J. Schwartzel

A quartz-like material: gallium phosphate (GaPO4); crystal growth and characterization

This investigation concerns GaPO4 crystal growth in sulphuric and phosphoric acid media through the slow heating and vertical reverse temperature gradient methods. Systematic study of growth parameters shows that the growth rate Vx is always much greater than the two other ones, Vz and Vy. The most interesting result is the ability to produce GaPO4 epitaxy on large berlinite seeds in sulphuric acid and to use them for GaPO4 crystal growth in phosphoric acid. The epitaxial fit and the crystalline quality have been checked by X-ray topography. The [OH] content, determined by infrared spectrometry, seems to prove a lower OH concentration than in case of berlinite when approximatively the same crystal growth conditions are used. First piezoelectric characterizations for resonators near the AT cut show GaPO4 to be a very promising piezoelectric material with a large coupling coefficient near 16%, a quartz-like thermal stability and a Q factor already nearly sufficient for the applications.

Bulk wave propagation and energy trapping in the new thermally compensated materials with trigonal symmetry

In this communication, we compare the properties of the new piezo-electric materials that belong to crystal class 32: the aluminium phosphate, the gallium phosphate and langasite with those of quartz. In a first part, a comparison of the main piezo-electric properties of these crystals is made. Computed and experimental results concerning the Y rotated cuts and particularly the compensated cuts are given. The most important facts observed are the increase of the coupling coefficient from quartz, to berlinite, langasite and gallium phosphate, and the simultaneous shift of the angular position of the most interesting compensated cuts towards the angles of maximum coupling coefficient. New determinations of the angular positions of the corresponding compensated cuts of gallium phosphate and doped langasite are also reported; the former one displays the largest coupling coefficient and an outstanding thermal stability. In the second part, the energy trapping properties of these four materials are compared. It is concluded that filters having more than 4 times the bandwidths obtained with quartz can be made using the new materials. Extremely high Q factors and the ability to withstand large excitation levels were observed in langasite resonators making use of energy trapping by the geometry (plano-convex). They appear very promising for low phase noise applications. The materials were found to possess an unique set of complementary properties, a high crystalline perfection, superior thermal behaviours, and different coupling coefficients adapted to an extremely broad range of filtering and frequency generation applications.<<ETX>>

Study of gallium phosphate and langasite crystals and resonators by X-ray topography

The gallium phosphate (GaPO/sub 4/) is, as berlinite, a close crystallographic analogue of quartz with the advantage that it has no /spl alpha/-/spl beta/ phase transition. It was shown that this material has very attractive properties for the applications to piezoelectric devices, due to its large coupling coefficients and to the existence of compensated cuts. Furthermore, it can be used up to extremely high temperatures (900/spl deg/C). To obtain much larger crystals, epitaxial growth of GaPO/sub 4/ on berlinite plates with several orientations was performed. The langasite crystals (LGS: La/sub 3/Ga/sub 5/SiO/sub 14/) were obtained by the Czochralski method. This new material has probably one compensated cut with a large coupling coefficient and very reduced angular sensitivity. Using the synchrotron radiation delivered by the DCI storage ring at the LURE (Orsay, France), we have studied by the X-ray topography technique the crystalline perfection of new GaPO/sub 4/ samples and different langasite crystals of different sources. For this study we have used traverse and section topography.<<ETX>>

Energy Trapping in Plane and Corrugated Resonators: Application to Quartz and Berlinite

Trapped energy resonators of plane and bevel led geometry are widely used for frequency generation and filtering. A model using a solution of the approximate equation governing the lateral dependance of thickness modes is established for plane resonators having nearly arbitrary electrode shape. This model uses solutions in the form of serie of products of Bessel and trigonometric functions and considers the expression of the approximate continuity conditions at a discrete number of points of the -1ectrode edge. This method of solution is applied to study the influence of the shape of the electrodes on the properties of the resonators and to demonstrate on a few examples that the usual circular geometry is not optimal with respect to several criterions. Resonators with electrodes respecting approximatively the lateral anisotropy of the plate (rectangular and elliptical) are considered in these examples. An extension of the model is made to consider plane resonators having shallow grooves outside the electrodes to improve the energy trapping.

Air-gap determination of the cut-off frequency of unelectroded plates and effects of local thickness modifications in plane resonators

A method is proposed for obtaining precise measurements of the cutoff frequencies of unelectroded plates. These quantities can then be used in a model, similar to that which has permitted the extraction of the cutoff frequency, to determine the other parameters of the resonator (electrode geometry and mass loading). Two successive applications of these models permit one to remove most of the uncertainties relative to the material constants and to obtain precise values of the equivalent scheme and, if necessary, a response free from anharmonic modes. A model of the resonators with embedded electrodes proposed by T.J. Lukaszek (1971) has been constructed and the properties of this type of resonators computed. The models made for the three types of resonators described here are based on the approximate equations governing the thickness vibrations of piezoelectric plates established by H.F. Tiersten and coworkers (1979). Two methods of resolution of these equations were used: a semialgebraical one and the finite-elements method.<<ETX>>

Energy trapping resonators and integrated filters using the AT cut of quartz like materials

The properties of AT resonators made with quartz, berlinite, and GaPO4 are compared using calculations made with a three-dimensional model that takes into account the energy trapping phenomena existing in real resonators. These computations show that the high coupling quartz-like materials lead to very interesting properties in terms of inductance and capacitance ration. The AT resonators using berlinite and GaPO4 achieve much greater filter bandwidth or oscillator shifts than AT quartz. For several applications, e.g., VHF filters with suppression of the antisymmetrical anharmonics, the use of berlinite appears to constitute an interesting compromise. For applications requiring the largest bandwidth or oscillators shifts, the use of gallium phosphate appears to be very promising.<<ETX>>

Berlinite: Characterization of Crystals with a Low Water Concentration and Design of Bulk Wave Resonators

Several modifications to crystal growth methods were successfully investigated to decrease the water concentration in crystals.

Linear model of the contoured resonators

An analysis based on the approximate equation for the thickness vibration established by H.F. Tiersten (1976, 1979, 1982, 1986) and coworkers is presented. A semi-algebraic method of resolution are investigated for partially or totally contoured resonators. In this method, the eigensolutions at V=0 are obtained by separation of the approximate equation in transformed rectangular or polar coordinates for the different regions of the resonator. A totally numerical solution of the approximate equation by the finite-element method is then proposed. The method can be used for practically any type of thickness-mode resonator. It is applied here to some typical examples of contoured resonators. The results are compared with those obtained with the previous method and with experimental results.<<ETX>>

Lateral field excitation and coupled modes in AT quartz: synchrotron radiation X-ray topography

Using the synchrotron radiation delivered by a DCI storage ring, plano convex AT resonators excited by a lateral field are studied by the X-ray topography technique. Different overtones and anharmonics of the three types of the thickness modes are observed. Coupled modes in fundamental AT plane resonators are shown and the reasons for their appearance are analyzed.<<ETX>>

Studies of Quartz Resonators by Stroboscopic Topography

Summary Stroboscopic X-ray topography have been carried out to observe the states of acoustic vibrations in quartz resonators. These experiments have been done using the storage ring of D.C.I. (Orsay, France) as a pulsed light source. The studied AT resonators have shown that the vibration mode is directly related to the density and the distribution of the defects.