The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation
N- and p-type samples of Si-Ge solid solution with the resistivity of (4...7) 10⁻³⋅ Ohm·cm, unannealed after high-temperature baking have been investigated. Samples were irradiated up to the fluence ~10²⁰ n⁰·cm⁻² in reactor active zone at the temperature ~500 ºC in mixed neutron field. It has b...
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irk-123456789-801472015-04-13T03:02:08Z The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation Dolgolenko, A.P. Физика радиационных повреждений и явлений в твердых телах N- and p-type samples of Si-Ge solid solution with the resistivity of (4...7) 10⁻³⋅ Ohm·cm, unannealed after high-temperature baking have been investigated. Samples were irradiated up to the fluence ~10²⁰ n⁰·cm⁻² in reactor active zone at the temperature ~500 ºC in mixed neutron field. It has been observed that in the process of reactor irradiation not only phosphorus or boron precipitation, but the annealing of samples occurs resulting in the increase of doped substituting impurities solubility and hence in the reduction of resistivity. It is shown that the radiated redistribution can be described by diffusion and relaxation processes. The dose dependence on resistivity as a function of fast-pile neutron fluence was calculated and interpreted in terms of the effective medium theory. Activation energies of the doping impurities annealing process and characteristic dimensions of defect clusters have been defined. Исследованы образцы n- и p-типа проводимости твердого раствора кремний-германий с удельным сопротивлением (4...7) 10⁻³⋅ Ом/см, не прошедшие отжига после высокотемпературного спекания. Образцы облучались до флюенса ~10²⁰ n⁰·•cм⁻² в активной зоне реактора ВВР-М при температуре ~500 ºC в смешанном нейтронном поле. В процессе облучения наблюдались не только преципитация легирующей примеси бора и фосфора, но и увеличение их растворимости, обусловленное кластерами дефектов. Показано, что радиационное перемешивание можно описать на языке диффузионных и релаксационных процессов. Изменение удельного сопротивления в зависимости от флюенса быстрых нейтронов описано в рамках теории эффективной среды. Определены энергии активации процесса отжига легирующих примесей и характерные размеры кластеров дефектов. Досліджені зразки n- та p-типу провідності твердого розчину кремній-германій з питомим опором (4...7) 10⁻³⋅ Ом/см, що не пройшли відпал після високотемпературного спікання. Зразки опромінювались до флюєнсу ~10²⁰ n⁰·•cм⁻² в активній зоні реактора ВВР-М при температурі ~500 ºC в змішаному нейтронному полі. В процесі опромінювання спостерігались не тільки преципітація легуючої домішки бору та фосфору, але й збільшення їх розчинності, що обумовлено кластерами дефектів. Показано, що радіаційне перемішування можна описати в термінах дифузійних та релаксаційних процесів. Зміна питомого опору в залежності від флюєнсу швидких нейтронів описана в рамках теорії ефективного середовища. Визначені енергії активації процесу відпалу легуючих домішок та характерні розміри кластерів дефектів. 2006 Article The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation / A.P. Dolgolenko // Вопросы атомной науки и техники. — 2006. — № 4. — С. 65-70. — Бібліогр.: 20 назв. — англ. 1562-6016 PACS: 61.80.HG; 61.72.JI; S5.11-12 http://dspace.nbuv.gov.ua/handle/123456789/80147 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах |
| spellingShingle |
Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах Dolgolenko, A.P. The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation Вопросы атомной науки и техники |
| description |
N- and p-type samples of Si-Ge solid solution with the resistivity of (4...7) 10⁻³⋅ Ohm·cm, unannealed after high-temperature
baking have been investigated. Samples were irradiated up to the fluence ~10²⁰ n⁰·cm⁻² in reactor active zone at the temperature
~500 ºC in mixed neutron field. It has been observed that in the process of reactor irradiation not only phosphorus or boron precipitation,
but the annealing of samples occurs resulting in the increase of doped substituting impurities solubility and hence in
the reduction of resistivity. It is shown that the radiated redistribution can be described by diffusion and relaxation processes.
