Electro-physical properties of γ-exposed crystals of silicon and germanium
The paper represents a review of research data upon changing electrophysical properties of n-Si and n-Ge when radiation defects arise under action of different γ-irradiation doses. Analyzed are consequences of arising deep levels of radiation defects in the forbidden band of silicon and germanium, w...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
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| Цитувати: | Electro-physical properties of γ-exposed crystals of silicon and germanium / Yu.P. Dotsenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 47-55. — Бібліогр.: 63 назв. — англ. |
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irk-123456789-1179332017-05-28T03:04:08Z Electro-physical properties of γ-exposed crystals of silicon and germanium Dotsenko, Yu. P. The paper represents a review of research data upon changing electrophysical properties of n-Si and n-Ge when radiation defects arise under action of different γ-irradiation doses. Analyzed are consequences of arising deep levels of radiation defects in the forbidden band of silicon and germanium, which leads to the considerable increase of resistivity gradients caused by non-uniform compensation of shallow donor centers. In addition, considered are characteristics of radiation defects energy levels which determine both regularities of electrophysical properties changes and peculiarities of tensoeffects in γ-irradiated crystals. It is noticed that neutron-doped n-Si (P) has larger radiation hardness in respect to γ-irradiation as sompared to silicon doped with phosphorus in the course of crystal growth. 1999 Article Electro-physical properties of γ-exposed crystals of silicon and germanium / Yu.P. Dotsenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 47-55. — Бібліогр.: 63 назв. — англ. 1560-8034 PACS 72.15.E, 72.20, 61.72.T, 72.80.C., 71.55.A http://dspace.nbuv.gov.ua/handle/123456789/117933 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The paper represents a review of research data upon changing electrophysical properties of n-Si and n-Ge when radiation defects arise under action of different γ-irradiation doses. Analyzed are consequences of arising deep levels of radiation defects in the forbidden band of silicon and germanium, which leads to the considerable increase of resistivity gradients caused by non-uniform compensation of shallow donor centers. In addition, considered are characteristics of radiation defects energy levels which determine both regularities of electrophysical properties changes and peculiarities of tensoeffects in γ-irradiated crystals. It is noticed that neutron-doped n-Si (P) has larger radiation hardness in respect to γ-irradiation as sompared to silicon doped with phosphorus in the course of crystal growth. |
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Dotsenko, Yu. P. |
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Dotsenko, Yu. P. Electro-physical properties of γ-exposed crystals of silicon and germanium Semiconductor Physics Quantum Electronics & Optoelectronics |
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Dotsenko, Yu. P. |
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Dotsenko, Yu. P. |
| title |
Electro-physical properties of γ-exposed crystals of silicon and germanium |
| title_short |
Electro-physical properties of γ-exposed crystals of silicon and germanium |
| title_full |
Electro-physical properties of γ-exposed crystals of silicon and germanium |
| title_fullStr |
Electro-physical properties of γ-exposed crystals of silicon and germanium |
| title_full_unstemmed |
Electro-physical properties of γ-exposed crystals of silicon and germanium |
| title_sort |
electro-physical properties of γ-exposed crystals of silicon and germanium |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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1999 |
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http://dspace.nbuv.gov.ua/handle/123456789/117933 |
| citation_txt |
Electro-physical properties of γ-exposed crystals of silicon and germanium / Yu.P. Dotsenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 47-55. — Бібліогр.: 63 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT dotsenkoyup electrophysicalpropertiesofgexposedcrystalsofsiliconandgermanium |
| first_indexed |
2025-07-08T13:02:29Z |
| last_indexed |
2025-07-08T13:02:29Z |
| _version_ |
1837083920190930944 |
| fulltext |
47© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 1. P. 47-55.
1. Introduction
Because the semiconductor exposure by high energy par-
ticles can be used with the objective to necessary change
their properties, the investigations of the influence of dif-
ferent γ-exposure doses on the defect structure and char-
acteristics of materials have not only scientific interest,
but are also important and from the practical point of
view. Besides that, due to the exposure action the change
of the properties of the semiconductor materials, struc-
tures and devices, which operate in the radiation fields
take place. Thus, from the point of view of prediction of
the parameter stability of such devices the investigations
of the regularities of creation and transformation of radi-
ation defects in semiconductors under the radiation expo-
sure is becoming more and more actual.
