Nucleation, growth and transformation of microdefects in FZ-Si
The physical model of microdefects formation in dislocation-free FZ-Si single crystals is offered. Experimental results and theoretical data allows to approve that recombination between vacancy and self-interstitials at high temperatures is hampered by an entropy barrier. Established is that the pro...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2004
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irk-123456789-1181082017-05-29T03:03:52Z Nucleation, growth and transformation of microdefects in FZ-Si Talanin, V.I. Talanin, I.E. The physical model of microdefects formation in dislocation-free FZ-Si single crystals is offered. Experimental results and theoretical data allows to approve that recombination between vacancy and self-interstitials at high temperatures is hampered by an entropy barrier. Established is that the process of microdefects formation in silicon proceeds simultaneously by two independent mechanisms: the vacancy and interstitial ones. 2004 Article Nucleation, growth and transformation of microdefects in FZ-Si / V.I. Talanin, I.E. Talanin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 16-21. — Бібліогр.: 50 назв. — англ. 1560-8034 PACS: 61.72.Bb; 61.72.Ji; 61.72.Yx http://dspace.nbuv.gov.ua/handle/123456789/118108 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The physical model of microdefects formation in dislocation-free FZ-Si single crystals is offered. Experimental results and theoretical data allows to approve that recombination between vacancy and self-interstitials at high temperatures is hampered by an entropy barrier. Established is that the process of microdefects formation in silicon proceeds simultaneously by two independent mechanisms: the vacancy and interstitial ones. |
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Talanin, V.I. Talanin, I.E. |
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Talanin, V.I. Talanin, I.E. Nucleation, growth and transformation of microdefects in FZ-Si Semiconductor Physics Quantum Electronics & Optoelectronics |
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Talanin, V.I. Talanin, I.E. |
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Talanin, V.I. |
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Nucleation, growth and transformation of microdefects in FZ-Si |
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Nucleation, growth and transformation of microdefects in FZ-Si |
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Nucleation, growth and transformation of microdefects in FZ-Si |
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Nucleation, growth and transformation of microdefects in FZ-Si |
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Nucleation, growth and transformation of microdefects in FZ-Si |
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nucleation, growth and transformation of microdefects in fz-si |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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Nucleation, growth and transformation of microdefects in FZ-Si / V.I. Talanin, I.E. Talanin // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 16-21. — Бібліогр.: 50 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT talaninvi nucleationgrowthandtransformationofmicrodefectsinfzsi AT talaninie nucleationgrowthandtransformationofmicrodefectsinfzsi |
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2025-07-08T13:22:43Z |
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2025-07-08T13:22:43Z |
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1837085193116057600 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 1. P. 16-21.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine16
PACS: 61.72.Bb; 61.72.Ji; 61.72.Yx
Nucleation, growth and transformation
of microdefects in FZ-Si
V.I. Talanin, I.E. Talanin*
Zaporozhye Institute of State & Municipal Government, 70B, Zhukovskii str., 69002 Zaporozhye, Ukraine
E-mail: V.I.Talanin@mail.ru
*Zaporozhye State Engineering Academy, 226, prospect Lenina, 69006 Zaporozhye, Ukraine
Fax: +380 (612) 601498
Abstract. The physical model of microdefects formation in dislocation-free FZ-Si single crys-
tals is offered. Experimental results and theoretical data allows to approve that recombina-
tion between vacancy and self-interstitials at high temperatures is hampered by an entropy
barrier. Established is that the process of microdefects formation in silicon proceeds simulta-
neously by two independent mechanisms: the vacancy and interstitial ones.
Keywords: microdefects, silicon, interstitial, vacancy.
Paper received 29.11.03; accepted for publication 30.03.04.
1. Introduction
During the production of dislocation-free silicon single
crystals, it is necessary to solve the problem of their struc-
tural perfection. After the crystals are grown, structural
microdefects form during cooling, which may include
agglomerates of point defects (vacancies or silicon self-
interstitials) and impurities. These structural defects can
detrimentally affect the reliability of semiconductor de-
vices and their performances.
