Instabilities in binary compounds under irradiation
A simulation of radiation-induced instability in binary semiconductor, such as GaAs, was fulfilled. The instability is connected with antisite defects accumulated. It was shown that the number of antisite defects in crystal under irradiation can significantly exceed their equilibrium concentration....
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Cite this: | Instabilities in binary compounds under irradiation / V.V. Mykhaylovskyy, V.I. Sugakov // Вопросы атомной науки и техники. — 2000. — № 4. — С. 10-13. — Бібліогр.: 15 назв. — англ. |
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| citation_txt | Instabilities in binary compounds under irradiation / V.V. Mykhaylovskyy, V.I. Sugakov // Вопросы атомной науки и техники. — 2000. — № 4. — С. 10-13. — Бібліогр.: 15 назв. — англ. |
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| description | A simulation of radiation-induced instability in binary semiconductor, such as GaAs, was fulfilled. The instability is connected with antisite defects accumulated. It was shown that the number of antisite defects in crystal under irradiation can significantly exceed their equilibrium concentration. We have found that the instability with respect to periodical defect distribution appear at some conditions of irradiation. The wavelenght of the periodical distribution was estimated as 100 nm - 10 nm depending on crystal parameters .
Моделирование радиационно-индуцированной нестабильности в двоичной полупроводника, например, GaAs, было выполнено.Нестабильность связана с антиструктурных дефектов накапливается. Было показано, что число антиструктурных дефектов в кристалле при облучении может значительно превышать их равновесная концентрация. Мы обнаружили, что неустойчивость по отношению к периодического распространения дефектов появляются в некоторых условиях облучения.Длина волны периодического распределения была оценена как 100 нм - 10 нм в зависимости от параметров кристаллической.
Моделювання радіаційно-індукованої нестабільності в двійковій напівпровідника, наприклад, GaAs, було виконано. Нестабільність пов'язана з антиструктурних дефектів накопичується. Було показано, що число антиструктурних дефектів в кристалі при опроміненні може значно перевищувати їх рівноважна концентрація. Ми виявили, що нестійкість по відношенню до періодичного поширення дефектів з'являються в деяких умовах опромінення. Довжина хвилі періодичного розподілу була оцінена як 100 нм - 10 нм залежно від параметрів кристалічної.
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УДК 539.12.04:669.018
INSTABILITIES IN BINARY COMPOUNDS UNDER IRRADIATION
V. V. Mykhaylovskyy, V. I. Sugakov
Institute for Nuclear Research, pr. Nauki 47, Kiev, Ukraine, 03650, vvmih@ukrpack.net
A simulation of radiation-induced instability in binary
semiconductors, such as GaAs, was fulfilled. The
instability is connected with antisite defects
accumulated. It was shown that the number of antisite
defects in crystal under irradiation can significantly
exceed their equilibrium concentration. We have found
that the instability with respect to periodical defect
distribution appears at some conditions of irradiation.
The wavelength of the periodical distribution was
estimated as 100 nm - 10 μm depending on crystal
parameters.Introduction
Radiation is an effective tool for studying properties
of materials. In multicomponent systems radiation can
cause transitions to new phases (see review [1]).
Because irradiated substances are far from equilibrium,
effects of self-organization can be found in these
systems [2]. For instance, the periodical distribution of
point defects can appear even in the case of uniform
radiation and uniform sink density.
Spatial modulation of composition of different
materials was observed experimentally in many works
[3 - 5]. For instance, in [3, 4] the oscillations of the
composition of Fe-Ni and Fe-Ni-Cr alloys were detected
after irradiation by Ni+ ions with the energies of 5 MeV.
This effect has been investigated earlier for simple
substances ([6, 7]). The possibility of oscillation
appearance is discussed in [8]. In [9] we predicted this
phenomenon for ordered multicomponent alloys. In this
work we analyze such an effect in binary
semiconductors.
First, we shall calculate the stationary values of
defect concentration assuming uniform defect
distribution. Then we shall perform the stability analysis
of such distribution.
1 Defect concentrations in the case of uniform
distribution
Let us consider how the radiation influences
materials. A binary compound consists of two types of
atoms, which we denote as A and B. In a fully ordered
compound each type of atom forms the sublattice (Fig.
