(\text{disc on half-space})$	$R_{int}:tip-sampleinterface$ $R_{spr}:spreadinginthesample$ $R_{BD}:buried-interfaceterm$ $f:dilutionfactor$ $b:sourceradius$ $\begin{array}{r}{k}_s:sampleconductivity;Mundeetal.:\\ decomposition,5.41MK/WonSiO2and2.60\\ MK/WonAl,with1.84,0.68and0.08MK/W\\ (70.8,26.2and3.1percent),interface\\ atmost1\times 10^{7}K/W;discformula(background\\ knowledge,Majumdar)\end{array}$ $\begin{array}{r}(computed:thethreetermssumto2.60\\ MK/W;treatingSiO2asbulkwiththesame\\ R_{i}ntgivesbabout51\mathrm{nm})\end{array}$
Thin-film spreading and dilution	$L_{spread}=t\sqrt{\frac{k_{film}}{k_{sub}}}$	$f={\left(\frac{b}{b+t\sqrt{k_{film}/k_{sub}}}\right)}^2$	$L_{spread}:lateralspreadinglength$ $\begin{array}{r}t:filmthickness;Mundeetal.:Labout\\ 80\mathrm{nm},f=0.148,14\mathrm{nm}Alfilmwithk=\\ 45.1W/(\mathrm{m}\mathrm{K})againstFuchs-Sondheimer\\ 49.5andbulk237W/(\mathrm{m}\mathrm{K}),SiO21.38\\ W/(\mathrm{m}\mathrm{K}),buriedinterface200MW/({\mathrm{m}}^2\mathrm{K})\end{array}$ $\begin{array}{r}(computed:14\mathrm{nm}timesthesquarerootof\\ 45.1/1.38gives80\mathrm{nm};f=0.148impliesb\\ =50\mathrm{nm};thefilmhas19percentofbulk\\ conductivity)\end{array}$
Conductivity sensitivity range	$\frac{\partial R_{ss}}{\partial k_s}=-\frac{1}{4k_s^{2}b}$	$k_s\approx 0.1\text{to a few tens W/(m K) (vacuum)},<10\text{(air)}$	$\begin{array}{r}Toveeetal.:sensitivityrangeinvacuum\\ andair,contact/non-contactratios1.028\\ (dopedSi)and1.11(Pd)invacuum,tip\\ temperaturerisehalvedinair,\\ interfacialconductance80to300\\ MW/({\mathrm{m}}^2\mathrm{K}),contactresistancelimiting\\ high-conductivitysamples,CNTapex\\ predictedtoreach100to1000W/(\mathrm{m}\mathrm{K});\\ PMMA0.19andSi130W/(\mathrm{m}\mathrm{K})\end{array}$ $\begin{array}{r}(computed:atb=50\mathrm{nm},R_{s}pris3.6MK/W\\ forSiO2and38K/WforSiat130\\ W/(\mathrm{m}\mathrm{K}),belowthe1.84MK/Winterface)\end{array}$

Resolution, Modes and Calibration

Name	Formula	Related Formulae	Variables/Constants
Spatial resolution	$d_{SThM}\sim 2b$	$r_{tip}:\sim 10\mathrm{nm}(\text{doped Si}),\sim 50\mathrm{nm}(\text{Pd})$	$\begin{array}{r}{d}_{SThM}:thermalresolution;Toveeetal.:\\ Wollastonmicrometreresolution,doped-Si\\ apexabout10\mathrm{nm},Pdapexabout50\mathrm{nm},\\ modelled50\mathrm{nm}contact;Mundeetal.:\\ sub-100\mathrm{nm},below70\mathrm{nm}inafigure,SThM\\ tipradiusbelow100\mathrm{nm};Ge:passiveand\\ activemodes\end{array}$ $(computed:b=50\mathrm{nm}givesabout100\mathrm{nm})$
Active and passive modes	$\text{active: }I\text{heats the probe},\Delta V\propto \frac{R_{nc}}{R_{nc}+R_c}$	$\text{passive: small }I,\tilde{T}\approx T_s(\text{thermometry})$	$\begin{array}{r}Ge:resistiveelementusedinpassiveor\\ activemodes;Mundeetal.:activeJoule\\ heatingwithvoltageabove0.5Vandgain\\ 1000;Toveeetal.:self-heatingabove100\\ {}^{\circ }Cpossible;passivemappingofdevice\\ hotspots(backgroundknowledge,Gomeset\\ al.)\end{array}$ $\begin{array}{r}(computed:inpassivemode,0.1\mathrm{K}\\ resolutionneeds3.8\times 10^{-4}fractional\\ resistanceresolution)\end{array}$
Calibration of probe thermal resistance	$R_{nc}=\frac{d\Delta T}{d{P}_{tip}}(\text{linear regression})$	$\Delta T=aV$	$\begin{array}{r}a:calibrationslopefromprobevoltageto\\ temperaturerise;Mundeetal.:\\ circuit-basedmethodavoiding\\ thermal-stageerrors,sevenscans,+/-0.1\\ \mathrm{K}instrumentaluncertainty;Toveeetal.:\\ Peltierhot-coldplatefromroom\\ temperatureto100{}^{\circ }C\end{array}$ $\begin{array}{r}(computed:the0.40\times 10^{4}K/Wuncertaintyis\\ 6.7percentof{R}_{n}c)\end{array}$

Important Questions

Ques: How does an SThM probe measure temperature?

