Thick film technology has been used to produce high frequency (>20 MHz) transducers. Alumina or silicon substrates appear to be inappropriate as backing material because of their low attenuation and high acoustic impedance. Alternatively, porous materials have a sufficient attenuation but their acoustic impedance lowers the sensitivity. In this context, the use of a Bragg cell between the piezoelectric film and the substrate is investigated for high frequency ultrasonic transducers for non destructive testing or medical applications. A recursive transmission/reflection model is presented. The influence of the constitutive layer properties of a Bragg cell is studied for two compatible sets of materials (Au/PZT or Pt/Al 2 O 3 ). This model is then used to highlight the interest of a periodic structure loaded with a substrate. Finally, experimental results on a Bragg cell are reported and discussed.Key words: periodic structures, piezoelectric transducer, high frequency.
A. IntroductionThe elaboration of thick-film high frequency ultrasonic transducers requires a compromise between theoretical design and fabrication possibilities in terms of material properties and sizes. All the substrates adapted to the fabrication process have an acoustic impedance close to that of the active film or even higher, leading to a strong damping of the piezoelectric resonance. Therefore, it is necessary to adapt the input impedance at the rear face of the piezoelectric layer to avoid excessive lowering of its resonance frequency and of transducer sensitivity. Here, the proposed solution is the insertion of a Bragg cell between the piezoelectric layer and the substrate. Available material combinations are restricted by thermal and chemical compatibility. Thus, the ratio of acoustic impedance between the two layers constituting the Bragg cell is limited. First, the recursive model and related formulas for the reflection and transmission coefficients are presented without restriction to periodicity. Then, the case of a Bragg cell on a substrate is presented as a way to modify the input impedance of the backing. Second, the influence of the acoustic impedance ratio on the transmission coefficient is presented and two available compatible sets of materials (Au/PZT or Pt/Al2O3) are discussed. The influence of the number of layers is discussed both in terms of minimum value and bandwidth. Then, the high frequency transducer design is presented, using a recursive calculation of the input impedance of the backing. Finally, experimental results are presented for a Bragg cell made of Au/PZT.
B. ModelingThe modeling of a periodic structure is developed here on the basis of a one dimensional assumption. It takes into account multiple reflections between the interfaces.
B.1. Reflected and transmitted pressure fieldsUsing the notation proposed by Conoir [1], the Fresnel reflection and transmission coefficients, R and T, at the interface between layers indexed n and n+1 are:reciprocally,andwhere Zn is the acoustic impedance, ϕn = knzn = ω ...