The investigations by different methods have estab-
lished [1-11], that at the growth of bulk semiconductor
crystals in the planes, perpendicular to the growth direc-
tion, the practically periodical distribution of the doping
impurity arises. Depending on the crystal growth condi-
tions [2] the periodicity of such structures is character-
ized by the width in the range of 10-6 - 10-3 m and is
connected with the different impurity distribution coeffi-
cient between liquid and solid phases of crystal, which is
grown from the melt. The impurity concentration in the
layers can differ by several times [12], because due to the
charge carriers diffusion in the crystal volume, the intrin-
sic electrical field arises, which is modulated in the direc-
tion of the growth axis with the same periodicity as that of
the impurity distribution [5]. A theoretical approach to
the methods of taking into account in the kinetic phenom-
ena the contribution of statistically distributed impurities
in the crystal bulk was proposed by Herring [8]. It was
shown, in particular, that transverse magnetic resistance
connected with the growth layers, in classically strong
fields is determined by the dependence ∆ρ ρ⊥ / 0 ∼ H 2 ,
and in the region of quantizing magnetic fields: ∆ρ ρ⊥ / 0 ∼
∼ H . The experimental investigations have confirmed the
theoretical conclusions [ 9, 13, 14]. The corresponding
PACS 72.15.E, 72.20, 61.72.T, 72.80.C., 71.55.A
Electro-physical properties of γγγγγ-exposed crystals of silicon
and germanium
Yu. P. Dotsenko
Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, 252028, Ukraine
Abstract. The paper represents a review of research data upon changing electrophysical proper-
ties of n-Si and n-Ge when radiation defects arise under action of different γ-irradiation doses.
Analyzed are consequences of arising deep levels of radiation defects in the forbidden band of
silicon and germanium, which leads to the considerable increase of resistivity gradients caused
by non-uniform compensation of shallow donor centers. In addition, considered are character-
istics of radiation defects energy levels which determine both regularities of electrophysical
properties changes and peculiarities of tensoeffects in γ-irradiated crystals. It is noticed that
neutron-doped n-Si (P) has larger radiation hardness in respect to γ-irradiation as sompared to
silicon doped with phosphorus in the course of crystal growth.
Keywords: radiation defects, γ-irradiation, electron silicon, electron germanium, radiation hard-
ness.
Paper received 10.02.99; revised manuscript received 17.05.99; accepted for publication 24.05.99.
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
4 8 SQO, 2(1), 1999
choice of orientation for current J and magnetic field H
vector enabled to determine the transverse magnetic re-
sistance of n-Ge which is directly connected with the pres-
ence of the defect structure in the form of growth layers.
Because as a result of γ-exposure in the crystal vol-
ume the defects are created which have the acceptor lev-
els in the forbidden gap and which cause the compensa-
tion of the donor impurity, the properties of semicon-
ductors with the increase of radiation dose are sufficiently
changed, in particular, due to the essential growth of the
gradients of the crystal specific resistance, which are de-
termined by the presence of the growth layers [15-18].
It was proved that the most informative methods for
the investigations of the origin and properties of the ra-
diation defects are the combinations of different experi-
mental methods (electron paramagnetic resonance
(EPR), capacitance spectroscopy (DLTS), nuclear mag-
netic resonance (NMR), optical methods, etc.) with the
high pressure methods, in particular, strong directed
stresses. Therefore, considerable attention was paid to
the investigation of the electro-physical and, in particu-
lar, tensor resistive properties of the γ-exposed semicon-
ductors [15-21].
At present work the review of the literature and orig-
inal data concerning the investigations of the electro-
physical properties of the strongly deformed γ-exposed
crystals of silicon and germanium of n-type will be ad-
duced.
2. Influence of the γγγγγ-radiation on the electro-
physical properties of n-type silicon
Because the most informative from the stand point of
studying the influence of γ-radiation on the properties
of materials are the investigation results at different ex-
posure doses, including those ones which lead to the
drastic changes of the semiconductor properties (for ex-
ample, strong compensation, n-p conversion, essential
increase of tensor sensitivity, etc.) the investigation re-
sults of the influence of different γ-exposure doses on
electro-physical and, in particular, tensoresistive prop-
erties of silicon and germanium will be presented in
present review.
