CALCULATION OF THE SAW VELOCITY CHANGE OF
PROTON- EXCHANGED LiNbO3 CRYSTAL
B. Lin, G. Chen, X. R. Zhang, D. Zhang and J. C. Chen
State Key Lab. of Modern Acoustics and Institute of Acoustics,
Nanjing University, Nanjing 210093, China
ABSTRACT. We calculate the velocity of SAW propagating in the yz-, xy- and zx- planes of
proton-exchanged LiNbO3 as the function of propagation direction (angle), based on the theory of
SAW propagating in thin film and considering the anisotropy and piezoelectricity of the film and
substrate. The calculation results can be compared with the measured results. The velocity change of
SAW propagating along x-axis is larger than that along z- axis for y-cut substrate. The detail results,
the comparison between theoretical and experimental results and discussions will present in this
paper.
INTRODUCTION
It is well know that LiNbO3 undergoes ion exchange in acid media, replacing some
or all of the lithium ions with protons are called proton exchange (PE) [1]. When this
reaction is carried out in strong acid (for example, aqueous nitric acid), complete exchange
results, accompanied by a structural transformation from the rhombohedral LiNbO3
structure to the cubic perovskite structure [2]. With weaker acids, partially exchanged
materials can be prepared with retain the LiNbO3 structure. These materials are of
particular interest because they can be prepared as thin layers at the surface of LiNbO3
crystal without affecting their optical quality, and cause large optical and acoustic
refraction index increases which have been used in a number of optical devices and
surface acoustic waveguides. A great deal of study has taken place concerning the
fabrication and behavior of PE LiNbO3 waveguides and devices [3,4]. Rice studied the
properties of Li: xkxNbO3 as a function of x, temperature, and stoiciometry of the LiNbO3
used for its preparation [5].
The acoustic property of PE LiNbO3 used in surface acoustic waveguides has been
studied by using the Brillouin Scattering method [6], acoustic microscopy method [7] and
the interdigital transducers (here after IDT) method [8-13]. Hinkov fabricated the first time
SAW waveguides on y-cut LiNbO3 substrates by PE and studied the influence of the
source dilution, the annealing, or the Ti prediffusion on the SAW velocity, by using IDT as
SAW excitation source and optic probe as detector [4]. They reported that: The exchange
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
1284
in pure acid always leads to a velocity decrease, and the decrease value is larger for y-x
sample and smaller for x-z sample. The absolute value of the velocity change decreases
with the dilution of the proton source. In contrast to the exchange in pure acid, the SAW
velocity increases for y-z samples exchanged in a diluted source. The velocity change in
Ti-prediffused samples is smaller as compared to samples without Ti due to the lower
exchange rate caused by the presence of Ti [[14].
We are interested in Hinkov et al [6] and Burnett et al. [7] works because they
measured the SAW velocity change due to PE by using different wavelength of SAW
propagating in LiNbO3 wafers, which were PE exchanged under different PE conditions.
Hinkov et al. did not make theoretical calculation for comparing with their measured
results. Burnett et al. made approximations and calculation. However, their calculated
results are different with the measured results for yz-, xz- planes, except for xy-plane. We
also interesting in Biebl's work because he first evaluated the elastic constants of PE
LiNbO3 [15].
We respectively calculate the velocity of SAW propagating in the yz-, xy- and zxplanes of proton-exchanged LiNbO3 as the function of propagation direction (angle), based
on the theory of SAW propagating in thin film and considering the anisotropic and of the
film and substrate, and including piezoelectricity of substrate. The calculation results, the
comparison between our calculation and their measured results and discussions are present
in this paper.
CALCULATIONS
Brief Review of the Previous Results
Firstly, we review the results obtained by Brunett et. al., Hinkov et al. and Biebl.
Figure 1 to Figure 3 show the variation of SAW velocity with azimuthal angle
(propagation direction) for all cuts of virgin and proton-exchanged (PE) crystal
respectively measured by Burnett et al., by using acoustic microscopy method, The
frequency of SAW used by them is of 215 MHz (i.e., >-SAW~20 |um) and the depth of the PE
layer is of dpE= 2.03 |um. From Fig. 1 to Fig. 3, we can only see the attend of the velocity
decrease for the sample with PE layer and the relation between the velocity and
propagation direction, but not the absolute change of the SAW velocity due to PE, since
the SAW wavelength is more less than the depth of the PE layer. We regard that the SAW
velocity measured by them are contributed by the PE layer and pure LiNbO3. The
fabrication conditions of proton-exchange for x-cut, y-cut and z-cut LiNbO3 crystal are
listed in Table 1 respectively. They made approximations as: the PE had the same
proportional effect on all elastic constants, and for each propagation direction the system
could be modeled as an isotropic layer on an isotropic half space. They made calculations
by using a computer program implementing Brekhovskikh's method. So, their calculated
results are different with the measured results for yz-, xz- planes, except for xy-plane.
