Features of a shock wave in CdTe by pulsed laser irradiation
Analyzed on the example of CdTe are formation and propagation of shock waves during pulsed laser irradiation of a solid surface. It is shown that before the appearance of a shock wave in a solid, a gradual increase in pressure gradient leads to formation of dislocations, density of which increases w...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| Cite this: | Features of a shock wave in CdTe by pulsed laser irradiation / B.K. Dauletmuratov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 130-134. — Бібліогр.: 17 назв. — англ. |
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| citation_txt | Features of a shock wave in CdTe by pulsed laser irradiation / B.K. Dauletmuratov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 130-134. — Бібліогр.: 17 назв. — англ. |
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| description | Analyzed on the example of CdTe are formation and propagation of shock waves during pulsed laser irradiation of a solid surface. It is shown that before the appearance of a shock wave in a solid, a gradual increase in pressure gradient leads to formation of dislocations, density of which increases with depth. The dislocation density is maximum at the place of shock wave formation.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 130-134.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
130
PACS 61.72.Lk, 61.80.Ba, -x
Features of a shock wave in CdTe by pulsed laser irradiation
B.K. Dauletmuratov
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
E-mail:boribai_7@rambler.ru
Abstract. Analyzed on the example of CdTe are formation and propagation of shock
waves during pulsed laser irradiation of a solid surface. It is shown that before the
appearance of a shock wave in a solid, a gradual increase in pressure gradient leads to
formation of dislocations, density of which increases with depth. The dislocation density
is maximum at the place of shock wave formation.
Keywords: pulsed laser irradiation, CdTe, dislocation density.
Manuscript received 02.09.10; accepted for publication 02.12.10; published online 28.02.11.
1. Introduction
Up to date, the method of pulsed laser processing and
modification of subsurface layers has been increasingly
used to form inverse and graded layers in
semiconductors, to create ohmic and barrier contacts, for
solid and liquid phase doping when manufacturing the
structures and devices based on them in photo- and
optoelectronics, sensor electronics, and especially
ionizing radiation detectors based on CdTe and
CdZnTe [1].
Pulsed laser doping the samples of CdTe is
produced using nanosecond irradiation of the structure
Іn/CdTe and accompanied by the simultaneous
occurrence of various physical processes at a high
velocity. In this case, particularly important phenomenon
is the emergence and spread of a shock wave (SW) in
solid [1-7], which is essentially a nonlinear process and
leads, in particular, to changes in the defect system of
semiconductor [2-4]. This, in its turn, leads to changes in
electrical and optical parameters of devices based on
CdTe.
Therefore, the purpose of this study was to
determine the characteristics of the shock wave in the
structure of CdTe and In/CdTe after nanosecond laser
irradiation.
2. Some properties of shock waves
The shock wave is a discontinuity surface at the
intersection where the pressure, density and temperature
increase dramatically, and the velocity of operating
medium motion is dramatically reduced. The shock
wave is an example of normal hydrodynamic
discontinuity, and through it a flow of matter goes (as
opposed to a tangential discontinuity, through which the
substance does not flow). From the macroscopic point of
view, the shock wave is an imaginary surface on which
the thermodynamic quantities of the medium (which
tend to vary continuously in space) make finite jumps.
When passing through a shock front, changed are
pressure, temperature, density of matter, entropy
environment, and its velocity relatively to the shock
front. Here, as the shock wave we mean the “inverted”
profile (front) according to [8-10], which moves in the
material surface of discontinuity of the thermodynamic
quantities. Shock waves do not possess the additivity
property in the sense that the thermodynamic state of the
environment that occurs after the passage of a shock
wave is impossible to get with a consistent passing of
two shock waves with lower intensities. Acoustic waves
are oscillations of the density of the medium, which
propagate in space. The equation of state of ordinary
matter is that in the high-pressure velocity of acoustic
waves (i.e., the speed of perturbation spread) increases
(it means that the acoustic wave is the nonlinear one).
When spreading, it inevitably leads to the phenomenon
of overturning solutions that give rise to shock waves.
By this mechanism, the shock wave in normal
environment is always a wave of compression. However,
in those systems where the speed of perturbation spread
decreases with increasing the density, rarefaction shock
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 130-134.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
131
wave is observed. For the rapid transformation of the
density oscillations to the shock wave, it requires strong
initial deviations from equilibrium. This can be achieved
by creation of acoustic waves with a very high intensity
provided, for example, by pulsed laser irradiation (PLI).
The length of the shock front in semiconductors is
of the order of interatomic distances. The characteristic
difference between the shock and stress waves is that the
transfer of momentum from the shock compressed
matter to a non-excited its part has a character of
individual collisions and not a collective atomic motion.