The dose dependence on resistivity as a function of fast-pile neutron fluence was calculated and interpreted in terms of the effective
medium theory. Activation energies of the doping impurities annealing process and characteristic dimensions of defect clusters
have been defined. |
| format |
Article |
| author |
Dolgolenko, A.P. |
| author_facet |
Dolgolenko, A.P. |
| author_sort |
Dolgolenko, A.P. |
| title |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation |
| title_short |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation |
| title_full |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation |
| title_fullStr |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation |
| title_full_unstemmed |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation |
| title_sort |
annealing of high - level doped materials on the base of the n – and p – si₀.₇ ge₀.₃ solid solution under reactor irradiation |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2006 |
| topic_facet |
Физика радиационных повреждений и явлений в твердых телах |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80147 |
| citation_txt |
The annealing of high - level doped materials on the base of the n – and p – Si₀.₇ Ge₀.₃ solid solution under reactor irradiation / A.P. Dolgolenko
// Вопросы атомной науки и техники. — 2006. — № 4. — С. 65-70. — Бібліогр.: 20 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT dolgolenkoap theannealingofhighleveldopedmaterialsonthebaseofthenandpsi07ge03solidsolutionunderreactorirradiation AT dolgolenkoap annealingofhighleveldopedmaterialsonthebaseofthenandpsi07ge03solidsolutionunderreactorirradiation |
| first_indexed |
2025-07-06T04:04:01Z |
| last_indexed |
2025-07-06T04:04:01Z |
| _version_ |
1836868846843068416 |
| fulltext |
THE ANNEALING OF HIGH - LEVEL DOPED MATERIALS ON THE
BASE OF THE n – AND p – Si0.7 Ge0.3 SOLID SOLUTION UNDER
REACTOR IRRADIATION
A.P. Dolgolenko
Institute for Nuclear Research NASU, Kиїv, Ukraine
N- and p-type samples of Si-Ge solid solution with the resistivity of 310)7...4( −⋅ Ohm·cm, unannealed after high-temperature
baking have been investigated. Samples were irradiated up to the fluence ~1020 no·cm-2 in reactor active zone at the temperature
~500 ºC in mixed neutron field. It has been observed that in the process of reactor irradiation not only phosphorus or boron pre-
cipitation, but the annealing of samples occurs resulting in the increase of doped substituting impurities solubility and hence in
the reduction of resistivity. It is shown that the radiated redistribution can be described by diffusion and relaxation processes.
The dose dependence on resistivity as a function of fast-pile neutron fluence was calculated and interpreted in terms of the effec-
tive medium theory. Activation energies of the doping impurities annealing process and characteristic dimensions of defect clus-
ters have been defined.
PACS: 61.80.HG; 61.72.JI; S5.11-12
INTRODUCTION
Silicon-germanium alloys have been used in
practical thermoelectric energy conversion applications
for a relatively great number of years [1]. Study of the
high-temperature properties of Si-Ge solid solution
under nuclear irradiation is of great importance.
The directed search is possible at thorough study of
material properties under nuclear irradiation, that
induces the intense temperature spikes (Θ-spikes).
Mathematical study of this process was carried out in
[2]. It was shown that the sample shape and boundary
conditions determine only the average temperature of
the sample volume and don't influence the probability
density of spikes. The local heating gives rise to melting
of small volume region, properties of which are
changed after recrystallization. The melt regions and
dimensions of the created defect clusters are determined
by the energy of primary knock-on atoms, which was
spent on elastic collisions.
The volume of cascades has nearly 100 impurity
atoms, and the number of the primary displaced atoms
exceeds the thousand. The whole process of
displacement of atoms in cascades is completed for
~10-13 s. For the period of ~10-12 s received kinetic
energy is transmitted to the lattice and only chaotic,
similar to liquid, distribution of atoms has time to be
realized [3].
In order to study the influence of irradiation on the
material properties the measurements of conductivity,
diffusion coefficients and others are usually carried out.
Time of measurements considerably exceeds the
duration of Θ-spike. Thus, the changes of measured
macroscopic parameters will be observed only under the
conditions of the overlapping of the local melting
regions and the plastic deformation regions [4].
The diffusion processes both within thermal peak
and out of its limits have no time to occur [5], as the
diffusion of atoms of overheated liquid for such period
does not exceed 0.1...1.0 nm.
EXPERIMENT
The samples of n- and p-type conductivity of silicon-
germanium alloys with the resistivity ~ 310)7...4( −⋅
Ohm·cm, obtained by the method of high-temperature
baking after the doping by natural mixed isotopes of
phosphorus and boron are investigated, but long-lasting
annealing at ~900 ºC has not been carried out. The irra-
diation was executed by total spectrum of neutrons in
active zone of the WWR-M reactor at temperature
~500o C. The measurement of resistivity was executed in
the process of irradiation and received information was
processed using the computer programs. In Fig. 1, 2 the
experimental data of resistivity of n- and p-Si0.7Ge0.3
samples after various doses of irradiation by fast neu-
trons are shown as points. The solid lines show the theo-
retical curves of resistivity as a function of fast neutron
fluence in frameworks of the effective medium theory.