The systematic study of microdefects began in 1960s,
using methods of selective etching, decoration and X-ray
topography [1�3]. On the basis of these studies, two types
of microdefects were identified: A-microdefects (usually
revealed as large etch-pits with smaller concentration)
and B-microdefects (small etch-pits with higher concen-
tration) [4]. Experience of crystal quenching [5] has shown
that B-microdefects are formed first. Using transmission
electronic microscopy (TEM) it was established that
A-microdefects [6] and B-microdefects [7, 8] have an in-
terstitial character. Typical A-microdefects are observed
in stratified distribution at crystal growth rates of
V = 1�3.5 mm/min�1, and in uniform distribution at
V < 1 mm/min�1. B-microdefects are observed in strati-
fied distribution at V ≤ 4.5 mm min�1. Such a distribution
of microdefects reflects the distribution of their nuclea-
tion sites. During crystal growth, there is a fluctuation in
the temperature due to the rotation of the crystal and a
melt convection occurs [9]. Therefore, the microdefects
grow, repeating crystal growth and stopping growth [10].
Further studies of silicon single crystals grown at high
growth rates (more than 4.5 mm/min�1) have shown that
these monocrystals contain uniformly distributed micro-
defects; this was revealed under selective etching as matt
areas. Veselovskaya et al. [11] observed these defects in
FZ-Si by selective etching and decoration techniques, and
classified them as C- and D-microdefects depending on
their distribution and concentration. Both these types of
microdefects were found as areas of uniformly distributed
defects with high densities. The difference between C-
and D-defects is in the distribution of microdefects in these
areas. D-microdefects are primarily concentrated as chan-
nels in a central part of the crystal whereas C-microdefects
are revealed as rings or contours of an incorrect form.
Later, Roksnoer et al. [12], using X-ray topography follo-
wed by decoration with copper, suggested that D-mic-
rodefects have a vacancy characteristic in Czochralski
grown (Cz-Si) silicon.
Various theoretical models were suggested to explain
the regularities of formation of microdefects in silicon.
Main problems were in the assumptions about the domi-
nant type of point defects in crystal, their concentration,
and interaction between them. In some models [6, 10,
13], it was assumed that the dominating type of point
defects in crystal are self-interstitials. In other models
[14, 15], it was supposed that the dominating type of de-
fects are the vacancies. In contrast, authors of Refs [16,
V.I. Talanin, I.E. Talanin: Nucleation, growth and transformation of microdefects in FZ-Si
17SQO, 7(1), 2004
17] suggested simultaneous independent coexistence of
both main types of point defects at high temperatures.
However, none of these models could explain experimen-
tal results, which were obtained later with TEM [18].
According to the commonly accepted Voronkov
theory [19�21], the recombination rate between isolated
vacancy and interstitial defects is high and further the
diffusivity of interstitials is higher than the diffusivity of
vacancies near the melting point, and finally the concen-
trations of vacancies is higher than the concentrations of
interstitials at the melting point where both concentra-
tions are in thermal equilibrium. Only the microdefects
of either interstitial type (A- and B-microdefects, if the
concentration of self-interstitials is higher than the con-
centration of vacancies) or only the vacancy type (D-mic-
rodefects, if the concentration of vacancies is higher than
the concentration of interstitial atoms) are formed in the
crystal. According to [19], the type of dominating point
defects depends on the parameter V/G (V � growth rate of
crystal, G � axial temperature gradient): if V/G < Ccrit,
then interstitial atoms of silicon dominate in the crystal, if
V/G > Ccrit, then the vacancies dominate. Furthermore,
these results based on data from Refs. [10, 12].
