Modelling and control of coupled AFM arrays for parallel imaging verified through a macro scale experiment.

Atomic Force Microscopy (AFM) is a mature imaging technology that is utilised in a wide range of applications for the purpose of obtaining high resolution images of sample topography and sample property measurements. Currently, AFM technology is centred around the use of single cantilevers to obtain data for one point on the sample at a time. There is currently a drive to extend AFM technology beyond the capabilities of established measurement techniques, including the ability to measure multiple sample points simultaneously, increase acquisition rate, increase measurement sensitivity to sample variations, and to obtain detailed, localised information about material properties. One possible way to address some of these issues is to use arrays of cantilevers instead of a single beam. Using multiple active sensing cantilevers in close proximity allows for true simultaneous data acquisition across multiple points of interest on a sample, as well as increasing measurement density. The main drawback is that cantilevers in a closely spaced array become mechanically coupled, altering the dynamic response of the system. To ensure reliable functionality, a full understanding of the coupled system dynamics is required, including how response is altered by nonlinear force interactions at each cantilever tip. In this research, a detailed dynamic analysis is conducted for a set of fabricated micro-cantilever AFM arrays fabricated by our collaborators at the Technische Universit at Ilmenau (TUI), for the purpose of understanding the system response during Amplitude Modulation operation (AM-AFM). A mathematical model was developed for an array of M beams, each with nearest-neighbour mechanical coupling and individual nonlinear tip-sample force interaction terms. It is shown that this model is able to capture the system eigenmodes, and how the spatial shape of the eigenmodes is altered by tip-sample force interactions. To complement the model, an equivalent macro scale experimental setup was developed to mimic the response of the micro arrays. The macro scale test rig allows for easy and quick parameter variation to gain a better understanding of the micro system response. This approach provided insight into the micro scale dynamics and provided experimental validation of the mathematical model. Using the developed model and macro scale experiment, the observed response of the micro arrays could be linked to the parameter space of the system. This information has been used to determine the cause of observed nonlinear phenomena in the array response. Recommendations have been made as to how the array parameters may be optimised to avoid unwanted phenomena which may result in erroneous data. It is believed that this information will be valuable to our collaborators and will be a signi cant step towards commercialisation of their array technology for parallel throughput AFM. In addition, a new method of enhanced sensitivity AFM has been proposed, utilising the change in spatial mode shape as a measurement signal. This method utilises mechanical coupling as an advantage, as opposed to trying to eliminate coupling as a unwanted feature. The proposed concept has been validated through mathematical modelling and experimental investigation, and the preliminary steps required to implement the technology with the TUI arrays have been proposed