Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons
We have studied the high-resistance samples of p-Si (р00 = (3.3 ± 0.5) × × 10¹² cm⁻³ ) and n-Si (n₀ = (2.0 ± 0.3) × 10¹² cm⁻³ ) grown by the floating-zone technique after the irradiation by fast-pile neutrons at 287 К. The dose and the temperature dependences of the effective concentration of c...
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Dolgolenko, A.P. Varentsov, M.D. Gaidar, G.P. Litovchenko, P.G. 2017-05-29T19:37:10Z 2017-05-29T19:37:10Z 2007 Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons / A.P. Dolgolenko, M.D. Varentsov, G.P. Gaidar, P.G. Litovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 4. — С. 9-14. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS 61.72.Ji, 61.80.Hg, 61.82.Fk, 71.55.Cn https://nasplib.isofts.kiev.ua/handle/123456789/118342 We have studied the high-resistance samples of p-Si (р00 = (3.3 ± 0.5) × × 10¹² cm⁻³ ) and n-Si (n₀ = (2.0 ± 0.3) × 10¹² cm⁻³ ) grown by the floating-zone technique after the irradiation by fast-pile neutrons at 287 К. The dose and the temperature dependences of the effective concentration of carriers have been measured. The calculation has been carried out in the framework of Gossick's corrected model. It is shown that the radiation hardness of n- and p-Si, on the one hand, is defined by clusters, and, on the other hand, by vacancy defects (acceptors) in n-Si and by interstitial defects (donors and acceptors) in p-Si. We have determined that, during the irradiation of p-Si by small doses of neutrons, the change of a charge state of interstitial defects leads to the annealing of these defects and to a decrease of their introduction rate. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons Article published earlier |
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| title |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons |
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Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons Dolgolenko, A.P. Varentsov, M.D. Gaidar, G.P. Litovchenko, P.G. |
| title_short |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons |
| title_full |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons |
| title_fullStr |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons |
| title_full_unstemmed |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons |
| title_sort |
dependence of the defect introduction rate on the dose of irradiation of p-si by fast-pile neutrons |
| author |
Dolgolenko, A.P. Varentsov, M.D. Gaidar, G.P. Litovchenko, P.G. |
| author_facet |
Dolgolenko, A.P. Varentsov, M.D. Gaidar, G.P. Litovchenko, P.G. |
| publishDate |
2007 |
| language |
English |
| container_title |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| format |
Article |
| description |
We have studied the high-resistance samples of p-Si (р00 = (3.3 ± 0.5) ×
× 10¹² cm⁻³
) and n-Si (n₀ = (2.0 ± 0.3) × 10¹² cm⁻³
) grown by the floating-zone technique
after the irradiation by fast-pile neutrons at 287 К. The dose and the temperature
dependences of the effective concentration of carriers have been measured. The
calculation has been carried out in the framework of Gossick's corrected model. It is
shown that the radiation hardness of n- and p-Si, on the one hand, is defined by clusters,
and, on the other hand, by vacancy defects (acceptors) in n-Si and by interstitial defects
(donors and acceptors) in p-Si. We have determined that, during the irradiation of p-Si by
small doses of neutrons, the change of a charge state of interstitial defects leads to the
annealing of these defects and to a decrease of their introduction rate.
