Comparative Between (LiNbO3) and (LiTaO3) in Detecting Acoustics Microwaves Using Classification
Comparative Between (LiNbO3) and (LiTaO3) in Detecting Acoustics Microwaves Using Classification
Comparative Between (LiNbO3) and (LiTaO3) in Detecting Acoustics Microwaves Using Classification
Corresponding Author:
Hafdaoui Hichem,
Electronics Department, Faculty of Technology,
University of Batna 2 (Mostefa Benboulaid),
Algeria.
Email: hichemhafdaoui@yahoo.fr
1. INTRODUCTION
Multiferroic materials exhibiting ferroelectricity and ferromagnetism in the same phase have attracted
much attention due to their basic physics and potential technological applications in recent years [1, 2].
Lithium tantalate (LiTaO3) and lithium niobate (LiNbO3) are well-known materials for ferroelectric,
piezoelectric, acoustooptical, electro-optical and nonlinear optical applications [3, 4]. The interest in the use of
piezoelectric materials as the wave propagation medium lies in the propagation of appearance. These waves in
this case, spread in a resilient part (or acoustic) and power; hence the name electroelastic or electroacoustic [5].
Various types of transducers such as bulk acoustic wave (BAW) (Bulk acoustic waves) transducers, shear wave
transducers and interdigital transducers IDTs (Inter-Digitized transducers) are reported for generation and
reception of acoustic waves in SAW (Surface acoustic waves) devices. IDTs are widely used transducer in
SAW devices and they are metallic comb shaped electrodes fabricated over a piezoelectric substrate [6]. Theory
on generation and propagation of BAW in a SAW device with IDTs is well explained in [5, 7].
Some materials, when deformed, become electrically polarized.This effect is known as piezoelectricity [8, 9].
In this work, we searched for all Acoustic velocity and Attenuation coefficients on the level of Piezoelectric
substrate (LiNbO3) and then we compared it with the results of Piezoelectric substrate (LiTaO3) ,to conclude
wich of them is better in utilization for generating bulk acoustic waves.
Interdigital transducer
Input of signal Z
Output of signal
Surface
waves X
Piezoelectric substrate
(LiNbO3) or (LiTaO3)
D = ε .E + eT .S (1)
The electric polarization of the medium under the effect of deformation, also involves the creation of stresses
under the effect of an external electric field. This constraint is:
T = C. S.− e. E (2)
In one form the stress tensor and the electric induction are defined as follows: [8-11]
D i = e jkl . S kl + ε ik . E k (4)
! ∂D i
div. D = =0 (5)
∂X i
The movement of the particles under the action of stress is described by Newton's equation:
∂u ²
∇T = ρ. (6)
∂t ²
Substituting (3) and (4) in (5) and (6) we obtain the piezoelectric tensor phenomenological equations:
2 2 2
∂ Uk ∂ U ∂ Uj
C ijkl + e lij 4 =ρ
(7)
∂ .Xi ∂ .X l ∂ .X k ∂ .Xi 2
∂ .t
2 2
∂ Uk ∂ U
e ikl − ε ik 4 =0
(8)
∂ .Xi ∂ .X l ∂ .X k ∂ .Xi
U i = u i exp(jβ. α i X ) (9)
3
where ui(i=1,2,3) are displacement amplitudes, ui(i=4) represents the amplitude of the electric
potential, β is the propagation constant, αi are the attenuation coefficients of the wave within the piezoelectric
crystal (axis Y show in Figure 1) and ω is the angular pulsation.We will be interested in the coefficient αi. With
a chosen LiNbO3 (Lithium Niobate) or LiTaO3 (Lithium Tantalate). Solutions of this type of wave correspond
to waves propagating with or without attenuation along the direction X. The elastic displacements Ui and the
electric potential U4 may vary from the normal direction to the flat surface (Y), but following invariant Z as
show in Figure 1. Substituting (11) into (9) and (10) we obtain the system:
8 i
Det ( A) = ∑ Bi .α = 0 (11)
i=0
This polynomial is called dispersion equation or secular equation.
The solution of (11) gives for each β (β = 2.π.f / Vs: constant propagation) eight roots. These roots are based
on Vs (acoustic velocity). Each root generates three displacement components of the particle and an electric
potential. Thus, the general solution is a combination of eight roots (8 secondary wave) given by the expression:
n =1
{
U i = ∑ C n . D in .exp jβ. α n . X 3 + jβX 1 (1 + j. γ ) − j. β. V. t} (12)
i=1,4
where D in are the components of the eigenvector of the system (10) associated with the eigenvalue α n
Cn: constant to be determined by the boundary conditions.