Fig. 1. Resistivity of n- Si0.7Ge0.3 as a function of fast-
pile neutron fluence:
- experimental values;------ - theoretical dependence:
1 -unannealed sample; 2 - annealed sample
______________________________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2006. №4.
Серия: Физика радиационных повреждений и радиационное материаловедение (89), с. 65-70.
65
Fig. 2. Resistivity of p-Si0.7Ge0.3 as a function of fast-pile
neutron fluence:
• - experimental values; -------- - theoretical dependence:
1 - unannealed sample; 2 - annealed sample
THEORY
At high temperatures the continuous redistribution of
atoms of the solid, stipulated by thermal movement,
occurs. Atoms in diamond-like lattices can migrate both
by vacancies and by interstitials, and in the most
common case - simultaneously. Thus, the atoms from a
lattice site can go to tetrahedral and octahedral
interstitials and back to sites, annihilating with the
vacancies located therein. The appropriate transitions of
impurity atoms can be characterized by the relaxation
time (τ ). If relaxation time reaches values 10-2 s and
more, it is possible to neglect the diffusion, but one can
not neglect the relaxation. Due to statistical nature of
this process the time of presence of atom in lattice in
one of the balance position varies with temperature
according to the exponential law. Under the radiation
the redistribution of atoms occurs, depending upon the
exposure dose. So it is known [6], that the neutrons with
energy higher than 36 keV transmit to lattice atom the
energy, sufficient for formation of the whole cascade of
knocked-out atoms, after reorganization of which the
damage regions with high density of defects in local
volume are created. The probability of their formations
in n-Si0.7Ge0.3 samples will be determined by the
macroscopic cross-section ( 15.0=Σ cm-1) of fast-pile
neutron scattering in assumption, that each scattered
neutron creates cluster irrespective of the irradiation
temperature. Such assumption is based on the fact that if
the increased irradiation temperature causes the
annealing of small size clusters, high doping level of Si-
Ge samples can result in space division of formed
subcascades. The authors of the work [7] have
calculated by Monte-Carlo method cascade sizes,
created by primary knocked-out atoms (PKA) from
bismuth to nitrogen in Si. It is shown, that with
reduction of PKA weight the size of average cascade
grows and the formation of isolated subcascades is
possible. In the case of p-Si0.7Ge0.3 it is necessary to take
into account the clusters, created by the reaction
10B(n,α)7Li [1]. It is possible to calculate the number of
defect clusters (Nc) created by neutrons in the unit of
time and volume, according to the expression:
INc ⋅= Σ , (1)
where I is the flux of fast-pile neutrons with energy
100>nE keV )scmn101.3( -1-2o13 ⋅⋅⋅=I .
The volume fraction, occupied by defect clusters of
the average radius ro, in dependence on the irradiation
time (t), is equal ([3], p. 252):
⋅⋅⋅⋅⋅−−= tIrf o Σπ 3
3
4exp1 . (2)
In the cascade of knocked-out atoms the intensive re-
distribution of lattice atoms and the doped impurities oc-
cur. These discrete stochastic events are connected with
instantaneous local increase of temperature during the
creation of defect clusters. The temperature in these lo-
cal regions increase for a short time to the melting tem-
perature. But only high temperatures (about the tempera-
ture of Si0.7Ge0.3 melting) make the main contribution
into the frequency of the impurity jumps. Therefore, it
can be supposed that all changes, which take place in the
local regions of melting due to Θ-spike, began to appear
under condition that their fraction of sample volume
tends to the unit. Then the radiated redistribution can be
described by diffusion and relaxation processes in the
whole of volume.
At such approach the "front" of temperature within
sample in dependence on irradiation dose (Φ ) will be
changed proportional to the fraction of recrystallization
volume and can be presented as:
( )[ ]ΦΣΦ ⋅⋅−−⋅+= VTTT oir exp1)( ;
irmo TTT −= ; 3
23
4 rV ⋅⋅= π , (3)
where tI ⋅=Φ is the fluence of fast-pile neutrons; V is
the volume of intensive redistribution of atoms with the
radius 2r ; irT , mT are the sample irradiation and
melting temperatures.