1,a). Even in the absence of radiation, there is a great
number of point defects in the crystal. The typical
defects for ordered multicomponent compounds are
antisite defects, i.e. atoms that occupy the wrong
sublattice (Fig. 1b). The radiation knocks the atoms of
both types out of their sites, creating interstitial atoms
and vacancies. Then these point defects diffuse over the
crystal and participate in different reactions. For
example, an interstitial atom and a vacancy can
recombine mutually. After recombination of interstitial
atom and vacancy of the same type the ideal crystal is
restored. But if their types are different, the antisite
defect appears (Fig. 1c). Unlike the interstitial atoms
and the vacancies, the antisite defects migrate very
slowly and they are accumulated in the crystal. In thin
samples radiation creates defects almost uniformly. This
is true for neutron and electron irradiation, which can
penetrate deep into the sample. So we assumed that the
distributions of defects are also uniform. Defect
concentrations can be determined with the reaction rate
method. We considered the following point defects:
interstitial atoms of both types (their concentrations we
denoted as IA and IB), vacancies on both sites (Va and
Vb) and antisite defects (Ab and Ba). We used
dimensionless units for concentrations, in which the
volume of one crystal unit cell is equal to 1.
Fig. I, a - ordered binary compound; b - antisite
defects; c - recombination ofla and Vb that leads to
creation of the antisite defect
Time dependence of radiation defect concentrations
is determined by the following kinetic equations:
dt
dIA = A
aiK Aa – A
iaK IA Va – A
ibK IA Vb + A
biK Ab –
– AB
ibK IA Bb + BA
ibK IB Ab + BA
iaK IB Aa – AB
iaK IA Ba –
– αIA (IA – nIA) + K0 [Aa + Ab – z (Va + Vb)/2];
(1)
dt
dVa = A
aiK Aa – A
iaK IA Va – B
iaK IB Va + B
aiK Ba –
– B
baK Va Bb + B
abK Vb Ba + A
abK Vb Aa – A
baK Va Ab –
– αVa (Va – nVa) + K0 (1 – z Va) (Aa + Ba);
(2)
10
dt
dAb = A
ibK IA Vb – A
biK Ab + AB
ibK IA Bb – BA
ibK Ab
IB +
+ A
abK Vb Aa – A
baK Va Ab – α IA (IA – nIA) Ab / 2 +
+ α IB(IB – nIB) Bb/2 + αVa(Va – nVa)/2 –
– K0(Ab – zVb).
(3)
The remaining three equations for IB, Vb and Ba can
be written analogously after changing A↔B and a↔b.
The equations for Aa and Bb can be obtained from the
conservation of site numbers: Aa + Ba + Va = 1 and Bb +
Ab + Vb = 1.
The following defect reactions were included in
these equations:
1) recombination of interstitial atoms with the same
or different types of vacancies (i.e. reactions like IA + Vb
→ Ab or IA + Va → Aa );
2) thermal creation of Frenkel pairs from antisite
defects and from atoms localized on their own sites (i.e.
Ab → IA + Vb and Aa → IA + Va );
3) substitution of atoms or antisite defects with
interstitial atoms (e.g. IA + Ba ↔ Aa + IB);
4) atom transition to the vacancy in the other
sublattice with ordering or disordering (e.g. Ab + Va ↔
Aa + Vb);
5) capture of interstitial atoms and vacancies by
unsaturable sinks, such as dislocations and surface
(terms with α; nIA, nIB, nVa, nVb are the thermal
concentrations of corresponding defects);
6) creation of Frenkel pairs by radiation (terms with
K0; the terms containing z take into account the dynamic
recombination of interstitials and vacancies, where z is
the number of atoms in the region of dynamic
recombination [10]).
Coefficients K can be evaluated from diffusion
parameters. Some of them are related by the detailed
balance principle. In this work we assumed that defect
energies and diffusion barriers do not depend on the
order parameter. So, we restricted ourselves to low
concentration of antisite defects, i.e. up to several
percent.
There are a lot of parameters needed to obtain all
coefficients. Most of them have been determined
experimentally using different techniques (see [11]).
