A contribution to solve the problem of coating properties extraction in quartz crystal microbalance applications

The problem of coating properties extraction in quartz crystal resonator (QCR) applications is one of the challenging tasks of QCR applications, not completely solved even in theoretical conditions. The present work demonstrates that the problem is determined only for a set of three parameters of the coating, which concentrate the four coating properties. The following parameters are chosen: the surface mass density m8 = p1h1, the loss tangent tan delta1 = G''1/G'1, and the magnitude of the characteristic impedance /Z1(c)/ = (p1/G1/)(1/2). An algorithm is proposed that permits, in ideal conditions, an unambiguous extraction of these parameters, starting only from the admittance spectrum of a three-layer compound resonator, obtained from the one-dimensional transmission-line model (TLM) around the resonance. The algorithm introduces three additional improvements in relation to other routines: the calculation time is drastically reduced, the problem of erroneous solutions related to relative minima in typical fitting routines is eliminated, and a systematic error analysis in the extraction of the coating properties in real practice can be carried out. The use of the proposed algorithm as a tool for studying the effects of different phenomena such as slipping or surface roughness is introduced.