Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates
Group and phase velocities of the lowest orders of Lamb waves in <100>, <110> directions for (100) Cd₀.₂Hg₀.₈Te plates are calculated. Frequency dispersion of a₀ and s₀ Lamb modes velocities were measured on (111)-plates in the range of frequencies from 0.2 to 10 MHz. The frequency depen...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2002
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| Цитувати: | Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates / I.O. Lysiuk, V.F. Machulin, Ja.M. Olikh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 31-35. — Бібліогр.: 11 назв. — англ. |
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irk-123456789-1195622017-06-08T03:04:15Z Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates Lysiuk, I.O. Machulin, V.F. Olikh, Ja.M. Group and phase velocities of the lowest orders of Lamb waves in <100>, <110> directions for (100) Cd₀.₂Hg₀.₈Te plates are calculated. Frequency dispersion of a₀ and s₀ Lamb modes velocities were measured on (111)-plates in the range of frequencies from 0.2 to 10 MHz. The frequency dependencies of relative efficiency of the Lamb modes excitation using two geometrical versions: symmetrical - with two piezoelectric transducers, and antisymmetrical - with one piezoelectric transducer, have been studied. Possible applications of studied waves including ultrasonic treatment of semiconductors have been discussed. 2002 Article Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates / I.O. Lysiuk, V.F. Machulin, Ja.M. Olikh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 31-35. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS: 62.30.+d http://dspace.nbuv.gov.ua/handle/123456789/119562 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Group and phase velocities of the lowest orders of Lamb waves in <100>, <110> directions for (100) Cd₀.₂Hg₀.₈Te plates are calculated. Frequency dispersion of a₀ and s₀ Lamb modes velocities were measured on (111)-plates in the range of frequencies from 0.2 to 10 MHz. The frequency dependencies of relative efficiency of the Lamb modes excitation using two geometrical versions: symmetrical - with two piezoelectric transducers, and antisymmetrical - with one piezoelectric transducer, have been studied. Possible applications of studied waves including ultrasonic treatment of semiconductors have been discussed. |
| format |
Article |
| author |
Lysiuk, I.O. Machulin, V.F. Olikh, Ja.M. |
| spellingShingle |
Lysiuk, I.O. Machulin, V.F. Olikh, Ja.M. Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Lysiuk, I.O. Machulin, V.F. Olikh, Ja.M. |
| author_sort |
Lysiuk, I.O. |
| title |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates |
| title_short |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates |
| title_full |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates |
| title_fullStr |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates |
| title_full_unstemmed |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates |
| title_sort |
properties and application of ultrasonic lamb waves in cdxhg₁₋xte plates |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2002 |
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http://dspace.nbuv.gov.ua/handle/123456789/119562 |
| citation_txt |
Properties and application of ultrasonic Lamb waves in CdxHg₁₋xTe plates / I.O. Lysiuk, V.F. Machulin, Ja.M. Olikh // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2002. — Т. 5, № 1. — С. 31-35. — Бібліогр.: 11 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT lysiukio propertiesandapplicationofultrasoniclambwavesincdxhg1xteplates AT machulinvf propertiesandapplicationofultrasoniclambwavesincdxhg1xteplates AT olikhjam propertiesandapplicationofultrasoniclambwavesincdxhg1xteplates |
| first_indexed |
2025-07-08T16:10:43Z |
| last_indexed |
2025-07-08T16:10:43Z |
| _version_ |
1837095762811420672 |
| fulltext |
31© 2002, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2002. V. 5, N 1. P. 31-35.
PACS: 62.30.+d
Properties and application of ultrasonic Lamb waves
in CdxHg1-xTe plates
I.O. Lysiuk, V.F. Machulin, Ja.M. Olikh
Institute of Semiconductor Physics, NAS of Ukraine, 45 prospect Nauky, 03028 Kyiv, Ukraine
Phone: 380 (044) 265 6256; fax: 380 (044) 265 8342; e-mail: olikh@class.semicond.kiev.ua
Abstract. Group and phase velocities of the lowest orders of Lamb waves in <100>, <110>
directions for (100) Cd0.2Hg0.8Te plates are calculated. Frequency dispersion of a0 and s0
Lamb modes velocities were measured on (111)-plates in the range of frequencies from 0.2 to 10
MHz. The frequency dependencies of relative efficiency of the Lamb modes excitation using
two geometrical versions: symmetrical � with two piezoelectric transducers, and antisymmetrical �
with one piezoelectric transducer, have been studied. Possible applications of studied waves including
ultrasonic treatment of semiconductors have been discussed.
