The kinetic of point defect transformation during the annealing process in electron-irradiated silicon

The A-centers (VO) annealing and transformation of precursors to form stable СiОi defects during these processes are described. It was found the necessity to take into account annihilation of vacancy type defects with the interstitial type mobile defects to describe the annealing of defects. I...

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Дата:	2011
Автори:	Gaidar, G.P., Dolgolenko, A.P., Litovchenko, P.G.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2011
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon / G.P. Gaidar, A.P. Dolgolenko, P.G. Litovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 213-221. — Бібліогр.: 32 назв. — англ.

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spelling	irk-123456789-1177072017-05-27T03:04:05Z The kinetic of point defect transformation during the annealing process in electron-irradiated silicon Gaidar, G.P. Dolgolenko, A.P. Litovchenko, P.G. The A-centers (VO) annealing and transformation of precursors to form stable СiОi defects during these processes are described. It was found the necessity to take into account annihilation of vacancy type defects with the interstitial type mobile defects to describe the annealing of defects. It was shown that the energies of migration for vacancy (V) and interstitial carbon atoms Сi that are defined by the degree of their localization in silicon lattice at the temperature close to 550 K are equal Emv = 1.1 eV and Emc = 1.16 eV, accordingly. 2011 Article The kinetic of point defect transformation during the annealing process in electron-irradiated silicon / G.P. Gaidar, A.P. Dolgolenko, P.G. Litovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 213-221. — Бібліогр.: 32 назв. — англ. 1560-8034 PACS 61.72.Cc, Ji; 61.80.Fe, 61.82.Fk http://dspace.nbuv.gov.ua/handle/123456789/117707 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The A-centers (VO) annealing and transformation of precursors to form stable СiОi defects during these processes are described. It was found the necessity to take into account annihilation of vacancy type defects with the interstitial type mobile defects to describe the annealing of defects. It was shown that the energies of migration for vacancy (V) and interstitial carbon atoms Сi that are defined by the degree of their localization in silicon lattice at the temperature close to 550 K are equal Emv = 1.1 eV and Emc = 1.16 eV, accordingly.
format	Article
author	Gaidar, G.P. Dolgolenko, A.P. Litovchenko, P.G.
spellingShingle	Gaidar, G.P. Dolgolenko, A.P. Litovchenko, P.G. The kinetic of point defect transformation during the annealing process in electron-irradiated silicon Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Gaidar, G.P. Dolgolenko, A.P. Litovchenko, P.G.
author_sort	Gaidar, G.P.
title	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon
title_short	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon
title_full	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon
title_fullStr	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon
title_full_unstemmed	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon
title_sort	kinetic of point defect transformation during the annealing process in electron-irradiated silicon
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2011
url	http://dspace.nbuv.gov.ua/handle/123456789/117707
citation_txt	The kinetic of point defect transformation during the annealing process in electron-irradiated silicon / G.P. Gaidar, A.P. Dolgolenko, P.G. Litovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 213-221. — Бібліогр.: 32 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
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fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. PACS 61.72.Cc, Ji; 61.80.Fe, 61.82.Fk The kinetic of point defect transformation during the annealing process in electron-irradiated silicon G.P. Gaidar, A.P. Dolgolenko, P.G. Litovchenko Institute for Nuclear Research, NAS of Ukraine, 47, prospect Nauky, 03680 Kyiv, Ukraine E-mail: gaidar@kinr.kiev.ua Abstract. The A-centers (VO) annealing and transformation of precursors to form stable СiОi defects during these processes are described. It was found the necessity to take into account annihilation of vacancy type defects with the interstitial type mobile defects to describe the annealing of defects. It was shown that the energies of migration for vacancy (V) and interstitial carbon atoms Сi that are defined by the degree of their localization in silicon lattice at the temperature close to 550 K are equal and , accordingly. The values for potential barriers and their positions on the migration path of interstitial carbon atoms to oxygen (О eV1.1V =mE eV16.1iC =mE i) in the region for capture of Сi atom by Оi atom (with the radius 14.7 Å) are determined. It was brought evidences that vibration band of absorption at is attributed to center modified by carbon, and the band is attributed to a metastable state of С 1cm9.865 − -A 1cm4.967 − іО2і defect associated with an oxygen dimer. The position of the center donor level in the forbidden band of silicon is determined as Е -A V + 0.415 eV. Keywords: silicon, point defects, electron irradiation, annealing. Manuscript received 21.10.10; accepted for publication 16.03.11; published online 30.06.11. 