Acoustic pulse in a solid, due to physical
nonlinearity, is the nonlinear wave [5]. As the physical
nonlinearity, we mean the difference modules of the
elastic constants and density Сijkl along the coordinate of
wave propagation at each point of pulse. In other words,
there arises the dependence of Сijkl and ρ on the strain,
i.e., Gooke’s law violation. The speed of sound in solids
is commonly expressed as
ijklС
, the velocity
increment due to changes in elasticity and density is as
follows
d
dС
d ijkl .
Therefore, a more “fast” component of the pulse
will catch the more “slow” ones. This corresponds to the
energy transfer from the low-frequency harmonics to the
higher frequency ones. Respectively, the pulse profile
will be distorted and more sharp. Profile distortion of the
sound wave leads to several effects. First, steepening the
profile may lead to the formation of gaps, so the initial
sine wave becomes a sawtooth wave with time.
Moreover, steepening the profile, leaving the movement
in a wave to be periodic, alters the spectral composition
of the wave. In the original monochromatic wave with
the frequency ω, both distribution and distortion of the
profile are related with increasing high-frequency
harmonics. Moreover, high overtones nω with larger n
reach a maximum in the place of the greatest slope.
Thus, there is a continuous transfer of energy from the
fundamental harmonic to the high overtones. Since the
attenuation of sound is proportional to the square of
frequency, this leads to stronger damping. Steepening
the wave front will take place until it stabilizes the
dissipative processes. Thus, the wave profile depends on
the ratio of non-linear and dissipative effects, and its
intensity. If the wave amplitude is sufficiently high non-
linear effects dominate, and the wave profile in the end
is “turned over”, which generates a shock wave.
Otherwise, the wave due to dissipation is damped out
earlier than it accumulates non-linear effects [10].
It should be noted that the equation of state for
solids is absent, which hinders the theoretical description
of occurrence and propagation of SW. Therefore, it
seems reasonable to use the model of gas for which it is
known. In the solid state, analogue of the adiabatic
exponent is the index of isentropy [6, 7].
In homogeneous isotropic gas with equilibrium
values of the pressure P0 and density ρ0, in a non-linear
wave, small perturbations of pressure P' and density ρ'
will give a small increment a0 to the propagation
velocity u (u<<a0), 0u . The speed of sound is
SPa )/( . In the linear acoustic approximation
u = 0, and all points of the sound wave profile spread at
the same speed a0. In the following first approximation
for the rate of displacement of points υ in the sound
wave profile in ideal gas
,
2
1
000 ua
u
a
γ – adiabatic exponent. Therefore, over time, the profile
of running wave will be distorted, and formation of the
gap, rollover will take place (without account of
dissipation). In the case of evolution of a plane harmonic
acoustic wave excited in ideal gas for the plane at x = 0,
i.e., tuu sin0
at x = 0 the solution for the time and
coordinates of the discontinuity, or turnover of the
profile will be
)1(
1
0
u
ts
,
)1(0
0
u
a
xs
,
where /2 0a [10]. Common, but more
complicated expressions for the time and coordinate of
SW formation in a solid are given in [9].
3. Results and discussion
The depth of shock wave formation in indium and CdTe
exposed on their surface by the laser pulse can be
calculated using the expression from [6, 7]
2/12
11
2
1
2
ERm
c
l l
SW
(1)
where сl is the velocity of the longitudinal acoustic
wave, τ – laser pulse duration, ρ – density, ζ – setting the
value of acceleration of the surface layer, m – isentrope
index, – the effective value of the distortion
coefficient for the pulse front, γ – adiabatic exponent,
R – coefficient of optical reflection, E – energy density
of the laser pulse, αλ – optical absorption coefficient. As
in [6], we take = 1, ζ = 1, m = 3, γ = 5/3. Taking into
account that according to [11] in metals, the value of
propagation velocity for pressure pulses in the
nanosecond pulsed laser irradiation is 15-30% higher
than the longitudinal speed of sound.
Fig. 1 shows the results of calculation for the depth
of SW formation in In and CdTe as dependent on the
density of laser pulse intensity /EI .
Following the plot in Fig. 1, selection of the CdTe
thickness allows to avoid formation of SW in the bulk,
and to locally influence the defect subsystem at various
depths of semiconductor.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 130-134.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
132
0 1x10 7 2x10 7 3x10 7 4x10 7 5x10 7
0
100
200
300
400
500
1
2
I, МВт/см 2
l У
В
,м
к
м
Fig. 1. The depth of shock wave formation in CdTe (1) and
Іn (2) versus the intensity of ruby laser pulse. For CdTe
R = 0.43, for indium R = 0.9.
