A method as for producing a laterally limited, single-crystal region on a substrate with selective epitaxy, said substrate comprised of single-crystal semiconductor material at least in the region of a surface of said substrate, said method comprising the steps of:
- generating a mask layer consisting essentially of dielectric material on said surface of said substrate by generating a first auxiliary layer on said surface of said substrate, generating a second auxiliary layer over said first auxiliary layer, and generating a main layer over said second auxiliary layer, said first auxiliary layer, said second auxiliary layer and said main layer, in combination, forming said mask layer producing an opening in said mask layer through which said surface of said substrate is exposed, said opening having a first extent parallel to and adjacent said surface of said substrate laterally projecting beyond a second extent of said opening at an upper surface of said mask layer, and said first and second extents being connected by a sidewall of said opening having a step-shaped profile in a cross-section of said opening proceeding. perpendicularly relative to said surface of said substrate, said opening in said mask layer being produced by etching said main layer in an anisotropic etching process to produce an opening in said main layer defining said first extent of said opening in said mask layer, selectively etching said second auxiliary layer relative to said main layer and relative to said first auxiliary layer in an isotropic etching process by under-etching said second auxiliary layer beyond the opening produced in said main layer to expose said first auxiliary layer and to define said second extent of said opening in said mask layer, and selectively etching the exposed portion of said first auxiliary layer relative to said second auxiliary layer in said isotropic etching process.