# AFM cantilevers driven below resonance?

Is there a physical reason why AFM cantilevers are driven below their resonance frequencies?

In all of the AFMs I have used, once you measure the resonance frequency of the cantilever, it is set up to be driven slightly below this frequency for measurement. Is this a convention? Does driving at resonance cause damage? If not, then why is the cantilever not also driven above resonance? I seem to recall an engineer telling me that driving below resonance improves the resolution and referenced a paper - but I can't find this.

## 1 Answer

The resonance curve is a Lorentzian shape (which looks similar to a Gaussian bell-shaped curve). When the slope of the Lorentzian is at a maximum (i.e. slightly off resonance), the driven system will be most sensitive to changes in the resonant frequency. In the linked article, notice that the amplitude $A_0$ is marked on the steep part of the Lorentzian, which makes $A_+$ and $A_-$ very different from $A_0$. https://en.wikipedia.org/wiki/Non-contact_atomic_force_microscopy#Amplitude_modulation

• But why below resonance and not above? Also, why is the resonance Gaussian? Resonances are so often Lorentzian... – DanielSank Dec 3 '15 at 6:02
• I don't know why below resonance. Maybe the idea is to try to avoid going to large amplitude as you near the surface, risking a crashed tip. – Spirko Dec 3 '15 at 6:10
• Yes, it's probably Lorentzian. Looking at the driven damped harmonic oscillator, that looks more appropriate. – Spirko Dec 3 '15 at 6:18