High-throughput Parasitic-independent Probe Thermal Resistance Calibration for Robust Thermal Mapping with Scanning Thermal Microscopy

TL;DR

The work addresses the challenge of obtaining quantitative nanoscale thermal properties with scanning thermal microscopy by introducing a circuit-based calibration of the probe thermal resistance $R_p$ to decouple parasitic heat pathways. It combines non-contact resistance calibration $R_{nc}$ with finite-element-contact modeling to extract the film’s thermal resistance $R_{th}$ and, via spreading-resistance analysis, the effective conductivity $k_{eff}$ of ultrathin films. Demonstrated on a 15 nm Al film on SiO$_2$, the method achieves sub-100 nm spatial resolution and yields $k_{eff} = 2.87 \pm 0.18\ \mathrm{W\,m^{-1}\,K^{-1}}$, consistent with size-dependent phonon-dominated transport in nanoscale metals. The approach provides a robust framework for quantitative nanoscale thermal metrology, enabling insight into defects, grain boundaries, and interfacial effects in nanostructured films.

Abstract

Nanostructured materials, critical for thermal management in semiconductor devices, exhibit a strong size dependence in thermal transport. Specifically, studying the variation of thermal resistance across grain boundaries is of critical importance in designing effective thermal interface materials for heterogeneous integration. Frequency-domain Thermoreflectance (FDTR)-based techniques can provide thermal resistance mapping at the micrometer length scale. Scanning Thermal Microscopy (SThM) has the potential for quantifying local thermal transport with orders of magnitude higher spatial resolution (<100 nm). However, challenges in accurately converting the raw signal to thermal conductivity and accounting for surface sensitivity limit its widespread adoption as a characterization standard for understanding nanoscale heat transport and defect-mediated modulation of thermal properties in nanostructured films. Here, we introduce a circuit-based probe thermal resistance (Rp) calibration technique that is independent of parasitic heat transport pathways; this calibration enables accurate measurement of the heat dissipated from the SThM probe and the resulting tip temperature change to extract the thermal resistance of the film (Rth). Following calibration, SThM achieved sub-100 nm spatial resolution in mapping thermal resistance across a 15 nm-thick Al film deposited by e-beam evaporation on a SiO2 substrate. Finally, the thermal resistance mapping is converted to thermal conductivity using a finite-element-modeling-based calibration approach, where the average of the pixel-level Rth values yields an effective thermal conductivity of 2.87 +/- 0.18 W m^-1 K^-1, in good agreement with published theoretical frameworks describing heat transport in ultrathin Al.

Figures (6)

• Figure 1: (a) Schematic of a Kelvin Nanotechnology (KNT) thermistor probe with an integrated Wheatstone bridge for high-precision thermal signal detection. The input voltage ($V_{in}$) supplied using integrated software, while variable resistor balances the bridge by matching tip resistance at the equilibrium conditions. (b) SThM topography and (c) SThM thermal signal maps of a 5 $\mu$m × 5 $\mu$m Cu-Through Silicon Via (TSV) sample. The thermal signal in (c) reveals local thermal conductivity contrast arising from grain boundary and surface roughness variation. (d) SThM topography [nm] signals and (e) SThM thermal signal [V] profiles along line 1. Consecutive changes in thermal signal peaks, with no corresponding change in topography, demonstrate that the spatial resolution of local thermal conductivity mapping is < 70 nm.
• Figure 2: (a) The heat transfer pathways of the probe just before contacting the sample are dominated by radiative ($R_{rad}$) and convective ($R_{air}$) thermal resistances. (b) Heat transfer pathways when the probe is in contact with the sample, introducing additional thermal resistance channels through the solid-solid ($R_{ss}$) and water conduction ($R_{water}$).
• Figure 3: SThM non-contact thermal resistance ($R_{nc}$) measured with monitored Joule heating. Linear regression fitting is applied to extract $R_{nc}$, considering $\pm 0.1$ uncertainty in tip-temperature rise ($\Delta T$).
• Figure 4: (a) Temperature distribution along the arc length of data line for different thermal interface resistances ($R_{int}$). Data points are downsampled for clarity, with distinct markers and dotted lines highlighting the temperature trends for each $R_{int}$ value. (b) Temperature difference ($\Delta T = T_{tip} - T_{sample}$) versus $R_{int}$, illustrating the monotonic increase of thermal decoupling with higher contact resistance. Together, these plots highlight the influence of $R_{int}$ on probe–sample thermal coupling in SThM measurements.
• Figure 5: (a) Custom meshed geometry of the SThM probe and the sample. The probe consists of a $Si_3N_4$ cantilever with Au connection pads and a Pd tip resistor. A 5 nm Ni–Cr thin layer is deposited between the Au pads and the Pd tip to suppress reverse heat transfer and to avoid sudden increases in Joule heating. (b) Effect of $R_{int} = 10^6 \mathrm{K/W}$ on the surface temperature of the SiO$_2$ sample and the SThM tip contact. (c) Temperature variation at the contact interface for $R_{int} = 10^7 \mathrm{K/W}$. (d) Reduced surface heating due to the higher thermal resistance of $R_{int} = 10^8 \mathrm{K/W}$. (e) Schematic representation of the sample surface in contact with the SThM tip. (f–h) Effect of $R_{int}$ on the Cu surface for $10^6$, $10^7$, and $10^8 \mathrm{K/W}$, respectively.