|
| issn |
1560-8034 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118342 |
| citation_txt |
Dependence of the defect introduction rate on the dose of irradiation of p-Si by fast-pile neutrons / A.P. Dolgolenko, M.D. Varentsov, G.P. Gaidar, P.G. Litovchenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2007. — Т. 10, № 4. — С. 9-14. — Бібліогр.: 11 назв. — англ. |
| work_keys_str_mv |
AT dolgolenkoap dependenceofthedefectintroductionrateonthedoseofirradiationofpsibyfastpileneutrons AT varentsovmd dependenceofthedefectintroductionrateonthedoseofirradiationofpsibyfastpileneutrons AT gaidargp dependenceofthedefectintroductionrateonthedoseofirradiationofpsibyfastpileneutrons AT litovchenkopg dependenceofthedefectintroductionrateonthedoseofirradiationofpsibyfastpileneutrons |
| first_indexed |
2025-11-26T01:42:45Z |
| last_indexed |
2025-11-26T01:42:45Z |
| _version_ |
1850605160316796928 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
9
PACS 61.72.Ji, 61.80.Hg, 61.82.Fk, 71.55.Cn
Dependence of the defect introduction rate on the dose
of irradiation of p-Si by fast-pile neutrons
A.P. Dolgolenko, M.D. Varentsov, G.P. Gaidar*, P.G. Litovchenko
Institute for Nuclear Research, NAS of Ukraine,
47, prospect Nauky, 03680 Kyiv, Ukraine, fax: 380-44-5254463
*Corresponding author: e-mail: gaidar@kinr.kiev.ua
Abstract. We have studied the high-resistance samples of p-Si (р00 = (3.3 ± 0.5) ×
× 1012 cm−3) and n-Si (n0 = (2.0 ± 0.3) × 1012 cm−3) grown by the floating-zone technique
after the irradiation by fast-pile neutrons at 287 К. The dose and the temperature
dependences of the effective concentration of carriers have been measured. The
calculation has been carried out in the framework of Gossick's corrected model. It is
shown that the radiation hardness of n- and p-Si, on the one hand, is defined by clusters,
and, on the other hand, by vacancy defects (acceptors) in n-Si and by interstitial defects
(donors and acceptors) in p-Si. We have determined that, during the irradiation of p-Si by
small doses of neutrons, the change of a charge state of interstitial defects leads to the
annealing of these defects and to a decrease of their introduction rate.
Keywords: silicon, neutron irradiation, radiation hardness, radiation defect, cluster.
Manuscript received 19.10.07; accepted for publication 19.12.07; published online 30.01.08.
1. Introduction
The radiation hardness of semiconductor devices keeps
the attraction of researches. The actuality of the data on
the type and the characteristics of radiation defects in
such materials increases significantly due to the
realization of the project of a Super Large Hadron
Collider (SLHC) with a luminosity of ~1035 cm−2s−1.
This demands the detectors with radiation hardness more
than ~1016 noсm−2. The high carrier mobility in n-type Si
(by 3.5 orders more than that for p-type) and its working
capacity after n → p conversion make the ionizing
radiation detectors fabricated on n-type Si very
attractive.
It should be noted that the formation of defects
substantially depends on the temperature, at which the
samples are irradiated. For example, the irradiation
below 120 K decreases the defect introduction rate by
several orders [1]. In [2], it was shown that the intensity
of near-edge absorption and the rate of post irradiation
annealing of defect clusters are considerably higher for
silicon crystals irradiated by fast neutrons at 100 K. This
can be explained by the high introduction rate of non re-
orientation divacancies, which are strongly annealed
under the temperature higher than 140 K. The low-
temperature irradiation also suppresses the participation
of oxygen in the formation of electrically active oxygen-
contained defects.
Taking into account the above-mentioned, the main
objectives of the present paper are: (i) to measure and to
describe the temperature dependence of the hole effect-
tive concentration in p-Si irradiated by various fluences
of fast neutrons; (ii) to compare the radiation hardness of
n- and p-Si; (iii) to calculate the dependence of the
defect introduction rate on the irradiation dose.