Then characteristic time of relaxation in the
annealing of doped impurity ( 1τ ) becomes the function
of the irradiation dose:
⋅=
)(
exp)(1 Φ
τΦτ
kT
Ea
o , (4)
where oτ is a constant, which by order of value is
inversely proportional to the frequency factor of defect
clusters annealing; aE is energy of activation of doped
impurity annealing.
It was noticed [1], that samples of n- and p-Si0.7Ge0.3
exposed to the long annealing after high-temperature
baking at the beginning of irradiation increase the
resistivity due to phosphorus or boron precipitation.
This loss of electrical activity of doped impurity occurs
in conducting matrix of samples and can be determined
by the removal constant time ( 2τ ) of doped impurity on
66
sinks. Nature defects, dislocations and crystal
boundaries of thermoelectric materials, and as well as
defect clusters, created by irradiation can act as for
doped impurity sinks. The theory of effective medium ,
containing defect clusters with the conductivity 1σ in
the conducting matrix with conductivity oσ is presented
by the following expressions [8]:
oef f σσ ⋅= ; ( ) 5.02 2/xaaf ++= ;
( ) ( )[ ]2/15.05.15.0 xxCa +−⋅−⋅⋅= ; ox σσ /1= , (5)
where efσ is the sample conductivity with introduced
defect clusters; C is the fraction of conducting volume.
Taking into account the known expression (2) for the
fraction of non-conducting volume occupied by defect
clusters, C is equal to:
( )Φ⋅⋅Σ−= kVC exp ; 3
13/4 rVk ⋅⋅= π , (6)
where Vk
is the average volume of defect clusters,
including space charge region of a radius 1r .
As one can see from fig. 1, 2 the resistivity of
samples increases with irradiation dose. But when the
volume fraction of thermal peaks during formation of
defect clusters comes nearer to 70 %, the resistivity of
conducting matrix )(Φρ m decreases, according to the
expression:
1
1
1
2
11
)(
expexp)(
−
−−−
−⋅−
−⋅+=
Φτ
Φρ
τ
ΦρρΦρ
II aaom ,
(7)
where oρ is the resistivity of sample before irradiation;
aρ is the change of resistivity of sample, if the
annealing was performed after thermal baking.
Therefore effective conductivity ( efσ ) of such
sample without preliminary annealing changes with
irradiation dose according to (5), if the resistivity of its
conducting matrix equals )(Φρ m , according to the
expression (7).The joint solution of equations (5) at
condition (1) and (6) has allowed to calculate the
average radius of defect clusters, created by irradiation
in reactor of n- and p-Si0.7Ge0.3 at temperature ~810o C
and to describe the change of the effective resistivity of
samples after 2o19 cmn10)3...5.1( −⋅⋅ doses of
irradiation (see fig. 1, 2; curves 2). Then it was assumed,
that the samples have been annealed after high-
temperature baking before irradiation. For detailed
description of experimental data at any irradiation dose
in given work (calculation of effective conductivity,
according to (5)) the change of resistivity in the
conducting matrix of samples, according to expressions
(4, 7) was taken into account. Then the process of the
precipitation of doping impurity with characteristic time
( 2τ ), occurring during irradiation and is distributed to
its fraction, which was caused due to the lack of
annealing of samples after high-temperature clinkering.
The results of the calculations are given in table.
Parameters of defect clusters: the radius of the disordered
(r1) and liquid (r2) regions and also the activation energy (
aE ) of phosphorus and boron under radiation annealing
with the relaxation characteristic times ( 2τ , 0τ ) for high-
doped n- and p-Si0.7Ge0.3 were calculated
Parameters Type of Si0.7Ge0.3
n p
Σ , cm-1 0.15 0.39
cmOhm, ⋅oρ 3.2·10-3 3.0·10-3
cmOhm, ⋅1ρ 8.1·10-2 2.9·10-2
cmOhm, ⋅aρ 7.5·10-3 1.4·10-2
1r , cm 40·10-8 44·10-8
2r ,cm 50·10-8 50·10-8
oτ , s 1.5·10-5 3.5·10-6
2τ , s 7·103 7·103
aE , eV 3.3 3.45
DISCUSSION
One can see from the table, that the fast-pile
neutrons in n- and p-Si0.7Ge0.3 create defect clusters with
approximately equal average radius. The rate of their
introduction differs more than two times. The defined
activation energy for boron and phosphorus migration
during irradiation process has appeared to be less, than
in silicon [9].Characteristically, that the phosphorus and
boron diffusivities in Ge are equal only at the
temperature, close to its melting. It is known, that it can
be explained by the dependence of diffusivity of these
impurity on vacancies charge in Ge. And nearly the
same diffusivities of phosphorus and boron in Si in wide
temperature region are connected with the neutrality of
vacancies. Let us evaluate the diffusion coefficients of
phosphorus and boron of n- and p-Si0.7Ge0.3 at irradiation
process in active zone of reactor. One can consider, that
in solid solutions Si-Ge, with increase of Ge content the
diffusivity of phosphorus will increase and the boron
diffusivity will decrease. Such diffusivity change of
these doping impurities would be symmetric in
comparison with their diffusion in Si, if the introduction
of Ge in Si is only the result of the increase of fraction
of charged vacancies. The authors [10] have shown, that
the diffusion of phosphorus in Si0.7Ge0.3 is subject to the
Arrhenius law:
−⋅=
kT
E
DD a
o
P exp , (8)
where PD is the P diffusivity in Si0.7Ge0.3 at temperature
( 1050...800 ) oC; 7107.3 −⋅=oD cm2/s is the pre-
exponential factor; 62.1=aE eV is the activation
energy for phosphorus migration.
