Sensitivity

High force and force-derivative sensitivity can be obtained with soft cantilevers having a high resonance frequency and a high quality factor. Low temperatures are beneficial. The sensitivities for forces [N/sqrt(Hz)] and force-derivative [(N/m) / (sqrt(Hz)∙m] are given by


      

 


(1)


(2)

where kB is the Boltzmann constant, T the temperature, kc the cantilever force constant, B the measurement bandwidth, fc the resonance frequency of the cantilever, and Q the quality factor of the cantilever.

Note for a cantilever with a resonance frequency of 50 kHz, a force constant of 0.3 N/m and a quality factor of Q = 106, a force sensitivity of 125 aN/sqrt(Hz) is obtained at room temperature!