CALCULATION OF THERMAL NOISE IN ATOMIC-FORCE MICROSCOPY

Thermal fluctuations of the cantilever are a fundamental source of noi se in atomic force microscopy. We calculated thermal noise using the e quipartition theorem and considering all possible vibration modes of t he cantilever. The measurable amplitude of thermal noise depends on th e temperature, the spring constant K of the cantilever and on the meth od by which the cantilever deflection is detected. If the deflection i s measured directly, e.g, with an interferometer or a scanning tunneli ng microscope, the thermal noise of a cantilever with a free end can b e calculated from root kT/K. If the end of the cantilever is supported by a hard surface no thermal fluctuations of the deflection are possi ble. if the optical lever technique is applied to measure the deflecti on, the thermal noise of a cantilever with a free end is root 4kT/3K. When the cantilever is supported thermal noise decreases to root kT/3K , but it does not vanish.