A. Deolia, A. Raman, R.B. Wagner
Keywords: atomic force microscopy, photothermal excitation, vibrations, heat transfer
Summary:Photothermal excitation (PTE) of atomic force microscope (AFM) microcantilevers generates a smooth transfer function free from spurious resonances as a consequence of localized microcantilever heating. PTE is usually used to excite the resonance dynamics of the microcantilever; however, it can also be utilized in sub-resonance AFM modes such as force modulation microscopy, force-displacement curves, photothermal-assisted tip scanning, tip-based mass spectroscopy, and thermomechanical indentation. The utilization and optimization of PTE done at sub-resonance frequencies of an AFM microcantilever is relatively unexplored. To understand the physics driving microcantilever bending and to optimize the performance of PTE AFM in the sub-resonance regime, models that capture the thermoelastic response of the microcantilever at these frequencies are needed. We have experimentally and theoretically studied the sub-resonance photothermal vibrational response of coated and uncoated AFM microcantilevers as a function of laser modulation frequency and spot location. The sub-resonance microcantilever response shows distinct thermoelastic regimes. Below the microcantilever’s thermal roll-off frequency, the vibration amplitude is mostly constant. Past the thermal roll-off frequency, the vibration amplitude decreases with increasing frequency. For both coated and uncoated microcantilevers, the photothermal laser spot location that maximizes microcantilever vibration per unit input laser power is near the free end of the microcantilever. This is the opposite of the usually employed optimization of placing the photothermal laser spot near the microcantilever’s fixed end that is commonly used in tapping mode AFM experiments. For the tested coated microcantilevers, the most efficient photothermal laser spot location migrates to the microcantilever’s fixed end as modulation frequency increases. For the tested uncoated microcantilever, the most efficient photothermal laser spot location remains unchanged at the tested modulation frequencies of 0.1 kHz to 50 kHz. We implement a one-dimensional heat transfer analysis and bilayer thermoelastic model to better understand the coated microcantilever’s response. This model shows good qualitative agreement with the experimental data but quantitively underpredicts the coated microcantilever’s bending by up to 90%. This underprediction may be related to neglecting microcantilever bending contributed by a through-thickness temperature gradient. To explain the underprediction and highlight the limitations of the bilayer model, we implemented a full three-dimensional heat transfer analysis using a finite element approach. Our results illustrate different aspects of sub-resonance frequency-dependent photothermal laser spot optimization that can guide users to understanding and maximizing AFM microcantilever response to a given photothermal laser input power.