The similar dependence was received for the B
diffusivity in Si [11] in the range of )1150...700( oC at
7106 −⋅=oD cm2/s and 68.1=aE eV and at more
high temperature with 1.17=oD cm2/s and 66.3=aE
eV [9]. The calculation shows, that at temperature
67
~1330 K these both dependencies give close values of B
diffusivity in Si. This temperature, according to [12], is
the point of transition from vacancy mechanism of the
Ge-diffusion in Si to self-interstitials mechanism at more
high temperature.
The theory [13] predicts, that this temperature in Si
is equal 1220 K. The authors [10] consider, that the
diffusion of phosphorus in Si0.7Ge0.3 is caused by the
same defects, as in Si, i.e. at temperature below 1250 K
it is caused by monovacancy mechanism. According to
data (table 1), the recovery of electrical activity of
phosphorus in n-Si0.7Ge0.3 at irradiation by fast-pile
neutrons at temperature 810 K one can describe as the
relaxation process (4) with characteristic time
5105.1 −⋅=oτ s and Ea = 3.3 eV. Therefore, the
diffusion coefficient of phosphorus in Si0.7Ge0.3 can be
usually described by Arrhenius equation:
( )kTDD P
o
P /3.3exp −⋅= . Comparing the expression
(8) with the latter at temperature 1250 K one can
receive, that the pre-exponential factor P
oD is equal
2.1 cm2/s. At such comparison the observed process of
radiationally accelerated diffusion of the doped impurity
is caused only by higher temperature of their diffusion in
thermal peaks. So, the diffusion coefficient of
phosphorus in Si0.7Ge0.3 is ~ 5.6 times higher, than in Si
at 1250 K. In Si0.8Ge0.2 the values of B diffusion
coefficient are one order less, than in Si, because of the
Ge and B atoms interaction [14, 15].
The formation of B complexes with Ge can happen
probably due to the elastic deformation of lattice, the
minimum condition of which requires, that the atoms,
causing this deformations, were joined in complexes. In
our case one can assume, that at such fast melting of
cascade regions in p-Si0.7Ge0.3 boron will not participate
in the creation of the complexes with Ge atoms. Then at
temperature 1250 K B diffusivity in Si0.7Ge0.3 will only
be in 5.6 times less, than in Si. According to data (table
1) the recovery of boron electrical activity in p-Si0.7Ge0.3
during reactor irradiation by neutrons at temperature
810 K is also possible to describe by the relaxation
process (4) with parameters 6105.3 −⋅=oτ s,
45.3=aE eV. After the comparison at temperature
1250 K, as in case of phosphorus, we receive the pre-
exponential factor of B diffusion in p-Si0.7Ge0.3
44.0=B
oD cm2/s. Irradiation temperature of samples
n- and p-Si0.7Ge0.3, equal 810 K, is not enough, to
observe directly the diffusion of boron or phosphorus
even at such irradiation times. But one can study at this
temperature the relaxation of electrical properties of
solids, connected with the transition of doped atoms
from one site to other. Then it is possible to determine
the appropriate relaxation times and corresponding
diffusivity. Therefore, one can think, that in research
samples studied at irradistion in the active zone of
reactor the increase of electrical activity of doped
impurity is caused by radiation-accelerated diffusion. It
can be connected with the melting, though extraordinary
fast, of sample regions due to PKA thermal peaks
formation. In the process of the cooling such regions
become homogeneous, causing the effect of radiation
acceleration of diffusion. The PKA on average spends
on elastic collisions ~28 keV. The other energy is spent
on ionization and is scattered by lattice electrons during
period of ~ 16105 −⋅ s. In our experiment small-sized
clusters are annihilated at irradiation temperature
without creating the melting regions and the average
cluster is disintegrated on 3...2 subclusters. Therefore
the mean energy for the formation of thermal peak is
equal ~10 keV, which is spent on elastic collisions with
atoms of lattice by PKA. Authors [16] has shown, that
the size of cascade, created by 10 keV PKA, is equal L
~100 Å in Si. Brinkman [17] has argued, that regions of
size approximately ~ 104 atoms are extraordinary fast
melted with significant redistribution of particles
because of turbulent flows. The strict mathematical
description of the radiation-induced diffusion (RID)
have given by Dienes and Vineyard [18] :
( ) 512/ LND oRID ⋅= , (9)
where Σ⋅= INo is the number of thermal spikes,
formed in volume of 1 cm3 by 1 second, and Σ is the
cross-section of formation of thermal spikes.