Thus, the sense of the Voronkov model consists of the
following: a) existence of recombination between self-
interstitials and vacancies for temperatures close to the
temperature of smelting; b) supposed was the only va-
cancy nature for primary grown-in microdefects; c) inde-
pendent existence of areas with only interstitial and only
vacancy microdefects (see Fig. 1).
2. Experimental methods
Non-doped monocrystals of high resistivity (2200�
�4000 cm) n-type silicon by diameter of 30 mm were
grown by floating zone technique in vacuum. The number
of passes of a melting zone varied from 2 up to 10. The
concentration of oxygen and carbon, defined by IR-ab-
sorption was less than 5·1015 cm�3. The crystals received
at a constant growth rate in a range 1�9 mm/min�1. Some
crystals were obtained with modification of growth rate
on fixed length.
In these crystals, if growth conditions are changed,
we can observe all the types of microdefects. When the
crystals diameter is increased, the growth condition are
changed. As a result, in largescale crystals we can ob-
serve only some types of microdefects.
The method of selective etching of the cross-sections
of crystal [22] with subsequent TEM-analysis was used
to reveal the distribution of grown-in microdefects. The
TEM studies were performed using the methods of the
�black-white contrast�[23], 2,5D [24] and �inside-out-
side contrast�[25]. Also applied were electron microscopes
JEM-7A and TSEM-200 with accelerating voltage up to
100 kV. For such voltage the introduction of radiation
defects is excluded, i.e. the quality of experiment is im-
proved.
3. Results and discussion
Summarizing all the experimental results about the physi-
cal nature of microdefects in dislocation-free single crys-
tal FZ-Si with a diameter of 30 mm, then using classifica-
tion [11] it is possible to conclude that:
1. A-microdefects are interstitial dislocation loops with
sizes of 1�50 µm with a Burgers vector of b = 1/2
[110], which are in planes {111} and {110}.
2. B-microdefects are agglomerates of point defects of
an interstitial type with sizes of 20�50 nm, some of
which are in the plane {100}. Using TEM these are
represented as rectangles and rhombs in the plane
{111} with the parties on directions [110] and [100],
respectively.
3. D-microdefects of an interstitial type are agglomer-
ates of point defects with sizes of 4 to 10 nm. Consid-
ering these as small dislocation loops, it is possible to
conclude that they can be in planes {100}, {110},
{111} and have the Burgers vector b = 1/2 [100] and
b = 1/2 [110].
4. C-microdefects are completely identical to D-micro-
defects in TEM images, sign of deformation of crys-
talline lattice and their sizes.
5. D-microdefects are uniformly distributed B-micro-
defects.
6. In crystals obtained at high growth rates (more than
6 mm/min�1) microdefects of the vacancy type are
formed simultaneously with microdefects of the inter-
stitial type in the same regions of the crystal.
The experiments have shown that the nucleation and
growth of microdefects depends on conditions of crystal
growth (growth rate of crystal, cooling rate and tempera-
ture gradient) and on the concentration of impurities of
carbon and oxygen. Therefore, it is possible to offer a quali-
tative model of formation, growth and transformation of
microdefects in dislocation-free single crystals FZ-Si.
The analysis of literary data and the experiments in
this work show a significant role of self-interstitials in
high-temperature experiments. All the known types of
Fig. 1. Defect formation scheme according to the Voronkov theo-
retical model.
�defect-free�
regime
�vacancy�
regime
�interstitial�
regime
V, mm/min
N, cm�3
18
SQO, 7(1), 2004
V.I. Talanin, I.E. Talanin: Nucleation, growth and transformation of microdefects in FZ-Si
microdefects in FZ-Si (i.e. A-, B-, D-defects) have an in-
terstitial nature. Furthermore, in researches of a gold
diffusion in silicon it was shown that the atoms of gold
take substitutional (Aus) and interstitial positions (Aui)
in silicon. The diffusion of gold in silicon is not explained
using the Frank-Turnbull mechanism (Aui + V ↔ Aus)
[26], but logic explanation may be given in the kick-out
mechanism [27]: Aui ↔ Aus + I.
