2.12 Secondary effects of IDT fabricated on piezo-substrate
2.12.1 Simulation to study the mass loading effects of IDT
The mechanical properties of IDT electrodes which are fabricated on the device substrate strongly affect the physical and electrical properties of the propagation of SAW in SAW
devices [7], [17]. Acoustic wave perturbs as it propagates under the IDT electrodes [17]. The presence of metallic IDT over the piezo-substrate gives mechanical loading or mass loading effects. The mass loading effects due to the presence IDT electrodes can be separated into three primary categories: inertial effects, energy trapping, and intrinsic stress [41], [23].
(a) (b)
(c) (d)
Figure 2.20 Results of simulation of a conventional SAW delay line device, (a) Total displacement profile at time 10 ns, and (b) Output electric potential, (c) x displacement, (d) y displacement at the receiver IDT.
Inertial effects caused by addition of mass to the surface of piezo-substrate provide a convenient means of frequency adjustment and are significant source of frequency aging due to contamination. In energy trapping, the mass loading combined with the size of the electrodes plays an important role in energy trapping under the electrodes [41], [51].
It creates the regions with different cut-off frequencies and it allows the confinement of acoustic energy. The number of trapped modes to only one can be controlled by controlling mass loading and electrodes dimensions. The final effect is due to intrinsic stresses in the electrodes layers and mechanical strains due to mismatch in thermal expansion of the electrodes and substrate interface [41]. At low temperature this effect is less than the other two effects. Accurate prediction of mass load due to IDT electrode is crucial for the development of high frequency devices. At high frequency the IDT electrode thickness is no longer negligible compared to the SAW wavelength. Consequently, the mass loading effects are significant and result in slowing of SAW and strong reflections [23]. The mass loading effect on SAW device response due to IDT electrodes is well-known and reported by many researchers [7], [41], [22], [23]. The velocity change due to loading effects of IDT can be expressed as a power series expansion on the relative electrode thickness he as [23]
...
e e
e m m
v v v v h v h
v v v v
2 0
1 1
0
(36)
where, v0 denotes the free surface SAW phase velocity. The expansion coefficients depend on the electrode geometry. The first term on the right side in equation (36) shows the electrical loading which is explained in subsection 2.12.2. The second and third terms show the linear shift in velocity due to mechanical loading. In practical case mass loading must be controlled to avoid undue dispersion [3]. The mass loading effect is well explained through Auld’s perturbation theory [3]. In this section, a series of simulations of a one port SAW resonator with infinitely long IDT are performed to study the electrode mass loading effects. The SAW phase velocity is calculated for different metallization ratios and electrode thicknesses of IDT and change in SAW phase velocity is observed. The reduction in metallization ratio and thickness of electrodes are considered as reduction of mass loading on SAW device. The metallization ratio (MR) is defined as the ratio of width of the IDT finger d and pitch of the
IDT finger p, [11] as shown in Figure 2.21. The electrode thickness he is normalized with the SAW wavelength λ. The expression for MR is given below.
MR d
p (37)
A one port SAW resonator of wavelength of 16 μm is simulated to study the effects of MR and electrode thickness on SAW phase velocity. The dimensions and boundary conditions used for simulation are as given in section 2.9. The eigenmode analysis is performed to find the SAW phase velocity for various MRs and electrode thicknesses. The SAW phase velocities for various MRs and electrode thicknesses are calculated using equation (33). The MR is varied from 0.0125 to 0.9 and thickness is varied from 0 to 0.6 μm. The normalized SAW phase velocity as a function of MR for various values of electrode thickness is shown in Figure 2.22 (b). The normalized SAW phase velocity is given as v/v0 where, v is the velocity of SAW resonator for various values of MR and electrode thickness, and v0 = 3477.914 m/s is the free surface SAW phase velocity as calculated in section 2.8. From Figure 2.22 (b) it is observed that the SAW phase velocity of the resonator decreases as the MR and electrode thickness increase.
A one port SAW resonator with massless IDT electrodes with different MR is simulated. The normalized SAW phase velocity as function of MR for massless IDT SAW resonator is given in Figure 2.22 (b). From Figure 2.22 (b), it is observed that the SAW phase velocity of SAW resonator with massless IDT electrodes is more than SAW resonator with metallic IDT electrodes. However the velocity is less than the free surface SAW phase velocity due to electrical loading effects.
The absolute value of the reflection coefficient per period p of SAW resonator is expressed as [23]
p
Piezo-substrate
d he
Figure 2.21 IDT metallization ratio and finger thickness.
sc sc p
f f
f
0
(38)
where, f0 is the center frequency of stopband of resonator. The absolute value of the reflection coefficient per period of one port SAW resonator for various values of MR and electrode thickness he is calculated. The reflection coefficient per period p as a function of MR for various values of electrode thicknesses is shown in Figure 2.22 (b). In order to get minimum reflection coefficient for a given MR a suitable electrode thickness can be chosen.
This allows the design of IDT without internal reflections [52].
The effective electromechanical coupling coefficient Keff2 of SAW resonator is expressed as [53]
%
a r
eff
r
f f
K f
2 2 100 (39)
where, fa and fr are the antiresonance and resonance frequency of the resonator [53].
The effective electromechanical coupling coefficient Keff2 as a function of MR for various values of electrode thickness is shown in Figure 2.22 (c).
The change in electrode width or MR influences the SAW phase velocity and reflection coefficient of the device. The increase in the MR reduces the phase velocity and increases the electromechanical coupling coefficient. By this way the antiresonance frequency fa is also shifted. The change in electrode thickness causes the shift in resonance frequency fr and change in electrode width results shift in both resonance frequency fr and antiresonance frequency fa [23].
(a) (b)
(c)
Figure 2.22 (a) Normalized SAW phase velocity as a function of MR at various electrode thicknesses he. (b) Absolute value of the reflection coefficient per period p as a function of MR at various electrode thicknesses. (c) Effective electromechanical coupling coefficient Keff2 as a function of MR at various electrode thicknesses.
0.965 0.970 0.975 0.980 0.985 0.990 0.995 1.000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized SAW phase velocity
MR
ha/λ = 0% ha/λ = 0.625%
ha/λ = 1.25% ha/λ = 1.875%
ha/λ = 2.5% ha/λ = 3.125%
ha/λ = 3.75%
ha/λ= 1.25%
ha/λ= 1.25%
hhae/λ/λ= 1.25%= 0 % he/λ= 1.25 % he/λ= 2.5 % he/λ= 3.75 %
he/λ= 3.125 % he/λ= 1.875 % he/λ= 0.625 %
0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Reflection coefficient |κp|
MR
ha/λ = 0% ha/λ = 0.625%
ha/λ = 1.25% ha/λ = 1.875%
ha/λ = 2.5% ha/λ = 3.125%
ha/λ = 3.75%
ha/λ= 1.25%
ha/λ= 1.25%
hhae/λ/λ= 1.25%= 0 % he/λ= 1.25 % he/λ= 2.5 % he/λ= 3.75 %
he/λ= 3.125 % he/λ= 1.875 % he/λ= 0.625 %
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 EffectiveK2(%)
MR
ha/λ = 0% ha/λ = 0.625%
ha/λ = 1.25% ha/λ = 1.875%
ha/λ = 2.5% ha/λ = 3.125%
ha/λ = 3.75%
ha/λ= 1.25%
ha/λ= 1.25%
hhae/λ/λ= 1.25%= 0 % he/λ= 1.25 % he/λ= 2.5 % he/λ= 3.75 %
he/λ= 3.125 % he/λ= 1.875 % he/λ= 0.625 %