oscillation 52 along the layer thickness 7 of the piezoelectric layer 4 an arrangement according to fig1 b in which the two electrodes 5 and 6 are disposed on one side of the piezoelectric layer 4 leads to a thickness shear mode oscillation 51 the arrangement according to fig1 c likewise leads to the development of a thickness shear mode oscillation 51 the resonator 2 has a surface section 8 on which a substance of a fluid 9 can be sorbed for this purpose the resonator 2 has a chemically sensitive coating 10 the chemically sensitive coating 10 is applied to the electrode 5 fig1 a as an alternative to this the chemically sensitive coating is applied to the two electrodes 5 and 6 fig1 b the chemically sensitive coating 10 can also be applied to the piezoelectric layer 4 fig1 c alternatively a protective layer 12 is applied to the resonator 4 onto which protective layer the chemically sensitive coating 10 is applied in turn fig1 d in an embodiment that is not shown the protective layer 12 itself acts a chemically sensitive coating 10 fig1 e shows a further alternative according to which the chemically sensitive coating 10 is disposed in a recess 13 of the semiconductor substrate 3 on a membrane 14 made of a nitride the recess 13 is produced by backside etching of the semiconductor substrate 3 according to fig1 f in contradistinction.