Comparative between (LiNbO3) and (LiTaO3) in detecting acoustics microwaves… (Hafdaoui Hichem)
36 r ISSN: 2252-8938
6 i
∑ β i .α = 0 (13)
i =0
This polynomial is called dispersion equation or secular equation.
The solution of (13) gives for each β (β = 2.π.f/Vs: constant propagation) six roots. These roots are based on
Vs (acoustic velocity). Each root generates three displacement components of the particle and an electric
potential. Thus, the general solution is a combination of six roots (6 secondary wave) given by the expression:
n =1
{
U i = ∑ C n . D in .exp jβ. α n . X 3 + jβX 1 (1 + j. γ ) − j. β. V. t} (14)
i=1,3
where D in are the components of the eigenvector of the system (10) associated with the eigenvalue α n
, Cn: constant to be determined by the boundary conditions.
[ ]
U (i 1) ≈ exp j. β. α (re1) . X 3 − β. α (im1) . X 3 .exp( jβ. X 1 ) (15)
[ ]
U (i 2 ) ≈ exp j.β. α (re2 ) . X 3 + β. α (im2 ) . X 3 .exp( jβ. X 1 ) (16)
[ ]
U (i 1) ≈ exp −β. α (im1) . X 3 .exp j.β α (re1) . X 3 + X 1 [ ] (17)
[ ]
U (i 2 ) ≈ exp +β. α (im2 ) . X 3 .exp j.β α (re2 ) . X 3 + X 1[ ] (18)
Remarks
if α im(i ) = 0 and α (1)
re < 0, the bulk waves will be obtained [12-14].
zero imaginary
part and the
minimal negative
value of real part
imaginary part
We set the value of the real part for (α4), which we will look for it in the Classification show in Figure 4.
Comparative between (LiNbO3) and (LiTaO3) in detecting acoustics microwaves… (Hafdaoui Hichem)
38 r ISSN: 2252-8938
Real part
imaginary part
zero imaginary
part and the
minimal negative
value of real part
Comparative between (LiNbO3) and (LiTaO3) in detecting acoustics microwaves… (Hafdaoui Hichem)
40 r ISSN: 2252-8938
zero imaginary
part and the
minimal negative
value of real part
Figure 10. Neural Network Bayesian Classifier - Acoustic velocity (Acoustic velocity)
Table 1. Summarizes the full work where we can notice bulk waves detection.
Coefficient Attenuation Imaginary part Real part Acoustic velocity Bulk waves (BAW)
α1 All values All values All values No Detection
α2 All values All values All values No Detection
α3 0 -0,5654 4050 m/s Good Detection
α4 0 -0,57212 4000 m/s Good Detection
α5 All values All values All values No Detection
α6 All values All values All values No Detection
α7 All values All values All values No Detection
α8 All values All values All values No Detection
5,4
3,4
Real part
1,4
-0,6
zero imaginary
part and the
-2,6 minimal negative
value of real part
-4,6
-2 0 2 4 6
Imaginary part
Comparative between (LiNbO3) and (LiTaO3) in detecting acoustics microwaves… (Hafdaoui Hichem)
Real part
-1,6
-4,594
-1,59999
-4,19979
-1,58
-4,18011
-1,56001
-4,14465
-1,49231
-4,12408
Scatterplot -1,48454
42 r -4,08499
ISSN:-1,47654
2252-8938
-4,08339
-1,42987
-4,07547
-1,41232
5,4 Imaginary
Imaginary
-4,00947
part part -1,4
Scatterplot -2 -2 -2,34345
Scatterplot -1,39765
-1,9321
-1,9321 -1,41232
-1,34345
-1,9 -1,4
3,4 -1,9
-1,8 -1,32454
5,4 5,4 -1,8 -1,32454
-1,7 -0,01997
-1,69001
-1,7 -0,4
-0,01996
Real part
-1,68011 -0,39901
-0,01988
1,4 3,4
3,4 -1,69001
-1,66
Real part 0 -0,39878
-1,68011
-1,6
-0,38765
-4,594
-1,59999 1,16874
-1,66
Real part
1,4 -1,58 -4,19979 -0,37878
1,18432
Real part
-0,6 1,4 -1,6
-1,56001
-4,18011 -0,35672
-1,49231
-4,14465
-1,59999 1,19723
-0,6 -1,48454
-4,12408 -0,34769
1,2
zero imaginary -1,58
-1,47654
-4,08499 -0,28999
1,41232
-2,6 -0,6 part and the -1,56001
-1,42987