Figure 4 shows the variation of SAW velocity with propagation direction for y-cut
of virgin and PE crystal measured by Hinkov et al., by using the Brillouin Scattering
1285
method. Hinkov et al. reported the reduction of the effective elastic constants amounting to
about 40% for the PE LiNbO3, but did not make theoretical calculation for comparison. In
their experiments, the acoustic wavelengths used are considerably smaller than the
exchange depths of the samples, the wavelength of longitudinal wave (L-wave) >-LA=0.11
|um, the SAW wavelength >-SAW=0.251 |um and 0.276 |um, but the depths are near to 4 |um.
We regard that all of the velocity decrease are contributed by the PE part of the sample
because the >-SAW and >-LA are more less than the dpE. They fabricate PE y-cut LiNbO3 in
benzoic acid at PE temperature is TPE=250 °C and PE times is tpE=several h, and with Ti
film (250 A ) prediffused at 1060 °C.
Biebl fabricated PE Y-cut LiNbO3 crystal plate in benzoic acid diluted by 1 mole%
lithium benzoate, take TPE=240 °C and three exchange times. We summarize his
fabrication conditions in Table 2. Biebl measured the dispersion curves for y-cut
x-propagation (y-x) and y-z LiNbO3 respectively by using IDT method with frequency of
100 MHz for y-z 108 MHz for y-x LiNbO3. The SAW velocities on pure H^Li^NbO, (kh-»
oo) are vYX=3190 m/s (-15.4%), and vYZ=3490 m/s (almost unchanged) in X-direction and in
z-direction, respectively. Then they did theoretical calculation to fitting that curves based
on the theory given by Solie to obtained the elastic constants (109N m"2) listed in Table 3.
4000 -,
3800 -,
3900-
*
for pure X-cut LiNbO3, f=215 MHz
o
for PE: X-cutLiNbO3, f=21 5 MHz MHz
A
for pure Y-cut LiNbO3, f=2 1 5 MHz
•
for PE: Y-cutLiNbO3, f=2 15 MHz MHz
A
A
3700-
3800-
'
3700A
36003500-
1
*
<;
o
oo
A
0 ° 2 °
A
A
360
C
/
°-
3
AA
o
.
*
«
^
•
°
*
/y>*
A
g 3500-
•
A
A°
A
3400Y
0
Q
A
0
A
.
>
^ A4 o o °
z
340
Y
°-
20 40 60 80 100 120 140 160 180
x
z
0
Angle (deg.)
20
40
60
80
100
Angle (deg.)
FIGURE 1 The variation of SAW velocity with
FIGURE 2 The variation of SAW velocity with
azimuthal angle (propagation direction) for x-cut of
azimuthal angle (propagation direction) for y-cut of
virgin and proton-exchanged (PE) crystal, measured
virgin and PE crystal, by using acoustic microscopy
by Burnett et al., by using acoustic microscopy
method, A,SAW~20 |um, dPE= 1.36 |um.
method, ^SAW~20 |um and dPE= 1.46 |um.
1286
4000-,
3700-
for pure Y-cut LiNbO3, f=215 MHz
—
iui puie i^\.i_«ii>u\_;3, A_AW^L;.^,JI(J,
o
for YX H+LiNbO3, ^SAW=0.251|om
3600-
for PE: Y-cutLiNbO,, ^215 MHz MHz
3900-
3500-
A
A
^
A
A
A
3400-
A
* A *
A
*
0
0
A
3300-
3800-
32000
3700-
3100-
3600-
2900-
0
3000=
20
40
0
60
z
, , , , , , , J ,,
?7m0
0
00°
28003500
° »
x
20
40
60
80
100
Angle a (deg.)
Angle (deg.)
FIGURE 3 The variation of SAW velocity with
FIGURE 4 The variation of SAW velocity with
azimuthal angle (propagation direction) for z-cut of
azimuthal angle (propagation direction) for y-cut
virgin and proton-exchanged (PE) crystal measured
of virgin and proton-exchanged (PE) crystal
by Burnett et al., by using acoustic microscopy
measured by Hinkov et al., by using the Brillouin
method, ^SAW~20 urn, dPE= 2.03 urn.
Scattering method, ^SAW=0.251, dPE= 4 urn.
TABLE 1.
The fabrication conditions of proton-exchange for LiNbO3 crystal [7].
Crystal cut direction
TPE °r-
tp E h
dPE (um)
X
200
16
2.03
Y
220
5
1.36
Z
200
16
1.46
TABLE 2.
