Consistency of the Surface Roughness Determined from Soft-X-Ray Reflectance and Surface Profiles Measured Using a Scanning Tunnelling Microscope: Coherence Length of the Soft X-Rays

There exists serious inconsistency between the rms surface roughness determined from the Debye-Waller factor for the soft-x-ray reflectance analysis and that measured with an optical surface profiler. We have measured the surface profile of evaporated films using a scanning tunnelling microscope, and reproduce the profile with the Fourier components whose spatial wavelength is shorter than the coherence length of the incident soft x-rays in the reflectance measurement. The rms surface roughness derived from the high-pass filtered profile agrees well with that determined using the reflectance measurement. This result explains straightforwardly the photon-energy dependence of the surface roughness estimated by the soft-x-ray reflectance method.