2. Experiment
High-resistance samples of p-Si (p00 = (3.3 ± 0.5) ×
× 1012 cm−3) and n-Si (n0 = (2.0 ± 0.3) × 1012 cm−3)
grown by the floating-zone technique with a specific
resistance of near 10 kOhm·cm were irradiated by
various fluences of fast-pile neutrons at a temperature of
287 K. The irradiation was performed in the horizontal
channel of a water-moderated research reactor
(WWR-M) with a neutron beam intensity of
5 × 108 noсm-2s-1 and the fluences from 1011 till
2 × 1014 noсm−2. The neutron fluence was determined by
a 32S threshold detector with accuracy of 10 % for the
energy of neutrons starting from ~100 keV. The
measurements of conductivity and the Hall coefficient
were carried out by the van der Pauw compensatory
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
10
method on samples of 10 × 10 × 1 mm in size with
accuracy of 3 %. Contacts were formed by the rubbing
of aluminum into the silicon polished surface.
3. Results
The temperature dependences of the effective hole
concentration for p-Si irradiated by different fluences of
fast-pile neutrons are presented in Figs. 1 and 2. The
evaluated values for the parameters of radiation defects
are presented in Table 1.
Fig. 3 shows the dependences of the effective
concentrations of carriers in n- and p-type Si on the
fluence of fast-pile neutrons.
The dependences of the introduction rates of
radiation defects on the irradiation time (at 287 K) are
presented in Fig. 4.
Table 1. Radiation defect parameters for p-Si irradiated by
fast-pile neutrons at 287 K.
Φ ,
noсm−2
p00,
сm−3
Nai, сm−3 νi, cm−1 Ev + Eai,
eV
R1, Ǻ
5 × 1012 2.96 ×
× 1012
1.5 × 1013
1.5 × 1012
8.0 × 1011
3
0.3
0.16
0.42
0.51
0.45
36
7.55 ×
× 1012
3.22 ×
× 1012
8.0 × 1012
1.6 × 1012
4.9 × 1011
1.0 × 1012
1.06
0.21
6.5 × 10−2
0.13
0.42
0.51
0.33
0.45
36
1.0 ×
× 1013
2.68 ×
× 1012
6 × 1012
1.7 × 1012
6.2 × 1011
0.6
0.17
6.2 × 10−2
0.42
0.51
0.45
36
1.89 ×
× 1013
3.16 ×
× 1012
1.7 × 1012
1.16 × 1012
8.5 × 1011
9 × 10−2
6.2 × 10−2
4.5 × 10−2
0.42
0.51
0.45
36
2.26 ×
× 1013
2.84 ×
× 1012
2.2 × 1012
1.04 × 1012
9.7 × 10−2
4.6 × 10−2
0.42
0.51
36
2.64 ×
× 1013
3.18 ×
×1012
2.5 × 1012
1.3 × 1012
9.5 × 10−2
4.9 × 10−2
0.42
0.51
36
2.83 ×
× 1013
3.17 ×
× 1012
2.15 × 1012
1.13 × 1012
7.6 × 10−2
4 × 10−2
0.42
0.51
36
3.02 ×
× 1013
2.97 ×
× 1012
2.1 × 1012
7.25 × 1011
7 × 10−2
2.4 × 10−2
0.42
0.51
36
3.21 ×
× 1013
3.18 ×
× 1012
2.5 × 1012
6.3 × 1011
7.8 × 10−2
2 × 10−2
0.42
0.51
36
Annealing at 292 К; 8.04 × 106 s
5 × 1012 2.96 ×
× 1012
1.0 × 1011
1.25 × 1012
1.6 × 1011
2.0 × 1011
2 × 10−2
2.5 × 10−2
3.2 × 10−2
0.1
0.42
0.36
0.33
0.26
20
Note. The level with energy Ev + 0.42 eV is the acceptor level
and all other levels with energy Ev + Eаi are the donor ones. Φ
is a fluence of fast-pile neutrons, р00 is a carrier concentration
before the irradiation; Nаi is the concentration of the i-th defect
with energy level in the forbidden band Ev + Eаi; νi is the
introduction rate of the i-th defect; and R1 is the average radius
of the clusters of defects.