1. Introduction In spite of considerable number of works concerning the annealing of radiation defects in silicon, in our opinion, this process is described only partially. For example, many authors usually use only two annealing mechanisms: migration to sinks and dissociation of defects. Therefore, when these two dominant defects in silicon (CiOi and VO) are annealed in the same temperature range 300…400 °С and their centers coincide at the annealing stages, it is difficult to clearly define: either vacancies generated in the course of centers dissociation are captured by C-A iOi, or Ci atoms released from CiOi interact with VO ( center). But in any case, the C -A sOi defects are formed as a result of annealing [1]. Point defects (vacancies and interstitial atoms) as well as their complexes with impurity atoms in silicon are the most completely studied. The activation energy of migration is one of the most important characteristics of the defects. So, the authors [2] compared the migration energy of interstitial atoms (ІSі) and Frenkel pairs ( )VI − with the migration energy of vacancy (V++, 0.33; V0, 0.45; V=, 0.18 еV) measured by Watkins [3]. Herewith, the hydrogen molecules (Н2) were used as sinks for vacancies and interstitials silicon atoms created by irradiation of 6-MeV electrons. It was shown that the migration energy (Em) of and almost do not differ from the migration energy of vacancies in the respective charge states. Investigation of the annealing of defect clusters, the main defects in which the di- and tri-vacancy defects are, allowed to determine the activation energies of their annihilation with the interstitial and di-interstitial silicon atoms ( and , respectively), as well as the migration energy of vacancies ( ) at the temperature about 380 K [4]. I VI − eV91.0I =aE eV74.02I =aE eV8.0V =mE © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 213 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. Knowing the value of the barrier ( eV41.0=bE ) [5], the migration energies and at the temperature about 100 °С can be determined. These small migration energies of vacancies and interstitial atoms sometimes were used (without direct experimental evidences) at high temperatures up to the silicon melting point. The experiments on radiation-accelerated self- diffusion of eV5.0I =mE eV33.0 2I =mE 30Si to the region of 28Si (99.926 %) with the thickness 280 nm were performed, and the migration enthalpy of vacancies = (1.8 ± 0.5) еV within the temperature range 780…872 °С was defined by the authors of [6]. The migration enthalpy of interstitial atoms = (1.77 ± 0.12) еV was determined in [7]. Thus, at low temperature the migrating vacancy is more localized than at high temperatures that confirms the opinion of the authors [8] about the delocalized nature of defects in silicon. The authors of [9] suppose that the thermally-activated movement of interstitial atoms and vacancies in the neutral charge states occurs at temperatures higher than 150 and 175 K, respectively. mH V mH I Extremely high mobility of ІSі at the temperatures Т < 10 K appears only in the process of irradiation, and it has no activation character (as a result of sequential recharge of ІSі) [10]. The interstitial Si atoms, according to the Watkins substitution mechanism, crowd out the C, B, In, Al impurities from the lattice points to the interstitial position without the need to overcome the barrier [11]. Herewith, their free path is . The interstitial atom I cm1010 65 −− − ++ from its tetrahedral (T) position by capturing one electron becomes I+ and can moves to the B-position (the configuration centered by bonds). The hole capture will convert it back to І++ state, which results in displacing it to T-position again [12]. It is known that the vacancy and interstitial silicon atom have negative correlation energy, which makes energy-favourable changing of charge state of defect from double positive to neutral state directly. The neutral level of vacancy is equal EV + 0.37 еV [13], therefore the appearance of level (EV + 0.04 еV)+/++ is observed when studying by the EPR method, since the hole generated by photon with energy of 0.35 eV was captured on the neutral level of vacancy. The migration