Through the resistance of a small sensor at the tip apex. Munde et al. use $\Omega ={\Omega }_0[1+\alpha (\tilde{T}-T_0)]$ for a Bruker Pd-on-silicon-nitride probe with 177 $\Omega$ at 294 $\mathrm{K}$ and a TCR of 3800 $ppm/K$. A 0.1 $\mathrm{K}$ change, the stated temperature resolution, alters 177 $\Omega$ by only 0.067 $\Omega$, a fraction of $3.8\times 10^{-4}$ (computed), so a bridge and amplifier with gain 1000 are needed. Tovee et al. compare the original 5 $\mu \mathrm{m}$ Pt Wollaston wire, which served as heater and sensor with micrometre resolution, against doped-silicon probes of about 3 $\mathrm{k\Omega }$ usable to 500 ${}^{\circ }\mathrm{C}$ and Pd probes of 300 $\Omega$ limited to 150 ${}^{\circ }\mathrm{C}$. Ge notes the resistive element can work in passive or active modes. Reference: R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary); P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary); Y. Ge, ‘Quantitative measurement using scanning thermal microscopy’, PhD thesis, University of Glasgow (2016) (abstract only).

Ques: Where does the heat from an active SThM probe go?

Mostly into the cantilever and air; only a small fraction crosses the contact. Munde et al. write the heat balance out of and in contact and decompose the contact conductance into radiation, air, solid-solid and water-meniscus paths. Their non-contact resistance is $5.97\times 10^4$ $K/W$, so a 50 $\mathrm{K}$ rise needs about 0.84 $\mathrm{mW}$ (assumed rise; computed). On contact, the bridge signal changes by $R_{nc}/(R_{nc}+R_c)$: about 1.08 per cent on SiO2 and 2.2 per cent on Al from their measured values (computed). Tovee et al. note that air conduction from the whole cantilever gives a large-scale background with no spatial information, while Munde et al. treat the water meniscus as a 6 per cent uncertainty in the contact resistance. Reference: R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary); P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary).

Ques: Is the non-contact thermal resistance of a Pd SThM probe $5.1\times 10^4$ or $6.0\times 10^4$ K/W?

Both are measurements. Tovee et al. measured $5.06\times 10^4$ $K/W$ for a Pd-on-nitride probe in air against a simulated $3.39\times 10^4$ $K/W$, while Munde et al. obtained (5.97 +/- 0.40)e4 $K/W$ by regression of temperature rise against Joule power. The two measurements differ by 18 per cent, about twice Munde’s 6.7 per cent uncertainty (computed). Probe batches and ambient air conditions can differ, and Munde’s circuit method avoids thermal-stage errors, so it is more likely representative of current probes, with 5 to $6\times 10^4$ $K/W$ a fair working range (my reading). The simulation is lower in both papers’ comparisons, suggesting models underestimate parasitic heat paths. Tovee’s doped-Si probe gave $4.16\times 10^4$ $K/W$. Reference: P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary); R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary).

Ques: Why does SThM lose sensitivity on good thermal conductors?

Because the tip-sample interface resistance dominates. Munde et al. split the measured 2.60 $MK/W$ on an Al film into 1.84 $MK/W$ interface, 0.68 $MK/W$ spreading and 0.08 $MK/W$ buried-interface terms, 70.8 per cent from the interface. Spreading resistance of a disc, $1/(4k_{s}b)$, is 3.6 $MK/W$ for SiO2 but only 38 $K/W$ for silicon with b = 50 $\mathrm{nm}$ (background knowledge, Majumdar; computed), far below the interface term, so materials above about 10 $W/(\mathrm{m}\mathrm{K})$ look almost the same. Tovee et al. give a vacuum sensitivity range of 0.1 to a few tens of $W/(\mathrm{m}\mathrm{K})$, reduced below about 10 $W/(\mathrm{m}\mathrm{K})$ in air, and predict that a carbon-nanotube apex could extend it to 100 to 1000 $W/(\mathrm{m}\mathrm{K})$. Reference: R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary); S. Gomes, A. Assy and P.-O. Chapuis, ‘Scanning thermal microscopy: A review’, Phys. Status Solidi A 212, 477 (2015), and A. Majumdar, ‘Scanning thermal microscopy’, Annu. Rev. Mater. Sci. 29, 505 (1999) (background knowledge; not opened); P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary).

Ques: How can SThM measure the conductivity of a thin film?