3 4 5 6 7 8106
107
108
109
1010
1011
1012
1013
54
3
2
1
p ef
f ,
сm
-3
103/T, K-1
Fig. 1. Temperature dependences of the effective carrier
concentration (peff) for p-Si irradiated by fast-pile neutrons
with fluences: 1 - 5 × 1012; 2 – 7.55 × 1012; 3 - 1.0 × 1013; 4 -
1.89 × 1013 nосm−2; 5 – after annealing (8.04 × 106 s) under a
fluence of 5 × 1012 nосm−2 at 292 K. Symbols present the
experimental data; solid lines are the results of calculations.
3.5 4.0 4.5 5.0
108
109
1010
1011
103/T, K-1
p ef
f ,
сm
-3
4
3
2 1
Fig. 2. Temperature dependences of effective carrier
concentration (peff) for p-Si irradiated by fast-pile neutrons
with fluences: 1 – 2.264 × 1013; 2 – 2.64 × 1013; 3 -
2.83 × 1013; 4 - 3.02 × 1013 nосm−2. Symbols present the
experimental data; solid lines are the results of calculations.
1011 1012 1013 10141010
1011
1012
p ef
f ,
сm
-3
Φ , nocm-2
1
2
1'
2'
Fig. 3. Dependence of the effective concentrations of carriers
(peff) on the fluence (Ф) of fast-pile neutrons at 292 K in
silicon samples, grown by the floating-zone technique: ∆ – p-
Si (p00 = 3.2 × 1012 сm−3) and ○ – n-Si (n0 = 2.0 × 1012 сm−3);
the results of calculations with (1, 1') and without (2, 2')
account of the additional overlapping of defect clusters are
presented by solid lines.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
11
10-1
100
t , с
5⋅1044⋅1043⋅1041⋅104
Ev+ 0,51 eV
Ev+ 0,45 eV
Ev+ 0,42 eV1
3
2ν
, c
m
-1
2⋅104
Fig. 4. Dependence of the introduction rate of defects with
energy levels Еv + 0.42 eV (1), Еv + 0.45 eV (2), and
Еv + 0.51 eV (3) on the irradiation time of р-Si samples at 287 К.
4. Calculation of the temperature and dose
dependences of the effective carrier concentration
The primary knock-on silicon atoms, originated due to
the irradiation of Si by fast-pile neutrons, produce the
vacancies and interstitial defects along trajectories of
motion. At the end of a trajectory, the high local
concentration of defects is created (after their athermic
realignment), which leads to the formation of the
clusters of vacancy- and also interstitial-type defects in
the conductive matrix of a sample.
The process of accumulation of the clusters of
defects in a separate volume is similar to the activation
and decay of radioactive nuclei. Thus, the volume
fraction (f ), occupied by clusters (due to the introduction
of point defects), with regard for the overlapping of
clusters in accordance with [3], can be evaluated as
)exp())exp(1( 1 ΦΣ−⋅ΦΣ−−= VVf , (1)
where Σ = 0.15 cm−1 is the macroscopic cross-section of
the introduction of clusters due to the irradiation by fast-
pile neutrons; Σ1 is the probability of the overlapping of
the clusters of defects, cm−1; V is the separate volume of
an average defect cluster, cm3; Ф is the fluence of fast-
pile neutrons, nocm−2.
The probability of the overlapping of the clusters of
defects is substantially smaller than that of the formation
of the clusters of defects: Σ1 << Σ.
Within Gossick's model for the cluster volume
[4], the effective concentration of carriers depending on
the temperature and a small fluence is given by the
formula [5]
,
),(
)(
ln
),(
4
exp
),(),(
2
2
2
10
eff
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
Φ
−µ
Φ
Φ∑εεπ
−×
×Φ=Φ
TP
TN
Tk
qTP
R
TpTp
V
p
(2)
where ( )Φ,Tp is the concentration of carriers in the р-Si
conduction matrix; ),(2 ΦTP is the concentration of
screening centers in the space charge region of defect
clusters; )(TNV is the effective density of states in the
valence zone of p-Si; R1 is the average radius of defects
gathering regions; ε and ε0 are the dielectric constants of
a material and vacuum, respectively; q is the carrier
charge; µp is the Fermi level position relative to the top
of the valence zone at the center of the damage region of
a defect cluster.
