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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Published in:Вопросы атомной науки и техники
Date:2000
Main Authors: Mykhaylovskyy, V.V., Sugakov, V.I.
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Language:English
Published: 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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author Mykhaylovskyy, V.V.
Sugakov, V.I.
author_facet Mykhaylovskyy, V.V.
Sugakov, V.I.
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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container_title Вопросы атомной науки и техники
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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fulltext 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
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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
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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.
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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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