Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type
The influence of γ-irradiation (⁶⁰Co) (within the dose range 1×10⁶ ≤ D ≤ 8×10⁷ R) on the concentration and mobility of major carriers in germanium and silicon has been investigated. In the oxygen-containing samples of n − AsGe and n − PSi , and in the compensated crystals of n −Si , the mobility...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1182402017-05-30T03:03:10Z Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type Gaidar, G.P. The influence of γ-irradiation (⁶⁰Co) (within the dose range 1×10⁶ ≤ D ≤ 8×10⁷ R) on the concentration and mobility of major carriers in germanium and silicon has been investigated. In the oxygen-containing samples of n − AsGe and n − PSi , and in the compensated crystals of n −Si , the mobility is shown to grow anomalously with the irradiation dose in the region of combined scattering of carriers. Proposed in this paper is the model based on accounting partial neutralization of charge of scattering centers by charge of radiation defects produced mainly around the scattering centers. This model qualitatively explains the experimental data. 2012 Article Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type / G.P. Gaidar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 26-31. — Бібліогр.: 12 назв. — англ. 1560-8034 PACS 61.80.Ed, 61.82.Fk, 72.20.-i http://dspace.nbuv.gov.ua/handle/123456789/118240 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The influence of γ-irradiation (⁶⁰Co) (within the dose range
1×10⁶ ≤ D ≤ 8×10⁷ R) on the concentration and mobility of major carriers in germanium
and silicon has been investigated. In the oxygen-containing samples of n − AsGe and
n − PSi , and in the compensated crystals of n −Si , the mobility is shown to grow
anomalously with the irradiation dose in the region of combined scattering of carriers.
Proposed in this paper is the model based on accounting partial neutralization of charge
of scattering centers by charge of radiation defects produced mainly around the scattering
centers. This model qualitatively explains the experimental data. |
| format |
Article |
| author |
Gaidar, G.P. |
| spellingShingle |
Gaidar, G.P. Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Gaidar, G.P. |
| author_sort |
Gaidar, G.P. |
| title |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type |
| title_short |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type |
| title_full |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type |
| title_fullStr |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type |
| title_full_unstemmed |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type |
| title_sort |
influence of γ-irradiation (⁶⁰со) on the concentration and mobility of carriers in ge and si single crystals of n-type |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2012 |
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http://dspace.nbuv.gov.ua/handle/123456789/118240 |
| citation_txt |
Influence of γ-irradiation (⁶⁰Со) on the concentration and mobility of carriers in Ge and Si single crystals of n-type / G.P. Gaidar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 1. — С. 26-31. — Бібліогр.: 12 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT gaidargp influenceofgirradiation60soontheconcentrationandmobilityofcarriersingeandsisinglecrystalsofntype |
| first_indexed |
2025-07-08T13:36:47Z |
| last_indexed |
2025-07-08T13:36:47Z |
| _version_ |
1837086077104422912 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
PACS 61.80.Ed, 61.82.Fk, 72.20.-i
Influence of γ-irradiation (60Со) on the concentration and mobility
of carriers in Ge and Si single crystals of n-type
G.P. Gaidar
Institute for Nuclear Researches, National Academy of Sciences of Ukraine,
47, prospect Nauky, 03680 Kyiv, Ukraine; e-mail: gaydar@kinr.kiev.ua
Abstract. The influence of γ-irradiation (60Co) (within the dose range
1×106 ≤ D ≤ 8×107 R) on the concentration and mobility of major carriers in germanium
and silicon has been investigated. In the oxygen-containing samples of AsGe−n and
PSi−n , and in the compensated crystals of Si−n , the mobility is shown to grow
anomalously with the irradiation dose in the region of combined scattering of carriers.
Proposed in this paper is the model based on accounting partial neutralization of charge
of scattering centers by charge of radiation defects produced mainly around the scattering
centers. This model qualitatively explains the experimental data.
Keywords: germanium, silicon, γ-irradiation, Hall effect, carrier mobility, electron
concentration, combined scattering.
Manuscript received 21.12.11; revised version received 11.01.12; accepted for
publication 26.01.12; published online 29.02.12.
1. Introduction
Authors of the monographs [1–5] and sources, cited
therein, investigated the influence of -γ radiation and
other nuclear radiation on generation of radiation defects
(RD) in crystals of n-type Si and Ge (as well as in more
complex semiconductor compounds) in order to
establish the nature of RD, kinetics of their accumulation
and annealing under different temperature conditions of
environment.