Then 18102.1 −⋅=P
RIDD cm2/s is the radiation-
induced diffusion coefficient of phosphorus in
n-Si0.7Ge0.3 presented at condition, that the radius of
melting region 5.62=r Å. The process of recovery of
electrical activity of phosphorus is completed at the dose
of fast neutrons ~ 19100.2 ⋅ cm-2 and boron dose ~
18107 ⋅ cm-2, that corresponds to radiuses of melted
zone ~62.5 Å and 58.6 Å, and melted volume fraction is
equal %95...90 , accordingly.
From expression TDc ⋅⋅= ρχ , where χ is the
thermal conductivity of n- and p-Si0.7Ge0.3 samples (
112 cmKW1085.2 −−−⋅=χ ), c is the specific heat (
-1-1-1 mothKsW2.31 ⋅⋅⋅=c ), ρ is density ( 38.3=ρ
gr/cm3) one can find the temperature conductivity
coefficient ( TD ) ( 2101.1 −⋅=TD cm2/s) at temperature
of 1500 K close to that of crystal melting [19].The
influence of thermal spikes, created by PKA on
radiation-induced diffusion of impurities have been
considered by the authors [20]:
( ) ⋅⋅⋅⋅= )/()3/2(3/5.1
TooRID DNDD Γπ
3/5))/(( mQcQk ⋅⋅⋅⋅ ρ , (10)
where 354.1)3/2( =Γ ; k is Boltzmann constant;
3.3=mQ eV is the activation energy for phosphorus
migrations; 10=Q keV is PKA energy, spent on elastic
collisions.
Then, according to (10) 18104.2 −⋅=P
RIDD cm2/s
for phosphorus. According to Brinkman the radiation-
accelerated diffusivity of boron 18102.2 −⋅=B
RIDD
68
cm2/s, and according to (10) this value is equal
18102.1 −⋅ cm2/s. At the beginning of irradiation (see
fig. 1, 2) the growth of the resistivity of
n- and p-Si0.7Ge0.3 samples is observed, that is connected
with the reduction of concentration of electrically active
impurities of phosphorus and boron and is characterized
by time constant 3107 ⋅=τ s. The irradiation, creating
vacancy-interstitial pairs, transfers the doped impurities
from sites to the interstitial positions. Therefore the
kinetics of formation of defect complexes, steady at
irradiation temperature 810 K, can be calculated and the
migration of doping impurity of boron and phosphorus
is described through self-interstitial mechanism. Usually
the diffusion is considered as the process of random
movement of diffusion particles, which jump in
succession along axes X on the distance x∆ . In the Fick
differential equation the value τ∆ 2/)( 2xD = is given,
representing a diffusivity during random movement of
particles in the given direction. In case of crystal lattice:
τ/2daD ⋅= ( 8105.5 −⋅=d cm, 12/1=a ,
3107 ⋅=τ s), so at irradiation in reactor of n- and
p- Si0.7Ge0.3 at temperature 810 K the diffusivities of
phosphorus and boron are equal 20106.3 −⋅=D cm2/s.
