Modeling and Simulation of the Interface Temperature Between a Heated Silicon Tip and a Substrate

Abstract

This article presents an analytical model and finite difference simulations that predict the interface temperature between a heated atomic force microscope (AFM) tip and a substrate. The thermal resistances for the tip, interfacial contact between the tip and substrate, and spreading into the substrate are all considered. The thermal properties and geometry of the tip closest to the apex govern heat transport through the entire tip. The models thus r uire boundary-constricted thermal conductivity in the tip and a separate thermal resistance to account for the geometry at the tip apex. The tip-substrate interface temperature depends upon the contact impedance, contact force, and ambient environment thermal conductivity. For a silicon tip, the combined thermal resistance of the substrate and contact is on the order of 10⁷–10⁸ K/W and dominates the heat transfer. The model identifies dimensionless parameters that govern the tip-substrate interface temperature, which can inform cantilever design and application development.

KEY WORDS:

• atomic force microscope
• point contact
• thermal resistance
• boundary scattering

The authors thank Z. Zhang and Y. Joshi for their helpful comments and discussion. We are grateful for the support of NSF CBET 07‐31930 and the Office of Naval Research.