Near-field radiative heat transfer in scanning thermal microscopy computed with the boundary element method

- Spheres and sphere-surface configurations are used to validate numerical results.
- We provide size and convergence criteria for finite and infinite objects.
- The tip-surface near-field radiation exchange is computed for dielectrics.
- The power exchanged depends on distance more softly than d−1.
- The radiative spatial resolution of scanning thermal microscopy can scale as d1/2.

We compute the near-field radiative heat transfer between a hot AFM tip and a cold substrate. This contribution to the tip-sample heat transfer in Scanning Thermal Microscopy is often overlooked, despite its leading role when the tip is out of contact. For dielectrics, we provide power levels exchanged as a function of the tip-sample distance in vacuum and spatial maps of the heat flux deposited into the sample which indicate the near-contact spatial resolution. The results are compared to analytical expressions of the Proximity Flux Approximation. The numerical results are obtained by means of the Boundary Element Method (BEM) implemented in the SCUFF-EM software, and require first a thorough convergence analysis of the progressive implementation of this method to the thermal emission by a sphere, the radiative transfer between two spheres, and the radiative exchange between a sphere and a finite substrate.