Design analysis of heated atomic force microscope cantilevers for nanotopography measurements

This paper considers the impact of electrical and mechanical design parameters on sensitivity and resolution of heated atomic force microscope cantilevers used for nanoscale topography measurements. A finite-difference simulation calculates heat generation and heat transfer from the cantilever, systematically varying heater impurity doping concentration, thickness, leg width, tip height and heater size. The highly nonlinear temperature-dependent electrical resistance of the doped silicon cantilever governs the cantilever performance and is tightly coupled with the generation and flow of heat in the cantilever, which are in turn governed by cantilever geometry. The topography sensitivity of the heated cantilever is on the order of 10^-3 νV nm^-1 at an operating point of ∼1 mW and <500 K, and the resolution is on the order of 0.1 nm Hz^-1/2. This analysis seeks to enable the rational design of heated atomic force microscope cantilevers for topography measurements.