Tadeusz Gryba

LEGENDRE POLYNOMIAL APPROACH FOR MODELING FREE-ULTRASONIC WAVES IN MULTILAYERED PLATES

Modeled on the Laguerre polynomial approach used for surface acoustic waves, a formulation is presented for the study of free-acoustic wave propagation in layered plates. It uses the Legendre polynomials. Each layer can be of arbitrary anisotropy and piezoelectricity with arbitrary crystal orientation with the only restriction that the parameters of the constituent materials are close to each other. Formulations are given for open-circuit and short-circuit surfaces. Phase velocity dispersion curves, attenuations, power distributions, and field profiles are easily obtained from an algorithm easily implemented on a computer using commercial software. Numerical results are given for AlAs/GaAs multilayered structures which illustrate the capabilities of the described method. Its major advantages are: (i) in a unified formulation, all types of modes, surface modes, interface modes, and plate modes are naturally encompassed. (ii) Large values of the frequency-thickness product as compared to the values allowed ...

A unified formalism using effective surface permittivity to study acoustic waves in various anisotropic and piezoelectric multilayers

A unified formalism is presented that uses the effective surface permittivity (ESP) to study surface acoustic waves (SAW) in layered substrates and guided waves in layered plates. Based on known mathematical tools, such as ordinary differential equation and transfer matrix, a generalized surface impedance (GSI) concept is developed and exploited to investigate the acoustic propagation in various anisotropic and piezoelectric layered structures. The ESP function, originally defined for the surface of a homogeneous and semi-infinite piezoelectric substrate, is extended to both the top surface of and an interface in a layered half space, as well as to either surface of a finite-thickness plate. General ESP expressions for all mentioned configurations are derived in terms of an equivalent GSI matrix. It is shown that, when using the appropriate GSI matrices, the same form of the ESP expressions applies no matter whether the structure is a homogeneous half space alone or coated with a layered plate or a layered plate alone. GSI matrices are explicitly given in terms of the bulk partial mode solutions for a substrate and via the transfer matrix for a plate. Modified GSI matrices for structures consisting of both a plate and a substrate are also specified. Analytical development is fully detailed to suit program implementation. To illustrate its versatility, the formalism is also applied to two-substrate configurations, allowing one to analyze guided waves in a plate sandwiched between and interfacial waves existing along the boundary of two different media. Numerical examples are given to illustrate the spectrum features that the ESP shows for various structures. Deduced ESP expressions allow one to locate directly all piezoelectrically active waves in any structure including at feast one piezoelectric layer. Acoustic modes that are not piezoelectrically active and those in non-piezoelectric materials can be also obtained by using the intermediate results, such as derived GSI matrices.

Conceptual advantages and limitations of the Laguerre polynomial approach to analyze surface acoustic waves in semi-infinite substrates and multilayered structures

Laguerre polynomial approach is used to calculate velocities, coupling coefficients, and field distributions of surface acoustic waves in both semi-infinite substrates and multilayered structures. Approximation used in boundary conditions for applying the Laguerre polynomial method is investigated. Effectiveness of the method to calculate the coupling coefficient is checked. Its capabilities with regard to the various types of waves are reviewed. It is shown that Laguerre polynomial method cannot be used to study leaky surface acoustic waves. For true surface acoustic waves it can, but for deep penetration, computing time becomes prohibitive. Laguerre polynomial method is interesting for true surface acoustic waves modes if decay length is of the order of one acoustic wavelength: velocities, coupling coefficient and, continuous field profiles are quite well returned. However, for multilayered structures, very dissimilar parameters of the constituent materials give rise to significant field level discontinuities at the interfaces. It is shown that the Laguerre polynomial method does not return, within reasonable computing time and required memory, these discontinuities of which multiple quantum well-based devices can take advantage.

Modeling of bulk acoustic wave devices built on piezoelectric stack structures: Impedance matrix analysis and network representation

The fundamental electro-acoustic properties of a solid layer are deduced in terms of its impedance matrix (Z) and represented by a network for modeling the bulk acoustic wave devices built on piezoelectric stacked structures. A piezoelectric layer is described by a three-port equivalent network, a nonpiezoelectric layer, and a short- or open-circuit piezoelectric layer by a two-port one. Electrical input impedance of the resonator is derived in terms of the Z-matrix of both the piezoelectric layer and an external load, the unique expression applies whether the resonator is a mono- or electroded-layer or a solidly mounted resonator (SMR). The loading effects of AZ-electrodes on the resonating frequencies of the piezoelectric ZnO-layer are analyzed. Transmission and reflection properties of Bragg mirrors are investigated along with the bulk radiation in SMR. As a synthesizing example, a coupled resonator filter (CR.F) is analyzed using the associated two-port equivalent network and by calculating the power transmission to a 50 Omega-load. The stacked crystal filter is naturally included in the model as a special case of CRF. Combining a comprehensive matrix analysis and an instructive network representation and setting the problem with a full vectorial formalism are peculiar features of the presented approach.

Analysis of Frequency Response of IDT/ZnO/Si SAW Filter Using the Coupling of Modes Model

A monolithic integration of filters on Si or GaAs substrates is highly desirable to miniaturize the outer dimensions of the cellular phones. But, direct monolithic integration of surface acoustic wave (SAW) filters is impossible with Si, which is nonpiezoelectric, and difficult with GaAs, which is weakly piezoelectric. One alternative is the deposition of a piezoelectric film on the semiconductor substrate. In this paper, we propose a modified coupling-of- modes (COM) approach, which can be used in the practical design of a layered ZnO/Si SAW filter. This is a dispersive SAW-layered filter, and some of the COM parameters become frequency dependent due to the phase velocity dispersion. The frequency response of the 3-step ladder type ZnO/Si SAW filter is analyzed and compared with the experimental results.

Modelling of radiofrequency MEMS bulk acoustic wave resonators with Legendre polynomial method

Radio‐Frequency electro‐acoustic resonators and filters are key components for wireless communication devices. The next generation of mobile systems requires for these components a strict size reduction, higher operating frequency and better power resistance. So, MEMS BAW (Bulk Acoustic Wave) devices have emerged as an efficient alternative to established Surface Acoustic Wave filtering solutions. Knowledge of the electromechanical coupling coefficient and the Q‐factor are of primary importance for the MEMS BAW device design. In our model, the Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to calculate these parameters. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach are, in a unique formulation, to take into account the presence of sources, existence of electrodes losses and dissimilarity of the constituent material...

Design of dispersive layered SAW filters with CMOS low noise amplifier

Up to now, RF front‐end surface acoustic wave (SAW) filters for mobile communication are mainly fabricated on LiNbO3 and LiTaO3 substrates. A monolithic integration of these filters on Si substrates is highly desirable, but Si is non piezoelectric. One alternative is the deposition of a piezoelectric film on the semiconductor substrate. CMOS technology is very attractive for integrating the radio frequency modules in a single chip. This paper presents the analysis and realisation of a SAW passband filter on silicon substrate based on a piezoelectric ZnO thin film working near 1 GHz , integrated with a CMOS low‐noise amplifier. We propose a modified coupling of modes (COM) approach for a layered ZnO/Si surface acoustic wave filter. The COM parameters in this formulation are the Rayleigh wave velocity, the electromechanical coupling coefficient, the complex reflection coefficient, the transduction coefficient and the inter‐digital capacitance C. This is a dispersive SAW layered filter some parameters of whi...