energy of vacancy in double positive charge state (Em = 0.32 ± 0.02 еV) was determined in [3]. In the case of interstitial silicon atom, the neutral level in the forbidden band of Si should be located at EV + 0.09 еV, because has the position at E0/I − c - 0.70 еV [14]. Thus, the donor levels of ІSі should be deep in the valence band. Therefore, the positively charged interstitial atoms in silicon ІSі have not been found up to date. However, irradiation with electrons at the temperature of 4.2 K in silicon containing С, Ga, In, Al substitution atoms leads to appearance of vacancies and interstitial ions Al++ in approximately equal amounts with the introduction rate of at the Rutherford scattering of electrons. Apparently, the EPR signal for interstitial silicon atom does not occur, since is in the zero-charge state in this experiment. The crowdion and dumbbell configuration can be formed by embedding the incuse atom into the chain of crystal atoms. Herewith, the consistent shift of chain atoms will take place [5]. In other words, the deformation wave along the chain of atoms (“the tsunami wave”) will extend. When the wave reaches the atom that has the covalent radius different from the one of silicon atoms, then the wave energy is spent on pushing this atom out the lattice point. Since the deformation field around this atom spreads on a distance of about three or four lattice parameters, the vacancy will be located at this distance from the interstitial ion Al 1cm03.0 − 0/ SiI − ++, but not in the immediate vicinity to him. It is very likely that both vacancy and interstitial silicon atoms in the crystal lattice can move only using the activation way, and the migration energy depends not only on the charge state, but also on the localization of the defect in the lattice. 2. Results and discussion To restore the electrophysical and optical properties of semiconductor materials and devices based on them, the annealing of radiation defects created by nuclear radiation is commonly used. In addition to migration of defects to the sinks and their dissociation, it must be taken into account the annealing of vacancy-type defects with interstitial and di-interstitial atoms. When the concentration of defects in solids exceeds the equilibrium level at a given temperature, then, under appropriate conditions, these defects will interact not only with each other but also with background impurities and thus will reduce the free energy of the crystal. The annealing can be described as equations similar to those used in the chemical kinetics. Accumulation or disappearance of the concentration of defects P caused by the annealing process of the first order can be defined through the constants of rate K: 0)( =−+ i m i i i PPK dt dP , j j j PK dt dP −= . (1) It should be noted that the use of first-order kinetics is valid in the case, when the concentration of sinks is at least an order of magnitude greater than the concentration of radiation defects [15]. Usually the rate constant is equal , where )/(exp ,, , TkEAK ji a ji ji −= jiA , are the frequency factors; are the activation energies of processes; k is the Boltzmann constant; Т is an absolute temperature; j, ji aE , i is the number of channels for annealing and accumulation of defects, respectively. Integrating the equation (1) and adding the various channels of annealing or accumulation of defects, one can obtain the following approximation © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 214 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine ] ] ( )[ ( )( )[ ,/expexp1 /expexp)( 1 00 1 1 0 ∑∑ ∑ == = −−−−+ +−−= n l l m i i a ii m k j j a jj PTkEtAP TkEtAPTP (2) at the condition that Р(200 K) = 1.0 in relative units. The latter term is related with the fact that the annealing process is not completed. Here is the share of annealing of defect concentration in j-manner; is the share of accumulation of defect concentration in i-manner; t is the annealing time. The more stable defect can be formed, for example, by the annealing of another defect. Interstitial silicon atoms movable at room temperature can anneal not only centers but also divacancies. The change in rates of concentrations inherent to vacancies and centers are equal lP00 jP0 i mP -A -A badt d ττ ]V[]I[]V[ −= , b i dt d τ ]V[]VO[ = , (3) where ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ == Tk Ea aa a exp11 0νν τ and ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ == Tk Eb bb b exp11 0νν τ are the lifetimes of interstitial atom and vacancy, respectively, up to the capture by di-vacancy and interstitial oxygen; [V], [І], [VOі] are the concentrations of vacancies, interstitial atoms, and centers, respectively; , are the frequency pre-exponential factors; E -A 0 aν 0 bν a, Eb are the activation energy of divacancy annealing and the