Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon
Low-frequency internal friction and dynamic shear modulus (Geff) in Si monocrystal were investigated in the range of 20 to 200 ºC. Temperature hysteresis of internal friction was found and effective shear modulus was studied in the unirradiated and a series of irradiated silicon samples. The appeara...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2005
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| Цитувати: | Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon / B.I. Gutsulyak, A.V. Oliynych-Lysyuk, I.M. Fodchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 25-29. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1209672017-06-14T03:04:45Z Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon Gutsulyak, B.I. Oliynych-Lysyuk, A.V. Fodchuk, I.M. Low-frequency internal friction and dynamic shear modulus (Geff) in Si monocrystal were investigated in the range of 20 to 200 ºC. Temperature hysteresis of internal friction was found and effective shear modulus was studied in the unirradiated and a series of irradiated silicon samples. The appearance of a hysteresis loop is due to interaction of genetic microdefects with crystal point defects and their nonsymmetric distribution in the process of samples heating-cooling. 2005 Article Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon / B.I. Gutsulyak, A.V. Oliynych-Lysyuk, I.M. Fodchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 25-29. — Бібліогр.: 19 назв. — англ. 1560-8034 PACS: 62.20.Dc, 81.40.Jj http://dspace.nbuv.gov.ua/handle/123456789/120967 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Low-frequency internal friction and dynamic shear modulus (Geff) in Si monocrystal were investigated in the range of 20 to 200 ºC. Temperature hysteresis of internal friction was found and effective shear modulus was studied in the unirradiated and a series of irradiated silicon samples. The appearance of a hysteresis loop is due to interaction of genetic microdefects with crystal point defects and their nonsymmetric distribution in the process of samples heating-cooling. |
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Article |
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Gutsulyak, B.I. Oliynych-Lysyuk, A.V. Fodchuk, I.M. |
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Gutsulyak, B.I. Oliynych-Lysyuk, A.V. Fodchuk, I.M. Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Gutsulyak, B.I. Oliynych-Lysyuk, A.V. Fodchuk, I.M. |
| author_sort |
Gutsulyak, B.I. |
| title |
Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
| title_short |
Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
| title_full |
Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
| title_fullStr |
Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
| title_full_unstemmed |
Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
| title_sort |
character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2005 |
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http://dspace.nbuv.gov.ua/handle/123456789/120967 |
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Character of elastic energy absorption in well developed genetic-impurity defect structure in monocrystalline silicon / B.I. Gutsulyak, A.V. Oliynych-Lysyuk, I.M. Fodchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 25-29. — Бібліогр.: 19 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T18:56:36Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 25-29.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
25
PACS: 62.20.Dc, 81.40.Jj
Low-temperature hysteresis of dynamic shear modulus Geff in silicon
B.I. Gutsulyak, A.V. Oleynich-Lysyuk, І.М. Fodchuk
Yu. Fed’kovych Chernivtsi National University, 2, Kotsyubinsky str., 58012 Chernivtsi, Ukraine
Abstract. Low-frequency internal friction and dynamic shear modulus (Geff) in Si
monocrystal were investigated in the range of 20 to 200 ºC. Temperature hysteresis of
internal friction was found and effective shear modulus was studied in the unirradiated
and a series of irradiated silicon samples. The appearance of a hysteresis loop is due to
interaction of genetic microdefects with crystal point defects and their nonsymmetric
distribution in the process of samples heating-cooling.
Keywords: silicon, shear modulus, hysteresis.
Manuscript received 24.06.05; accepted for publication 25.10.05.
1. Introduction
The greatest problem that arises in the course of using
semiconductor devices is a change in their parameters
with time and due to external factors, such as tempe-
rature and hard radiation. The processes occuring in a
semiconductor under thermal treatment and irradiation
are accompanied by formation of new and interaction of
the existing crystal structure defects that mainly affect its
photoelectric properties. Any change in photoelectric
properties is caused by changes in crystal structure,
particularly by changes in defect impurity structure and
strain distribution in crystal as a whole [1-4].
Silicon grown by the Czochralsky method has a
reasonably complicated system of genetic (hereditary)
defects. The absence of dislocations that are effective
sinks for point defects (intrinsic and impurity), results in
crystals oversaturation with them. Owing to this, in the
course of cooling after growing in the dislocation-free
silicon monocrystals, various kinds of point defect
clusters will be formed. Here belong growth bands and
precipitates that resulted from the dissociation of over-
saturated solid solutions of background impurities, as
well as microdefects of various types (А, В, С, D) [4-6].