Also we have the experimental results that the signifi-
cant role is played by vacancies [16, 28]. Thus, the corre-
lation of thermodynamic accounts and experimental data
is possible only in the model that suppose coexistence of
self-interstitials and vacancies in a thermal equilibrium
at high temperatures. In this model, the diffusivity of im-
purities is the sum of diffusivities on interstitials and on
vacancies [28]. In Ref. [29] theoretical models of a
selfdiffusion in silicon with simultaneous participation
of self-interstitials and vacancies were offered. It was
shown [29] that interstitial and vacancy contributions to
a self-diffusion are equalized in the vicinity 1100 0C,
and for higher temperatures during a self-diffusion the
selfinterstitials dominate whereas for a lower tempera-
tures the vacancies dominate. The results obtained in Refs
[30, 31] particularly confirm this model.
In our TEM-researches, it is established that vacancy
microdefects occur together with interstitial microdefects
in crystals grown at V > 6 mm/min�1. A ratio of vacancy
and interstitial microdefects in samples obtained at V =
= 7.5 mm/min�1 is approximately 1 : 4. In crystals ob-
tained at V = 9 mm/min�1, interstitial and vacancy de-
fects coexist approximately in the identical concentra-
tion, i.e. 1 : 1. Thus, the critical growth rate of the crystal
for which vacancy microdefects occur is in the interval of
6 mm/min�1 < V < 6.5 mm/min�1 (Fig. 2).
If the concentration of vacancy and interstitial micro-
defects are approximately identical, it is possible to as-
sume that in equilibrium conditions vacancies and self-
interstitials exist simultaneously and also in approxi-
mately identical concentrations. The estimates from Ref.
[19] give the concentration of vacancies at the smelting
temperature are 1.5·1014 cm�3, but selfinterstitials are
1.3·1014 cm�3.
In the Voronkov theory [19], it is suggested that the
main role at the initial stage of disintegration of
oversaturated solid solution of point defects is played by
the process of a recombination between vacancies and
self-interstitials.
However, in Refs [16, 32] it was supposed that the
direct recombination between vacancies and self-
interstitials is hampered by the existence of an energy
barrier. Tempelhoff et al. [32] argued that the recombi-
nation takes place only on some centres (B- and A-micro-
defects, dislocations, surface of crystal), and the direct
recombination is impossible. In Refs [17, 33], it was dis-
cussed the theory of the energy barrier which is ham-
pered by direct recombination between vacancies and self-
interstitials.
In the Ref. [17], the local equilibrium was considered
eqv
V
eqv
IVI CCCC = , (1)
where CV is the concentration of vacancies; CI is the con-
centration of self-interstitials.
The order of values for times when the system achieves
an equilibrium in the absence of a recombinational bar-
rier can be calculated according to the formula:
04 rDSπ
τ
Ω
≤ , (2)
where Ω is the volume of an elementary cell; DS is the
self-diffusion constant; r0 is a recombination cut.
Estimates from Ref. [33] at DS = 10�15 cm2/s, Ò =
= 1100°Ñ, r0 = 5⋅10�8 cm give the values τ ≤ 0.05. This
value is 105 less than the experimentally observed values
[33]. Thus, the conclusion can be made that the recombi-
nation is determined not by a diffusion, but overcoming
the recombinational barrier exceeding the free energy of
diffusion by ∆G. The value 105 arises from the Boltzmann
factor )(exp kT
G∆ .
In Ref. [33], it was supposed that the recombinational
barrier is the enthalpy barrier and entropy component
Ò∆S is very small:
STHG ∆−∆=∆ (3)
However, in Ref. [34] remarked was that the intrinsic
point defects behave variously for the various tempera-
tures. Hence, the fluctuations of barrier values take place
whereas the barrier ∆H = 1.4 eV was considered to be
constant [33].
