A method for etching a chromium layer in a vacuum chamber which may comprise introducing a halogen compound into the vacuum chamber, directing an electron beam onto the area of the chromium layer to be etched and/or introducing an oxygen including compound into the vacuum chamber. A further method for the highly resolved removal of a layer out of metal and/or metal oxide which may be arranged on an isolator or a substrate having poor thermal conductivity, may comprise arranging the layer inside a vacuum chamber, bombarding the layer with a focused electron beam with an energy of 3-30 keV, wherein the electron beam may be guided such that the energy transfer per time and area causes a localized heating of the layer above its melting and/or vaporization point and wherein the removal of the layer may be performed without the supply of reaction gases into the vacuum chamber.