Study of the fractal character of surfaces by scanning tunnelling microscopy: Errors and limitations

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Abstract
SUMMARY: The possibility of using the intrinsic three‐dimensional imaging capability of scanning tunnelling microscopes to study the fractal character of surfaces by Mandelbrot's method of ‘filling’ with water up to a given height is discussed. By plotting on a log‐log plot the area against the perimeter of the ‘lakes' that appear, the fractal dimension is obtained from the slope of the straight line fitting the data points. The possible errors and limitations of the method are discussed from results obtained from both simulated and real surfaces. The effect of noise and resolution in the scanning tunnelling microscope on the calculation of the fractal dimension is also discussed.

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