But exact values for some parameters are still unknown.
For example, determination of energy barriers for
vacancy jumps is very difficult due to variety of
mechanisms existing in binary semiconductors. In this
work we used the parameter values determined for
GaAs.
To estimate the stationary values of defect
concentrations, we set time derivatives in kinetic
equations to zero and solved the set of eight algebraic
equations. Four of them turn out to be linear and the
others are quadratic. This set was reduced analytically
to that of two equations, both of ninth order. Further
solving was performed numerically. It is necessary to be
extremely careful while performing numerical
calculations in such systems. Terms in these equations
can be of different orders and computational errors can
be significant. To avoid this, we worked with high
precision numbers using software from [12].
The temperature dependences of these stationary
values at defect production rate K0 = 10-5 dpa/s are
presented in Fig. 2.
1
3
K,T
10 −
nα
10-2
10-4
10-6
10-8
10-10
10-12
10-14
2.01.00.5
IGa
IAs
AsGa
VGa
VAs
1.5
Figure 2: Dependence of point defect concentration on
temperature at defect production rate = 10-5 dpa/s. The
scale on the x axis is proportional to the inverse
temperature
Dashed lines represent the defect concentration in
the absence of radiation. The minimum in vacancy and
antisite defect concentration is caused by competition of
two mechanisms of defect creation. At high
temperatures the thermal fluctuations determine thes
defect concentrations. At low temperatures the defect
concentrations are determined by the rates of radiation
defect creation and thermally activated annealing. From
Figure 2 it is seen that the antisite defect concentration
is large, particularly at low temperatures of the
environment.
DEVELOPMENT OF PERIODICAL
STRUCTURES
Now we should check the stability of the uniform
defect distribution obtained above. Let us consider
qualitatively why the uniform distribution can be
unstable. The lattice gets deformed around the antisite
defects due to the different size of atoms. This field of
deformation affects migration of interstitial atoms and
vacancies to antisite defects, hence, the processes of
their recombination. If interstitial atoms are attracted to
the regions of higher concentration of antisite defects,
then they recombine mostly there. This leads to further
increase of antisite defect density in these regions and to
its decrease in other regions. As a result, the defect
distribution function becomes periodic in space. Such
type of distribution is a superlattice of defect density.
To analyze this phenomenon quantitatively the
kinetic equations were modified to include diffusion
terms, which appear in non-homogeneous fields. Let us
consider the diffusion of the interstitial atoms of type A
as an example. The migration of interstitial atoms can
11
be described with a reaction IA(r) ↔ IA(r + dr), where
dr is the vector connecting two neighbor interstitial
positions. We took into account that both concentration
and energy of interstitial atoms are functions of
coordinates. As a result the following term was added to
the time derivative of interstitial atom concentrations:
∇+∇⋅=
∂
∂ )
kT
)(U )(I)(I(Ddiv
t
)r(I IA
AAIA
diff
A rrr
(4)
Index "diff" means that we wrote here only the terms
describing the diffusion of interstitial atoms, ∇ is the
gradient operator. UIA(r) is the external potential that
describes the interaction of point defects. In this work
only interaction with antisite defects was taken into
account, because their concentrations are larger than
those of other defects. Thus the potential for interstitial
atoms of type A was written as
( ) ( )[∫ +′⋅′−= rrrr bIA,AbIA AU)(U
( ) ( ) ] VdBU aIA,Ba ′′⋅′−+ rrr
(5)
UAb,IA(r – r') is the interaction energy of the antisite
defect Ab situated in r and the interstitial atom IA in r'. It
is seen that if defect concentrations are uniform, then
UIA(r) is constant and both gradients in (4) are equal to
0.
For defect-defect interaction the following equation
was used [13]:
Uα,β(r) = 3r8
VV3
π
∆∆ βα
2
11C
K
(–Ca) [3 – 5 (cos4 θx +
+ cos4 θy + cos4 θz)],
(6)
where Ca is the anisotropy parameter, which is
negative for most of crystals. C11, K are the elastic
constants, θi is the angle between the radius vector r and
i-th crystal axis, ∆V is the parameter that characterizes
the volume change due to introduction of the defect. In
the case of cubic crystals with weak anisotropy, when
the distance between the defects is much larger than the
lattice period, this formula describes the defect-defect
interaction. If the radius vector connecting the defects is
oriented along the crystal axis, the defects of the same
type attract each other.