Irradiation of semiconductor crystals by high-energy
particles results in generation of radiation defects. Due
to versatility of secondary processes, the present state of
collisions theory prevents from making conclusion on
the nature and possible types of radiation defects based
on calculations alone [3, 4]. The major role in solving
this problem is played by experimental research.
Therefore, the purpose of this paper is to study the
processes of formation and diffusion of point defects,
growth and decay of microdefects in the process of long-
term natural aging of silicon crystals irradiated and
unirradiated by high-energy particles.
2. Investigation results
The processes of diffusion, migration, as well as
formation of point defect sets will involve changes in the
temperature and amplitude spectra of elastic energy and
Geff absorption [7-15]. Therefore, to control and study
the behaviour of defects (radiation-induced or con-
ventional, growth-induced) in semiconductors [10-15] it
is interesting to use the internal friction (IF) method that
has been long and successfully used in the investigation
of metals [16]. The internal friction method is a
resonance technique possessing high structural
sensitivity, allowing to determine not only the type, but
also the symmetry of defects, their relaxation chara-
cteistics, concentration and thermodynamic parameters.
In this paper, the low-frequency IF and dynamic
shear modulus Geff in silicon were studied. Silicon
monocrystal (p-type) grown by the Czochralsky method
in direction [111] comprising horizontal and radial
growth bands with period of order 150 – 200 μm was
chosen as the object of the study. The oxygen
concentration, according to IR spectroscopy data, is close
to 1018 сm−3, boron concentration is about 1016 сm−3. Si
washers, cut perpendicular to the crystal growth direc-
tion, were cut to parallelepipeds 1.5×1.5×60÷80 mm.
The samples were subjected to polishing to the depth
from 40 to 80 μm and chemical etching to remove the
layer damaged on cutting. The direction of applied
strain, orientation of faces and the method of samples
securing are shown in Fig. 1.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 25-29.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
26
Fig. 1. Orientation of silicon monocrystal faces prepared for
investigation by internal friction method and direction of
applied alternating-sign strain.
Two groups of samples that were aging at room
temperatures for 9 years were studied: the group in the
initial state and the group of crystals after irradiation by
high-energy electrons of energy 18 MeV, particles flow
Фе = 1.8⋅1013 el/сm2 and γ-quanta (irradiation doses
made 1.8 and 3.6 kGy for electrons and 4⋅104 rad for γ-
quanta, respectively).
IF investigations were performed by torsional oscil-
lations method at frequencies ∼2.5 Hz in vacuum ∼103 Pa
at average heating-cooling rate 2–5 degrees per minute,
meeting optimal rates of temperature change, when the ef-
fects related to point defects in silicon are manifested [8].
Fig. 2 shows the results of studying the elastic energy
absorption and dynamic shear modulus in the
temperature range of 20 to 200 °C for the unirradiated
silicon in the initial state. On the curves of temperature
dependence of IF, one can observe a wide weakly
differentiated maximum of a complicated nature. Since
in these Si crystals linear defects are almost absent, the
discovered maximum can be related only to point defects
and their sets.
Fig. 2. Temperature dependences of IF (1, 2) and f2 ~ Geff
(3, 4) of Si. 1, 3 − heating; 2, 4 − cooling.
Fig. 3. Defect configuration: а – with neutral boron atom in
silicon interstice; b – with negatively charged boron atom
forming a double bond to silicon atom.
Maximum energy absorption can be observed only on
heating. On cooling, it was essentially smoothed, which
testified to its not purely relaxation nature.
Maxima of elastic energy absorption in IF spectra, as
a rule, are related to migration of point defects or their
sets and originate when the symmetry of field around the
point defect or set is lower than lattice symmetry. These
defects should include impurities of boron, oxygen,
carbon and interstitial silicon. Boron atom, implanted in
Si lattice, forms a split interstice with silicon atom – a
“dumb-bell”, which is asymmetric, since boron atom in
it is lighter than the silicon atom [7, 9]. As long as boron
in silicon crystal lattice can form several configurations
(Fig. 3) with lower than cubic symmetry, each of them
can lead to the occurrence of maxima on temperature
dependence of IF. The elastic energy absorption is
caused by migrations of boron atoms into equivalent
positions around the silicon atom. Each such process can
be accompanied by maximum absorption with activation
energies 0.29 and 0.49 eV. On conversion to frequency
2.5 Hz, we get that IF maxima related to the occurrence
of boron must be observed at lower than room
temperatures. Thus, the maximum on IF temperature
spectrum in Fig. 2 is not related to sets that can be
formed by boron in Si lattice [7, 9].