By modelling how heat spreads through the film into the substrate. Munde et al. define a spreading length $L=t\sqrt{k_{film}/k_{sub}}$ and a dilution factor $f=(b/(b+L){)}^2$. For their 14 $\mathrm{nm}$ Al film on SiO2, 14 $\mathrm{nm}$ times the square root of 45.1/1.38 gives 80 $\mathrm{nm}$, matching their stated 80 $\mathrm{nm}$, and f = 0.148 implies a contact radius of 50 $\mathrm{nm}$ (computed). Their extracted 45.1 $W/(\mathrm{m}\mathrm{K})$ is 19 per cent of bulk Al and about 9 per cent below the Fuchs-Sondheimer prediction of 49.5 $W/(\mathrm{m}\mathrm{K})$ (computed), showing strong boundary scattering. A buried-interface conductance of 200 $MW/({\mathrm{m}}^2\mathrm{K})$ adds a small 3.1 per cent term. Uncertainty comes mainly from the interface conductance and thickness variation (Munde et al.). Reference: R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary).

Ques: What spatial resolution does SThM reach?

From micrometres with wire probes to below 100 $\mathrm{nm}$ with microfabricated tips. Tovee et al. note that early SThM with a 5 $\mu \mathrm{m}$ Wollaston wire was micrometre-scale, while doped-silicon tips have apex radii near 10 $\mathrm{nm}$ and Pd tips near 50 $\mathrm{nm}$; they modelled a 50 $\mathrm{nm}$ contact. Munde et al. report sub-100 $\mathrm{nm}$ resolution, below 70 $\mathrm{nm}$ in one figure, and an 80 $\mathrm{nm}$ heat-spreading length in their Al film. A 50 $\mathrm{nm}$ contact radius suggests roughly 100 $\mathrm{nm}$ resolution (computed), consistent with those reports. Resolution is set by the thermal contact, not the geometric apex alone, because the meniscus and air paths broaden the exchange area in ambient conditions (Tovee et al.; background knowledge, Gomes et al.). Reference: P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary); R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary); S. Gomes, A. Assy and P.-O. Chapuis, ‘Scanning thermal microscopy: A review’, Phys. Status Solidi A 212, 477 (2015), and A. Majumdar, ‘Scanning thermal microscopy’, Annu. Rev. Mater. Sci. 29, 505 (1999) (background knowledge; not opened).

Ques: How is an SThM probe calibrated?

By relating probe resistance to temperature and then measuring its thermal resistance. Tovee et al. used a Peltier hot-cold plate from room temperature to 100 ${}^{\circ }\mathrm{C}$ and found resistance close to linear in temperature. Munde et al. avoid thermal-stage errors with a circuit method: tip power $P=V^2/\Omega$ is compared with the temperature rise, and $R_{nc}$ is the regression slope, giving (5.97 +/- 0.40)e4 $K/W$, a 6.7 per cent uncertainty (computed), over seven scans with 0.1 $\mathrm{K}$ instrumental uncertainty. Contact resistance is then extracted from the in-contact voltage ratio. Reference samples of known conductivity, such as PMMA at 0.19 and silicon at 130 $W/(\mathrm{m}\mathrm{K})$ used by Tovee et al., anchor the conductivity scale (background knowledge, Gomes et al.). Reference: P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, ‘Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials’, arXiv:1110.6055 (fetch-tool summary); R. Munde, H.-R. Chuang and R. Islam, ‘High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy’, arXiv:2511.09960 (2026) (fetch-tool summary); S. Gomes, A. Assy and P.-O. Chapuis, ‘Scanning thermal microscopy: A review’, Phys. Status Solidi A 212, 477 (2015), and A. Majumdar, ‘Scanning thermal microscopy’, Annu. Rev. Mater. Sci. 29, 505 (1999) (background knowledge; not opened).

References

1. R. Munde, H.-R. Chuang and R. Islam, “High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy,” preprint arXiv:2511.09960, 2026. Available: https://arxiv.org/pdf/2511.09960
2. P. Tovee, M. Pumarol, D. Zeze, K. Kjoller and O. Kolosov, “Nanoscale spatial resolution probes for Scanning Thermal Microscopy of solid state materials,” preprint arXiv:1110.6055. Available: https://arxiv.org/pdf/1110.6055
3. Y. Ge, “Quantitative measurement using scanning thermal microscopy,” PhD thesis, University of Glasgow, 2016 (abstract only). Available: https://theses.gla.ac.uk/id/eprint/7474
4. S. Gomes, A. Assy and P.-O. Chapuis, “Scanning thermal microscopy: A review,” physica status solidi (a), vol. 212, pp. 477-494, 2015; A. Majumdar, “Scanning thermal microscopy,” Annual Review of Materials Science, vol. 29, pp. 505-585, 1999 (cited from background knowledge).

Related pages in this vault: Atomic Force Microscope (AFM), Thermal and Electro-Thermal Simulation, Interconnect Joule Heating, Emission Microscope, OBIRCH and Lock-In Thermography, Kelvin Probe Force Microscope (KPFM), Scanning Capacitance Microscope (SCM), Scanning Spreading Resistance Microscope (SSRM), Scanning Microwave Impedance Microscope (sMIM), Spreading Resistance Profiler (SRP), Pyrometers and Wafer Temperature Sensors.