The values of the elastic constants for GaAs were
taken from [14]. Calculations of ∆V for GaAs were
made in [15] using ab initio simulations.
The diffusion of other interstitial atoms and
vacancies can be described in a similar way. Also all
reactions in equations (1) - (3) have additional terms in
the non-homogeneous case.
Now we can check the stability of the uniform defect
distribution. To do this, we represent all the
concentrations as stationary uniform values and small
non-uniform deviations around those values. For
example, the concentration of the antisite defects Ab was
written as
Ab = Ab0 + δAb exp(ikr + λ t)
(7)
where Ab0 is the uniform stationary value obtained
earlier in this work. All other concentrations were
written in such a form also. Then we substituted them in
the equations (1) - (3) modified to non-uniform
distributions. After substitution of (7) into (5) we
obtained Fourier transform of the defect-defect
interaction potential (6). It has the following form:
Uα,β(k) =
2
11C
K
(–Ca) ∆Vα ∆Vβ
4
4
z
4
y
4
x
k
kkk ++
8)
One can see from this formula that interaction is
maximum if the wavevector is directed along the crystal
axis.
λ(k) k
Fig. 3. The typical λ(k) for different irradiation
intensities and temperatures
Because we needed only to check the stability of
roots, we assumed that the deviations are small.
Keeping only the linear terms in deviations, we obtained
a system of linear equations. This system has a
nontrivial solution if its determinant is zero, which
enabled us to determine λ(k). The stationary solution is
stable if and only if real parts of all λ(k) values are
negative.
The typical λ(k) for different irradiation intensities
and temperatures are shown in Figure 3. When defect
concentrations are small and the interaction is not
significant, λ(k) is negative and the absolute value of λ
is higher for large values of k. It is seen as the effect of
diffusion, which suppresses the non-uniform
fluctuations. When defect concentration increases, the
interaction becomes more important. Some fluctuation
obtains positive feedback, i.e. Re λ(k) takes positive
values in some region of k values. It means that small
fluctuations with such k grow, which leads to the
development of the superlattice. The absolute value of k
gives us the period of the superlattice. Results of
stability analysis of the uniform solutions are presented
in the plane of irradiation intensity (K, dpa/s) and
environment temperature (T0) (see Figure 4). In the
region 1 the uniform values of defect concentrations are
stable. In the region 2 the system becomes unstable,
which leads to the development of the superlattice. It
should be noted that in the cubic crystals the instability
appears simultaneously for several states with different
12
values of k, which have the same modulus but different
directions. As the result complex structures like Bйnard
cells may develop. The typical period of the
superstructures depends on the crystal and external
parameters and varies from 102 to 105 lattice periods. It
is possible to vary the period of the superstructure by
changing the intensity and temperature of irradiation.
T0
lg K0 350 K
-4
1
2
400 K 450 K 500 K
-5
-4.5
-3.5
Fig. 4. Regions of instabilities on the plane of
irradiation intensity and environment temperature
REFERENCES
1.K. C. Russell, Progress in Materials Science. 1984,
28, 229.
2.V. I. Sugakov, Lectures in Synergetics, World
Scientific, Singapore, 1998.
3.F.A.Garner, H.R.Brager, R.A.Dodd and T.Lauritzen,
Nucl. Instr. and Meth. Phys. Res. B16, 244, 1986.
4.K.C.Russell and F.A.Garner, Met. Trans. A23, 1963,
1992.
5.V.S.Khmelevskaya, V.G.Malynkin and
S.P.Solovyev.//J. Nucl. Mater. 1993, v.199,.p.214.
6.V. I. Sugakov "A superlattice of defect density in
crystal under irradiation", in "Effect of Radiation on
Materials", 14th Int. Symp. American Society for
Testing and Materials, Philadelphia, 1, 510-522, 1989.
7.P. A. Selishchev and V. I. Sugakov, // Rad. Effects
and Def. in Solids.1995, 133, 237.
