Characterization of heat transfer in 3D CMOS structures using Sideband Scanning Thermal Wave Microscopy

TL;DR

This work tackles nanoscale heat transport in deeply buried CMOS BEOL structures under cryogenic operating conditions by introducing Sideband Scanning Thermal Wave Microscopy (S-STWM). The method modulates a buried heater at $f_{\mathrm{mod}}$ and senses with a high-frequency probe at $f_{\mathrm{car}}$, extracting sidebands at $f_{\mathrm{car}}\pm f_{\mathrm{mod}}$ to obtain phase information about heat propagation. By analyzing phase delays with a semi-infinite-wave model, the authors extract effective thermal diffusivity $\alpha$ and, with estimates of heat flux $Q_0$, effective thermal conductivity $\kappa$ across a CMOS BEOL structure containing a buried DTSCR heater in a 22-nm FDSOI process. The results reveal frequency- and geometry-dependent heat transport, including routing-dominated conduction along metal paths and insulator-dominated regions, and establish a foundation for in situ cryogenic thermal characterization and predictive 3D thermal modeling of cryo-CMOS devices. This technique offers a pathway to improved thermal management and packaging for quantum and HPC hardware by enabling quantitative, noninvasive mapping of heat flow in complex multilayer CMOS architectures.

Abstract

Efficient thermal management is critical for cryogenic CMOS circuits, where local heating can compromise device performance and qubit coherence. Understanding heat flow at the nanoscale in these multilayer architectures requires localized, high-resolution thermal probing techniques capable of accessing buried structures. Here, we introduce a sideband thermal wave detection scheme for Scanning Thermal Microscopy, S-STWM, to probe deeply buried heater structures within CMOS dies. By extracting the phase of propagating thermal waves, this method provides spatially resolved insight into heat dissipation pathways through complex multilayer structures. Our approach enables quantitative evaluation of thermal management strategies, informs the design of cryo-CMOS circuits, and establishes a foundation for in situ thermal characterization under cryogenic operating conditions.

Figures (6)

• Figure 1: a Schematic of the sideband-SThM setup used in this work. A high-frequency carrier signal $f_\mathrm{car}$ probes the resistance of the thermometer embedded in a Wheatstone bridge, while a low-frequency excitation $f_\mathrm{mod}$ is applied to a heater buried beneath the sample surface. The resulting SThM signal at the Wheatstone bridge is an amplitude-modulated $f_\mathrm{car}$, which can be demodulated to extract the sideband signals. Input and output signals are shown schematically and are not to scale. b Isophase curves for the heat waves propagating around a buried heating element. Another material with a different thermal diffusivity is shown in grey. The added colorbar shows the conversion from phase to propagation time of the heat wave. Color scale indicates the conversion to a propagation time.
• Figure 2: a Simplified cross-sectional diagram of buried DTSCR heater structure (not to scale) showing diodes D1, D2, and D3. b Measured DC I-V response of the diode string, which can be modeled as an ideal diode string with 30 $\Omega$ inline series resistance (reducing the effective voltage across the diode string at high bias compared to the sourced voltage). c Modeled transient waveforms for effective voltage, current, and dissipated power at the diode string. d Resulting modeled spectral content of power dissipation in the diode string. The fundamental frequency and 2$^{\textrm{nd}}$ harmonic are dominant, though the 3$^{\textrm{rd}}$ harmonic is also significant.
• Figure 3: a Grayscale optical micrograph of the region of interest with the scan window indicated by the green rectangle. The buried DTSCR heater is indicated by the blue rectangle. Red scale bar: 30 um. b Relative topography of the region. c Apparent DC temperature map. d Calibrated AC temperature obtained via the sideband detection. e Relative surface phase lag of the heat wave, obtained through the sideband detection, with the white square indicating the reference region used for the conversion of phase to heat wave velocity. f Effective heat wave velocity. g Effective thermal diffusivity. h Effective thermal conductivity.
• Figure 4: Representative 3D routing scheme for DTSCR signal and ground connections (not to scale). The routing regions indicated include both metal routing layers and vias. Metal-island fill and other routing unrelated to the DTSCR are not shown. A partially-transparent copy of Figure \ref{['fig:main_map']}d is overlaid to demonstrate the maximum AC heating directly above the near-surface signal routing.
• Figure 5: Measured and extracted thermal characteristics at the reference region as a function of the DTSCR's excitation frequency. The excitation is unipolar and its peak-to-peak amplitude is 3 V. The dashed lines highlight the $1$ kHz frequency. a Measured amplitude and phase of the first sideband signal. b Extracted effective thermal diffusivity. c Extracted effective thermal conductivity.