The Main Lateral Mode Approximation of a Film Bulk Acoustic Resonator With Perfect Metal Electrodes.

Using first principles and the constitutive equations of a piezoelectric crystal, we solve the 2-D problem inside a three-layer film bulk acoustic resonator (FBAR) in order to study the dispersion and parasitic lateral modes' characteristic of the structure. In our main lateral mode approximation, described here in detail, we construct the acoustic wave by combining the ideal "piston" mode and the main dispersion branch lateral mode. By limiting our analysis to the practical range of frequencies near the series resonance of the stack, where the lateral component $k_{x}$ of the ${k}$ vector is small, we find analytical expressions for the FBAR acoustic wave and for the dispersion of the three-layer stack. When lateral boundary conditions are added to the acoustic problem of a laterally finite resonator, we employ our theory to estimate the amplitude and the propagation of the lateral modes and then compare the theoretical predictions with the measurements of fabricated FBARs and finite-element simulation results. We are able to distinguish between a "clamped" and a "quasi-free" lateral interface by comparing the amplitude strength of the lateral modes produced, and we discuss how optimum lateral boundaries can be engineered with perimeter frames for realistic resonators.

An Investigation of Lateral Modes in FBAR Resonators.

Using first principles and the constitutive equations for a piezoelectric, we solve the 2D acoustic wave inside a single, infinite, piezoelectric membrane in order to study the dispersion of Thin Film Bulk Acoustic Resonator (FBAR) lateral modes, with and without infinitely-thin electrodes. The acoustic eigenfunction is a dual wave, composed of longitudinal and shear components, able to satisfy the 2D acoustic boundary conditions at the vacuum interfaces. For the single piezoelectric slab we obtain analytical expressions of the dispersion for frequencies near the longitudinal resonant frequency (Fs) of the resonator. These expressions are more useful for the understanding of dispersion in FBARs and more elegant than numerical methods like Finite Element Modeling (FEM) and various matrix methods. We additionally find that the interaction between the resonator's electrodes and the acoustic wave modifies the lateral mode dispersion when compared to the case with no electrodes. When correctly accounting for these interactions the dispersion zero is placed clearly at Fs, unlike what is calculated from a 2D model without electrodes where the dispersion zero is placed at Fp. This is important since all experimental evidence of measures FBAR resonators shows that the dispersion zero is at Fs. Furthermore, we introduce an electrical current flow model for the propagating acoustic wave inside the electroded piezoelectric and based on this model we can discuss an electrode-loss mechanism for FBAR lateral modes which depends on dispersion. From our model it results that lateral modes with real kx have higher electrode dissipation if they are closer to the resonant frequency. This is consistent with the typical behavior of measured FBAR filters where the maximum lateral mode damage on the insertion loss takes place for frequencies immediately below Fs.

A digitally compensated 1.5 GHz CMOS/FBAR frequency reference.

A temperature-compensated 1.5 GHz film bulk acoustic wave resonator (FBAR)-based frequency reference implemented in a 0.35 microm CMOS process is presented. The ultra-small form factor (0.79 mm x 1.72 mm) and low power dissipation (515 microA with 2 V supply) of a compensated FBAR oscillator present a promising alternative for the replacement of quartz crystal frequency references. The measured post-compensation frequency drift over a 0-100 degrees C temperature range is < +/- 10 ppm. The measured oscillator phase noise is -133 dBc/Hz at 100 kHz offset from the 1.5 GHz carrier.

Interlaboratory validation of a real-time PCR 24-hour rapid method for detection of Salmonella in foods.

The efficacy of a 24-h Salmonella real-time, or quantitative, PCR (qPCR) detection method was assessed through a collaborative effort involving eight Federal and state laboratories. Eleven foods including mashed potatoes, soft cheese, chili powder, chocolate, eggs, sprouts, apple juice, fish, shrimp, ground beef, and ground chicken were tested. For each food, seven blind samples were distributed to each participant for testing. These included six samples equivalently inoculated with 1 to 5 CFU/25 g of various serotypes of Salmonella (Gaminara, Weltevreden, Heidelberg, Senftenberg, Enteritidis, Newport, Typhimurium, and Kentucky for each food) and 10 to 50 CFU/25 g of the competitor Enterobacter cloacae. The seventh sample was inoculated with 10 to 50 CFU/25 g of the competitor, E. cloacae, only. These samples were tested for Salmonella by using four methods in parallel: (i) 24-h qPCR method detecting Salmonella from modified buffered peptone water enrichment medium; (ii) 48-h qPCR method detecting Salmonella from a secondary selective enrichment broth; (iii) modified Bacteriological Analytical Manual method; and (iv) VIDAS, an immunoassay system. The results of the statistical analysis showed there was no significant (P > or = 0.05) difference between either of the qPCR methods and the modified Bacteriological Analytical Manual method for 10 of 11 foods. For the one exception, sprouts, detection by qPCR required 48 h. Both qPCR methods showed a detection limit of 0.08 to 0.2 CFU/g. These results provide a solid basis for using this 24-h qPCR rapid screening method to detect Salmonella in foods.