Keywords: CdxHg1�xTe solid solutions, ultrasonic treatment, Lamb waves, efficiency of ultrasonic
mode generation.
Paper received 15.01.02; revised manuscript received 25.02.02; accepted for publication 05.03.02.
1. Introduction
Taking into account low structural perfection of
CdXHg1-XTe solid solutions including blocks, high dis-
location density, impurity and clusters, it is useful to ap-
ply intense ultrasonic waves for improving their struc-
ture [1, 2]. Usage of ultrasonic waves during manufac-
turing semiconductor devices allows to create new de-
vices with controlled characteristics [3]. Improvement of
parameters of CdXHg1-XTe chips was reached with treat-
ment by bulk waves [1-3]. But from the other point of
view, allowance for plate geometry of bulk crystals using
plate waves seems more suitable for treatment of such
crystals. The properties of plate waves called normal
waves in plate (NWP) is much more various than bulk
waves, so they can find more wide applications including
design of acousto-electronic sensors [4]. NWP are char-
acterized by a great dispersion of phase and group veloc-
ity of propagation, complicated distribution of elastic
deformation along thickness, frequency intervals where
certain mode exists. Because of simple, method for gen-
eration of such waves in piezoelectric A2B6 compounds
was carefully studied [5]. A number of physical results on
influencing ultrasonic waves on properties of semicon-
ductors are obtained on non-piezoelectrics [5,6].
Let�s pay attention to the fact that the applied dy-
namical ultrasonic treatment of semiconductor devices
in technological processes has some difficulties because
of limited access space, high requirements to uniformity
of deformation fields in the bulk or surface.
In order to show an advantage of used Lamb waves
for ultrasonic treatments of CdXHg1-XTe crystals, let`s
have a brief review of mechanism of ultrasonic interac-
tion with defects. The crystals have a high density of dis-
locations (104�106 cm-2) and point defects (more than
1015 cm-3). When a dislocation is in ultrasonic field stress
with sufficient intensity, it can oscillate with enormous
(macroscopic) ampitude [7]. There are possible processes
of redistribution of nonequilibrium points defects in the
crystal bulk and their recombination during oscillations
of a dislocation, which cause an improvement of
electrophysical parameters of the crystal [1,2]. Maximum
of a dislocation oscillation amplitude is effected in geom-
etry, when vector of deformation is perpendicular to dislo-
cation line. Therefore, ultrasonic treatment of semiconduc-
tor specimen with bulk or SH normal waves, which have
only one direction of deformation, involves only part of
dislocation into oscillatons and take part in redistribution,
recombination process of defects. In the case of ultrasonic
treatment with Lamb waves that have an elliptic
32 SQO, 5(1), 2002
I.O.Lysiuk et al.: Properties and application of ultrasonic Lamb waves...
polarisation, an arbitrary oriented dislocation can
oscillate. Thus, the type of treatment enables to in-
crease the number of dislocations involved into the
process of redistribution and recombination of de-
fects.
The purpose of the work is to analyze elastic
properties for Lamb waves as particular case of
NWP in CdXHg1-XTe plates in general and to study
possible applications of certain modes.
2. Normal waves in Cd0.2Hg0.8Te plates
The ultrasonic waves in a plate crystal with free
boundaries are determined by the following equa-
tion and edge conditions:
(1)
ni
l
ijnli xx
U
CU
∂∂
∂=
2
&&ρ
))((
))((
11111222
22111211
1
2
γββγ
γββγ
β
β
cc
cc
qhtg
qhtg
++
++=
))((
))((
22111211
11111222
1
2
γββγ
γββγ
β
β
cc
cc
qhtg
qhtg
++
++=
0=jij nT
where Ui - deformation along direction xi, Cijnl -
elastic modulus, Tij - stresses, ni - unit vector along
xi direction, r- density. Dispersion curves, which
define the velocity of NWP various modes as a func-
tion of frequency, can be determined by solving the
elastic equations of motion (1) and edge condition
(2), as discussed by Victorov [8] and Tursunov [9].