The implanted silicon atom in the nonequivalent
positions with a double or single bond (positively
charged) can be also considered as a mechanical dipole
with lower than lattice symmetry (Fig. 4) [2-5]. This can
also result in the appearance of peaks in elastic energy
absorption with activation energies 0.7 and 0.92 eV. On
conversion to frequency 2.5 Hz, the temperature
positions of these maxima will be, respectively, at 13
and 115 °С, actually coinciding with maximum energy
absorption in our case. At the same time, a peak caused
by reorientation of the silicon mechanical dipole is a
relaxation one, that is it should be observed both on
heating and cooling and be accompanied by elastic
modulus relaxation.
Behaviour of Geff with temperature in Fig. 2 also
proves this conclusion, since the presence of relaxation
process is not registered. Moreover, on cooling, modulus
passes much higher than on heating, which can indicate
to considerable structural inhomogeneity of our samples
and their different “response” to heating and cooling.
а b (110)
(111)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 25-29.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
27
The effective (dynamic) shear modulus can be arbitrarily
divided into “lattice” and “deformation” components
(Geff = Glat + Gdef). The hysteresis of dynamic elastic
modulus can be caused either by a change in Glat during
polymorphous transformation (or a different phase
precipitation, as mentioned above), or a change in its
“deformation” component during the reconstruction of
defective structure. Obviously, we are dealing more with
a change in the deformation component of dynamic
modulus, since, as we know, silicon in this temperature
range does not undergo classical temperature
polymorphous transformations [11]. The results of
amplitude dependences of internal friction of silicon
measured at room temperatures and presented in Fig. 5
can serve as a peculiar proof of the above said. A
divergence of curves Geff(γ) obtained with increasing and
decreasing the deformation degree γ, testifies to the
increase in Gdef of silicon during measurement. One of
possible reasons for this discrepancy can be the motion
of dislocation segments (dislocation bends) and their
liberation from impurity atoms due to diffusion.
Analysis of possible behaviour of dislocation-
impurity structure under the influence of external
periodic force and temperature shows that liberation of
dislocation (or dislocation segments) from impurity
atoms can really cause the diversity of Geff on heating
and cooling, if in the course of measurement the
impurity atmosphere has no time to return to the
dislocations. As is shown in paper [11] by example of
aluminum, the “evaporation-condensation” of impurities
from dislocations can bring about the appearance of
“direct” hysteresis of dynamic shear modulus: on the
temperature dependences of Geff (heating curves pass
above cooling curves).
However, in silicon with its high value of the Peierls
barrier it is very difficult to shift or at least bend the
dislocation, and this can occur at temperatures higher
than 600 °С [17]. Though, as shown in Ref. [13],
breaking dislocation off the fixing point does not call for
reaching critical strain of activation-free overcome of
energy barrier, and the motion of dislocation bends in
silicon becomes possible even at room temperatures
[14]. The bends on dislocations are those places that
absorb or emit impurity atoms most easily.
Fig. 4. Defect configuration: а – with neutral interstitial silicon
with double bonds, b – with positively charged silicon.
Fig. 5. Amplitude dependences of IF (1, 2) and f 2 ~ Geff (3, 4)
of Si with increased deformation amplitude γ (1, 3) and with
reduced γ ( 2, 4).
As a rule, dislocation-free crystals can contain a large
number of prismatic dislocation loops (swirl-defects) [2,
4, 6], created due to formation of clusters of excess
interstitial atoms on crystal cooling. Cluster formation
takes place heterogeneously on some nuclei that include
carbon atoms [5].
Crystals under study include a large number of
prismatic dislocation loops (swirl-defects). According to
accepted classification, these are А-microdefects that are
interstitial dislocation loops with the Burgers vector b
r
=
1/2 [110], lying in the planes {111} and {110} [2, 4-6].