-4,08339 -0,0399
2,24656
-2,6 -1,41232
-4,07547
minimal negative -1,49231
-1,4 -4,00947
-0,038
2,28876
value of real part -1,48454
-1,39765
-2,34345 -0,035
2,32454
-4,6 -4,6 -2,6 -1,47654
-1,34345
-1,41232 -0,03454
-2 0 2 4 6 -1,32454
-1,4
4,34345
-2 0 2 Imaginary 4
part 6 -1,42987
-0,01997
-0,0328
5,39765
-1,32454
Imaginary part -1,41232
-0,01996
-0,4
-0,02987
5,4
-4,6 -0,01988 -0,02888
0
-1,4
-0,39901
-2 0 2 4 6
-0,39878
-1,39765 -0,0276
Figure 12. Neural Network Bayesian Classifier - Imaginary
Imaginary part part (Acoustic
1,16874 velocity)
-0,38765 -0,02448
Real part -1,34345
1,18432
-0,37878
1,19723
-0,35672 -0,02001
-4,5941,2-1,32454
-0,34769 -0,0128
5,4 -4,19979 -0,01997
1,41232
-0,28999
Real part -0,01001
5,4 2,24656
-4,18011
-4,594 -0,01996
-0,0399
2,28876
-0,038
0
-4,14465
-4,19979 -0,01988
2,32454
-0,035 0,02
5,4 3,4 -4,18011
-4,12408
-4,14465
0Acoustic
4,34345
-0,03454 Velocity(Vs)
0,0343
3,4 -4,08499
5,39765
5,4 -4,12408 5,41,16874
-0,0328
2400 0,0432
Acoustic Velocity(Vs)
3,4 -4,08339
-4,08499
-0,02987
1,18432 2400
0,0723
Real part
1,4 -4,07547
-4,08339
2450
-0,02888 2450
1,19723
Real part
0,0343
-0,01001 2750 4050
1,4 0,0432 2800 3600 4100
0
Real part
1,4 0,02
0,0821
2850 3650 4200
2900
0,090,03432950 3700 4250
-0,6 -0,6 0,04323000 3750
0,09899 4300
-0,6 4350
0,3 0,07233050
0,32454 3100
3800 4400
-2,6 0,0821 3850 4450
-2,6 zero imaginary part and 1,0576 3150 4500
-2,6 0,09 3200
real part= - 4,594 1,42987 3900 4550
0,09899
2,06783 3250 4600
and Vs=3450 m/s-4,6 0,3
2,09321 3300 3950 4650
-4,6 -2 0 2 4 6
-2 0 2 4 Imaginary60,32454
3,08 part 3350 4000 4700
-4,6 Imaginary part 4,0789 3400 4050
1,05763450 4750
5,06987 4800
-2 0 2 4 6 1,42987 3500 4100 4850
Imaginary part 2,06783 3550 4150 4900
2,09321 3600
3650 4200
Figure 14. Neural Network Bayesian Classifier - Acoustic velocity3,08 (Acoustic velocity)
3700 4250
4,07893750
5,06987
4300
3800
IJ-AI Vol. 8, No. 1, March 2019: 33 – 43 3850 4350
3900 4400
3950
4000 4450
4050 4500
4100
4150
4550
4200 4600
IJ-AI ISSN: 2252-8938 r 43
Table 2. Summarizes the full work where we can notice bulk waves detection.
Coefficient Attenuation Imaginary part Real part Acoustic velocity Bulk waves (BAW)
α1 All values All values All values No Detection
α2 0 -4,594 3450 m/s Good Detection
α3 All values All values All values No Detection
α4 All values All values All values No Detection
α5 All values All values All values No Detection
α6 All values All values All values No Detection
10. CONCLUSION
In this article, we explained that the phenomenon of bulk waves are relying on numerical results at
the level of attenuation coefficients. Changes in real and imaginary parts of the coefficients based on the
acoustic velocity to detect these waves. Since the bulk waves were detected in Lithium Tantalate (LiTaO3) in
one coefficient attenuation α2 and in Lithium Niobate (LiNbO3) were detected in two coefficients attenuation
α3 and α4 so we conclude that (LiNbO3) is the better to use in generating bulk acoustic waves. To compare
between many piezoelectric substrates in detecting acoustic micro waves using PNN classification you just
have to change the characteristics of the material parameters, and those results we need them in realization of
acoustic microwaves devices.
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Comparative between (LiNbO3) and (LiTaO3) in detecting acoustics microwaves… (Hafdaoui Hichem)