Fractal Characteristics of Film Surface

A fractal surface was generated on computer by random addition method. The simulated measurement on this surface shows that z resolution has little effect on calculating fractal dimension D while the lower x, y resolution causes larger statistic error. D was calculated for Au films on three kind of substrate using data from Scanning Tunneling Microscope(STM) images. D = 2. 15 for Au/ceramic, and D = 2. 06 for Au/optical glass. D has different values for different points on Au/general glass, the reason of mismatch between curves from STM images of different scan sizes was also discussed.