Using a formal mathematics software for SH-APM sensor modelling

Abstract

Shear horizontal acoustic plate mode (SH-APM) sensors have been receiving a great deal of attention in biochemical applications for a few years [1–3]. They consist of a quartz plate with two interdigital transducers (IDTs) deposited on one surface, and a sensitive and selective coating layered on the opposite surface along which the wave interferes. The sensor sensitivity to mass loading, the acousto-electric effects, and the influence of viscosity, conductivity and temperature depend strongly on the considered mode and on the geometrical parameters of the delay line. Moreover, the nature and the crystallographic cut of the substrate, the ratio between the plate thickness and the wavelength, and the operating temperature are also important parameters. Systematic experimental studies are all the more difficult to achieve since there are many propagation modes and various detection mechanisms. As a consequence, our research on SH-APM sensors involves modelling devices. The modelling based on a ‘matrix approach’ was carried out with the help of the formal mathematics software MapleV. In this paper are reported the analytical and numerical results obtained with the software, as well as the calculation of the SH-APM phase velocity that can propagate in thin quartz plates of particular crystallographic cuts. These theoretical results are compared with experimental responses.