are obtained at 413.71 MHz and 414.41 MHz. The total displacement profile of the SH wave for different piezoelectric substrates at the resonance frequency is shown in Fig. 2.19. For 36◦-YX LiTaO3 and 41◦-YX LiNbO3 substrates, the y axis is normal to the substrate surface (Y-cut), with wave polarized in thezaxis and propagating along thexdirection. On the other hand, the 90◦-AT/ST quartz substrates are also Y-cut with wave polarized in thex axis and propagating along the z direction
2.6. FE simulation of SH-SAW delay line
(a)
0.0
4.0x10 4
8.0x10 4
1.2x10 5
1.6x10 5 1.35
1.40 1.45 1.50 1.55
extremely
fine
extra-course
extra fine
finer
fine
normal
coarse
coarser
|Vout
|(V)
Number of DOF
(b)
(c)
Figure 2.20: (a) 3D simulation geometry of a SH-SAW delay line device. (b) Mesh refinement study showing the plot of magnitude of the maximum stable output voltageVout (at t>40 ns) versus number of degrees of freedom (DOF) for the device obtained by progressively increasing the physics-controlled mesh fromextra-coarsetoextremely-fine. (c) Geometry meshed using the extra-fine option.
versus number of degrees of freedom (DOF) of the device obtained by progressively increasing the physics-controlled mesh fromextra-coarse toextremely-fine. The output voltage value tends to stabilize as DOF increases and the convergence of the solution was observed with respect to the mesh refinement. Considering time, memory usage and sufficient accuracy of the simulation, an extra-fine mesh of tetrahedral elements is kept resulting in about 11000 elements and more than 80000 solvable degrees of freedom during simulation. The minimum element quality of the 3D mesh was above 0.1. Fig. 2.20b and 2.20c show the mesh-refinement plot and the meshed geometry, respectively.
(a) (b)
(c) (d)
Figure 2.21: Time response simulation showing displacement profile and propagation of SH-SAW at (a) 4 ns (b) 8 ns (c) 12 ns, and (d) 16 ns for 36◦-YX LiTaO3 substrate.
2.6.2 Time response
Time response simulation showing the 3D displacement profile and propagation of SH-SAW at different times for 36◦-YX LiTaO3 is shown in Fig. 2.21. The wave is generated at the input IDT, travels through the delay line path in shear horizontal manner and reaches the output IDT.
The damping conditions at the boundaries of the device ensure that the reflection from edges is minimized and does not affect the propagation of the wave. The variation of shear displacement component, vertical displacement component and voltage with time for a SH-SAW delay line device considering different substrates is shown in Fig. 2.22a,2.22b, and2.22crespectively. The SH nature of the wave is confirmed from the observation that the shear displacement components are larger than the vertical displacement components as shown in Fig. 2.22aand2.22b. Different input frequency is applied to each of the substrate, depending on the shear velocity supported by the crystal (Table2.2) to achieve SH-SAW of wavelength of 12µm. Application of sinusoidal input of 5 V at the input IDT results in the generation of a stable sinusoidal voltage at the output IDT. The 41◦-YX LiNbO3 substrate generates a maximum sinusoidal output voltage of 4.8 V while 36◦-YX LiTaO3 produces an output voltage of 1.5 V. Quartz crystals generate very less output voltage of 0.03 V because of large insertion losses. Table2.3lists the values of maximum output voltage, shear and vertical displacement, charge density and minimum insertion loss of each of the substrates. Although all these crystals generate wave with particle displacements
2.6. FE simulation of SH-SAW delay line
0 5 10 15 20 25 30 35 40 45 50
-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Sheardisplacement(nm)
t (ns) 41-YX LiNbO
3
36-YX LiNbO 3
90-AT quartz
90-ST quartz
(a)
0 5 10 15 20 25 30 35 40 45 50
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Verticaldisplacement(nm)
t (ns) 41-YX LiNbO
3
36-YX LiNbO 3
90-AT quartz
90-ST quartz
(b)
0 5 10 15 20 25 30 35 40 45 50
-5 -4 -3 -2 -1 0 1 2 3 4 5
Voltage(V)
t (ns) 41-YX LiNbO
3
36-YX LiNbO 3
90-AT quartz
90-ST quartz
(c)
Figure 2.22: Time response of SH-SAW delay line device showing variation in (a) shear dis- placement component, (b) vertical displacement component, and (c) output voltage with time for different substrates.
mainly of SH nature, it can be noted that the difference between SH and vertical displacements is much greater for ST and AT substrates. Thus, ST and AT substrates generate a much purer SH wave than LiTaO3 and LiTaO3 substrates.
2.6.3 Charge density
For calculation of charge density, a simulation geometry similar to Fig. 2.20awas considered with IDT fingers designed on the entire delay line path. Electrostatic stationary solver was used to calculate the charge density by applying alternating voltages of 1 V and 0 V on the fingers of IDT. Fig. 2.23shows the spread of static charge density across the length of the device. The charge density on the IDT finger is either positive or negative, depending on the polarity of the applied voltage on each finger. It is noted that the charge density is maximum near the electrode edges and diverges as 1/p
(x) [123]. Since coupling coefficient of LiNbO3 is largest, it provides the highest charge density, followed by LiTaO3. ST/AT quartz generates a low value of charge density because of their low K2 values [11].
Substrate Vout Shear displacement Vertical displacement ILmin Charge density
(V) (nm) (nm) (dB) (µC cm−2)
36◦-YX LiTaO3 1.5 0.12 0.01 -27.1 200
41◦-YX LiNbO3 4.8 0.29 0.07 -15.6 250
90◦-AT quartz 0.031 0.010 5.8×10−5 -37.8 20
90◦-ST quartz 0.030 0.012 4.3×10−5 -38.4 19.5
Table 2.3: Maximum values of output voltage, shear displacement, vertical displacement, charge density, and minimum insertion loss obtained for SH-SAW delay line device considering different substrates.
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 -300
-250 -200 -150 -100 -50 0 50 100 150 200 250 300
Electrostaticchargedensity(C/m
2 )
x ( m) 36-YX LiTaO
3
41-YX LiNbO 3
(a)
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 -25
-20 -15 -10 -5 0 5 10 15 20 25
0 0
0 0
+1 +1 +1
+1
0
Electrostaticchargedensity(C/m
2 )
x ( m)
35.25-AT Quartz 42.75-ST Quartz
+1
(b)
Figure 2.23: Variation in electrostatic charge density with device length for (a) 36◦-YX LiTaO3 and 41◦-YX LiNbO3 and, (b) 90◦-AT quartz and 90◦-ST quartz.
2.6.4 Insertion loss
The input IDT is excited with a unit impulse input of 1.5 ns duration. Fig. 2.24ashows the impulse response of the device. The electromagnetic feed-through effect seen at the beginning of the impulse response is about 100 times less than the applied unit impulse signal. The feed- through can be further reduced if device length is increased, but it would enhance the number of elements required for meshing, thus increasing the time and memory usage. The frequency response of the delay line was obtained by taking the Fourier transform of the impulse response voltage at the output IDT and is shown in Fig. 2.24b. Since the time response simulation contained a limited number of data points, the frequency response signal was improved by zero padding the output voltage signal [127]. The 41◦-YX LiNbO3 substrate gives a minimumILof -15.6 dB while 36◦-YX LiTaO3 provides a minimumILof -27.1 dB. In comparison, the ST/AT quartz because of their poor K2, gives largeILof about -38 dB. The obtained results of ILof SH-SAW device is consistent with results reported in [147], [148]