For the correct calculation of рeff(Т, Ф), the
compensation of the conductive matrix must be taken
into account, which leads to the additional overlapping
in the space charge region of defect clusters in
accordance with (1).
The Fermi level position is determined by
thermodynamical characteristics of the system. Thus, µ
and ( )),()(ln 2 ΦTNTNkT c for n-Si can be defined as
an increment of the free energy of the system (a cluster
and the conducting matrix) on the addition of one electron
at the constant volume and temperature. Then
ΦΣεεπΦ 102
2 4),( RTNq can be described as a
decrease in the free energy for the full system on the
formation of ΦΣ defect clusters per volume unit. If the
energy direction should be changed, the above-mentioned
considerations will correspond to holes in p-Si.
Divacancies are multi-charge centers, whose donor
(Еv + 0.25 eV) and acceptor (Ес − 0.42 eV) levels
determine the position of the Fermi level µ =
Еv + 0.475 eV in the defect clusters formed by fast
neutrons in p-Si. In the intrinsic silicon, the Fermi level
should be located at the level of a neutral divacancy
which becomes apparent in experiments as the
recombination level Еc − 0.62 eV under the full
overlapping of defect clusters. With decrease in
temperature, the electrons and holes are captured on the
level Еv + 0.52 eV and recombine with one another. The
Fermi level moves to the middle of the forbidden band.
At the capture of a free electron (supplied by the
ionization of dopants), the energy of a divacancy will
increase by 0.165 eV. Thus, with increase in the n-Si
doping level (n0), the Fermi level in a cluster can be
defined as
innE 0c log033.06.0 +−=µ , (3)
where n0 is the concentration of electrons in the
conduction band before the irradiation, cm−3;
ni = 1010 cm−3 is the concentration of carriers in intrinsic
silicon. Eq. (3) corresponds to the experimentally
determined position of the Fermi level in n-Si (with
different n0) irradiated by the fluence of fast-pile
neutrons, at which the defect clusters are fully
overlapped.
Let us consider р-Si doped by boron with non
compensated concentration Nа in the range from room
temperature to liquid nitrogen one. Let fast-pile neutrons
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
12
homogenously form the donor-type point defects (apart
from the defect gathering region) with concentration
Nd < Na and the acceptor-type defects. We consider p-Si
as non-degenerated (Na < 1014 сm−3). Then, as the
temperature of a p-Si sample increases from 77 K, we
obtain some concentration of holes (in the valence band)
due to the thermal excitation of holes from the Ed level
both in the conduction matrix p1(T, Ф) and in the space-
charge regions of defect clusters P3(T, Ф)
,1
)(
)(
)(4
1
)(
)(
2
1),,(
2
11
11
111
⎟⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎜
⎜
⎝
⎛
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
λ
Φ
−
+×
×⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
λ
Φ
−=Φ
d
d
a
da
d
d
ad
Ep
N
N
EpN
Ep
N
NETp
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
λ
−=
Tk
E
TNgEp d
Vd exp)()(11 , (4)
where g = 2 is the factor of donor level degeneration in
p-Si; Nd(Ф) is the concentration of radiation-introduced
donor defects after the irradiation by the fluence Ф;
р11(Еd) is the concentration of holes in the valence band
of p-Si under condition that the Fermi level coincides
with the Еd level in the conductive matrix or the
effective level Еd /λ in the space-charge regions of defect
clusters. Equation (4) was obtained from solving the
quadratic expression which follows from the condition
of electroneutrality [5].
