A method for producing a floating gate memory device comprising the steps of: • Providing a monocrystalline semiconductor substrate, • Forming a tunnel oxide layer on said substrate, • Producing one or more openings in said tunnel oxide, to expose areas of said semiconductor substrate, • Cleaning the exposed substrate with a cleaning liquid, • Loading the substrate into an epitaxial reactor, and thereafter: • Optionally, annealing the substrate, to thereby remove any remaining oxides from the areas, • Epitaxially growing a monocrystalline semiconductor layer on the substrate by selective epitaxial growth using the exposed substrate areas as source areas, • Planarizing the monocrystalline semiconductor layer, • Depositing a hard mask layer made of dielectric material on the planarized monocrystalline layer, • Depositing and patterning a layer of resist on the hard mask layer, • Etching the monocrystalline layer, stopping on the tunnel oxide layer, thereby forming columnar monocrystalline floating gate structures, • Etching trenches between said columnar floating gate structures, through the portions of the tunnel oxide layer situated between the columnar floating gate structures, • Filling said trenches with a dielectric material, leaving a portion of the columnar floating gate structures exposed, • Thermally growing an oxide layer on each of the lateral sides of the columnar floating gate structures, • Depositing a control gate layer between and on top of said columnar floating gate structures, so that the control gate layer is directly on the totality of the thermally grown oxide layer on the lateral sides of the columnar floating gate structures. • Providing a monocrystalline semiconductor substrate, • Forming a tunnel oxide layer on said substrate, • Producing one or more openings in said tunnel oxide, to expose areas of said semiconductor substrate, • Cleaning the exposed substrate with a cleaning liquid, • Loading the substrate into an epitaxial reactor, and thereafter: • Optionally, annealing the substrate, to thereby remove any remaining oxides from the areas, • Epitaxially growing a monocrystalline semiconductor layer on the substrate by selective epitaxial growth using the exposed substrate areas as source areas, • Planarizing the monocrystalline semiconductor layer, • Depositing a hard mask layer made of dielectric material on the planarized monocrystalline layer, • Depositing and patterning a layer of resist on the hard mask layer, • Etching the monocrystalline layer, stopping on the tunnel oxide layer, thereby forming columnar monocrystalline floating gate structures, • Etching trenches between said columnar floating gate structures, through the portions of the tunnel oxide layer situated between the columnar floating gate structures, • Filling said trenches with a dielectric material, leaving a portion of the columnar floating gate structures exposed, • Thermally growing an oxide layer on each of the lateral sides of the columnar floating gate structures, • Depositing a control gate layer between and on top of said columnar floating gate structures, so that the control gate layer is directly on the totality of the thermally grown oxide layer on the lateral sides of the columnar floating gate structures.