In order to immobilise bio-material, e.g. enzymes, micro-organisms, cells, organelles, etc., on a substrate with a Si3N4 surface with bonding-active NHx groups, use is made of a hetero-functional cross-linking agent with a bio-material coupling function on the one hand and a NHx-reactive group on the other. The immobilisation substrate preferably takes the form of a 10-1000 mm thick Si3N4 layer which is separated from SiH4/NH3 by CVD and coated with bonding-active NHx groups by hydrolysing surface cleaning, especially with dilute acid. Advantageously, a hetero-bifunctional cross-linking agent is first caused to react with an NH2-reactive aldehyde, ester, halide, epoxide, imine or isocyanate group and, after the removal of unbonded superfluous cross-linking agent, coupled to the biomaterial by means of the bio-reactive group.