In this article we discuss how to pole piezoelectric materials in OnScale and walk through an example of how to rotate the material properties of Lithium Tantalate for the Y-cut angle in an LT-SAW.
Piezoelectric Effect
Piezoelectric Effect is the ability of certain materials to generate an electric charge in response to applied mechanical. The inverse is also true, when an electric field is applied to the material, it causes mechanical deformation. Some naturally occurring materials which exhibit this property are quartz, topaz, bone and sugar cane. However, engineers have developed man-made materials such as Lithium Tantalate for use in sensing applications.
Piezoelectric Poling
Piezoelectric materials are made up of a crystalline structure.
Figure 1: Structure of perovskite material
This crystalline structure is made up of multiple unit cells which have a polarization. Naturally, the polarization of each cell is random. To enhance the piezoelectricity, the materials are ferroelectrically polarized so that the electric dipoles become aligned with the same orientation making one side of the material positive and the other side negative.
Figure 2: Dipole orientation throughout the poling process for piezoelectric materials
How to Pole Piezoelectric Materials in OnScale
Axis Poling
It is very simple to set the orientation of piezoelectric materials in OnScale. For poling along an axis you would simply set the ‘Poling’ option in the material database to the positive or negative XYZ axis. For example, if we wanted to simulate a PZT plate vibrating in thickness mode (up and down) we would set the poling in the Y axis.
Figure 3: Y + poling of piezoelectric plate
Figure 4: OnScale Material Database poling option
The positive and negative sign determines which way the wave will propagate. For the wave to propagate upwards in Figure 2 the poling would be set to Y+.
This poling is then coded automatically using the following code:
Figure 5: Axis command for axis poling, matr command for Y+ poling
The axis command in general defines a local Cartesian system (x’, y’, z’) which orients the desired coordinate system relative to the global Cartesian space. For plane poling the local system axes is defined by one spatial location and two vectors.
Figure 6: axis defn syntax for axis poling
- x0, y0, z0 – The global co-ordinates of the origin
- vx1, vy1, vz1 – The X,Y,Z components of Vector 1 (vector for new z-axis z’)
- vx2, vy2, vz2 – The X,Y,Z components of Vector 2 (vector for new x-z plane)
Figure 7: How local system axes relates to global system
Axis poling uses the cartesian system definition as shown above.
Cylindrical Poling
For cylindrical poling, the material must be broken up into smaller elements to be individually poled. There is no way to define cylindrical poling automatically, this must be done in code, for example:
For cylindrical poling, the local system axes is defined by one spatial location and three rotation angles.
Figure 8: Axis defn syntax for cylindrical poling
- x0, y0, z0 – The global co-ordinates of this co-ordinate axis
- rotatex – Rotation about the global X axis to align with the local system (degrees)
- rotatey – Rotation about the global Y axis to align with the local system (degrees)
- rotatez – Rotation about the global Z axis to align with the local system (degrees)
Figure 9: Piezoelectric disc with cylindrical poling
This example is an aluminium nitride disc, radially poled, split up into 120 different orientations from 0° to 360°. To check if you have poled a material correctly you can use the following code to display poling arrows:
Figure 10: Code to display poling arrows
Spherical Poling
Similar to cylindrical poling, for spherical poling the material must broken up into smaller elements to be individually poled. This is done in code, for example:
For spherical poling, the local system axes is defined by one spatial location and three rotation angles.
Figure 11:Axis defn syntax for spherical poling
- x0, y0, z0 – The global co-ordinates of this co-ordinate axis
- rotatex – Rotation about the global X axis to align with the local system (degrees)
- rotatey – Rotation about the global Y axis to align with the local system (degrees)
- rotatez – Rotation about the global Z axis to align with the local system (degrees)
Figure 12: Piezoelectric sphere with spherical poling
This example is a piezoelectric sphere, spherically poled, split up into 10 different orientations from 0° to 360° and 10 orientations from -45° to 45°.
How to Rotate Lithium Tantalate to Represent Y-cut Angle in LT-SAW
Lithium Tantalate (LiTaO3) is a piezoelectric material commonly used in Surface Acoustic Wave (SAW) filters. SAW filters use thin layers of this material as a substrate. The cut angle of the material influences the surface velocity and propagation direction and therefore filter performance. OnScale enables designers to explore many non-standard cut angles, offering better control over RF performance and thermal stability.
This example simulates the Y-cut of Lithium Tantalate . The direction of the SAW propagation is in the X direction, so the cut is rotated to modify the device behaviour (beta rotation in Euler angles).
Figure 13- LT-SAW Model in OnScale
The Y-cut rotation is done using the axis command in OnScale. The initial cut angle is -90 degrees (in X direction) and is rotated by the Y-cut angle which is a variable.
Figure 14: axis command syntax for y-cut rotation
Then in the LiTaO3 material definition the rotation is applied using the code:
Figure 15: Matr command for lithium tantalate with Y-cut
As the cut angle is a parametric variable $cut_angl, multiple simulations can run for different Y-cut angles. To sweep a variable on the cloud, the variable must be defined with symbx instead of symb.
OnScale ran a design study to analyse how the cut angle of a Unit Cell LT-SAW affected the electrical performance. The orientation of the Y-cut angle was swept from 0° to 180° in 1° steps and these simulations were run in parallel. The impedance results from the sweep showed a clear picture of the electrical performance of the LT-SAW in terms of Y-cut angle with the non-leaky and leaky SAW modes clearly visible. Leaky SAWs are more common as the piezoelectric layers are significantly stiffer than the soft substrates, resulting in acoustic losses through the substrate. Studies like this allow engineers to identify which cut angle is optimal for a non-leaky SAW and therefore higher performing filter.
Figure 16: LT-SAW Impedance
If you would like more detail on this design study or wish to try this for yourself, click here!
