In conventional contact resonance (CR) AFM methods, the AFM tip is brought into contact with the sample, and a mechanical, thermal, or electrical excitation is applied to the tip or sample at a drive frequency equal to a resonance frequency of the coupled tip-sample system. Mechanical or thermal excitation is used to probe nanomechanical properties, while electrical excitation is used to probe piezoelectric properties (piezo response force microscopy, PFM) or ionic conduction (electrochemical strain microscopy, ESM). The motivation for driving the system at a resonance frequency is that the cantilever motion is amplified by up to several orders of magnitude (relative to off-resonance), thus enhancing the small-signal sensitivity. Conventional CR-AFM has the disadvantage that the resonance frequency and hence the vibrational shape of the cantilever varies during a scan, due to spatial variation of the elastic modulus or surface morphology. Hence, for a fixed position of the detection laser on the cantilever, the deflection amplitude may vary all the way from maximum response (at a node) to zero response (at an antinode). This shape-related amplitude variation is a roadblock to quantification of the material properties of interest.
Here, we propose and demonstrate a new type of CR-AFM measurement, isomorphic CR, in which the resonance frequency and vibrational shape is equal for all pixels in a scan, thus eliminating the unwanted shape-related amplitude variation. As a result, relative amplitude contrast is inherently reliable, quality factor contrast is directly related to material damping, and calculated elastic stiffness is free from modeling uncertainties. Furthermore, the detection laser position can be specifically optimized for the selected vibrational shape. Isomorphic CR-AFM is accomplished as follows. First, the AFM scan is conducted in force-mapping mode: the tip is brought into contact with the sample; the contact force is increased and then decreased; and the tip is retracted and moved to the next sample location (this sequence is repeated for each pixel in the scan). Simultaneously, the tip or sample is excited at a sum of two fixed drive frequencies, and the amplitude and phase response at each frequency is measured as a function of time and hence contact force. The resonance frequency is deduced to be equal to fmean , the mean of the two fixed drive frequencies, at the point in the force curve where the vibration amplitudes are equal. Finally, the amplitude, phase, and Q factor at fmean are calculated from the measured amplitudes and phases based on a harmonic oscillator model. We will present experimental results for a variety of samples, including mapping elastic and viscous properties of a polymer blend, bias induced strain of a piezoelectric material (PFM mode), and bias induced strain of a lithium battery cathode material (ESM mode), to illustrate the utility and scope of the isomorphic contact resonance method.