Glass element with structured wall and method for the production thereof

A method for producing a panel-shaped glass element, comprising:

• providing a vitreous material having a thickness defined between two opposing surfaces, the vitreous material having a thermal expansion coefficient of less than 10×10-6 K-1;
• directing a laser beam of an ultrashort-pulse laser onto one of the two opposing surfaces through focusing optics in order to form an elongate focus in the vitreous material until a plurality of filamentary channels are generated in the thickness by incident energy of the laser beam, the plurality of filamentary channels having a depth that runs transverse to the thickness and being arranged at a distance from one another;
• exposing the vitreous material to an etchant that erodes the vitreous material to widen the plurality of filamentary to define a recess through the thickness of vitreous material with a recess wall adjoining the two opposing surfaces and with a plurality of depressions in the recess wall, wherein each of the plurality of depressions have a rounded dome-shape hollow and a ridge enclosing the rounded dome-shape hollow;
• and
• adjusting parameters of the laser beam so that the recess wall has a mean roughness value that is at least 50 nm and less than 5 µm.