The results of the investigations of the γ-exposure in-
fluence on the tensor resistive properties of silicon, doped
by the phosphor during growth process [22, 23], are pre-
sented in Fig. 1. Let us notice that the silicon crystals
which were grown in the [100] direction, were doped by
the phosphor impurity from the melt up to concentrations
1.2 × 1014 cm-3 . It can be seen from the presented in Fig. 1
data, that after the certain γ-exposure doses Φ ≈
≈ 1.7×1017 quanta/cm2 ) the essential anisotropy of
ρ ρX f X/ ( )0 = dependencies for the samples fabricated
in equivalent crystallographic directions ([100] � sam-
ples of I group and [001] � samples of II group [22, 23]),
but with different orientation relative to the direction of
the crystal growth (curves 3-3´, 4-4´) arises. The type of
the ρ ρX f X/ ( )0 = dependencies testify that at certain
γ-exposure doses the mechanism of the redistribution of
the charge carriers between ∆
1
valleys of conduction band,
which lead to the increase of crystal resistance with pres-
sure Xº[100] increase, is accompanied by the mechanism
of the deformation-induced ionization of the radiation
defect energy level (A-center, to which in the forbidden
gap the acceptor level E
c
- 0.17 eV [ 15,24,25] corre-
sponds). This leads to the increase of the current carriers
concentration at the cost of decreasing energy difference
between bottom of the conduction band and the level E
c
- 0.17 eV with the pressure and respective resistance de-
crease. Because of the phosphor impurity donor con-
centration is essentially changed through the growth lay-
ers at time of γ-exposing, the resistance value and its de-
pendence on the pressure for the samples of I group will
be determined by the layers with smaller phosphor im-
purity concentration, that is by the parts with the bigger
compensation degree (in series connection of the growth
layers resistance). In samples of the second group, on
the contrary, due to the parallel connection of the growth
layers resistance, the resistance of the layers and its de-
pendence from the pressure will be determined by the
properties of the layers with the lesser degree of compen-
sation. Presented considerations on the possible origin
Fig. 1. Anisotropy of longitudinal tensoresistive effect ρ
x
/ρ
0
=
= f(X) for equivalent crystallographic orientations of samples
at T = 78 K using different doses of γ-irradiation, Φ, 1017 quan-
ta/cm2: 1, 1' � 0; 2, 2' � 1.36; 3, 3' � 1.76; 4, 4' � 2.08.
X, 103 kG⋅cm2
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
49SQO, 2(1), 1999
of the tensoresistive effect anisotropy in γ-exposed sili-
con doped by phosphor during growth time are also con-
firmed in sufficient degree by the dependencies of the
current carriers mobility on the exposure dose and by
temperature dependencies of the resistance for the sam-
ples of I and II groups (Fig. 2).
Thus, the analysis of the presented results of the ten-
soresistive effect investigations for silicon doped during
growth process by phosphor are testifying about the es-
sential growth of the inessential for the initial samples
gradients of the specific resistance at certain doses of γ-
radiation due to different degree of donor impurity com-
pensation by radiation defect (A-center) with the accep-
tor properties.
More perfect method of semiconductor doping is, as
is known, the doping by exposure of thermal (slow) neu-
trons [26]. In silicon, in particular, at exposure by ther-
mal neutrons atoms of 30Si isotope are transformed due
to nuclear reaction into 31P phosphor atoms (30Si(n,γ) →
→31Si → 31P + β). Because the atoms of 30Si isotope, which
comprise approximately 3 % from the number of silicon
isotopes, are uniformly distributed in the crystal volume,
method of transmutation doping enables to obtain also
the uniform distribution of phosphor impurity, which
gives a possibility to produce the semiconductor devices
with the improved parameters in comparison with the
devices on the base of semiconductors doped during the
growth process by adding the impurity into the melt.
The electro-physical properties of the transmutation
doped silicon were studied in series of work [26-30].
