Effective stiffness of qPlus sensor and quartz tuning fork

• We measure the effective stiffness of seven types of qPlus sensors as well as QTFs.
• The widely used cantilever beam theory is found to overestimate their stiffness.
• We suggest a new formula to determine the stiffness of qPlus sensors and QTFs.
• The measured results are well described by the proposed formula.
• The effective stiffness of QTF is twice that of qPlus sensor for the same type.

Quartz tuning forks (QTFs) have been extensively employed in scanning probe microscopy. For quantitative measurement of the interaction in nanoscale using QTF as a force sensor, we first measured the effective stiffness of qPlus sensors as well as QTFs and then compared the results with the cantilever beam theory that has been widely used to estimate the stiffness. Comparing with the stiffness and the resonance frequency in our measurement, we found that those calculated based on the beam theory are considerably overestimated. For consistent analysis of experimental and theoretical results, we present the formula to calculate the stiffness of qPlus sensor or QTF, based on the resonance frequency. We also demonstrated that the effective stiffness of QTF is twice that of qPlus sensor, which agrees with the recently suggested model. Our study demonstrates the use of QTF for quantitative measurement of interaction force at the nanoscale in scanning probe microscopy.