3.5 Different aspects of NCIDT SAW devices
3.5.2 Effect of air gap on SAW phase velocity
the effect of short-circuiting of electric field by NCIDT is more prominent than the effect of permittivity of the holding substrate. The effect of short circuiting of electric field due to metallic IDT is discussed in section 3.6.
coupling between a piezoelectric half-space and a plane at a height. Coupling decreases exponentially with increase in the air gap, thus the gap has to be a small fraction of wavelength for the concept to be practically effective. Lakin [13] reported the perturbation theory for electromagnetic coupling to elastic surface waves on piezoelectric substrate and stated the following results. The normalized relative change in SAW phase velocity (v) is given by
tanh
tanh
a v
a
kh kh 1
1 (46)
where ha is air gap, k is the wave number, and ε is the permittivity of the material. The theoretical results for the decrease in the normalized perturbation coupling due to an increased air gap ha are presented. The relative change in the coupling with air gap spacing is strongly influenced by the effective relative dielectric constants of the piezoelectric material.
Ingebrigtsen [20] reported that a small air gap between piezo-substrate and adjoining medium may drastically reduce the coupling. Kino et al. [66] gave the normal mode theory for the Rayleigh wave amplifier. The relative velocity perturbation for a conducting plane at a distance of ha with that at zero separation is expressed as
tanh
tanh
a ah a a a
p a a
h e
v h
v h
2
0
1
0 1 (47)
where βa is the unperturbed Rayleigh wave propagation constant, εp is the effective permittivity of the piezo-substrate[66]. The result obtained for YZ LiNbO3 from equation (47) is verified with the direct field calculation reported by Campbell and Jones [67].
The results of simulation of a one port SAW resonator with NCIDT having infinite number of IDT fingers patterned on Si substrate are given below. Owing to the periodic nature of IDT structure, one pair of IDT fingers as described in Section 3.1 is used with periodic boundary conditions. The simulation is carried out by FEM using piezo plain strain application mode provided by COMSOL Multiphysics. The 2D geometry of a periodic segment of NCIDT SAW resonator considered for simulation is shown in Figure 3.13. The dimensions used for simulation are as given in Section 3.1. The thickness of holding substrate is 16 μm. The air gap (ha) between NCIDT and piezo-substrate is varied from 0.06 λ to 1.5 λ. The boundary conditions and meshing used for simulation are as given in Section 3.1. The eigenmode analysis is performed to determine the resonance frequency and anti-resonance frequency.
A series of simulations is performed to calculate the resonance frequency and anti-resonance frequency of the resonator for various values of air gap between NCIDT and the piezo- substrate. The SAW phase velocity v is calculated using equation (33). The plot of normalized SAW phase velocity (v/v0) as a function of normalized air gap (ha/2p) is shown in Figure 3.14.
With the increase in the air gap, the effects of the permittivity of the holding substrate and the conductivity of IDT on the SAW velocity reduce, and the SAW phase velocity approaches the free surface velocity v0 of the piezo-substrate.
IDT
Air gap
λ ΓL
≈ ≈
ΓR
p
Piezo-substrate Non-piezoelectric
substrate x3
x1 x2
ha ≈ ≈
Figure 3.13 2D geometry of one port SAW resonator with NCIDT used in the simulation to study the effect of air gap between NCIDT and piezo-substrate.
The electromechanical coupling coefficient K2 of the NCIDT SAW device for various values of air gap between NCIDT and piezo-substrate is calculated. The electromechanical coupling coefficient K2 is calculated from free surface velocity vf for NCIDT configuration and metalized surface velocity vm for NCIDT configuration. The expression for electromechanical coupling coefficient K2 is expressed below [3], [70].
f m
f
v v
K v
2 2 (48)
The plot of electromechanical coupling coefficient K2 as a function of normalized air gap between NCIDT and piezo-substrate is shown in Figure 3.15. The K2decreases sharply as the air gap increases. The K2 of the NCIDT SAW resonator is 0.001 % for air gap of λ/4 (4 μm) and is close to zero for air gaps greater than λ/2. The low coupling of the device can be overcome to a large extent by using the large number of IDT finger pairs [6]. Owing to the reduced coupling, the NCIDT SAW device needs to be operated with adequately high gain amplifier and often high voltage excitation.
Figure 3.14 Normalized SAW phase velocity versus normalized air gap between NCIDT and piezo- substrate.
0.9995 0.9996 0.9997 0.9998 0.9999 1.0000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Normalized SAW phase velocity
ha/2p
The presence of metallic electrodes on the surface causes changes in electrical and mechanical impedances at the surface and results in reflections whenever SAW encounters an IDT [4]. In conventional SAW devices, these reflections are significant as the substrate possesses strong electromechanical coupling and the material used for IDT has mechanical impedance very different from that of substrate material. In NCIDT, the effects related with the mechanical properties of the electrodes are completely eliminated due to separation of IDT from the piezo-substrate, and the effects related with the electrical properties of the electrodes are reduced to great extent due to the air gap between the piezo-substrate and NCIDT. The reflection coefficient p is one of the important parameters in the design of SAW resonators. The reflection coefficient of a transducer should be ideally zero while the reflection coefficient of a reflector should be one [3]. The reflections from electrodes cause considerable distortion, and reduce the frequency at which the conductance is maximum and susceptance is zero as reported by Skeie [71] and Morgan [3]. The reflections from IDT fingers can be reduced by splitting fingers into two [4].
The reflection coefficient per period of the NCIDT SAW resonator is calculated for various values of air gap between NCIDT and piezo-substrate. The reflection coefficient per period of the resonator is calculated from the upper and lower edges fsc+ and fsc- of the stopband. The reflection coefficient per period p can be expressed as
sc sc
p
f f
f
0
(49)
where, f0 is the center frequency of the stopband [23]. The plot of reflection coefficient per periodp as a function of normalized air gap between NCIDT and piezo-substrate is shown in Figure 3.16. The reflection coefficient per period of NCIDT SAW resonator decreases sharply as the air gap increases. The reflection coefficient per period of the NCIDT SAW resonator is 0.014 × 10-3 for air gap of λ/4 (4 μm), and is close to zero for air gaps greater than (λ/2). If the reflectivity is weak, the SAW amplitude will not vary much over a distance of a few electrodes [3].
Figure 3.15 Electromechanical coupling coefficient versus normalized air gap between NCIDT and piezo-substrate.
Figure 3.16 Reflection coefficient per period versus normalized air gap between NCIDT and piezo- substrate.
0.000 0.005 0.010 0.015 0.020 0.025 0.030
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 K2(%)
(ha/2p)
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Reflection coefficient |κp| (10-3)
ha/2p