It was found in [6] that in single crystals of
PSi−n grown by Czochralski method with a high
content of residual oxygen impurities after high
temperature annealing (at Т = 1200 °С for t = 2 h), the
concentration of EPR-active phosphorus NP sharply (up
to ~45%) decreases with almost constant concentration
of carriers nе. According to [6], the conditions of
deionization of phosphorus impurity during the lowering
of temperature (up to ~20 K) for EPR-measurements
were deteriorated as a result of high temperature
annealing. This could be conditioned by several factors:
а) some neutralization of the positively charged
ionic residues by the negatively charged vacancies
diffusing to them in the process of annealing;
b) formation of the traps that can more efficiently
(in comparison with ionic residues Р+) capture electrons
during lowering the temperature, thereby reducing the
ESR-activity of phosphorus atoms (since in order to the
phosphorus atoms reveal the EPR-activity, it is required
that the electrons with uncompensated spins were
captured by these atoms during the temperature
decrease). Dislocation loops, for example, can act in the
role of such traps. The appearance (as a result of high
temperature annealing of Czochralski-grown silicon
crystals) of the dislocation loops is proved in [7, 8] using
X-ray studies and electron microscopy methods.
Capturing the electrons at low temperatures, the traps
located near the ion residues will partially neutralize the
charge of these residues, reducing the efficiency of
electron scattering by the ions. This will lead (as in the
case a) to an anomalous increase in the mobility of
carriers, which is observed in the experiments with heat-
treated Si crystals with a high content of oxygen
impurities.
If the assumptions in [6] concerning the mechanism
of increasing the mobility due to the partial
compensation of positively charged ionic residues by the
negatively charged vacancies or their complexes is true,
then any damage of the crystal lattice (which occurs, for
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
26
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
example, under the radiation treatment of this material),
that causes the appearance of point centers with opposite
charges with respect to the ionic residues within the
range of their Coulomb interaction, must also lead to the
increase in the mobility of carriers.
The aim of this work is an attempt to validate this
assertion by studying the radiation changes in the basic
parameters of AsGe−n and PSi−n single crystals
(concentration ne and mobility μ of carriers) under
-γ irradiation (60Со) in the region of the combined
scattering of carriers.
2. Results and discussion
The experiments described below were carried out with
Si and Ge single crystals of n-type conductivity.
Changes in the concentration nе and mobility of carriers
μ = R × σ (R – Hall coefficient, σ – electrical
conductivity), depending on the monotonous increase in
the -γ irradiation dose within the range
1×106 ≤ D ≤ 8×107 R were investigated. Irradiation was
carried out at room temperature. Measurements of the
Hall effect at temperatures of 300 and 77 K allowed to
overlap the range from conditions of predominant
phonon scattering to conditions characterized by
significant contribution of the conduction electron
scattering by impurity centers.
The Hall effect and resistivity at 300 and 77 K were
measured before and after irradiation on the five
cruciform samples made from the same crystal of
grown by the Czochralski method and weakly
doped by As impurity (ρ
Ge−n
300K = 45.7 Ohm·cm, ne,77K =
). In the initial crystals the measured
values of the mobility are in a good agreement with the
values of the mobility, calculated within the framework
of the theory of anisotropic scattering [9, 10]. The
averaged (by the data for 5 samples) results of carried
out experiments for two different temperatures (300 and
77 K) in the range of non-monotonic change in
parameters with growth of irradiation doses are
summarized in Table 1.
313 cm102.48 −×
The dose changes of the mobility and concentration
in samples of AsGe−n (obtained both for the room
temperature and for the temperature of liquid nitrogen)
represented in Fig. 1.
In addition to the typical decrease of the carrier
mobility under the monotonous increasing of irradiation
dose, the most interesting results (for both temperatures,
at which these experiments were conducted) were
obtained at the minimum and maximum values from the
used range of doses: in the first case – some increase and
in the second case – a sharp decrease in the mobility μ
with increasing the irradiation dose.
Presence of maximum in μ = μ (D) (see curves 1
and 3 in Fig. 1), probably, results from two factors:
a) growth of μ (D) associated with the radiation-
induced introduction of the acceptor (negatively
charged) centers that, at small doses, are mainly
produced in the vicinity of the positively charged ion
cores of phosphorus (where the lattice is slightly
stressed) and partly neutralize charges of the cores; this
effect reduces the efficiency of the Rutherford scattering
and enhances the mobility μ.
b) natural decrease in μ (D) with the further
increase in the radiation dose, which is due to the
marked growth of the integrated concentration of
scattering centers (Ni = Nd + Na) and the further rise
(with the dose D) of their compensation factor.