Received expressions for the diffusivity of phosphorus
and boron:
( )kTD P /3.3exp1.2 −⋅= ,
( )kTD B /45.3exp44.0 −⋅= , which are correct at high
temperature (T >1250 K), can be used correctly at
810 K during the irradiation process (the monovacancy
diffusion mechanism should not result in electrical
activity loss of doped impurity). Then the diffusion
coefficient of boron and phosphorus ( 20106.3 −⋅=D
cm2/s) received above can be realized at 840 K - local
temperature for the P interstitial diffusion and at 910 K -
local temperature for the B interstitial diffusion, that
testifies to radiation-accelerated diffusion of these
impurities. Atom Ge, receiving the energy of 41 keV
creates in Ge lattice overheated to 1060 K region of
radius 95 Å and the duration of existence of thermal
spike is equal 12103 −⋅ s ([3], p. 248). The mentioned
calculations had shown that in the alloy of n- and
p-Si0.7Ge0.3 on the average the region of 60 Å, existence
of which was 12109 −⋅ s, was melted. The P and B
diffusivities being equal ~ 4103 −⋅ cm2/s at the melting
point are quite sufficient for atoms to overcome one
internuclear distance during melting time existence.
The processes of doped impurity annealing is com-
pleted at quite definite dose of the irradiation of n- and
p-Si0.7Ge0.3 by fast-pile neutrons (see fig. 1, 2). One can
characterize them according to (4), by constant times of
restoration of electrical activity of phosphorus
61025.1 ⋅=Pτ s and boron 61029.1 ⋅=Bτ s. Such
process of restoration take place in each region, which
is equal to the size of thermal spike. Then one can
assume that the coefficient of radiation-induced
diffusion can be determined according to the expression:
τπ 2/4 2rDRID ⋅= , (11)
where r is radius of thermal spike, τ is constant time of
restoration of electrical activity of dopant.
Then the coefficient of radiation-induced diffusion
for phosphorus in Si0.7Ge0.3 is equal P
RIDD = 18100.2 −⋅
cm2/s and for boron =B
RIDD 18107.1 −⋅ cm2/s at 810 K,
according to (11).
CONCLUSION
Dose dependence of the n- and p-Si0.7Ge0.3 resistivity
after high-temperature baking without annealing is
described in frameworks of effective medium theory and
theory of radiation - induced diffusion of doped
impurities. The observable features of the dose
dependence of resistivity of n- and p-type SiGe solid
solutions are connected with doped impurities annealing
in the process of irradiation in reactor and are explained
by the defect clusters formation. Coefficients of
interstitial diffusion of phosphorus and boron in
n- and p-Si0.7Ge0.3 are determined.
REFERENCES
1.A.P. Dolgolenko. The influence of defect clusters on
redistribution of doping impuriyies in n- and p- Si0.7Ge0.3
under reactor irradiation //Fiz. Tech. Poluprov. 1999, v.
33, N4, p. 405–409.
2.I.М. Lifshitz. About thermal spikes in the medium ir-
radiated by nuclear radiation //DAN USSR. 1956,
v. 109(6), p. 1109–1111.
3.М.J. Thompson. Defects and Radiation Damage in
Metals. M.: “Mir”, 1971, p. 367.
4.I.М. Lifshitz, М.I. Kaganov, L.B. Tanatarov. To the
theory of radiation changes in metals //Atomnaja En-
ergija. 1959, v. 6(4), p. 391–402.
5.F.F. Komarov, A.P. Novikov, V.S. Solovjev,
S.Yu. Shirjaev. Defect structures in ion-implanted sili-
con //Mn.: University, 1990, p. 86.
6.A.P. Dolgolenko. About the averedge defect concen-
tration in clusters formed by fast-pile neutrons in n-Si
//Radiation defects in silicon //Kyiv, 1976 (Preprint
KINR-76-23), p. 12–13.
7.R.S. Walker and D.A. Thompson. Computer Simula-
tion of Ion Bombardment Collision Cascades //Radia-
tion Effects. 1978, v. 37, p. 113–120.
8.Coher H.Morrel and Jortner Joshua. Effective Medium
Theory for the Hall Effect in Disordered Materials
//Phys. Rev. Letters. 1973, v. 30, N15, p. 696–698.
9.B.I. Boltaks. Diffusion and point defects in semicon-
ductor. L.: "Nauka", 1972, p. 384.
10.D. Mathiot, J.C. Dupuy. Phosphorus diffusion in
Si0.7Ge0.3 //Appl. Phys. Lett. 1991, v. 59, N1, p. 93–95.
11.G.L. Vick, K.M. Whittle. Solid Solubility and Diffu-
sion Coefficients of Boron in Silicon //J. Electrochem.
Soc. 1969, v. 116, N 8, p. 1142–1144.