Consider the criterion of SW formation under
single-pulse irradiation. The left-hand side of (2) is a
dimensionless combination of variables that characterize
the parameters of radiation-absorbing body. On the left
in (3), there are values that characterize the laser
radiation, on the right – those of absorbing medium
,7
11
81
2224
2
mc
ERl
l (2)
or .6
4
2
lcQ
(3)
Here, l is the characteristic size that is lower than
the values of 2 variables – the crystal thickness and
radius of the radiation beam. Q = E·S is the laser
radiation energy, S – irradiated area, τ = 20 ns. Table 1
shows the physical parameters of CdTe and In.
According to the criterion (2) for the CdTe crystal
2-mm thick, the inequality holds up to the energy density
E = 6 mJ/cm2 (I = 0.3 MW/cm2), for In of the same
thickness – 0.1 mJ/cm2 (I = 5 kW/cm2). At the same
time, the melting threshold of CdTe is 2...6 MW/cm2 in
accord with various data, while calculations of the
maximum heating temperature for the surface of CdTe
and In, made using the expression
Table 1.
Material сl,
m·s-1
ρ,
kg·m-3
=0.694,
m-1
R Тmelt,С
CdTe 3300 5860 2.94106 0.43 1092
In 1400 7310 5.4107 0.9 157
12
2
IA
T
(here, χ – coefficient of thermal diffusivity, τ – pulse
duration (20 ns), λ – heat conductivity, A – optical
absorption coefficient), indicate that this energy density
melting and, moreover, evaporation from the In surface
does not take place. Especially, since you can clamp the
surface by depositing a transparent material to radiation
or place it in transparent liquid. Then there will be no
unloading wave. Fig. 2 shows the surface temperature of
CdTe and In after nanosecond laser irradiation.
When irradiating structures In/CdTe to create
detectors of ionizing radiation, the right-hand side of
criterion (3) is 9·1018 J/s2 for In. For S = 16 mm2, the
minimum energy density required to implement this
criterion is 0.003 mJ/cm2 (150 W/cm2). Fig. 2 shows that
melting and, moreover, evaporation from the surface
will not occur. The same is valid for CdTe (Fig. 2). I.e.,
these unequalities are performed in a wide range (below
Tmelt within approximately three orders).
Thus, according to the criteria (2) and (3) [6, 7],
SW appears at energy densities up to melting and
evaporation of the surface layer. At the same time, there
[6, 7] used is the model of evaporation of the skin layer
to assess the depth of the shock wave, but nevertheless,
evaporation is not necessary and/or sufficient condition
for the emergence of the shock wave. This is such a
model, which assumes that the skin layer is evaporated.
The fact that it is convenient to use gas (but not solid) in
the model of SW formation, because there is no equation
of state for solids and the speed of sound as dependent
on the internal energy. There is a simple relationship for
ideal gas, but for a rigid body it is very complex.
Respectively, calculation is very complicated, in
particular, the index of isentropy – analogue of heat
should be used. By their values for gas and solid, these
quantities are almost identical (3 and 4). In principle,
“gas” model is satisfactory for estimating the depth of
the shock wave in solid, but gives large uncertainties in
the problem of laser exposure (as indicated in [6]). The
theory of formation and propagation for shock waves in
gases is well developed [10].
0.0 2.0x10
5
4.0x10
5
6.0x10
5
8.0x10
5
1.0x10
6
0
50
100
150
200
250
2
T
, d
e
g
I, MW/cm2
1
Fig. 2. Theoretical dependence of the surface temperature of
CdTe (1) and In (2) on the intensity of pulsed laser radiation.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 1. P. 130-134.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
133
At the same time, the general condition of the
shock wave appearance is accumulation of non-linear
effects that dominate over the processes of dissipation of
acoustic nonlinear pulse during its propagation after
laser irradiation of solids. The first makes the pulse front
sharper, while the second is broadens it. Especially
because there can be 4 causes (joint) of SW formation in
a solid during PLI, in general. I.e., shock deformation
and, accordingly, generation of compression pulse by
nanosecond laser irradiation is due to:
1. Very fast, within 20 ns, heating (thermal shock)
and, accordingly, deformation at a high rate of it.
2. Fast (with the shock velocity) phase transition at
the solid-liquid interface.
3. Rapid evaporation from the surface and thus
generation of the recoil pressure of non-equilibrium
vapor.
4. Optical breakdown and plasma formation in
vapor – there is the emergence and rapid expansion of
the plasma under absorption of radiation, then ionization
and breakdown.
The most intense defect generation takes place in
the area of the shock wave front in the instant of its
formation and the beginning of movement, when there
arises a maximum concentration of point defects in the
structure (Fig. 3 and [2, 3]), as well as the maximum
microhardness [13], indicating the local mass transfer.