A sharp reduction of carrier mobility at maximum
irradiation doses (≈7×107 R) is related, likely, not only
with the increased number of crystal lattice regions
damaged during irradiation, but also with change in their
shape and, perhaps, even with appearance of mutual
overlap some of them. It also leads to that the discussed
changes in the mobility of irradiated crystals almost
equally noticeable both at room temperature and at 77 K,
since they relate with changes both of the impurity
scattering and the carrier scattering by lattice vibrations.
When Ge−n crystals were irradiated by
-γ quanta (60Co, D = 106 R), the experimentally
measured values of mobility (at 77 K) grew up to
34400 cm2/V⋅s (curve 1 in Fig. 1). As shown by the
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Table 1. Influence of small doses of -γ irradiation (60Со) on the resistivity ρ, concentration of major carriers ne and
their mobility μ in single crystals of n – Ge〈As〉.
Т = 300 K Т = 77 K
Dose D, R ρ,
Ohm⋅сm
ne, сm–3 μ,
сm2/V⋅s
ρ,
Ohm⋅сm
ne, сm–3 μ,
сm2/V⋅s
0 45.7 3.86 × 1013 3560 7.47 2.48 × 1013 33840
1 × 106 46.8 3.48 × 1013 3830 7.52 2.42 × 1013 34400
2 × 106 45.2 3.74 × 1013 3700 7.59 2.41 × 1013 34160
3 × 106 46.9 3.67 × 1013 3690 7.76 2.36 × 1013 34140
27
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
calculations, this change of mobility could be caused by
decrease in the concentration of scattering centers from
2.5×1013 down to . However, the
concentration of scattering centers not only did not
become lower, but in fact increased slightly. This slight
decrease in the carrier concentration ∆n
313cm101 −×
e = (2.48 –
2.42)×1013 = is associated with 311cm106 −× -γ induced
generation of the corresponding number of acceptor
centers in the crystal volume, which capture exactly the
same number of conduction electrons.
In the case of , it is hard to speak about the
contribution of specific RD to mobility variations
because by now there is no common opinion about the
type of the generated RD including oxygen.
Nevertheless, it is clear that with increasing the
irradiation dose for these crystals, some changes take
place there, which restrains mobility lowering in the
region of liquid nitrogen temperatures. This assumption
gains further support from the fact that the growth of
efficiency of carrier removal from the conduction band
(in the region of D > 5×10
Ge−n
6 R; see curve 3 in Fig. 1) and,
consequently, the increase of concentration of scattering
centers do not affect practically on dependence μ77K =
μ (D) (Fig. 1, curve 2).
Decrease the carrier mobility related with
increasing the irradiation dose from 106 up to 7×107 R in
the region of mainly impurity scattering (i.e., at 77 K –
Fig. 1, curve 2) amounts to only 24%, while in the
region of preferential scattering by lattice vibrations (i.e.,
at 300 K – Fig. 1, curve 1) this change of μ300K (in the
same range of the increasing radiation dose) reaches
~39%. Thus, with respect to -γ irradiation of Ge−n ,
the change in mobility of major carriers in the direction
of its reduction in the region of mainly phonon scattering
is more vulnerable than in the region of preferential
scattering by impurities. This fact should be taken into
account, when the semiconductor devices (which operate
in the high radiation fields) are based on high-resistance
crystals of . Ge−n
Fig. 1. Dependences of the carrier mobility μ determined at
300 K (1) and 77 K (2), and their concentration ne (3)
determined at 77 K on the -γ irradiation dose D in
Czochralski-grown crystals of n – Ge〈As〉.
Fig. 2. Dependences of the carrier mobility μ (1) and their
concentration ne (3) determined at 77 K on the -γ irradiation
dose D in Czochralski-grown crystals of n – Si〈P〉. The dashed
curve 2 shows the mobility values calculated using the theory
of anisotropic scattering.