It was established that the barrier will be increased
with the increase of temperature [34]. Thus, the conclu-
sion was made that the recombinational barrier is deter-
mined as the entropy component from the equation (3)
[34].
The microscopic model of the entropy barrier was dis-
cussed in details in Refs [27, 35]. According to this model,
the point defects in silicon (vacancies and self-inter-
stitials) have an extended character at very high tempera-
Fig. 2. Experimental dependence of the ratio of concentration of
vacancy (N1) and interstitial (N2) microdefects on crystal growth
rate.
0
0.2
0.4
0.6
0.8
1
6 7 8 V, mm/min
N N/
1 2
V.I. Talanin, I.E. Talanin: Nucleation, growth and transformation of microdefects in FZ-Si
19SQO, 7(1), 2004
tures, i.e., one atom (or one vacancy) are extended on
some nuclear volumes (11 atoms occupied 10 cells). In
this model, the recombination happens only for of �si-
multaneous compression both from these defects in a
neighbourhood of one nuclear volume� [34]. The ex-
tended defect configurations have the greater number of
microstates than a point defect. Thus, the compression
lowered an entropy and, therefore, the entropy barrier
∆S < 0 exists. If the temperature is lowered the barrier is
considerably reduced and disappeared at low tempera-
tures when the defects easily recombine. Thus, the intrin-
sic point defects at high temperatures are extended, but
at low temperatures they have the dumbbell configura-
tion [34, 36]. The theory of extended defect configura-
tions and the recombinational barrier was confirmed in
Refs [37�39].
Thus, according to the theory [34] that was con-
structed in the correspondence with the Ref. [29] in sili-
con at high temperatures the joint coexistence of both
types of intrinsic point defects in equivalent concentra-
tion is observed. This fact determines the values of the
self-diffusion factor. Furthermore, �the condition of a
smallness� should be taken into account:
STH ∆<<∆ (4)
In Ref. [34], using the results of oxidizing experiments
and from the value 510)exp( =∆
kT
G the barrier was es-
timated as kS 5.11=∆ at T = 1373 K.
Our accounts according to (3)�(4) give the value of
the barrier at Ò = 1685 K (temperature of smelting) as
eV674.1=∆G .
Hence, the estimate of value from the equation (2)
needs to allow the recombinational barrier, i.e.:
)exp(4 0 kT
GrDS ∆−⋅
Ω
≤
π
τ (5)
The allowance of the barrier value gives the value of
53 min. Thus, for standard sizes of ingots and standard
time of its growth the recombination will have no time to
come true.
Therefore, we can estimate the length of area near to
crystallization front on which the recombination hap-
pens according to [19]:
GHH
kT
vi
m
)(
2 2
∆+∆
=l , (6)
where k is the Boltzmann constant; Tm is the smelting
temperature of; G is the axial temperature gradient; ∆Hi
and ∆Hv are energy of self-interstitial and vacancy for-
mation, respectively.
The value of G we can define from the equation (7)
with allowance that the gradient is defined on crystalli-
zation front:
)28.02.61exp(256100 −−+== VGL (7)
We did account for crystal that was grown at V =
= 9 mm/min�1 when the equality of concentrations of va-
cancy and interstitial microdefects was established. Thus,
from the equations (6)�(7) and at Tm = 1685 K,
,eV5.4=∆≈∆ vi HH V = 9 mm/ min�1 is established that
the mm25.6=l .
Then the time during which the intrinsic point defects
exist in recombinational area is define from the follow-
ing equation:
V
t
l= , (8)
where V is the growth rate of the crystal. At V = 9 mm/min�1
is established that t = 41.6 s. The accounts from equa-
tions (5)�(8) give at V = 2 mm/min�1 the following values:
mm25.3=l and min625.1=t . The results [19] show at
V = 2 mm min�1 the following values: mm2=l , min1=t
and s3.0≈τ .
We received the differences in accounts from the theory
[19]. It is possible because of that in Ref. [19] the theory
of enthalpy barrier is used and is used that the joint coex-
istence of both types of intrinsic point defects is denied.