1
V
The PE exchange time [15].
tp E h
22.25
43
90
dPE (um)
2.6
3.5
4.7
TABLE 3. The elastic constants Ca (109N m2) for LiNbO3 and HxLi1.xNbO3[15 ]. ©1992 IEEE.
Material
Cu
C12
C13
LiNb03
203
53
HxLi1.xNbO3
150
39
C*
C66
245
60
75
210
72
55
C14
C33
75
9
75
0
We regard that the elastic constants obtained by Biebl can be used to calculate the SAW
velocity surface and bulk wave surface in xy-, xz- and yz-planes because the elastic constants are
evaluated under the condition (kh^ oo), when the frequency is fixed, the thickness of the PE layer is
infinite.
1287
Calculations Results
We calculate the variation of SAW velocity with azimuthal angle (propagation
direction) for x-cut of virgin and proton-exchanged (PE) crystal in yz-, y-cut in xz- plane
and for z-cut in xy- planes of LiNbO3 substrate with or without a PE layer where both the
PE layer and substrate may be arbitrarily anisotropic and including piezoelectricity of
substrate based on the theory of SAW propagating in the anisotropic thin film deduced by
Farnell and Adler [16]. In calculation we use the elastic constants evaluated by Biebl et al..
The calculated results are shown in Figure 5 to Figure 8. The comparison of the variation
of SAW velocity with azimuthal angle between the results calculated by us and that
measured by Burnett et al. are shown in Figure 5 for x-cut of virgin and PE crystal, Figure
6 for y-cut of virgin and PE crystal, and Figure 7 for z-cut virgin and PE crystal,
respectively. Figure 8 illustrates the comparison of the variation of SAW velocity with
azimuthal angle for y-cut of virgin and PE crystal between the results calculated by us and
the results measured by Hinkov et al.
3800-,
^ Calculated for y-cut Pure LiNbO3
3700-
„ Measured for Pure
X-cutPureLiNbO,
3800-
Measured for pure sample
Calculated for PEUNbO3 //
3600-
Sa 3600-
Calculated for PELiNbCX
/
.IT 3500,8
> 3400-
> 3400-
0
Y
50
100
150
Measured by
Burnett PE
20
40
60
Angle (degree)
XI
Angle (degree)
V\
80 ^100
FIGURE 5 The comparison of the variation of SAW FIGURE 6 The comparison of the variation
velocity with azimuthal angle for x-cut virgin and PE
of SAW velocity with azimuthal angle for
crystal between the results calculated by us and that
y-cut virgin and PE crystal between the results
measured by Burnett et al.
calculated by us and measured by Burnett et
al.).
z-cut Pure LiNbO,
^
3200-
%' 3700 - • - -.1:^,Calculated for PE LiNbO,.» ' _ _ -
Y
20 30 40
Angle (degree)
50
CalculatedforPE
^
fsooo
Measured by Burnett
10
J -7--.
3400 - measured by Hinkov
for pure
Calculated for PELiNba
3oOO
XCalculated for pure
^3600
1
< 3800-
9
For Y-cut pure and PELiNbO3
3800-,
^3900-
measured byy Hinkov
measure
nov for
or PE____
> 2800
60
0
20
40
60
80
100
Angle (degree)
FIGURE 7 The comparison of the variation of
SAW velocity with azimuthal angle for z-cut of
virgin and PE crystal between the results calculated
by us and measured by Burnett et al.
FIGURE 8 The comparison of the variation of
SAW velocity with azimuthal angle for y-cut of
virgin and PE crystal between the results calculated
by us and measured by Hinkov et al.
1288
DISCUSSION
The comparison of the variation of SAW velocity with propagation direction for
y-cut PE LiNbO3 measured by Burnett et al with that measured by Hinkov et. al., is shown
in Figure 9. From Figure 9, it is clearly seen that the values of the velocity measured by
Hinkov et al., are much lower than that measured by Burnett et al., that is due to the
difference of the PE conditions (PE time tpE and PE temperature TPE), the surface cases
(with or without prediffused thin Ti film and post coating thin metal film), the thickness of
films are described by dTi for Ti-prediffusived film and by dmat for metal film are listed in
Table 4 respectively.