Similar experiments on the influence of
-γ irradiation on the mobility and concentration of
major carriers were carried out with silicon crystals. Five
samples, intended for subsequent -γ irradiation (60Co),
were cut from the ingot of , doped with
phosphorus N
Si−n
Р = nе = , grown in the 〈100〉
direction by the Czochralski method (with residual
oxygen impurity of
314 cm106.6 −×
( ) 317 cm101.71.5 −×− ).
For the initial samples of Si, the concentration of
free carriers nе practically corresponded to the doping
level of silicon by phosphorus (nе = Nd). It follows from
the coincidence with the error close to ~1.5% for the
experimentally determined values of μ with the data
calculated according to the theory of anisotropic
scattering, in which the concentration of scattering
centers is taken equal to the concentration of shallow
donors, i.e., for unirradiated samples (D = 0) can be
considered that the compensation factor is k = Na/Nd = 0.
Therefore, using the difference between the initial ( )
and final ( ) values (obtained after irradiation) of
carriers concentrations, it was possible to determine the
concentration of acceptor centers (N
0
en
∗
en
a) introduced into
the crystals during irradiation, namely: Na = ne
0 – ne
*.
These and other data for Si−n samples are presented in
Table 2.
Fig. 2 presents the changes (obtained at 77 K) in
the mobility and carrier concentration in the initial and
-γ irradiated samples of PSi−n as a function of the
dose within the range 0 ≤ D ≤ 8×107 R.
Fig. 2 shows that the carrier removal from the
sample bulk (curve 3) due to radiation introduction of
the acceptor centers is characterized by a function that is
smoothly decreased with increasing the radiation dose D.
Concerning the Hall mobility of carriers, it should
be seen that under the monotonical increase in the total
concentration of scattering centres Ni = Na + Nd, which is
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
28
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
Table 2. Carrier concentration ne and concentrations of donor Nd and acceptor Na centers (at 77 K) in the initial and
-γ irradiated using the maximal dose (D = 8×107 R) samples of n – Si〈P〉.
nе × 10–14,
сm–3 Na × 10–14, сm-3 Ni×10-14 = (Nd+Na)×10-14,
сm–3
Before
irradiation
nе ≡ Nd
After
irradiation ne
*
After irradiation
Na = ne
0–ne
*
Before
irradiation
Nd ≡ nе
After
irradiation
Ni = Nd+Na
d
a
N
Nk = k (%) Samples of
PSi−n
6.60 5.44 1.16 6.60 7.76 0.176 17.6
accompanied by a continuous decrease in nе with
increasing the irradiation dose, the mobility of carriers
should decrease in the region of combined scattering
(T = 77 K). However, the experimental dependence of
the mobility (as in the case of -γ irradiation of
AsGe−n samples) on the dose μ = μ (D) has a small
(but well-marked) maximum (Fig. 2, curve 1) in the
range of the minimal irradiation doses (at D = 1×107 R).
Although the maximum of mobility in its dependence on
the irradiation dose in the crystal of (Fig. 1)
appears within the range of doses that is an order of
magnitude lower than those at which this maximum is
observed in (Fig. 2).
Ge−n
Si−n
The radiation-induced lowering the efficiency of
scattering by the charged centers probably manifests
itself also within the region of the highest doses where
the general rise of the concentrations Nd + Na (and their
compensation factor) becomes most pronounced and
provides a marked lowering μ as compared with the
mobility in the initial crystals. The straightforward
substantiation of this interpretation is given by the
numerical values of mobility which were calculated in
the framework of the theory of anisotropic scattering [9–
11] (see Appendix) for the summarized values of Ni =
Na + Nd; they appeared to be much smaller than the
experimental ones (dashed curve 2 in Fig. 2). At the
same time, the testing calculations, performed for the
samples before their irradiation, are in a good agreement
with the experimental data within the errors less
than 1.5%.
The estimations showed that, at the concentrations
of phosphorus atoms approximately
already at the
31514 cm1010 −−
-γ quanta integral flows of ~107 R, the
probability of formation of the radiation defects, within
the limits of the overlapping of Coulomb cross-sections
for scattering by donor and acceptor centers, amounts
from 1 up to ~3%. With increasing the irradiation dose,
the fraction of neutralized ion residues of phosphorus
atoms increases. However, it should be taken into
account that the indicated probability of introduction of
the neutralized Coulomb charges (1…3%) was obtained
for the equiprobable generation of radiation defects in
the silicon bulk. At the same time, the probability of
appearance of radiation defects in the mechanically
strained regions of crystals is substantially higher than in
unstrained regions. Therefore, it is naturally to expect
that, at low doses of irradiation, the introduction of
defects occurs primarily in the locally strained lattice
regions, i.e. near the dopant atoms, and that ultimately
leads to the increase of μ, which is experimentally
observed.