In case of peculiar planes and directions of propa-
gation, the system of equations (1), (2) can be con-
verted into two independent systems. The first of
these systems describes transversal normal waves
(TNWP); the second does Lamb waves (LW). Each
of these two types of waves consists of two groups:
symmetrical and antisymmetrical. The division con-
nected with symmetry of deformation with respect
to median plate. Equations obtained from the sys-
tem of equations (1) and (2) for the Lamb wave in
(100) cube crystal plate along <100> and <110>
direction of propagation are as follows [9]:
for symmetric waves:
(3)
for antisymmetric waves:
2
2
22
2
2,1 BAA −±=β
( )
++−+++= 441211
11
441212
2
4411
4411
2 2
2
)2()(
2
1
ccc
c
ccccc
cc
A ρυ
+++
++−=
2
)2(
2
41 44121144212441142
4411
2
ñcccccc
cc
B ρυυρ
for <110> direction: ,
where
Group velocity is calculated by the formula
ω
ωυ
ω
∂
∂
=
∂
∂=
- 1
ph
ph
ph
gr V
V
V
V
Equations (3), (4) are transcendental, and their
solution cannot be found as an analytical function
υ from ω. The problem has additional difficulties
for solving in some phase velocity intervals when
the equations transform into the complex ones. In
the work, roots of equations (3), (4) were found by
means of finding minima of functions
))((
))((
)(
11111222
22111211
1
2
1 γββγ
γββγ
β
β
cc
cc
qhtg
qhtg
qf
++
++
−=
))((
))((
)(
11111222
22111211
2
1
2 γββγ
γββγ
β
β
cc
cc
qhtg
qhtg
qf
++
++−=
Then mode discrimination was made from the
found roots and group velocity of the Lamb waves
were calculated.
But such luck solution of the system of equations
(1), (2) occurs as written above in special case. In
an arbitrary crystal direction of wave propagation,
including (111) in whole, the system of equations
(1), (2) isn�t partitioned, and in this case we can not
speak about �pure symmetric waves� and �pure
antisymmetric waves�, we have one intricate sys-
tem of guide waves.
We calculated the frequency dispersion curves
of phase Vph and group Vgr velocities for Lamb mode
propagation along <100> direction in (100)-cut of
Cd0.2Hg0.8Te plate. For the calculations, values of
elastic moduli and density were taken from [10]. The
curves for the lowest Lamb modes (for symmetric -
si and antisymmetric - ai, order i = 0,1,2) are shown
in Fig. 1a, b, accordingly. It can be seen that there
are Lamb modes s1 and a2 characterized by existent
of negative values of the group velocity near fre-
quency of appearance. The negative sign of Vgr says
that phase velocity have opposite direction as com-
pared to the group velocity. Such waves are called
as a reverse waves [5].
Such narrow range of existence of reverse Lamb waves
and their super dispersion determine their
supersensibility to alteration of medium elastic constants
and finds its application in non-destructive testing of
Cd0.2Hg0.8Te plates.
(4)
(5)
where, fq πυ 2= = w, q-wave vector, V- phase velocity of
propagation.
For <100> direction: ,
where
1
2
11
2
2,1 BAA −±=β
4411
2
11441212
2
4411
1 2
)2()(
cc
cccccc
A
−+++
=
ρυ
4411
2
4411
42
1
)(
cc
cc
B
ρυυρ +−
=
(2)
44
2
2,111
2
44122,1
2,1
)(
ccV
cc
−−
+
=
βρ
β
γ
I.O.Lysiuk et al.: Properties and application of ultrasonic Lamb waves...
33SQO, 5(1), 2002
.
0
1
2
3
4
0 1 2
-1
0
1
2
a
s 2
a 2
s 1
a 1
s 0
a 0
V
p
h,
1
0
3
m
/s
b
s 2 a 2
s
1
a 1
s 0
a 0
V
g
r,
1
0
3
m
/s
fh , M H z m m
Fig. 1. Theoretical dispersion dependencies of ultrasonic Lamb
mode velocities for propagation along <100> direction in (100)-
cut of Cd0.2Hg0.8Te - plate: a) phase and b) group. Solid lines for
symmetric (si) and dash - for antisymmetric (ai) modes accord-
ingly. The values of elastic modulus are given from [7].