SW also causes hardening the material and alters the
yield [14]. The characteristic decay length of the shock
wave at E ≈ 10-16 J/cm2 is approximately 60-100 μm
[3, 13]. Calculations based on the expression (1) showed
that SW for I = 100 MW/cm2 is formed at the depth of
72 μm, which is consistent with Fig. 3, where the
dislocation density is the highest one. Dislocation
network after the passage of the shock wave was also
observed in [15].
The pressure gradient increases in a nonlinear
wave, as the latter propagates inside the bulk, reaching a
maximum in the points of the shock wave front. The
shock wave momentum is transfered both to matrix
atoms and defects (scattering centers). Increasing the
laser pulse energy results in a shift of the concentration
maximum of defects closer to the surface, i.e., we deal
with the influence of the pressure gradient of the
nonlinear wave and its front location. Thus,
experimental results indicate formation of dislocations in
CdTe by increasing the gradient of the non-linear wave
and formation of SW (Fig. 3b). Fig. 3 shows that in the
place of SW formation one can observe the maximum
concentration of dislocations. This is also consistent with
previous results [2, 3].
When shock waves possess a high intensity, the
pressure in the front is so high that the shear stiffness of
the material does not manifest itself, the atoms leave the
correct location in the crystalline layers (cleavage), a
crystalline body temporarily acquires the properties of
amorphous (glassy, liquid) body. These waves, in
contrast to the waves preserving the crystalline
properties of the body, are called as the plastic ones [8].
a
0 10 20 30 40 50 60 70
0.0
5.0x103
1.0x104
1.5x104
2.0x104
2.5x104
di
sl
, c
m
-1
l, m
b
Fig. 3. a) Pits from dislocations in CdTe after a shock wave
corresponding to the laser intensity I = 100 MW/cm2. The
depth: 0 (1), 24 (2), 48 (3), 72 μm (4). b) Dependence of the
dislocation density on depth.
Note that in some publications, in particular in [16,
17], mass transfer is explained by action of the shock
wave. In these works, the spiking concentration of
copper in nickel and carbon in iron is reached at the
depths 80 and 150 μm for I = 109 W/cm2, which is
explained by spreading SW, but the shock wave at this
intensity is formed at the depths 0.6 to 1 μm. Therefore
further in depth, if assuming this mechanism of the
shock wave, decrease in the concentration of impurities
and defects should occur like to that in [3, 13-15]. The
mechanism of mass transfer here is barodiffusion, and in
the same paper [17] solved is the equation of mass
transport with account of barodiffusion.
3. Conclusions
Using the example of CdTe, we have shown that the
shock wave in a solid during its formation and
movement, and also before the appearance leads to the
|
| id | nasplib_isofts_kiev_ua-123456789-117656 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-11-24T11:44:23Z |
| publishDate | 2011 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Dauletmuratov, B.K. 2017-05-25T18:46:14Z 2017-05-25T18:46:14Z 2011 Features of a shock wave in CdTe by pulsed laser irradiation / B.K. Dauletmuratov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 1. — С. 130-134. — Бібліогр.: 17 назв. — англ. 1560-8034 PACS 61.72.Lk, 61.80.Ba, -x https://nasplib.isofts.kiev.ua/handle/123456789/117656 Analyzed on the example of CdTe are formation and propagation of shock waves during pulsed laser irradiation of a solid surface. It is shown that before the appearance of a shock wave in a solid, a gradual increase in pressure gradient leads to formation of dislocations, density of which increases with depth. The dislocation density is maximum at the place of shock wave formation. The work was performed under the financial support of the State Fund for Fundamental Researches of Ukraine, project No F41.1/032 and State target scientific and technical program: project Nо І-2.1.1-08, state registration No 0108U003198 and No І-1.2.1-08, state registration No № 0108U004836.. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Features of a shock wave in CdTe by pulsed laser irradiation Article published earlier |
| spellingShingle | Features of a shock wave in CdTe by pulsed laser irradiation Dauletmuratov, B.K. |
| title | Features of a shock wave in CdTe by pulsed laser irradiation |
| title_full | Features of a shock wave in CdTe by pulsed laser irradiation |
| title_fullStr | Features of a shock wave in CdTe by pulsed laser irradiation |
| title_full_unstemmed | Features of a shock wave in CdTe by pulsed laser irradiation |
| title_short | Features of a shock wave in CdTe by pulsed laser irradiation |
| title_sort | features of a shock wave in cdte by pulsed laser irradiation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/117656 |
| work_keys_str_mv | AT dauletmuratovbk featuresofashockwaveincdtebypulsedlaserirradiation |