TSM Resonator Mass Sensitivity

The accumulation of an ideal mass layer at the crystal surface, which is an anti-node or maximum of displacement, causes an increase in the kinetic energy with no change in potential energy. This assumes that the mass layer is sufficiently thin and/or rigid and that displacement is uniform across its thickness, 

The peak potential energy density Up in the TSM resonator occurs at an instant (depicted in Rgure 3.4) when displacement is maximum in the crystal and velocity is zero. From Equation 2.40, this is given by 

Invoking the Rayleigh hypothesis by balancing peak kinetic and potential energy dfinsitips (Equations 3.6 and 3.7) gives a relationship between resonant frequency w and surface mass density p,  

Combining Equations 3.2, 3.3, and 3.9 gives the Sauerbrey equation commonly used to relate changes in TSM resonant frequency to surface mass density p, tl]  

Solution (a) From the detinition of sensitivity and Equation 3.9, S = dp, = foKPqh) = — 57 Hz-cmVpg. This means that for each 1 pg/cm of mass accumulation, the resonant frequency will decrease by 57 Hz. (b) The limit of mass resolution is the mass density that causes a frequency shift of 0.3 Hz R = 3(,Hf)/S = (0.3 Hz)/(S7 Hz-cmVpg) = 5 ng/cm.  

---