Quantitative measurements using multiple frequency atomic force microscopy
The imaging mode presented here combines the features and benefits of amplitude modulated (AM) atomic force microscopy (AFM), sometimes called AC mode AFM, with frequency modulated (FM) AFM. In AM-FM imaging, the topographic feedback from the first resonant drive frequency operates in AM mode while the second resonant drive frequency operates in FM mode and is adjusted to keep the phase at 90 degrees, on resonance. With this approach, frequency feedback on the second resonant mode and topographic feedback on the first are decoupled, allowing much more stable, robust operation.
1. An atomic force microscope, comprising:
an atomic force microscope cantilever, having a base and a probe tip;
a surface for holding a sample to be measured by the cantilever, adjacent to the cantilever;
a controller; and
a cantilever driving element, driven by said controller;
the controller receiving a signal indicative of cantilever motion,
and forming a feedback loop with the signal,
the controller exciting the cantilever at least at one both of first and second eigenmodes, wherein the first eigenmode excites in a first mode, and
the second eigenmode excites in a second mode, and in the absence of any second mode excitation, the first eigenmode is interacting with the surface in the attractive mode, and when the first eigenmode is exciting, and the second eigenmode is added to the exciting, after the second mode is added, the first eigenmode is in a repulsive mode, induced by the addition of energy of the second eigenmode,
the controller exciting the cantilever at the first and second eigenmodes while controlling a distance between the cantilever and the sample, and
the controller measuring the amplitude and/or phase of the cantilever at least at one of first and second frequencies associated with the first and second eigenmodes.
2. The microscope as in claim 1 , wherein the controller measures amplitude and/or phase at both of the first and second frequencies.
3. The microscope as in claim 1 , wherein the controller measures amplitude and/or phase at one of the frequencies, and keeps constant amplitude and/or phase of the other frequency.
4. The microscope as in claim 1 , wherein said first frequency is a resonant frequency of the cantilever.
5. The microscope as in claim 1 , wherein said first eigenmode is at a first resonant frequency of the cantilever, wherein said probe tip oscillates at said resonant frequency, and said resonant frequency is applied to said feedback loop to control interactions between the cantilever and sample to maintain an amplitude of oscillation at the first resonant frequency of the probe tip essentially constant at an amplitude setpoint.
6. The microscope as in claim 1 , wherein the measured amplitude and/or phase is used to determine information about the sample surface.
7. The microscope as in claim 1 , wherein said second eigenmode is at a second resonant frequency of the cantilever.
8. A method of operating an atomic force microscope, comprising:
exciting a cantilever driving element, using a controller, relative to a surface of a sample to be measured;
receiving, in the controller, a signal indicative of cantilever motion, and forming a feedback loop with the signal,
exciting the cantilever at least at one of first and second eigenmodes,
wherein the first eigenmode excites in a first mode, and the second eigenmode excites in a second mode, and in the absence of any second mode excitation, the first eigenmode is interacting with the surface in the attractive mode, and when the first eigenmode is exciting, and the second eigenmode is added to the exiciting after the second mode is added,
the first eigenmode is in a repulsive mode, induced by the addition of energy of the second eigenmode,
controlling a distance between the cantilever and the sample during said exciting, and
measuring the amplitude and/or phase of the cantilever at least at one of first and second frequencies associated with the first and second eigenmodes.
9. The method as in claim 8 , wherein the controller measures amplitude and/or phase at both of the first and second frequencies.
10. The method as in claim 8 , wherein the controller measures amplitude and/or phase at one of the frequencies, and keeps constant amplitude and/or phase of the other frequencies.
11. The method as in claim 8 , wherein said first eigenmode is at a first resonant frequency of the cantilever, wherein said cantilever oscillates at said resonant frequency, and said resonant frequency is applied to said feedback loop to control interactions between the cantilever and sample to maintain an amplitude of oscillation at the first resonant frequency of the probe tip essentially constant at an amplitude setpoint.