The results of the tensoresistive effect investigation
in crystals of neutron-doped silicon in the range of strong
directed deformations [29-30] testify about the noticeable
difference in the type of ρ ρX f X/ ( )0 = dependencies
recorded for the usually doped by phosphor silicon crys-
tals and neutron-doped silicon at small values of impuri-
ty concentration ( N
p
≤ 1.0 ⋅ 1014 cm-3). For silicon doped
by phosphor during growth process, the ρ ρX f X/ ( )0 =
dependencies in the region of strong directed pressures
have characteristic region of the tensoresistive effect sat-
uration at T = 78 K in pure crystals (N
p
≈ 1.0⋅1012 -
1.0⋅1014 cm-3) (Fig. 3, curve 1). The tensoresistive effect
for the samples of the neutron doped silicon with com-
parable phosphor impurity concentration is character-
ized by the absence of saturation in the region of the
strong directed pressures (X > 0.6⋅103 kG⋅cm-2, Fig. 3,
curves 2, 3), which testify about the absence of complete
ionization of phosphor impurity in such crystals at T =
= 78 K and their additional ionization under the action
of pressure in the [100]ºX direction. Thus, the Hall coef-
ficient temperature dependence for the neutron doped n-
Si(P) in strain-free crystal (X = 0) has the noticeable de-
crease in the 78-130 K temperature region (inset to the
Fig. 3, curve 2´). Similar interpretation is valid for the
absense of saturation in the ρ ρX f X/ ( )0 = dependen-
cies, when considering the region of strong pressures for
the doped during the growth process n-Si(P) which is com-
pensated by the acceptor impurity (compensation degree
Fig. 2. Dependencies of the Hall mobility for current carriers
(a) and resistivity (b) of n-Si (P) crystals (N
p
= 1.2⋅1014 cm-3) for
samples of the group I (curves 1 and 1', respectively) and sam-
ples of the group II (curves 2 and 2') on the dose of irradiation.
Fig. 3. Dependencies ρ
x
/ρ
0
= f(X) obtained at T = 78 K for n-Si
samples doped by phosphorus in the course of growing (curves
1, 4) and the transmutationally doped ones (curves 2, 3). Tem-
perature dependencies of the Hall coefficients for the samples
1, 2, 4, are shown in the inset.
µ H
,
10
3
cm
2 V
-1
s-1
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
5 0 SQO, 2(1), 1999
k = N
a
/ N
d
≈ 0,9 ) (Fig. 3, curves 4, 4 ´, respectively).
The deviation of the lg(n
2
/ n
1
) = f(X) dependencies
(where n
2
� concentration of the electrons in valley, which
is elevated in energy scale with the pressure, n
1
� concen-
tration of the electrons in the descending valley) from
linearity [31] (Fig. 4) also testify about the emergence of
the additional to the inter-valley charge carrier redistri-
bution mechanism of tensoresistive effect, determined
by the increase of electron concentration, as in neutron-
doped silicon crystals with phosphor concentration with-
in ≈ (2.5÷20)⋅1013 cm-3, as well as in the compensated sil-
icon. Therefore, it is apparent that for such crystals the
method of the determination of the deformation poten-
tial constant from the slope of linear dependence
lg(n
2
/ n
1
) = F(X) [32] (in which the n
2
/ n
1
ratio of electron
concentrations is expressed through the value of ρ
X
/ ρ
0
ratio, which is measured in the wide range of directed
pressure changes, including the region of pressure satu-
ration) cannot be used. The analysis of the main mecha-
nisms of the tensoresistive effects, which lead to the de-
viation of the lg(n
2
/ n
1
) = F(X) dependencies from linear-
ity, is presented in thesis works [21, 33].
As noted previously, transmutation doping of sili-
con enables to obtain the uniform distribution of the
phosphor impurity, therefore with the aim to determine
the influence of the γ-radiation on the properties of neu-
tron-doped silicon the investigations of the physical prop-
erties of strongly-deformed [29] and γ-exposed with var-
ious doses crystals [30], were performed.
Neutron doping of the high resistance p-Si crystals
which were grown in [100] direction was carried out in
the reactor of the Institute of Nuclear Research as at
NAS of Ukraine. After technological annealing which
has been carried out with the aim of radiation damage
removal, samples of n-Si had low phosphor concentra-
tion Np = 3.15⋅1014 cm-3. Two groups of samples for mea-
surements of longitudinal tensoresistive effects were ori-
ented as in the work [22] in equivalent crystallographic
directions [100] and [001]. Let us notice that the ratio of
electrons concentrations, n
2
/ n
1
, which determines the de-
pendence of the specific resistance of silicon and germa-
nium on pressure in the conditions of action of inter-
valley redistribution mechanism (Smith-Herring tenso-
effects) can be respectively written for the non-degener-
ated crystals as:
n
n
KX
sat
X
sat
2
1
1
1 2 2= −
−
−
ρ
ρ
ρ
ρ (1)
for n-Si in the conditions XºJº[111].
n
n
Ksat
X
sat
X
2
1
1
1
8 1
3
3= −
+
−
−
ρ
ρ
ρ
ρ (2)
for n-Ge in the conditions XºJº[111].