According to X-ray diffractometry data, their
concentration is n ~ 105 cm−3, and dimensions R ~ 5 – 20
μm [15, 18, 19]. As the temperature increases due to a
change in local strains around A-defects and non-
uniform distribution of strains in crystal as a whole and
under the influence of external alternating-sign strain,
the point defects can be redistributed and move either
toward the dislocation loop, or away from it depending
on the sign of thermal strains and defect type. Probably,
with cooling rate chosen, not all the point defects return
to their places. This may cause the appearance of
temperature hysteresis of effective shear modulus. It is
also proved by the fact that hysteresis loop area is
narrowed with reduction of cooling rate. At the same
time, the hysteresis of modulus Geff may be caused by
other reasons, for example, the interaction of oxygen
precipitates with applied strains or the growth of oxygen
precipitates or their decay.
Note that silicon annealing at 450 °С which is known
to stimulate a decay of oversaturated solid solution of
oxygen in silicon, damped temperature hysteresis in the
range of 20 to 200 °С, but did not cancel the amplitude
one: it became somewhat narrower, but did not disappear
(Fig. 6). Narrowing of the amplitude hysteresis is
attributable to formation of oxygen precipitates SiOx,
with the field of strains around them blocking the
increase or reduction of dimensions “motion” of А-
microdefects.
а б
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 25-29.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
28
2 3 4 5
0
10
20
30
40
f 2
, c
-2
Q
-1
, 1
04
γ, 10-5
1
2
3
4
2,65
2,66
Fig. 6. Amplitude dependences of IF (1, 2) and f 2(3, 4) of Si
on holding at 450 оС for 5 hours. 1, 3 − with increasing γ, 2, 4
− with reducing γ.
Fig. 7 shows the curves of the temperature
dependence of internal friction and the effective shear
modulus in silicon after irradiation with the electron dose
3.6 kGy and gamma-quanta. The irradiation initiated the
disappearance of IF maximum in the region of 100 °С
and temperature hysteresis of the elastic modulus. The
behaviour of Geff with temperature indicates that the
sample structure has become more homogeneous. For
the majority of samples the IF becomes more stable.
So, in the course of long-term silicon aging, IF
maximum and shear modulus hysteresis in the range of
20 to 200 ºC is probably caused by the interaction of
microdefects with point defects. Irradiation by high-
energy particles blocks the “motion” of these
microdefects. Dissociation of oversaturated solid
solution of oxygen in silicon and formation of SiOx
precipitates also restricts considerably such defects – the
elastic modulus hysteresis in the range of 20 to 200 ºC
disappears.
0 50 100 150 200
0
10
20
Q
-1
,1
04
T, oC
2,7
2,8
4
3
2
1
f 2
,c
-2
Fig. 7. Temperature dependences of internal friction (1, 2) and
f 2 ~ Geff(3, 4) in silicon after irradiation with electrons and
gamma-quanta. 1, 3 −heating, 2, 4 − cooling.
Thus, the analysis of temperature spectra of IF
combined with X-ray diffractometry data [15, 18, 19] of
silicon crystals irradiated with high-energy particles
allows making some assumptions as to possible
mechanisms and dynamics of structural changes in
silicon crystals in the course of long-term natural aging.
As long as for Si (Cz) the basic defects are B-type
microdefects, under the influence of high-energy
irradiation these microdefects may transform into A-type
with dimensions ≥ 10 μm.
In so doing, the scheme of possible transformation
is as follows [5, 12]:
(CsI) + Oi I⇒ n[(CsI) + Oi] ⇒ B-microdefects;
B + ISi ⇒ A-microdefects.
Moreover, one can assume the existence of another
type of defects – vacancy sets (VV-sets), as long as in
mechanical spectra of irradiated silicon (unlike control
samples of the first group), under dynamic thermal
cycling, maxima in the region of 180 to 220 ºC appear
and gain in magnitude. Such defects are typical exactly
of VV- clusters in silicon planes (111).
3. Conclusions
1. Selective sensitivity of low-frequency internal
friction to changes in “genetic defects-point defects”
system was discovered.
2. Occurrence of IF hysteresis loop and shear modulus
hysteresis in the range of 20 to 200 ºC is related to
the interaction between genetic microdefects and
point defects in crystal and their nonsymmetric
distribution in the course of samples heating-cooling.
3. Irradiation by high-energy particles blocks the
increase in dimensions of microdefects. Dissociation
of oversaturated solid solution of oxygen in silicon
and formation of SiOx precipitates results in the
disappearance of elastic modulus hysteresis in the
range of 20 to 200 ºC.
4. In the course of being held at room temperature for
nine years, the samples irradiated by high-energy
electrons (E ~ 18 MeV) with doses 3.6 and 5.4 kGy
became more homogeneous in structure as compared
to doses 1.8 and 2.7 kGy.
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