activation energy of center formation, respectively. -A The solutions of Eqs (3) are the functions of the annealing temperature T. The change in the concentration of centers as dependent on the annealing temperature (which entering into the formulas for ν -A а and νb) of the irradiated silicon is equal ( )[ ]( ( )[ ]) ( ) ./exp1 exp1]I[]VO[ 0 baab bai t t νννν νν −−−− −−−= (4) Changing of the concentration of vacancies depending on the temperature of annealing of irradiated silicon is equal ( ) ( )[ ( abbaa tt ] )ννννν −−−−= /expexp]I[]V[ 0 , (5) where [І0] is the initial concentration of interstitial silicon atoms. The obtained equations (1)-(5) can be applied to describe the isochronal annealing of centers by using the experimental data of R.E. Whan [16]. In this work, after irradiation of grown by Czochralski (Cz) with 2 MeV electrons at the temperature close to -A Si-n C50°− with the fluence and after annealing step by 25 °С during 20 min, the vibration band at at 80 K was measured. The samples of with specific resistance of 10 and 100 Ohm⋅cm, doped with phosphorus, contain about of interstitial oxygen atoms. 218 cm101 −× 1cm836 − Si-n 317 cm107 −× The oxygen-vacancy complex ( center) is one of the main radiation defects in silicon. When capturing the vacancy, the oxygen atom is shifted and, filling it, is located almost in the vacant lattice point. The results of the uniaxial compression show that the energy of atomic reorientation of center is about 0.38 eV [17] and reorientation can occur at room temperature. center has six possible orientations in the silicon lattice. Oxygen is displaced from the center of tetrahedral substitutional position in the line of 〈100〉 and linked with two silicon atoms, forming the Si-O -A -A -A i-Si bonds. Thus, center has no dangling bonds. Two vibrational absorption bands correspond to center: (in the state of VO -A -A 1cm830 − 0) and (in the state of VO1cm877 − –) when measuring at room temperature. The band at (VO1cm889 − 2i) grows with the activation energy of Еа = 1.86 еV and the frequency factor [18]. 111 s106 −×=ν As reported in [19], there observed is simultaneous appearance of two defects with levels in the silicon forbidden band ЕV + 0.35 еV and ЕV + 0.38 еV during the annealing of centers. The first level is not stable at room temperature, and its disappearance is accompanied by a further increase of the concentration of C -Ci iOi-defects with the level of ЕV + 0.38 еV. Interstitial carbon defect arises as a product of the interaction between the silicon atom and substitutional carbon (Cs) by the capture mechanism [20]. In the first configuration, C and Si atoms are placed along the 〈001〉 direction, occupying the vacant lattice point of silicon. This configuration is the most stable one for Сі in silicon. The reaction of Cs + ISi → Сі is considered as exothermic reaction with the release of 1.2 еV energy. Therefore, carbon shifts from the lattice point into the interstitial position and moves in the silicon lattice with the energy Еm = 0.87 еV. This Сі configuration interacts with Oі that immediately occupies a vacant lattice point, forming СіVOіISi-defect (ЕV + 0.35 еV). At room temperature, this defect is not stable, since ISi leaves to sinks, forming, in our opinion, СіVOі-defect (ЕV + 0.38 еV). The increase in energy of the СіVOі donor defect by 0.03 eV indicates that it is ISi that leaves to sinks at room temperature [21]. Сі in the interstitial position interacts with Oі with the activation energy 0.87 eV corresponding to this process, forming (СО)і-defect with the energy position ЕV + 0.34 еV [22]. However, the activation energy during the interaction with centers decreases down to 0.77 eV, since the barrier of С -A і interaction with VOі is less than that with Oі. Fig. 1 shows the isochronal annealing of centers described using Eq. (2) and nine channels of accumulation and disappearance of the vibrational band at . -A 1cm836 − 215 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. 200 300 400 500 600 700 0.0 0.2 0.4 0.6 0.8 1.0 D ef ec t c on ce nt ra tio n, re la tiv e un it Tanneal , K [V] x 10 [V] x 10 3 4 1 2 Fig. 1. Calculation of the isochronal annealing of defects in the electron-irradiated Cz-Si: 1 – A-centers (VO), 836 cm–1; 2 – Ci-centers (interstitial carbon), 922 cm–1 ; ○, ● – the experimental data obtained in [16]; –––– – the theoretical description made by the authors of this paper; 3 and 4 – the calculated dependences of vacancy generation (V) as consistent with reactions V3 + I2 → V and V2 + I → V, respectively, and annealing V + O = VO. Parameters for calculations and the reaction types for accumulation and annealing of centers are presented in Table 1, in which Е -A а and ν are the activation energy of accumulation and disappearance of centers and their frequency