8.V. V. Mykhaylovskyy, K. C. Russell, V. I. Sugakov
"Time and space instabilities in binary alloys at phase
transitions under irradiation", Symposium N:
Microstructural Processes in Irradiated Materials,
November 30 – December 4, 1998, Boston,
Massachusetts, USA.
9.V. V. Mykhaylovskyy, K. C. Russell, V. I. Sugakov,
Ukrainian Physical Journal, 44, 1280, 1999.
10.S. Banerjee and K. Urban, //Phys.st.sol., A81, 145
1984.
11.A.Sakalas and Z. Januskevicius, "Point defects in
semiconductors", Vilnius, 1988, (in Russian).
12.GNU multi precision library and its description can
be found at http://www.swox.com/gmp
13.G. Leibfried, N. Breuer, "Point defects in metals.
Introduction to the theory", Springer, Berlin, 1978.
14.H. Seong and L. J. Lewis, //Phys Rev B52, 5675,
1995.
15.D. Conrad and K. Scheerschmidt, //Phys Rev B58,
4538, 1998.
13
УДК 539.12.04:669.018
Instabilities in binary compounds under irradiation
Development of periodical structures
references
|
| id | nasplib_isofts_kiev_ua-123456789-78134 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:54:55Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Mykhaylovskyy, V.V. Sugakov, V.I. 2015-03-12T07:12:33Z 2015-03-12T07:12:33Z 2000 Instabilities in binary compounds under irradiation / V.V. Mykhaylovskyy, V.I. Sugakov // Вопросы атомной науки и техники. — 2000. — № 4. — С. 10-13. — Бібліогр.: 15 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/78134 539.12.04:669.018 A simulation of radiation-induced instability in binary semiconductor, such as GaAs, was fulfilled. The instability is connected with antisite defects accumulated. It was shown that the number of antisite defects in crystal under irradiation can significantly exceed their equilibrium concentration. We have found that the instability with respect to periodical defect distribution appear at some conditions of irradiation. The wavelenght of the periodical distribution was estimated as 100 nm - 10 nm depending on crystal parameters . Моделирование радиационно-индуцированной нестабильности в двоичной полупроводника, например, GaAs, было выполнено.Нестабильность связана с антиструктурных дефектов накапливается. Было показано, что число антиструктурных дефектов в кристалле при облучении может значительно превышать их равновесная концентрация. Мы обнаружили, что неустойчивость по отношению к периодического распространения дефектов появляются в некоторых условиях облучения.Длина волны периодического распределения была оценена как 100 нм - 10 нм в зависимости от параметров кристаллической. Моделювання радіаційно-індукованої нестабільності в двійковій напівпровідника, наприклад, GaAs, було виконано. Нестабільність пов'язана з антиструктурних дефектів накопичується. Було показано, що число антиструктурних дефектів в кристалі при опроміненні може значно перевищувати їх рівноважна концентрація. Ми виявили, що нестійкість по відношенню до періодичного поширення дефектів з'являються в деяких умовах опромінення. Довжина хвилі періодичного розподілу була оцінена як 100 нм - 10 нм залежно від параметрів кристалічної. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Физика радиационных повреждений и явлений в твердых телах Instabilities in binary compounds under irradiation Нестабільність в бінарних сполуках при опроміненні Нестабильность в бинарных соединениях при облучении Article published earlier |
| spellingShingle | Instabilities in binary compounds under irradiation Mykhaylovskyy, V.V. Sugakov, V.I. Физика радиационных повреждений и явлений в твердых телах |
| title | Instabilities in binary compounds under irradiation |
| title_alt | Нестабільність в бінарних сполуках при опроміненні Нестабильность в бинарных соединениях при облучении |
| title_full | Instabilities in binary compounds under irradiation |
| title_fullStr | Instabilities in binary compounds under irradiation |
| title_full_unstemmed | Instabilities in binary compounds under irradiation |
| title_short | Instabilities in binary compounds under irradiation |
| title_sort | instabilities in binary compounds under irradiation |
| topic | Физика радиационных повреждений и явлений в твердых телах |
| topic_facet | Физика радиационных повреждений и явлений в твердых телах |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78134 |
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