The validity of these estimations is based on the
macroscopic homogeneity of the investigated crystals.
Our conclusion concerning their homogeneity follows
from the fact that during the measurements of
magnetoresistance in a transverse magnetic field (under
Н⊥J) the changes of the direction of the magnetic field
and current J on the opposite (even at the maximum
values of the field H, which amounted to 32 kOe) did not
change the value of magnetoresistance within 0.05%.
The above-mentioned macroscopic homogeneity of
samples is not significantly deteriorated after irradiation,
too (Fig. 3).
In Czochralski-grown silicon, the oxygen-vacancy
complex ( −A center) is the predominant radiation defect
responsible for the radiation-induced changes of free
carrier concentration. Naturally, one may suppose that
the mobility μ is changed in the irradiated crystals just
owing to the localization of these negatively charged
acceptors near the phosphorus cores. Оne may expect
that in zone-melted silicon, where the vacancy-
phosphorus complex ( −E center) [12] is a dominant
RD, irradiation would not give rise to a mobility
increase. The latter suggestion follows from the fact that
the phosphorus atom is a component of center, thus,
during the introduction of centers only the sign of
charge of scattering centers is changed, but their
concentration is not changed.
−E
−E
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
In order to verify the supposition concerning the
mechanism of carrier mobility enhancement in
-γ irradiated oxygen-containing crystals of silicon, the
comparative experiments with samples cut from the
single crystals grown using the floating-zone method,
where the concentration of residual oxygen was low
( ), were carried out. These experiments
showed that such crystals did not exhibit the radiation-
induced mobility enhancement (Fig. 4), and the observed
decrease of μ was caused by additional scattering by RD
of other types, such as
316
O cm10 −≤N
−W , −K centers, etc.
29
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
Fig. 3. Dependences ( )HfH =
ρ
ρ⊥
0
obtained at 77 K in the
experiments with initial (D = 0) crystals of PSi−n (o) and
with the samples -γ irradiated using the dose D =
8×107 R (●).
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 4. Dependences of the free electron mobility μ at 77 K on
the -γ irradiation dose D in the silicon crystals grown using
the floating-zone method. The solid line gives our
experimental data; the dashed one presents the calculated
results.
Fig. 5. Dependences of the resistivity ρ on the -γ irradiation
dose D measured at 77 K in the samples of Si−n with
different compensation factors: 1 – nе =
; k = N313cm104.73 −× a/Nd = 0.83; 2 – nе =
; k ≈ 0. Both crystals were 313cm107.19 −× -γ irradiated
(60Co) at Т = 300 K.
The influence of small doses on the resistivity of
compensated and of practically uncompensated (in the
initial state) crystals of Si−n was also different, which
is illustrated by the data shown in Fig. 5.
Thus, the minimum of resistivity appears in the
compensated crystal at the radiation dose D ≅ 106 R,
while in the crystal with k ≈ 0 such minimum does not
exist. Since the compensated crystal is quite
heterogeneous, in this material there is a high probability
of the formation of clusters of dopant impurity in the
form of closely spaced positively charged ionic residues
of phosphorus (two or more). When such crystal was
irradiated by -γ quanta, mobile vacancies may be
trapped by one of the ionic residues of phosphorus,
which is contained in the cluster structure, with the
formation of negatively charged center. Scattering
efficiency of such a new formation (which is consisted
of the located near ionic residue of phosphorus P
−E
P
+ and
−E center) due to the effect of partial screening (or
neutralization) will be somewhat reduced. So, we would
obtain reduction in the resistivity (and, consequently,
respective increase in the carrier mobility) at low
-γ irradiation doses in the compensated crystal.
The inhomogeneity is significantly smaller in
almost uncompensated material. Therefore, the
formation of dopant impurity clusters is unlikely. The
-γ quanta irradiation of these crystals introduces
additional scattering centers (acceptors), which reduces
the mobility, and, consequently, the resistivity is
increased, and it is obtained by us in the experiment.