0 5 10 15
-1
0
1
2
a
b
2
1
2 4
31
a
0
s0
t , µ s
U
, V
Fig. 2. a) The scheme of experiment is shown: piezoelectric
transducers - 1,2,3; semiconductor sample - 4.
b) Measured waveforms of pulse of excitation (on transducer 1, curve
1) and ultrasonic pulse passed across Cd0.2Hg0.8Te-plate (111)-cut
(on receiver transducer 3, curve 2) at frequency of 0.67 MHz.
Curve 1 is shifted by 0.9V and reduced by 10 times. The arrows
correspond to arrival time of a0 and s0 mode s, accordingly.
3. Exciting and measuring techniques
The n- and ð-types of CdXHg1-XTe plates (x≈0.2;
square S ≈ 200-250 mm2; thickness h ≈ 1 mm) were stud-
ied in the work. The previous measurements of velocity
of bulk waves were carried out with ultrasonic interfer-
ometer continuous method in the range of frequencies from
0.5 to 10 MHz with precision 2%. The excitation of Lamb
waves were performed using piezoelectric transducers in
the form of bars made from ceramics PZT-19 polarized
along thickness or width and LiNbO3 (Y+36o)- crystal
cut. To measure group velocity Vgr and study efficiency
of generation of Lamb waves, the pulse method was used.
Modes were identified by comparison of experimentally
measured Vgr with the predicted ones. Experimental Vgr
values were determined by measurements of time delay
of a passed ultrasound pulse across sample. The scheme
of our experiment is shown in Fig. 2à. Two types of ge-
ometry of ultrasonic excitation were used: with one gen-
erating transducer 1 and double generating transducers1
and 2. Transducer 3 served as a receiver.
Oscillograms of ultrasonic pulses were excited in
(111)-cut of CdXHg1-XTe plates with one piezoelectric
transducer and corresponded to vibrations along trans-
ducer width, and direction of Lamb wave propagation is
shown in the Fig. 2b. The presence of two response pulses
shows that two different modes of the Lamb waves were
excited simultaneously and with approximate efficiency
of excitement. In this example, the two modes can be sepa-
rated, as they characterized by different time delays stem-
ming from a difference in velocities of mode propaga-
tion. (Vs0=0.8·103 m/s, Va0≈1.6·103 m/s ).
0 1 2
1
2
1
4
23
a0
s0
V
gr
,
1
03
m
/s
fh , M H z m m
Fig. 3. Computed group velocities of lowest Lamb modes s0 and
a0 propagation in Cd0.2Hg0.8Te-plate (100)-cut along <100> di-
rection (thick curves 1 and 2) and along <110> direction (thin
curves 3 and 4). Experimental sets of points in Cd0.2Hg0.8Te-
plate (111)-cut are shown as square (s0 -mode) and circle (a0 -
mode).
4. Identification of Lamb waves in (111)-
Cd0.2Hg0.8Te plates
The two experimental sets of Vgr for plate waves, which
were measured for a Cd0.2Hg0.8Te plate (111)-cut as fre-
quency dependencies, are shown in Fig. 3 as solid squares
34 SQO, 5(1), 2002
I.O.Lysiuk et al.: Properties and application of ultrasonic Lamb waves...
and open circles, accordingly. It should be noted that
comparison of results of measurements of these Vgr sets in
several different directions of propagation for the speci-
men shows that within the range of experimental error
Vgr are coincided. Therefore, Vgr in the plate studied ex-
hibits isotopic behavior. Surely, this result is caused ex-
istence of sub block structure in studied crystals.
It is known [1-3] that orientation of blocks in CdXHg1-XTe
crystals slightly changes by 1-3° from one to another [1,2].
