Raman and PL spectroscopy were carried out using a Horiba LabRAM instrument with a 532-nm laser and 100× long working distance objective with a numerical aperture (NA) of 0.6. Step sizes in the Raman maps varied between 0.4 and 0.6 μm, and the acquisition time of each device thermal map was ~20 to 30 min. The laser spot radius was ~0.4 μm, and the absorbed laser power was <5 μW to avoid laser heating in excess of the electrical heating and to maintain negligible photocurrent. The Raman spectra of the four-layer heterostructure of Gr/MoSe2/MoS2/WSe2 (Fig. 1B) showed peaks at 241.5 and 404.6 cm−1 corresponding to out-of-plane A1′ modes for MoSe2 and MoS2, respectively. The in-plane E′ modes for MoSe2 and MoS2 were represented by the peaks at 286.5 and 383.1 cm−1, respectively. Monolayer WSe2 showed the characteristic degenerate peak at 249.4 cm−1, which included both A1′ and E′, while the 2LA peak was at 259.3 cm−1. Furthermore, the G and G′ (sometimes called 2D) peaks of monolayer graphene were at 1585.3 and 2690.5 cm−1, respectively. We used the graphene G peak and the TMD out-of-plane modes for thermometry because they were less sensitive to strain.

For temperature-dependent Raman shift calibration, we used a Linkam THMS600 stage and carefully differentiated effects of strain (e.g., during the calibration on hot stage) and shifts due to electrical bias (gating effect from the substrate), following the calibration procedure outlined in section S7. The obtained Raman temperature maps were uniform (see section S6), similar to the SThM measurements shown in section S4. The uniform heating in the channel indicated that there was no measurable nonuniform doping or pinch-off, which simplified the extraction of interlayer TBC. Changes in the measured current along the graphene channel during mapping were smaller than 5%. All thermometry measurements were performed in ambient and at room temperature.

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