According to [36], should exist separately for �intersti-
tial� and separately for �vacancy� of growth regimes,
i.e. according to [40]:
,
)exp(4
1
)exp(4
1
kT
HCrD
kT
HCrD
vv
v
ii
i
∆−
≈
∆−
≈
π
τ
π
τ
(9)
where Di and Dv are diffusivities of a self-interstitials and
vacancies respectively; Ci and Cv are concentrations of
self-interstitials and vacancies, respectively.
However, experimental results in Refs [41-47] and
our results confirm the fact of joint coexistence of micro-
defects with various sign of strains and the fact of joint
coexistence of intrinsic point defects. These results can
be estimated only in the theory of joint coexistence of
intrinsic point defects [29] and theory of the entropy bar-
rier [34]. According to the theory [29], in the equation (5)
the factor of a joint self-diffusion of vacancies and self-
interstitials is taken into account.
Thus, the experimental results which are in the good
correlation with theoretical data allows to approve that
at the temperature of smelting in dislocation-free silicon
single crystals simultaneous coexistence of equilibrium
concentration of vacancies and self-interstitials takes
place. Concentration of vacancies and self-interstitials
are approximately identical near the crystallization
front. The recombination between them in an initial stage
of their interaction at a high temperatures is hampered
by the entropy barrier. Thus, the disintegration of
oversaturation solid solution of intrinsic point defects
proceeds simultaneously by two mechanisms: the vacancy
and interstitial ones. The microdefects are formed in the
result of interaction of intrinsic point defects with impu-
rities of oxygen and carbon.
20
SQO, 7(1), 2004
V.I. Talanin, I.E. Talanin: Nucleation, growth and transformation of microdefects in FZ-Si
For vacancy mechanism, theoretically possible are
only vacancy aggregation and joint vacancy-impurities
aggregation [19]. Vacancy-impurities aggregation begins
earlier than only vacancy aggregation. Interstitial at-
oms of oxygen are very mobile, and, therefore, the for-
mation of complexes is simulated by a leaving interstitial
oxygen in positions of substitution Os:
Oi + VSi → Os → 2Os + 3Os +�+ nOs.
At lower temperatures, Os can be centres of formation
of microprecipitates of oxygen. It is possible to estimate
the concentration of oxygen precipitates [20]:
2/3
2
2/1
24
≈
DCkT
VEnC
N ccrcrv
η
ρ
πγ
, (10)
where Ñv is the concentration of vacancies; ρ is the den-
sity of silicon stices; ncr is the nuclei critical size; C is the
concentration of oxygen; D is the diffusivity of oxygen;
Ecr is the binding energy to one atom of oxygen; Vc is the
cooling rate.
For FZ-Si at Ñv ~ 1014 ñm�3, C ~ 1016 ñm�3, D ~
~ 10�9 ñm2/s we receive N ~ 5⋅1012 ñm�3. Direct TEM-
researches of vacancy and interstitial microdefects give
the values of their concentration ~ 1013 ñm�3.
When microprecipitates are formed, there is a surplus
of volume, and one vacancy will be consumed by a grow-
ing precipitate for each two oxygen atoms precipitated.
The aggregation is accompanied by issue of atoms ISi.
The absorption of vacancies and impurity by growing
microdefects results in a decreased concentration of va-
cancies in a comparison with concentration of oxygen.
As a result, precipitates begin to absorb oxygen without
participation of vacancies, their sizes are increased and
then the type of a strain around them varies from vacancy
(tensile) to interstitial one (compressive). The similar re-
sults were obtained by HREM in Refs [38, 48] The bound-
ary of full transition can be determined from the relation
V/G. Thus, the parameter Ccrit of the theory [19] does not
describe a condition of change of growth regimes (�inter-
stitial� or �vacancy�). This parameter describes condi-
tions of emerging (or vanishing) of microdefects of a va-
cancy type in the result of diffusion and interaction of point
defects during cooling of the crystal. It is possible to deter-
mine Ccrit for the critical growth rate (Fig. 2). At V =
= 6.25 mm/min�1 we shall receive Ccrit = 9.31⋅10�5 cm2/(s⋅Ê).