12.G. Hettich, H. Mehrer and K. Maier. Tracer diffusion
of 71Ge and 31Si in intrinsic and doped silicon /Defects
69
and Radiation Effect in Semicondactors. Bristol and
London: Inst. Phys. Conf. Ser. N46, 1978. Chapter 9. p.
500–507.
13.Seeger and K.P. Chik. Diffusion Mechanisms and
Point Defects in Silicon and Germanium //Phys. Stat.
Solidi (b). 1968, v. 29, N 2, p. 455–542.
14.P. Kuo, J.L. Hoyt, J.F. Gibbons, J.E. Turner,
K.D. Jacowitz, Kamins. Comparision of boron diffusion
in Si and strained Si 1-x Gex epitaxial layer //Appl. Phys.
Lett. 1993, v. 62, N6, p. 612–614.
15.P. Kio, J.L. Hout, J.F. Gibbous, J.E. Turner, D. Lef-
forge. Effects of strain on boron diffusion in Si and Si 1-
xGex //Appl. Phys. Lett. 1995, v. 66, N5, p. 580–582.
16.V.M. Lenchenko. Radiation effects in monocrystals.
"FAN" UzbSSR, 1972, p. 53–90.
17.John A. Brinkman. On the Nature of Radiation Dam-
age in Metals //J. Appl. Phys. 1954, v. 25, N8,
p. 961–970.
18.D. Dins, J. Vinjard //Radiation defects in solid states.
1960, IL, p. 35.
19.М.G. Kekua, E.V. Khutsishvili. Solid solution of
germanium-silicon semiconductor system. Tbilisi:"Met-
sniereba", 1985, p. 174.
20.V.M. Lenchenko, T.S. Pugacheva //Proc. "Radiation
effects in solid states". Tashkent: "FAN" UzbSSR,
1963, p. 78.
ОТЖИГ ВЫСОКОЛЕГИРОВАННЫХ МАТЕРИАЛОВ НА ОСНОВЕ ТВЕРДОГО РАСТВОРА
n- и p-Si0.7Ge0.3 В ПРОЦЕССЕ РЕАКТОРНОГО ОБЛУЧЕНИЯ
А.П. Долголенко
Исследованы образцы n- и p-типа проводимости твердого раствора кремний-германий с удельным сопротивлением
310)7...4( −⋅ Ом/см, не прошедшие отжига после высокотемпературного спекания. Образцы облучались до флюенса
~1020 no·cм-2 в активной зоне реактора ВВР-М при температуре ~500 ºC в смешанном нейтронном поле. В процессе облу-
чения наблюдались не только преципитация легирующей примеси бора и фосфора, но и увеличение их растворимости,
обусловленное кластерами дефектов. Показано, что радиационное перемешивание можно описать на языке диффузион-
ных и релаксационных процессов. Изменение удельного сопротивления в зависимости от флюенса быстрых нейтронов
описано в рамках теории эффективной среды. Определены энергии активации процесса отжига легирующих примесей и
характерные размеры кластеров дефектов.
ВІДПАЛ ВИСОКОЛЕГОВАНИХ МАТЕРІАЛІВ НА ОСНОВІ ТВЕРДОГО РОЗЧИНУ
n- ТА p-Si0.7Ge0.3 В ПРОЦЕСІ РЕАКТОРНОГО ОПРОМІНЮВАННЯ
А.П. Долголeнко
Досліджені зразки n- та p-типу провідності твердого розчину кремній-германій з питомим опором 310)7...4( −⋅
Ом/см, що не пройшли відпал після високотемпературного спікання. Зразки опромінювались до флюєнсу ~1020 no·cм-2 в
активній зоні реактора ВВР-М при температурі ~500 ºC в змішаному нейтронному полі. В процесі опромінювання
спостерігались не тільки преципітація легуючої домішки бору та фосфору, але й збільшення їх розчинності, що
обумовлено кластерами дефектів. Показано, що радіаційне перемішування можна описати в термінах дифузійних та
релаксаційних процесів. Зміна питомого опору в залежності від флюєнсу швидких нейтронів описана в рамках теорії
ефективного середовища. Визначені енергії активації процесу відпалу легуючих домішок та характерні розміри
кластерів дефектів.
70
THE ANNEALING OF HIGH - LEVEL DOPED MATERIALS ON THE BASE OF THE n – AND p – Si0.7 Ge0.3 SOLID SOLUTION UNDER REACTOR IRRADIATION
PACS: 61.80.Hg; 61.72.Ji; S5.11-12
INTRODUCTION
Experiment
THEORY
DISCUSSION
CONCLUSION
REFERENCES
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