We can seen from the Table 4, it is reasonable that the velocities measured by
Hinkov et. al are lower than that measured by Burnett et al, since the values of velocity
measured in the sample PE exchanged in pure benzoic acid is lower than that in dilute
melts, in the sample with thickness PE depth is lower than that with thin depth, in the
sample with Ti and metal films is lower than that without films. In addition, Hinkov et. al
measured the velocity by using the SAW with wavelength ^SAW=0.251 \\m which much less
than the PE depth, thus all contribution of the PE depth are including in the results
measured and no influence from the substrate. In contrast, the wavelength of SAW >-SAW=20
|um used by Burnett et al. is more larger than the PE depth; the measured velocity
3800-
For Y-cut pure and PE LiNb)3crystals
A
I
3600-
<
V)
3400-
b
A
\
A
.;
:«*•'.
V
v
V
^
A
v
ft
v
v
& 3200-
1
> 30009»nn-
V
v
V
D
D
d
"
1
D
oX
n
x
0
DDD
,z
1
20
40
60
80
100
Angle a (deg.)
FIGURE 9 The comparison of the variation of SAW velocity with azimuth propagation direction for y-cut
PE LiNbO3 measured by Burnett et al with that measured by Hinkov et. al., where a: for pure crystal,
measured by Burnett et al., ^SAW=20 |um, b: for PE crystal, measured by Burnett et al., ^SAW =20 |um, d PE =
1.36 |um, c: for pure crystal, measured by Hinkov et al., A,SAW =0.25 l|um, d: for PE crystal, measured by
Hinkov et al., ^SAW =0.251 |um, d PE=4|um.
1289
TABLE 4.
The difference of the sample fabricated by Burnett et al. and Hinkov et al.
Authors
Burnett et al
PE solutions
tpE
Dilute melts
(h)
5
7.5
TPE
PE
^SAW
d,
•
dmet.
•
(Mm)
(Mm)
r .A ^
r .A ^
220
1.36
20
No
No
250
4.0
0.251
250
250
1
d
1% molar
Hinkov et. Al
Benzoic acid
value including the influence of the substrate except the contribution of the PE depth.
From Fig. 4 to Fig. 6, we can see that: the values of velocity calculated by us are
higher than that measured by Hinkov et al., but the attend of the curve of velocity as a
function of propagation direction calculated is near to the measured. It may cause by that
the elastic obtained from the sample photon exchanged in dilute melts 0.25%-2% and no
surface thin overlayer.
The curves of SAW velocity versus angle calculated is near to that measured by
Burnett et al., from the angle of 50° to 120° for x-cut PE LiNbO3, and from 45° to 90° for
y-cut PE sample. However, the reason of the difference appearing between the calculated
measured is not know now. But we also see that the calculated value is higher than that of
measured for the pure LiNbO3.
The tendency of the curve of SAW velocity versus angle for z-cut sample
calculated is near to that measured, but the value of the SAW velocity measured is more
less that calculated. We try to calculate the velocity surface of z-cut sample by using the
elastic constants (obtained by Biebl) multiplied 0.8. We see the calculated curve is the
same as the measured (c.f. Fig. 6), while the calculated curves for x-cut and y-cut PE
samples. Thus, we regard that we can not only consider the values of the elastic constants
change of the crystal, but also need to consider the change of the structure of them (from
trigonal to cubic structure and the fraction of the change.
CONCLUSIONS
As mentioned above some conclusions can be drawn:
The velocity of SAW propagating in the yz-, xy- and zx- planes of
proton-exchanged LiNbO3 as the function of propagation direction (angle) are calculated
based on the theory of SAW propagating in thin film and considering the anisotropic and
piezoelectricity of the film and substrate. Here, the film is PE layer. The calculation results
can be compared with the measured results of Hinkov et al., and Burnett et al.. The value
of SAW velocity change when the wave propagating along x-axis is larger than that along
z- axis for y-cut substrate. The values of velocity calculated higher than that measured by
Hinkov et al., but the tendency of the curve of velocity as a function of propagation
direction calculated is near to that measured. It may cause by that the elastic obtained from
the sample photon exchanged in dilute melts 0.25%-2% and no surface thin overlayer.
The curves of SAW velocity versus angle calculated is near to that measured by
Burnett et al., from the angle of 50° to 120° for x-cut PE LiNbO3, and from 45° to 90° for
y-cut PE sample. However, the reason of the difference appearing between the calculated
1290
measured is not know now.
The tendency of the curve of SAW velocity versus angle for z-cut sample
calculated is near to that measured, but the value of the SAW velocity measured is more
less that calculated. When we let the elastic constants decrease 20% from the values
obtained by Biebl, the curves calculated and measured is the same. We regard that we can
not only consider the values of he constants change of the crystal, but also need to consider
the change of the structure of the crystal (from trigonal to cubic structure and the fraction
of the change. It needs to investigate that the relation between the elastic constants and the
PE source, in the further.
ACKNOWLEDGMENTS
The State Key Lab. of Modern Acoustics, Nanjing University, Nanjing, China
support this work
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