Enhancing higher harmonics of a tapping cantilever by excitation at a submultiple of its resonance frequency

In a tapping-mode atomic force microscope, the frequency spectrum of the oscillating cantilever contains higher harmonics at integer multiples of the excitation frequency. When the cantilever oscillates at its fundamental resonance frequency w(1), the high Q-factor damps the amplitudes of the higher harmonics to negligible levels, unless the higher flexural eigenmodes are coincident with those harmonics. One can enhance the nth harmonic by the Q factor when the cantilever is excited at a submultiple of its resonance frequency (w(1)/n). Hence, the magnitude of the nth harmonic can be measured easily and it can be utilized to examine the material properties. We show theoretically that the amplitude of enhanced higher harmonic increases monotonically for a range of sample stiffness, if the interaction is dominated by elastic force.