简介: |
Abstract:
Derived from atomic force microscopy, Kelvin probe force microscopy (KPFM) is an important instrument for measuring surface potential and/or surface charge distributions on the sample of interest. The resolution of KPFM experiments is, however, limited by the finite curvature of the probe tip, which is on the same order of, or larger than, the desired spatial variation of sample features. In fact, the obtained images are functions of both the sample surface features and the KPFM probe-sample geometry. Reconstructing the sample surface charge distributions from measured KPFM images is an inverse problem.
To develop an algorithm for reconstructing the sample surface charges, we first generalize the boundary element formulation for the forward problem developed by Strassburg et al. [Rev. Sci. Instrum. 76 (2005) 083705] to account for dielectric samples, then derive the convolution relation that relates the KPFM images, the desired sample surface features, and the artifacts due to the finite curvature of the probe tip. Such convolution relation is exact for a sample with a flat surface but introduces approximations for a sample with surface topography. Finally, we develop an algorithm for the deconvolution with two methods to mitigate the edge effect: constant background approximation and periodic source approximation. Application of this algorithm to experimental data is presented for illustration.
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