Accurate assessment of the roughness exponent of a fracture surface via scanning tunnelling microscopy

A new straightforward method was proposed to measure the local roughness ex ponent of a scanning tunnelling microscopy (STM) image. Its reliability was tested against some ideal self-affine surfaces. Taking the mean value of a number of local roughness exponents for the STM images, which were randoml y recorded on a fracture surface, as the roughness exponent of the fracture surface, we quantitatively assessed the experimental error of the measured roughness exponent by statistical analysis. The experimental results for t wo different fracture surfaces showed that the difference between the two r oughness exponents was not produced by their experimental errors to a 90% p robability.