PURPOSE: To suppress the generation of defective substrates and to inexpensively obtain the AlN substrate by dispersing spherical alumina powder of a specific grain size into a solvent, coating the respective laminated surfaces of AlN green sheets with this solvent at a prescribed coating density, laminating plural sheets thereof and calcining the sheets in a nitrogen atmosphere.

CONSTITUTION: The spherical alumina powder having 5 to 100μm grain size is dispersed together with a binder (e.g.; methyl cellulose) into the solvent (e.g.: water). The resulted alumina powder slurry 1 is then sprayed onto the laminated surfaces of the green sheets 2 of the aluminum nitride so as to attain 10 to 300pieces/cm2 coating density and is dried. Plural sheets of such green sheets 2 are laminated and are calcined at 1800 to 1900°C in the nitrogen atmosphere, by which the aluminum nitride substrate is obtd. Since the spherical alumina powder having the uniform grain size is used as the laying powder, the deformation, warpage, etc., of the substrate are prevented in this way and the cost of production is reduced.