Effect of length, width, and mode on the mass detection sensitivity of piezoelectric unimorph cantilevers

Abstract

We have investigated both experimentally and theoretically the resonance frequency change of a piezoelectric unimorph cantilever due to the mass loaded at the tip of the cantilever. The piezoelectric cantilever was composed of a lead zirconate titanate (PZT) layer and a stainless steel layer. The dependence of the resonance frequency shift, Δf, with respect to a loaded mass, Δm, on the cantilever length, L, width, w, and the resonance modes was examined. For Δm much smaller than the effective mass of the cantilever, we showed that Δf/Δm increased with an increasing eigen value, νn2, and decreasing length, L, and decreasing width, w, as Δfn/Δm=−(νn2/4π)(1/L3w)(1/0.23612ρ̃)Ẽ/ρ̃, where Ẽ and ρ̃ are the effective Young’s modulus and effective density of the unimorph cantilever that depends on the thickness fraction, Young’s modulus and density of each of the individual layers. Thus, given the same Ẽ and ρ̃ by maintaining the same layer thickness fractions of the individual layers, Δf/Δm is increased by a factor of α−4 when a cantilever is reduced in size by a factor α in proportion in all dimensions. We also showed that the same scaling relationship can be applied to a strip mass loaded at the tip as well as uniformly distributed mass on the cantilever surface provided that the uniformly distributed mass does not form a continuous solid film rigidly bonded to the cantilever surface.

Real-Time Salmonella Detection Using Lead Zirconate Titanate-Titanium Microcantilevers

“…Thus, for this cantilever, each nanogram of mass adhered to tip surface will generate 10 Hz of frequency shift which is easily discernable using the impedance monitoring technique. This is already a great degree of sensitivity, further miniaturization will yield even greater sensitivity -calculation has shown that femtogram sensitivity can be reached by reducing the cantilever length to 0.1 mm [9] CONCLUSIONS It has been shown that the PZT-Ti microcantilever is an effective tool for direct, in-situ detection and quantification of Salmonella typhimurium in solution. By using a unique protein immobilization procedure that allows for the functionalization of titanium, the immobilization of CSA-1 antibody on the sensor tip surface was confirmed and successful dose response detections of S. typhimurium were performed using the PZT-Ti microcantilever.…”

“…When excited by an altemating current, the cantilever vibrates due to the piezoelectric effect. The resonance frequencies depend on the physical properties and dimensions of the cantilever, as well as the properties of the surrounding medium [9]. These resonant frequencies can be identified and monitored by measuring the electrical impedance spectrum with an impedance analyzer (Agilent 4294A, Agilent, Palo Alto, CA).…”

“…Binding of antigens or cells to the cantilever tip increases the cantilever mass which in turn decreases the cantilever's resonance frequency. Monitoring the shift in frequency of a resonant peak, Afr, can be translated into the amount of mass, Am, adhered to the tip under detection conditions by the following equation [9]:…”

“…The piezoelectric microcantilever developed by our group, [8,9] on the other hand, can maintain strong resonance peaks in water with Q value well over 40 by optimally incorporating a highly piezoelectric layer in the cantilever structure, thus allowing direct, in-water detection, while also presenting advantages such as highly sensitive, in situ, real-time quantification and low cost of production. This work is the basis for the microcantilevers used herein to directly detect the presence of Salmonella typhimurium in aqueous suspension.…”

Study of node and mass sensitivity of resonant mode based cantilevers with concentrated mass loading

“…9 Yi et al studied the effect of length, width, and resonance mode on mass sensitivity of a piezoelectric unimorph cantilever for concentrated mass loaded at the free end of the cantilever beam. 10 Besides shape effect, mass sensitivity is also dependent on mass loading conditions such as loading mass and positions. 11,12 Particularly, there are nodes on an acoustic wave device when the device is in resonance.…”