The centers of nucleation based on interstitial oxy-
gen atoms exist also in the case of the interstitial mecha-
nism. However, here the catalytic role is played by car-
bon atoms. Oversaturation by interstitial silicon atoms
results in appearance of complexes [CsISi]:
Cs + ISi ↔ [CsISi].
The number of interstitial defects can be estimated
using the equation [20]:
2/3
2
2/1
13,0
≈
kTD
VE
C
N
i
ccr
i
ρ
, (11)
where Ci is the concentration of self-interstitials before
condensation; Ecr = 1.5 eV is the binding energy for the
critical nuclei to one silicon atom.
The estimate for Ci ~ 1014 ñm�3 and Di ~ 3.5⋅10�4 ñm2/s
gives the value N ~ 106 ñm�3. The similar value is ob-
tained using TEM-researches of A-microdefects concen-
tration.
Lowering the critical radius [CsISi]-nucleis and ac-
celeration of a diffusion Cs here happens. As a result,
[CsISi] agglomerates are formed. Furthermore, during
supersaturation of ISi co-precipitation of Oi and Cs can
happen [49, 50]. Thus, for formation of B-microdefects:
ISi + Cs → [CI] + Oi → Â-microdefects.
The growth of interstitial microdefects results in sig-
nificant lowering the self-interstitial concentration. It
creates conditions for precipitation of impurities. In this
case, formation of particles of an impurity phase is ac-
companied by generation of self-interstitials in positions
between stices of the lattice. As a result, two types of
interstitial microdefects are formed: interstitial agglom-
erates (drains for interstitial atoms of silicon) and impu-
rity precipitates (sources of these atoms).
Both mechanisms (vacancy and interstitial) result in
formation of small interstitial agglomerate, i.e. D-
microdefects. This D-microdefects are uniformly distri-
buted B-microdefects. The B-microdefects is transformed
into A-microdefects. These mechanisms are described by
the following equations.
For the vacancy mechanism:
a) nOi + VSi → n(VO2) → vacancy microdefects.
b) n(VO2) + Oi +...+ nOi → n[(VmOn) + ISi] → D-
microdefects.
For the interstitial mechanism:
a) Ñs + ISi → (CsISi) → D-microdefects.
b) (CsISi) + Oi → n[(CsISi) + Oi] → B-microdefects.
c) B-microdefects + ISi → A-microdefects.
In Fig. 3, the scheme of microdefects formation proc-
ess in FZ-Si is shown.
Fig. 3. Schematic diagram of formation and transformation of
microdefects in FZ-Si crystals.
N, cm�3
V, mm/min
0
2
4
8
12
10
10
10
10
2 4 6 8
V- (vacancy) defects
D-defects
B-defects
A-defects
V.I. Talanin, I.E. Talanin: Nucleation, growth and transformation of microdefects in FZ-Si
21SQO, 7(1), 2004
4. Conclusions
Thus, the formation of vacancy and interstitial micro-
defects is caused by disintegration of oversaturated solid
solution of intrinsic point defects. All the known types of
microdefects are formed in the result of interaction of
intrinsic point defects with impurities of oxygen and car-
bon. The concentration of vacancies and self-interstitials
are approximately identical in the vicinity of the crystal-
lization front. The recombination between them at the
initial stage of their interaction at high temperatures is
hampered. Therefore, the formation of microdefects pro-
ceeds simultaneously by two mechanisms: the vacancy
and interstitial ones. Vacancy and interstitial micro-
defects coexist in crystal. The parameter V/G = Ccrit de-
scribes conditions of emerging (vanishing) of vacancy
microdefects in the crystal.
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