Modelling thermal expansion as a point spread function for nanoscale chemical imaging

Abstract

Atomic force microscopy-infrared (AFM-IR) is an AFM based technique that measures mid-IR absorption spectra at nanometre spatial resolution. The technique of AFM-IR relies on the detection of the pulsed wavelength tuneable IR laser induced thermal expansion of the sample area underneath the AFM tip. While this mode of signal generation sounds simple enough it is still not fully understood. In this work, we present a theoretical investigation of the laser heating induced thermal expansion process and model it as a point spread function (PSF). This approach draws parallels to super resolution microscopy where the PSF is used to determine spatial resolution and to resolve features below the diffraction limit. By solving the inhomogeneous heat equation with a volumetric heat source, we obtain the PSF of AFM-IR in time and frequency domain. To verify that simplified boundary conditions do not result in a significantly changed behaviour a finite element model of heat conduction in solids and fluids (implemented in COMSOL Multiphysics 5.6) of more realistic sample geometries is used. In this case we consider a cylindrically shaped sample with a single spherical element thermally heated by a laser pulse. The sample is placed on a thick substrate and covered by an air layer. Finally, the theoretical considerations yielding the PSF are compared to COMOSL simulated data. First results show that there is a frequency (pulse repetition rate), pulse length and sample geometry dependence of the PSF in AFM-IR. The achievable spatial resolution is improved for short pulses, high frequencies, small absorber size and when the absorbers are closer to the substrate. These results provide guidance for experimental parameters which can be considered as trade-off between spatial resolution and signal intensity.