In a similar manner with increase in the tempe-
rature of a p-Si sample from 77 K, we obtain some
concentration of holes in the valence band due to the
thermal excitation of carriers from the acceptor level Еа
both in the conducting matrix р0(Т, Φ ) and in the space-
charge regions of defect clusters Р4(Т, Φ )
( )
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
Φ
+=Φ 1
)(
)(4
1)(
2
1,,
11
110
a
a
aa Ep
N
EpETp ,
( ) ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
λ
−=
Tk
E
TNgEp a
Va exp)(111 , (5)
where g1 = 0.5 is the degree of acceptor level
degeneration in p-Si; and Na(Ф) is the concentration of
radiation-introduced acceptor-type defects after the
irradiation by the fluence Ф.
If the donor and acceptor defects are located in the
conducting matrix of p-Si, then λ = 1. But if they are in
the space-charge regions of defect clusters, then λ = 1.2.
The analysis of the temperature dependences рeff(Т, Ф)
shows that their better description will be obtained on
the supposition that defects (with effective level Еа /λ)
are present in the space-charge regions, which
compensates the screening effect of a shallow dopant
(boron). The energy position of the mentioned level in
the conducting matrix in p-Si is Ea. Then the additional
hole concentration in the valence band of the conducting
matrix of samples of p-Si is equal to р = р0 + р1, and the
supplementary concentration of screening centers in the
space-charge regions of defect clusters is P2 = P4 + P3.
Figures 1 and 2 show the calculated [according to
Eqs. (2), (4), and (5)] the temperature dependences of
effective hole concentrations in the valence band of p-Si
under irradiation by various fluences of fast-pile
neutrons. The parameters of calculations are presented in
Table 1. It was supposed that, in the case of the absence
of a statistical interaction between the levels of radiation
defects, the carrier concentration in the conducting
matrix of p-Si can be determined by the calculation of
the total concentration of holes ( )∑ Φ
i
ii ETp ,, , which
will be supplied into the valence band due to the
ionization of acceptor and donor levels:
( ) ( )∑ Φ+−Φ=Φ
i
Dii NpETpTp )(,,, 00 . (6)
Here, i is the index running from 1 to 3 (we assume
the presence of one acceptor and two donor defect levels
in the conductive matrix); p00 is the hole concentration in
p-Si before irradiation; and )(ΦDN is the concentration
of the deepest donor levels.
The concentration of screening centers in the
space-charge regions of defect clusters can be
determined with accordance to (4) and (5) for λ = 1.2 as
( ) ( ) ( )∑ λ
Φ
+−Φ=Φ
i
D
ii
N
pETPTP 0022 ,,, , (7)
where i is the index running from 1 to 3 (we assume the
presence of one acceptor and two donor defect levels in
the space-charge regions); and )(ΦDN is the concen-
tration of radiation-induced defects.
5. Discussion
The analysis of the literature data shows a lot of data
concerning the radiation defects, whose energy levels are
located in the forbidden band with a spacing from 0.02
to 0.05 eV [6]. Nevertheless, many defect levels are
undefined (see, e.g., [7]). However, the problem of
radiation defect levels is complicated by the fact that the
theoretical calculation of the energy level position for
deep states is unsolved so far despite some successful
results.
In [8], the original scheme of energy levels for
intrinsic radiation defects, which is based both on the
literature data and the original experiment, was
proposed. It takes the following positions into account:
(i) radiation defects form the additional energy levels in
the forbidden band, and the intrinsic defects in silicon
are amphoteric; (ii) under capture of one or two
electrons on acceptor levels of a divacancy or a di-
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
13
interstitial, the position of levels in the forbidden gap of
silicon is changed by the value ∆Е0 = 0.165 ± 0.005 eV,
and, in the case of vacancies or interstitials, the
mentioned value is added twice; (iii) the modification of
a divacancy by carbon increases the energy position of
acceptor levels by the value ∆Е1 = 0.035 eV and
decreases the energy of donor levels, whereas the
addition of oxygen to a divacancy decreases the acceptor
level energy and increases the donor level energy of a
divacancy by the value ∆Е2 = 0.06 eV.