factor; h is the concentration of defects on different stages of annealing in relative units; N -A 0 is the concentration of sinks; T is the temperature of center for annealing stage; D0 is the pre-exponential factor of the diffusion coefficient of the mobile defect; R is the radius of capturing the mobile defect by center at the temperature of center at the annealing stage. -A As seen from Table 1, accumulation of centers occurred in three temperature ranges. In the interval of 250-300 K, the migration energy of Frenkel pair is similar to the migration energy of vacancy [2]. It can be assumed that dissociation of Frenkel pairs occurs in the vicinity of О -A і. Second 300-400 K and third 350-500 K stages of centers accumulation are described by Eq. (4). Concentrations of vacancies captured by О -A і are presented as curves 3 and 4 in Fig. 1. They were determined using Eq. (5). In these stages the generation of vacancies is a process of annealing of V3 and V2 defects during the capture of I2 and I, respectively. As seen from Table 1, the annealing of centers occurs by capturing the di-interstitial and interstitial atoms of silicon, as well as the oxygen dimer. Moreover, center can be reorientated during the capture of interstitial atom. Then the activation energy of VО -A -A і annealing will increase up to 1.3 eV. Naturally, in grown using the Czochralski method, the free oxygen atoms (О Si-n і) are the main sinks, but in the vicinity of 500 K the deformation fields reduce the migration energy of centers on sinks down to Е-A а = 1.5 еV. It is possible that within this range clustering the vacancy- type defects occurs. Thus, made in the work [1] suggestion that within the range of annealing temperatures 300-400 °С dissociation of centers occurs was not confirmed. More likely that center only partially dissociates in the course of migration to the sink (O -A -A і) with formation of VO2i-defect (the band of ). It was showed in [23] that the capture radius of carbon by the interstitial atom of oxygen was equal to R = 17 Å. After revision of the oxygen contents in [24], the capture radius is 1cm889 − Si-Cz Table 1. Parameters of the isochronal annealing of Ci and A-centers in the electron-irradiated (the experimental data obtained by R.E. Whan [16]). Si-Cz Procedure Reaction Eа, eV 1s, −ν h, relative unit iii C,VO,ON 3cm− scm, 2 0D K,T R, Å V + Oi → VOi 0.8 10107× 0.035 17107× 0.05 282.75 16.2 I2 + V3 → V V + Oi → VOi 0.74 0.8 6105× 7102× 0.13 Formation of A-centers, 836 cm–1 I + V2 → V V + Oi → VOi 0.91 0.8 6105× 6101× 0.15 I2 + VO → Oi + I 0.74 12107× 0.025 171046.3 × 7.89 229.37 20.4 I + VOi → Oi 0.91 11101× 0.325 171097.2 × 0.13 318.17 21.5 I + → OiVO ← i 1.3 12101× 0.17 171056.2 × 1.25 425.04 24.9 Drift in the deformation field 1.5 12102× 0.15 481.03 O2i + VOi → VO3i 1.7 12103× 0.1 171006.2 × 4.77 539.13 24.3 Annealing of A-centers, 836 cm–1 VOi + Oi → VO2i 1.86 12105.1 × 0.53 17107× 1.06 601.26 16.2 Annealing of Ci, 922 cm–1 I + Cs → Ci Ci + VOi → CiVOi 0.5 0.77 7107.1 × 9108× 0.12 0.67 ~ 17103× 17105.3 × 51015.2 −× 31076.8 −× 240.5 295.5 21.5 20.3 © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 216 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. equal to R = 14.7 Å. The oxygen atom in the interstitial position creates deformation of the silicon lattice, therefore during migration of interstitial carbon toward oxygen, it needs to overcome the potential barrier depending not only on the distance to the oxygen atom, but also on the motion path of carbon. There are three such motion paths: TH, TB, THTB. Here TH is a transition of the interstitial atom from tetrahedral in hexagonal position in the silicon lattice; TB is a transition of the interstitial atom from tetrahedral in the bond centered position; THTB is a transition from tetrahedral in hexagonal position, then in tetrahedral and in bond centered position. The experimental data for the metastable complexes of СіОі are presented in [1]. According to the proposed model [25], the oxygen and carbon atoms do not form the direct bonds, therefore their local vibrational modes can be represented as “oxygen- related” or “carbon-related”. Accumulation and annea- ling of the concentration of various local vibrational bands were calculated according to Eq. (2) using the experimental data obtained in [24]. The direction of the movement of Сі to Оі depends on the value of barrier that should be overcome by Si atoms when moving to Оі. Herewith, it was taken into account that the deformation field decreases in inverse proportion to the square of the distance from the Оі atom. Let us assume that we consider an elastic medium with the center of expansion at the origin of coordinates, where the interstitial oxygen atom is located. It means that under some small radius r0 there is the radial displacement