If density of blocks is in the range from 10 to 60 cm-1
along any direction of crystal length (≈2 cm) orientation
of all subblocks can change by more than 60°, which
corresponds to symmetry period of elastic properties of
(111)-cut for plate of cubic crystals. Taking into account
this aspect and the fact of a non-existent analytical solu-
tion of (1), (2) for (111)-plates, the comparison of the
experimental data was made to identify them with theo-
retical curves of Vgr for s0-and a0- modes propagation
along [100]-direction and [110]-direction in (100)-cut of
Cd0.2Hg0.8Te plate (Fig. 3, thick curves 1, 2 and thin -
3,4, accordingly). Our experimental data find a good
agreement with our assumption, which states that veloc-
ity of the lowest Lamb wave modes in (111) plane in
Cd0.2Hg0.8Te cut are close to a0 and s0 in (100) cut along
<100>, <110> directions (with precision 8%.). As it
could be seen from Fig. 3, the dispersion curve of veloc-
ity marked by squares are in the range between curves 1
and 2, which enables us to identify it as the velocity of s0-
mode. The fact that the dispersion curve marked by cir-
cles is close to curves 3 and 4, permits to consider it as a0
mode.
5. Efficiency of ultrasonic mode generation and
application of NWP
From the viewpoint of application of the ultrasonic
treatment of semiconductor plate, the efficiency of ultra-
sonic excitement in plate is one of the main parameters.
0,2 0,4 0,6
1
2
1
ef1
ef2η ,
re
l.
u
n
.
fh, MHz-mm
Fig. 4. Experimental frequency dependencies of relative effi-
ciency of excitation a0 mode with respect to s0 mode η=Ua0/Us0
in (111)-cut Cd0.2Hg0.8Te plate, where Ua0, Us0, � amplitudes of
a0, s0 modes. Curve 1 - geometry with one transducer 1; curve 2-
geometry with double-transducer 1 and 2 (see Fig. 2)
Relative efficiency of excitation a0-mode with respect
to s0 mode (η=Ua0/Us0) in the frequency range from
0.2 to 2 MHz has been studied, where Ua0, Us0, �
amplitudes of a0, s0 modes. Curve 1 in Fig. 4 shows
that efficiency of generation of a0-mode with one
piezoelectric transducer is about 5 times higher than
the efficiency of s0-mode generation. Curve 2 in Fig. 4
and oscillogram curve 2 in Fig. 2 exhibits approxi-
mately equal efficiency of the Lamb mode genera-
tion with two piezoelectric transducers. Fulfilled
researches have led to conclusions: the method of
attached transducers enabled to excite the lowest
Lamb modes (a0 and s0) simply and reliably; the
usage of double -transducer improves the efficiency
of generation s0 mode; the greatest relative effi-
ciency of excitation of the a0 Lamb mode (η=5.7) is
achieved with one transducer generation at fre-
quency of fh ≈ 0.2 MHz⋅mm.
The Lamb waves are conventionally used in non-de-
structive testing of plates [11]. For this application the a0
and s0 modes are proposed. As shown in Fig. 1b, the
antisimmetrical a0 is very sensitive to the thickness of
plate if fh<1 MHz mm holds. As a0 has low velocity of
propagation, which increase accuracy of defect location
detection, it can be applied for nondestructive testing.
The dispersion of the symmetrical s0 mode if fh<0.25
MHz mm holds is negligible so it can be used for defect
location in plate with slight non-parallel side. s1-Lamb
mode in the range of 0.64�0.68 MHz-mm and a2 in the
range 1.19�1.31 MHz-mm are reverse Lamb waves and
can be used for non-destructive testing Cd0.2Hg0.8Te plate
which enables us to check uniformity of material.
Conclusions
In the paper, the frequency dispersion curves of
phase and group velocities for Lamb mode propa-
gation along <100> and <110> directions in (100)-
cut of Cd0.2Hg0.8Te plate are obtained. The meth-
ods of generation of specific NWP modes were elabo-
rated; the group velocity Vgr was measured in range
(0.5�10) MHz in (111)-cut of Cd0.2Hg0.8Te plate;
the lowest a0 and s0 Lamb wave modes were identi-
fied. The comparative study of the generation effi-
ciency of separate modes provides conclusion that
a0-mode has much more efficiency of generation
than the s0-Lamb mode and may be recommended
for ultrasonic treatment of Cd0.2Hg0.8Te samples.
Some features of the Lamb wave modes for ultra-
sonic diagnostics are discussed.
Taking into account that investigated materials
are widely used in infrared engineering in the form
of heterostructures and layered structures CdHgTe/
CdTe, there is the necessity in special researches of
the acoustic characteristics of NWP in such objects.
I.O.Lysiuk et al.: Properties and application of ultrasonic Lamb waves...
35SQO, 5(1), 2002
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