The analysis and the results presented in [8] gave
us a possibility to determined the fact that the energy of
acceptor levels is increased by value ∆Е = 0.33 / ξ under
the electron capture, where ξ is the number of vacancies
in the multivacancy defects (1 ≤ ξ ≤ 5).
The positions of acceptor levels relative to the
bottom of the conduction band and those of donor levels
relative to the valence band top for intrinsic radiation
defects in p-Si are presented in Table 2.
We assume (see the Table in [8]) that Еv + 0.42 eV
belongs to the acceptor level of interstitial levels (I−/0),
and Еv + 0.45 eV belongs to the donor level of di-
interstitials (I2
0/+). The increase in the number of
negatively polarized oxygen neighbors in the series of
Ci, CiOi, CiO2i leads to an upward shift of their donor
levels: Еv + 0.28 eV, Еv + 0.34 eV, Еv + 0.39 eV,
respectively. This can be explained by the effect of
increasing the repulsive electrostatic potential that
originates from oxygen atoms [9]. Thus, the observed
level Еv + 0.51 eV can be attributed to I2Oi
0/+ defects.
In Fig. 3, the results of theoretical calculations of
the dependence of the effective carrier concentration on
the fluence of fast-pile neutrons for n- and p-Si with and
without additional overlapping of defect clusters,
according to (1), are presented by solid lines. The
calculations were carried out in the frame of Gossick's
corrected model for the defect clusters with average radii
of defect gathering regions Rn = 40 Å and Rp = 36 Å for
the samples of n- and p-type silicon, respectively. While
calculating the carrier concentration in the conducting
matrix by (4) and (5), it was usually supposed that
Nа = р00, Na (Ф) = vа × Ф, and Nd (Ф) = vd × Ф, where vd
is the rate of hole removal by donor defects, and vа is the
rate of free hole generation by deep acceptor defects. In
the description of the dose dependence of the carrier
concentration, the introduction rate for a donor level
(Еv + 0.51 eV) is obtained as vd = 0.06 сm−1, and, for an
acceptor level (Еv + 0.42 eV), the value vа = 0.1 сm−1
was used. For n-Si, the introduction rate of three-
vacancy acceptor defects (Ес - 0.49 eV) was taken as
ν = 0.25 сm−1. It was found that the average value of the
introduction rate for defects allows one to get a
satisfactory description of the dose dependence рeff(Ф).
According to (3), the Fermi level position in the clusters
formed by fast-pile neutrons in n-Si is µ =
Ес − 0.524 eV. Fig. 3 shows that, after the irradiation
with a dose of ~5 × 1013 noсm−2, the carrier concentration
in p-Si reaches a constant value of 8 × 1010 cm−3, and,
consequently, with the defect cluster overlapping, the
Fermi level stands near Еv + 0.476 eV (in the p-Si
forbidden gap), which is still unchangeable in the wide
range of the doping levels of samples. The calculation
shows that the probability of the additional overlapping
in the space-charge region of defect clusters in n-Si is
Σ1 = 0.006 cm−1, whereas Σ1 = 0.001 cm−1 for p-Si.
The radiation hardness for n-Si can be confidently
determined as vnRh /0= , where ν is the removal rate of
electrons in the conducting matrix. Then, for p-Si, it is
**
0
*
**
0
2 add
da
h vv
p
v
vp
R
−
=
Φ−Φν+
= ,
where *
av = 0.08 cm−1, and *
dv = 0.06 cm−1 are, respect-
tively, the rates of introduction and removal of holes at
292 К. Hence, the radiation hardness of p-Si is by one
order higher than that for n-Si irradiated by fast-pile
neutrons. The above-determined radiation hardness is, in
fact, the dose at which the conductivity of a sample is
minimal.