of medium (δ0). The problem was solved in [26] in approximation of lattice deformation without changing its volume. The deformation energy is equal to 2 003 16 δμπ= rUdef , (6) where μ = 0.63 еV/Å3 is a modulus of elasticity under shift. At positive δ0 (it is expansion) the medium was compressed along the radius and was stretched tangentially. The radial shift is 0 2 0)( δ⎟ ⎠ ⎞ ⎜ ⎝ ⎛=δ r rr . (7) Parameters for the annealing of precursors for formation of the СiОi stable defect are presented in Table 2. The activation energies of accumulation and annealing of СiОi metastable defects were determined, and the directions of Сі motion were indicated. The value of the potential barrier (Еb) was defined as , where Е iC mab EEE −= а is the activation energy of Сі motion; is the migration energy of interstitial carbon atoms (С eV87.0iC =mE і). The migration energy of Сі was determined by the annealing of band (Fig. 2). The temperature of the center stage 1cm1.922 − ( )T and the frequency jumps of Сі at this temperature were also determined and presented in Table 2, where the concentration of defects was indicated in relative units (N). On the basis of the determinate barriers for movement of Сі to Оі, in Fig. 3 we show the schematic model of СiОi metastable pairs. According to the proposed model, the bands related to III group of precursors in СiОi formation can be annealed with the activation energy Еа = 2.5 еV, if the Сi atom will jump to II group or the Оі atom will migrate closer to the Сi atom. Annealing of these bands will also occur if the Сi atom with the migration energy shifts closer to oxygen, which will form herewith one bond more with the silicon atom. eV87.0iC =mE According to this model, the vibrational band of should be defined as related to two oxygen atoms (О 1cm4.967 − 2i), since only О2i has the migration energy of . From presence of the activation energy of annealing , the band of 967,4 cm eV7.12iO =mE eV87.0iC =aE –1 should be related to the III group of precursors for СiО2i formation. The description of the annealing of some bands is presented in Fig. 2. In spite of the fact that the band of was related to the III group of precursors, in which the С 1cm1.910 − і carbon atom is located closest to the Оі atom, its growth and annealing occurs 30 K earlier than these for the other precursors of СiОi. Therefore, it is assumed that this is related with different ways of Сі motion to Оі. Usually, the vibrational band of 865,9 cm–1 is considered as related to the СiОi stable defect that is annealed with energy of Еа = 1.86 еV. Herewith, the CsOi defect is formed with the activation energy of 1.86 еV, and in this region of temperatures the centers are also annealed with the migration energy of to the sinks (О -A eV86.1iVO =mE і atoms) with forming the band of 889 cm–1. This band increases with the VO2i-defect formation energy equal to Еа = 1.86 еV and with the frequency factor equal to . 111 s106 −×=ν 260 280 300 320 340 0.0 0.2 0.4 0.6 0.8 1.0 1.2 A bs or pt io n co ef fic ie nt , c m -1 Tanneal , K 922.1 865.9 910.1 x 5 1086.2 967.4 Fig. 2. Calculation of changes in intensities of absorption bands associated with interstitial carbon-related defects upon 20 min isochronal annealing of electron-irradiated samples. ■, □, ●, ▲, $– the experimental data obtained in [24]; ––––– – the theoretical description made by the authors of this paper. Si-Cz © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 217 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. Table 2. Parameters of the isochronal annealing of precursors of CiOi-defect formation in the electron-irradiated Cz-Si (the experimental data obtained by L.I. Khirunenko et al. [24]). Vibrational band absorption, сm-1 Motion of Сi Eа, eV Eb, eV K,T 1 0 s,expν − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − Tk Eb N, relative unit to Oi from Oi 1.1 1.7 0.23 0.83 275.6 286.15 4.67×1012 1.20×1012 0.27 0.13 iO1059.6 tо Oi 1.7 0.83 295.64 3.90×1011 0.4 tо Oi 1.1 0.23 286.0 1.24×1012 0.6 iC858 tо Oi from Oi 1.7 1.1 0.83 0.23 291.19 295.14 6.65×1011 4.14×1011 0.43 0.17 from Oi tо Oi 1.7 1.1 0.83 0.23 288.3 294.2 9.29×1011 4.59×1011 0.1 0.11 iC2.218 tо Oi from Oi 1.7 1.1 0.83 0.23 311.5 324.2 7.45×1010 2.13×1010 0.12 0.09 tо Oi 1.7 0.83 275.37 4.83×1012 0.195 iO3.1097 tо Oi 2.5 1.63 290.9 6.92×1011 0.195 tо Oi 1.7 0.83 279.35 2.87×1012 0.17 iC3.6011 tо Oi from Oi 2.5 1.7 1.63 0.83 293.6 299.8 4.93×1011 2.45×1011 0.07 0.10 tо Oi 1.7 0.83 291.27 6.53×1011 0.79 iC.20861 tо Oi from Oi 2.5 1.7 1.63 0.83 310.27 323.6 8.35×1010 2.13×1010 0.29 0.50 tо O2i 1.7 0.83 291.14 6.43×1011 0.65 2iO4.967 from O2i tо O2i 1.7 0.87 0.83 0 316.35 319.7 4.19×1010 3.0×1010 0.3 0.35 tо Oi 2.5 1.63 278.5 3.19×1012 0.10 iC0.119 from Oi tо Oi 2.5 0.87 1.63 0 290.15 290.5 7.31×1011 5.0×1011 0.06 0.04 tо Oi 2.5 