Methods of determining surface diffusion coefficients of molecules from signal fluctuations of a locally fixed probe are revisited and refined. Particular emphasis is put on the influence of the molecule's extent. In addition to the formerly introduced autocorrelation method and residence time method, we develop a further method based on the distribution of intervals between successive peaks in the signal. The theoretical findings are applied to STM measurements of copper phthalocyanine (CuPc) molecules on the Ag(100) surface. We discuss advantages and disadvantages of each method and suggest a combination to obtain accurate results for diffusion coefficients.

Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to molecules with circle-like shapes. Here we extend these treatments to molecules with rectangle-like shapes, for which also rotational diffusion needs to be taken into account. Focusing on the distribution of peak widths in the signal, we show how translational as well as rotational diffusion coefficients can be determined. We address also the question, how the distribution of interpeak time intervals and autocorrelation function can be employed for determining diffusion coefficients. Our approach is validated against kinetic Monte Carlo simulations.

We develop two methods for determining anisotropic diffusion properties of molecules on surfaces. These methods are based on the analysis of signal fluctuations recorded with moving probe tips, of, for example, a scanning tunneling microscope. In the first method, the probe tip oscillates along a straight line, which allows to quantify the effective diffusion perpendicular to the line. By varying the line orientation, the diffusion tensor is obtained. In the second method, the probe tip rotates along a circle and the diffusion tensor is determined by analysis of crosscorrelations between antipodal points. Both methods are successfully validated against surrogate data from kinetic Monte Carlo simulations.