Figure 3 shows that, at low radiation doses, the
experimental values of effective carrier concentration
don't blend with the overall picture of the peff
dependence on the fluence of fast-pile neutrons. The
defect introduction rates presented in Table 1 (from the
calculation of the temperature dependence of peff) are
decreased by factors of 3−5 with increase in the
irradiation dose in the range from 5 × 1012 to
1013 noсm−2. The sample storage at room temperature
during three months results in that the defect levels
Еv + 0.51 eV and Еv + 0.45 eV are fully annealed, and
the introduction rate of Еv + 0.42 eV level is
considerably decreased. After the irradiation with a dose
of near 5 × 1012 nocm−2, the Fermi level position into the
conductive matrix is Еv + 0.38 eV. This means that the
donor levels of I2
+ and I2Oi
+ are in the positively charged
state, and interstitial atom (I) with the acceptor level
(Еv + 0.42 eV) is, in general, in the neutral state. In [10]
with the use of the first-order annealing kinetics, the
activation energy (Еа = 0.6 ± 0.2 eV) and the frequency
factor ν ≅ 108 s−1 for the isothermal annealing of I2
+(Р6)
(at 370 and 344 K) were evaluated. After the irradiation
by gamma-rays (60Со) and by fast-pile neutrons of
Table 2. Radiation annealing of interstitial-type defects.
De-
fect
Tanneal,
K
Activa-
tion
energy,
eV
Frequen-
cy
factor,
s−1
Annealing
reaction
Level
energy,
eV
I=/− 287 0.4 2.0 × 103 I− → I= Еv + 0.42
I2
0/+ 287 0.42 4.0 × 103 I2
+ → I2
0 Еv + 0.45
I2Oi
0/+ 287 0.42 2.5 × 103 I2Oi
+ →
→ I2Oi
0
Еv + 0.51
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2007. V. 10, N 4. P. 9-14.
© 2007, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
14
intrinsic p-Si, the authors [11] observed the annealing of
defects with the energy level (Еv + 0.40 eV) and the
activation energy Еа = 0.85 eV. According to Table 2,
the level (Еv + 0.42 eV) is attributed to an acceptor
defect. The energy of migration for interstitial atoms in
the neutral charged state (I0) is Еm ≅ 1.5 eV;
Еm ≅ 0.85 eV is the energy of migration for interstitial
atoms in the negatively charged state (I−), and a twice
negatively charged interstitial atom (I=) has the energy of
migration Еm ≅ 0.4 eV, according to the literature data.
Therefore, a decrease in the introduction rate for defects
I0 (Еv + 0.42 eV), I2
+ (Еv + 0.45 eV), and
I2Oi
+ (Еv + 0.51 eV) is determined by the radiation
annealing under the irradiation by fast-pile neutrons at a
temperature of 287 K. The dependence of the defect
introduction rate on the time of irradiation by fast-pile
neutrons of p-Si ( 00p = 3.0 × 1012 сm−3) is presented in
Fig. 4. The obtained activation energies for the radiation
annealing of the above-mentioned defects and their
frequency factors are presented in Table 2.
6. Conclusions
We have found that, under the neutron irradiation of p-Si
at 287 K (see Table 2), only the changes of charged
states of interstitial and di-interstitial atoms lead to a
change of their activation energy and the annealing.
It is established that the radiation hardness of n-
and p-type silicon is determined by defect clusters, on
the one hand, and vacancy-type defects (acceptors) in n-
Si and interstitial-type defects (donors and acceptors) in
p-Si, on the other hand.
We have confirmed that the radiation hardness of
p-Si is higher than that for n-Si and clarified the reasons
for this fact. The radiation hardness is determined by the
n → р conversion of the conducting matrix in n-type
silicon and is related, in p-type silicon, to the dose, at
which the full overlapping of clusters takes place.
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