1.63 278.79 3.08×1012 0.055 iC2.749 from Oi 2.5 1.63 290.21 7.41×1011 0.055 iiOC65.98 0.77 2.5 0 1.73 289.0 317.25 1.7×1010 9.88×108 0.54 0.35 iC2.129 I + Cs → Ci 0.91 0.87 0.4 0 263.7 3.4×106 1.65×1012 0.16 1.39 Based on data obtained using a magnetic spectrometer in [27], it was found that center is the amphoteric defect, and it has not only the acceptor (Е -A с – 0.17 eV) but also the donor (Ес – 0.76 eV) level. Fig. 4 presents the isochronal annealing within the temperature range 300…800 K of ( ), doped with 1 % of germanium, after irradiation on WWR-M reactor by the fluence of fast neutrons at room temperature. The Fermi level position in such samples is Е 〉〈GeSi-p 314 0 cm1005.1 −×=p 2o13 cmn107.1 −⋅×=Φ v + 0.3 eV. Thus, we can observe only the annealing of defects that are located above this level. On the curve of annealing of effective carrier concentration (Fig. 4), experimentally obtained by us, three stages of changes in the concentration of holes in the valence band of were found, and one of these stages shows the annealing of donor level of center. Si-p -A At the first stage (Тann = 50…300 °С), the defect, possibly (Е+ 2I m = 0.6…0.2 eV [28]), is annealed with parameters and Е1s20 −=ν а = 0.4 eV. If it is (Е + 2I v + 0.45 eV), then germanium lowers the migration energy of this defect. It may be also joining the divacancies in the form of a tetravacancy. The second stage of annealing has parameters Еа = 1.86 eV and , and it is observed within the temperature range of Т 112 s102 −×=ν ann = 300…320 °С. Since both the energy of this process and the temperature range of annealing are related to center, moreover, we study the samples of the very , then, in our opinion, Fig. 4 shows the annealing of the donor level of center. The third stage of annealing within the temperature range 320…500 °С is formed with the following parameters: Е -A Si-p -A а = 1.5 eV and . Up to date, it is not clear exactly what the defect is annealed in this area. 17 s105.1 −×=ν The description of the annealing of 866 cm–1 (СіОі) and 836 cm–1 (VO) bands and the growth of (С1cm1104 − sOі) band is presented in Fig. 5 according to the experimental data [29] obtained for Cz-Si irradiated with 2.5-МеV electrons at room temperature with the fluence . The energy of dissociation or formation of defect is determined by the 218 cm101 −× © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 218 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. binding energy of components plus the migration energy of a mobile defect. Such mobile defects in this case are vacancy or interstitial carbon atoms (Сі). We were lucky in this case: within the range of temperatures close to 550 K (Fig. 5) the formation stage of СiОi and VOі is observed. Our calculation showed that the migration energy of Сі within this temperature range is equal to , and the migration energy of vacancy – . eV16.1iC =mE eV1.1V =mE Thus, in comparison with the migration energies of Сi and ISi at room temperature, their energy of migration increases by 0.3 еV under Т ~ 550 K, confirming the model that determines the migration energy of defect depending on the degree of delocalization of this defect [8]. In this case, most likely the defects exist in the neutral charge state. The most interesting is that the same concentration of vacancies and interstitial carbon atoms is generated. Thus, one can assume that in this temperature range dissociation of di-vacancy modified by the stable ISiCi defect occurs in accord with the reaction of V2ISiCi → V + Сi. o Ci (III)Ci (II) E, eV 1 2 -1 -2 -3 Ci Ci (I) Oi Em Oi Eb1. 63 r0 a 3r0 0. 83 0. 23 R=14.7 A Em C i 2a Fig. 3. Schematic model of CiOi metastable pair. Eb is the energy of deformation barrier around Oi; Em – the migration energy; Ea = Em + Eb – the energy of motion activation; r0 ≈ 2.35 Å – the minimum distance between atoms; a ≈ 5.43 Å – the lattice parameter of silicon. 8⋅1027⋅1026⋅1025⋅102 p ef f , cm -3 T, K 2⋅1013 4⋅1013 6⋅1013 8⋅1013 1.0⋅1014 3⋅102 4⋅102 Fig. 4. Dependence of the effective concentration of holes on the temperature of annealing for (~1%) (p〉〈GeSi-p 0 = = 1.05×1014 cm–3) after irradiation by the fluence Φ = = 1.7×1013n0 cm–2 of fast-pile neutrons. The isochronous annealing was carried out for 25 min within the temperature interval 300 to 800 K. 300 400 500 600 700 0 1 2 3 4 In te gr al a bs or pt io n co ef fic ie nt , c m -2 Tanneal , K 1104 cm-1 (CsOi) x 0.3836 cm-1 (VO) 866 cm-1 (СіОі) 1 2 3 Fig. 5. Changes in the integrated absorption intensity of the bands due to VO, CiOi and CsOi complexes upon isochronal (30 min) annealing of a sample ([Si-Cz 16О] = 1.05×1018, [12C] = 3×1017 cm–3), electron irradiated (1×1018 cm–2) at room temperature. □, ○, × – the experimental data obtained in [29]; – ––– – the theoretical description made by the authors of