Stiffness effects in piezoelectric devices

Details Stiffness effects in piezoelectric devices Stiffness effects in piezoelectric devices

1998-12-16

2001-05-08

Hafiz, Tariq R. (Department: 2163)

Data processing: structural design, modeling, simulation, and em

Structural design

C703S002000, C703S013000, C716S030000

Reexamination Certificate

active

06230113

ABSTRACT:

TECHNICAL FIELD
The present invention relates to the field of piezoelectric devices. More particularly, the present invention relates to designing piezoelectric devices to comply with design specifications.
BACKGROUND ART
A wide variety of piezoelectric devices are in common use in various electronics applications. One common type of piezoelectric device is a crystal resonator. A typical crystal resonator includes a layer of crystalline piezoelectric material having opposite faces, with each face having a corresponding electrode bonded thereto, thereby sandwiching the piezoelectric material between the electrodes. The crystal resonator vibrates in response to an electrical stimulus applied to the electrodes. The vibration induces a highly stable electrical oscillation across the electrodes that is useful for timing other devices. Another common type of piezoelectric device is the crystal filter. One variety of crystal filter includes a layer of crystalline piezoelectric material having opposite faces, an electrode affixed to one of the faces, and a pair of electrodes affixed to the other face. The pair of electrodes induces two frequency peaks in electrical conductivity of the crystal filter, with a bandpass filter being formed by suitably adjusting the location of the peaks.
For a piezoelectric device to operate properly, it is important for its elastic properties to fall within design specifications. For example, if the stiffness of a crystal resonator falls outside design specifications, the crystal resonator may not have the desired oscillation frequency. Similarly, if the stiffness in a crystal filter falls outside design specifications, the crystal filter may not have the desired magnitude response. Unfortunately, it has proven very difficult to provide piezoelectric devices with precisely determined elastic properties. One reason for this difficulty is that there is considerable interplay between the various elastic properties of a piezoelectric device. For example, increasing electrode mass to reduce acceleration sensitivity may yield an undesired side effect such as a shift away from desired resonant frequency.
Due to such difficulties, piezoelectric devices generally are formed in a rough state that is not guaranteed to be within final design specifications. The piezoelectric devices may then be brought into final design specifications by adding or removing material from the piezoelectric device. In one conventional approach, material is added or removed from electrodes. In another conventional approach, stiffening electrical fields are applied to a piezoelectric device during operation. In a third conventional approach, a piezoelectric device is stiffened to reduce acceleration sensitivity by adding one or more braces either on the electrodes or on the layer of piezoelectric material.
Such conventional approaches to providing piezoelectric devices with desired elastic properties are undesirable. They are not truly design based, but rather require extra fabrication steps, such as adding or removing material from electrodes, or special operating environments, such as appropriate stiffening electrical fields. Generation of stiffening electrical fields may require additional circuitry. Conventional approaches typically also require the formation of various prototype devices to determine how to fabricate the piezoelectric device with a suitable rough state as described above. Further, conventional approaches are believed to work poorly where electrode thickness exceeds about two percent of total device thickness.
There is accordingly a continuing need in the electronics arts for an improved system and an improved method for providing piezoelectric devices with desired elastic properties. Such system and method preferably should be designed based, so that extra fabrication steps and generation of special operating environments are avoided. Such system and method preferably should be usable with a wide variety of piezoelectric devices, including crystal filters and crystal resonators. Further, there is also a continuing need for improved piezoelectric devices which meet final design specifications without the need for post production processing of the devices.
DISCLOSURE OF INVENTION
It is an object of the present invention to provide a system and a method for verifying design characteristics of piezoelectric devices during a design process which conveniently can be performed before any manufacturing steps. It is another object of the present invention to provide improved piezoelectric devices having stiffness determined during a design stage, thereby reducing requirements for post production processing of the piezoelectric devices.
In accordance with one aspect of the present invention, a method for verifying a design for a piezoelectric device comprises forming a model of the piezoelectric device that expresses a stress component of the piezoelectric device as a weighting of strain components of a first device component of the piezoelectric device. The model is analyzed to verify whether the piezoelectric device, or a second device component thereof, meets a design specification. For example, the model may be analyzed to verify whether the piezoelectric device (or the electrode or electrodes thereof) are suitably stiff, and further to verify the stiffness quality of the piezoelectric device (or the electrode or electrode thereof) on an absolute or other scale. The first and second device components do not need to be the same. For example, an electrode may be verified for suitable stiffness by analyzing a weighting of strain components of the layer of piezoelectric material. This beneficially reduces computational complexity of the model of the piezoelectric device by eliminating expressed dependence therein on strain components of the electrodes while retaining useful information about the electrodes such as their stiffness quality.
In accordance with another aspect of the present invention, a method for verifying a design for a piezoelectric device comprises forming a first model of the piezoelectric device that expresses stress in the device as a function of an elastic property and deformation of the device. Such elastic property may be, for example, the stiffness of the piezoelectric device or the layer of piezoelectric material. Preferably the deformation is represented by the strain of the layer of piezoelectric material, with such strain expressed as a weighting of three or more strain components determined at the faces of the layer of piezoelectric material. The first model is then manipulated to form a second model of the device having a reduced computational complexity relative to the first model. For example, stress in the piezoelectric device as a whole can be expressed as a function of strain of the layer of piezoelectric material. This reduces computational complexity of the second model relative to the first model by eliminating express dependence in the second model on the strain or strain components of the electrodes. The second model is beneficially applied to generate a modeled property of the device, such as device or electrode stiffness quality, and the modeled property is analyzed to verify whether the design for the device meets design specifications.
In a preferred embodiment of the present invention, stress in the piezoelectric device is represented by stress components T
ij
(n)
of the piezoelectric device, where n takes on integer values between zero and three. To reduce computational complexity in this embodiment of the present invention, preferably only the first four stress components T
ij
(0)
, T
ij
(1)
, T
ij
(2)
, T
ij
(3)
are used. Each of the stress components T
ij
(n)
are expressed as a weighted sum of strain components S
kl
(m)
of the piezoelectric device, preferably the first four strain components S
kl
(0)
, S
kl
(1)
, S
kl
(2)
, and S
kl
(3)
. Using only the first four strain components S
kl
(0)
, S
kl
(1)
, S
kl
(2)
, and S
kl
(3)
is believed to yield highly accurate results and to reduce computational complexity by ignoring s

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