The present invention relates to a method for the preparation of samples having polished surfaces or facets suitable for the application of high resolution microscopy techniques such as electron microscopy, scanning probe microscopy and the like. In particular it relates to a method for forming highly flat and smooth cross-sections through device structures immediately adjoining a sample surface, to allow high resolution analysis of such device structures. For instance the invention relates to formation of facets on samples having epitaxial layers, multilayer structures, semiconductor thin films and the like where the structures and layers have sub-micrometre scale dimensions. When studying such device structures, it is desirable to achieve polished surfaces or facets with a roughness of the order of 1nm (root mean square peak-to-trough height) or better.