this paper. Fig. 6. Models for СіОі [1]. (а) Divalent oxygen model, (b) trivalent oxygen model. Gray, black, white atoms are Si, C, O. Crystallographic axes and principal directions of the B tensor are also shown. The calculation of the kinetics of formation of vibrational band showed that in the temperature region of 250-310 K the process passed with the activation energy Е 1cm9.865 − а = 0.77 еV, and within the temperature region 310 to 330 K with the activation energy Еа = 2.5 еV. The latter process can be explained as the movement of the interstitial atom Oі to the vacancy that is left by the carbon atom: CsОі → СіVOі. It is the interstitial atom Oі that has the activation energy of diffusion in silicon equal to 2.5 eV. The band of has also the activation energy of annealing Е 1cm2.1086 − а = 2.5 еV, but it is found in the II group, therefore only the movement of Оі tо Сі can be responsible for this stage of СiОi formation. And formation of СiОi with the activation energy of 0.77 еV begins at the temperature close to 250 K, when the precursors are absent yet. Therefore, it is more probable that carbon modifies center with formation of the vibrational band at and with the donor level location in the forbidden band at Е -A 1cm9.865 − V + 0.38 еV [19]. The authors of [30], using DLTS-measurements, related the donor level ЕV + 0.38 еV with the complex. According to the VO-C © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 219 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 213-221. © 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine ve charged states are deeply located in the valence band. References 1. R idd donors in Si // Phys. Rev. B 2. crystals // Phys. Rev. B 66, ). 3. Inst. of 4. hysics and Atomic Energy 5. aukova dumka, Кiev, p. 200, ssia 6. tures // Phys. Rev. 7. ns // Phys. Rev. B 52 (23), 8. // Phys. 9. cts in 10. Inst. of Phys. London and Bristol, p. 12-29, 11. model of modification of the donor and acceptor levels of radiation defects by the background impurities such as Сі and Oі, in the work [14] it was showed that the interstitial carbon increases the energy of acceptor levels in the silicon forbidden band and reduces the energy of donor levels by 0.035 eV. Therefore, the donor level of center in silicon will be the level of (0/+) Е -A V + 0.415 еV (ЕV + 0.38 + 0.035 еV = ЕV + 0.415 еV), and the donor level of СiОi will be ЕV + 0.34 еV and of СiО2i – ЕV + 0.39 еV, as indicated in [31]. In this case, the Сі carbon atom in the temperature range of 550 K pushes out Оі into the interstitial position, overcoming the barrier of Еb = 1.86 − 1.16 = 0.7 еV, and forms the CsOi defect. It is known [32] that under irradiation the stable defect of СiISi is formed and can be captured by the interstitial oxygen; herewith Сi and ISi in the СiISi defect occupy a vacant lattice point in silicon. Then, the reaction of СiISi + Оi → СiVОi + ISi will occur within the temperature range 310 to 330 K, moreover the oxygen atom with the migration energy of initiates this reaction. eV5.2iO =mE According to the simulation results carried out in [24], the lowest binding energy of Сі and Oі within the metastable СiОi complex related to the III group is equal to 0.7 еV. This energy results in a tangential displacement of Sі1 and Sі2 atoms as shown in Fig. 6 [1]. On the assumption that Сі and Оі atoms are found at the distance r0 ≈ 2.35 Å from each other, the tangential displacement δ0 = 0.17 Å is equal to the radial one, where the Сі atom overcomes the barriers. According to the expressions (6) and (7), the distances of Сі atom from Оі in the moments when Сі atom overcomes the barriers determined by us are calculated (Table 2). The first and third barriers are found at a distance from oxygen, equal two and one lattice parameter of silicon, respectively. The second barrier (0.83 eV) is located at the distance of three minimum distances (3r0) between atoms in the silicon lattice. 3. Conclusions The centers (VO) annealing and transformation of precursors for formation of the stable С -A iОi defect during the annealing are described. The distance between the interstitial atoms of carbon (Сі) and oxygen (Оі) at the moments when carbon overcomes the barriers during its migration inside the volume of the radius (14.7 Å) for capturing Сі by the atom Оі has been determined. From the description of the A-center formation in the annealing process, it has been experimentally found that the migration energy of vacancies ( at ~380 K and at ~550 K) and for the interstitial carbon ( at 280 K and at 520 K) in the silicon lattice depends on temperature. 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The kinetic of point defect transformation during the annealing process in electron-irradiated silicon

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