Subsurface atomic force microscopy: towards a quantitative understanding

Recent experiments in the field of subsurface atomic force microscopy have demonstrated that it is possible to nondestructively image micro- and even nanoparticles that are embedded significantly deep within the bulk of a sample. In order to get insights into the contrast formation mechanism, we performed a finite element analysis and an analytical study, in which we calculated the amplitude and phase variation on the surface of an ultrasound wave that has traveled through the sample. Our calculations were performed as closely as possible to the situation in the experiments to enable a (future) comparison based on our predictions. We show that Rayleigh scattering of acoustic waves accounts for the measured contrast and we verify the characteristic Rayleigh dependences. The numerical results show that the contrast is independent of the depth at which a particle is buried, whereas the analytical study reveals a 1/depth dependence. In addition, we find a large deviation in the width of the particle in the contrast at the surface when applying the numerical or the analytical calculation respectively. These results indicate the importance of both the reflections of sound waves at the sample interfaces and bulk damping, as both are treated differently in our two models.