Abstract: Unwanted distortion of the planar configuration of a carbon-based X-ray lithography mask, that would otherwise occur during selective etching of the (silicon) support substrate, is prevented by incorporating a compensation layer of inorganic material that effectively offsets the internal compressive stress characteristic of the carbon. For this purpose, on a top, planar surface of a silicon substrate, a multiple layer structure containing a first layer of carbon having an internal compressive stress characteristic and a second layer of inorganic material having an internal tensile stress characteristic, is plasma-deposited. The tensile stress characteristic of the inorganic layer compensates for the compressive stress characteristic of the carbon layer and causes the composite structure to retain its substantially planar configuration after the underlying silicon substrate has been etched in the course of obtaining a rim structure on which the X-ray transmissive structure is supported.