3. Conclusions
The dependences of concentration and mobility of
carriers in n-type crystals of germanium and silicon on
the dose of -γ irradiation (60Co) were investigated. It is
shown that under the influence of small doses of
-γ irradiation in oxygen-containing single crystals of
AsGe−n and PSi−n , as well as in Si−n
compensated crystals, increase of the carrier mobility
within the range of combined scattering of carriers was
experimentally observed. The proposed model that takes
into account partial neutralization of the charge of
scattering centers by the charge of radiation defects
explains the observed features.
Appendix
23
34
2/3
7
9.13
295.61051.3
JJ
JJ
T ′+′
′+′⋅
=μ , cm2/V⋅s, (A1)
where
30
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 1. P. 26-31.
∫
∞ −
+ϕ+
=′
0 0
2
2/3
1
662.0
d
bx
xexJ
x
,
∫
∞ −
+ϕ+
=′
0 1
2/32
2/3
2
d
bxx
xexJ
x
,
( )(
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
)∫
∞ −
+ϕ+++
=′
0 1
2/32
0
2/32
2/9
3
662.0
d
bxxbxx
xexJ
x
,
( )∫
∞ −
+ϕ+
=′
0
2
1
2/32
2/9
4
d
bxx
xexJ
x
, (A2)
( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−⎟
⎠
⎞
⎜
⎝
⎛++
−
+
+
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛−+−×
×
−
=ϕ
T
x
T
xe
T
x
e
T
x
T
xe
T
x
e
Tx
T
T
T
T
630630,θ630
1
1260
190,θ190190
1
5.28,
/630
/630
/190
/190
(A3)
with
( )
⎩
⎨
⎧
α<
α>
=αθ
.for0
,for1
,
x
x
x
The values of b0 and b1 depending on concentration
and temperature are given in detail in [11].
References
1. V.S. Vavilov, N.P. Kekelidze, L.S. Smirnov,
Influence of Radiation on Semiconductors. Nauka,
Моsсow, 1988 (in Russian).
2. P.I. Baranskii, А.V. Fedosov, G.P. Gaidar, Physical
Properties of Silicon and Germanium Crystals in
the Fields of Effective External Influence.
Nadstyr’ya, Lutsk, 2000 (in Ukrainian).
3. P.I. Baranskii, А.V. Fedosov, G.P. Gaidar,
Heterogeneities of Semiconductors and Urgent
Problems of the Interdefect Interaction in the
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V.V. Milenin, I.V. Prokopenko, Yu.A. Tkhorik,
Radiation Resistance of GaAs-based Microwave
Schottky-barrier Devices. Interpres LTD, Kyiv,
1998.
5. А.А. Groza, P.G. Litovchenko, М.І. Starchik,
Radiation Effects in Infrared Absorption and
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Ukrainian).
6. P.I. Baranskii, A.A. Bugay, V.M. Maksimenko,
V.V. Savyak, V.P. Shapovalov, Influence of heat
treatment on the EPR and electrical activity of the
phosphorus impurity in conventional and neutron-
doped silicon crystals // Fizika i tekhnika
poluprovodnikov, 14 (7), p. 1438-1441 (1980), in
Russian.
7. J.R. Patel, A. Authier, X-ray topography of defects
produced after heat treatment of dislocation-free
silicon containing oxygen // J. Appl. Phys. 46 (1),
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8. N.A. Vitovskii, V.V. Emtsev, T.V. Mashovets,
Yu.G. Morozov, The kinetics of the interaction of
point radiation defects of structure with impurity
atoms in semiconductors // Fizika i tekhnika
poluprovodnikov, 8 (11), p. 2276-2279 (1974), in
Russian.
9. A.G. Samoilovich, I.S. Buda, I.V. Dakhovskii, The
theory of anisotropic scattering // Fizika i tekhnika
poluprovodnikov, 7 (4), p. 859 (1973), in Russian.
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V.V. Kolomoets, Electrical and Galvanomagnetic
Phenomena in Anisotropic Semiconductors (Ed. by
P.I. Baranskii). Naukova Dumka, Kyiv, 1977 (in
Russian).
11. P.I. Baranskii, I.V. Dakhovskii, V.V. Kolomoets,
А.V. Fedosov, Investigation of the anisotropy of
carrier scattering in // Fizika i tekhnika
poluprovodnikov, 10 (7), p. 1345-1348 (1976), in
Russian.
Si−n
12. I.D. Konozenko, A.K. Semenyuk, and
V.I. Khivrich, Radiation Effects in Silicon.
Naukova Dumka, Kyiv, 1974 (in Russian).
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