Loss tangent imaging: Theory and simulations of repulsive-mode tapping atomic force microscopy

An expression for loss tangent measurement of a surface in amplitude modulation atomic force microscopy is derived using only the cantilever phase and the normalized cantilever amplitude. This provides a direct measurement of substrate compositional information that only requires tuning of the cantilever resonance to provide quantitative information. Furthermore, the loss tangent expression incorporates both the lost and stored energy into one term that represents a fundamental interpretation of the phase signal in amplitude modulation imaging. Numerical solutions of a cantilever tip interacting with a simple Voigt modeled surface agree with the derived loss tangent to within a few percent.