Parameter K of mobility anisotropy in relations (1)
and (2) is determined both for n-Si and n-Ge (for the
above mentioned orientations ) by ρ
sat
/ρ
0
ratio :
K sat= −
3
2
1
20
ρ
ρ . (3)
The results of the investigations of longitudinal ten-
soresistive effect (Fig. 5) testify about the absence of such
high anisotropy of the obtained ρ ρX f X/ ( )0 = depen-
dencies even for the exposure doses of γ-quanta 60Co,
which were essentially higher than those used in work
[22]. The data obtained testify on the higher radiation
stability in respect to the γ-exposure of neutron-doped
silicon, which is necessary to take into account during
the development of the solid state devices on the silicon
base. The transmutation doping also provides, at respec-
tive control of slow neutron exposure dose, the possibil-
ity to obtain with the necessary accuracy the required
concentration of the doping impurity with practical as-
surance of the creation of micro-nonuniformities, which
are connected with the association creation: impurity-
impurity or impurity - residual impurity atoms, which
enables to exclude the creation most dangerous defects
structures of single-crystal materials from the point of
view of devices functioning reliability [29, 34, 35].
3. Electrophysics properties of γγγγγ- exposed n-germa-
nium
The results similar to the results obtained of tensoresis-
tive effect anisotropy in γ-exposed n-Si were obtained by
the authors of works [19,36,37] under the investigations
of the transport phenomena in the γ-exposed directed
deformed n-Ge crystals. In the conditions of the crystal
Fig. 4. Dependencies ln[(n
2
/ n
1
)⋅104] = f(X) are plotted for T =
= 150 K (curve1) and T = 78 K (curves 2-5) for silicon crystals
doped by phosphorus in the course of growing (1, 2, 5) and
neutron-doped n-Si (P) (3, 4) with parameters: 1, 2 � ρ
300
=
= 102 Ohm⋅cm, k = N
a
/ N
d
≈ 0.25; 3 � ρ
300
= 220 Ohm⋅cm, k ≈
≈ 0.25: 4 � ρ
300
= 55 Ohm⋅cm, k ≈ 0.52; 5 � ρ
300
= 103 Ohm⋅cm,
k ≈ 0.9.
X, 103 kG⋅cm2
ln
[(
n 2
/ n
1)
⋅1
04 ]
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
51SQO, 2(1), 1999
growth in the [111] direction, the equivalent directions
[ ],[ ],[ ]
_ _ _
111 111 111 are placed at 1100 angle to the direction
of the growth, which also enables to carry out the com-
parative experiments with the aim to detect the influ-
ence of γ-exposure on the anisotropy of tensoresistive
properties of n-germanium, for which, as it is known,
the maximal tensosensitivity is observed for the samples
orientation along Xº{111}ºJ [38,39].
The results of the investigations of longitudinal ten-
soresistive effect in γ-exposed n-Ge crystals with the an-
timony impurity donor concentration ≈ 2.7⋅1013 cm-3 [36].
Presented in Fig. 6 results of measurements at 78 K tes-
tify about the increase of influence of the crystal defect
structure, which is connected with non-uniform distri-
bution of the doping impurity through the growing lay-
ers on the tensoresistive effect anisotropy, which was
measured in equivalent directions {111} º X, with the
increase of the γ -exposure dose (Fig. 6, curves 1, 1´ - 4,
4´). Contrary to the experimental data for the γ-exposed
n-Si(P), in γ-exposed n-Ge(Sb) crystals at T = 78 K no
additional ionization of charge carriers at pressures
which reach values 1.2⋅103 kG⋅cm-2 is observed. This data
testify that under the directed deformation Xº[111] the
shift of E
c
-0.2 eV energy level (which belongs to the V
2
D
defect of radiation origin [18]) in the direction towards
the bottom of conductivity band [11, 37] is not sufficient
for the additional ionization of the free charge carriers at
T = 78 K.
Taking into account that the mobility anisotropy pa-
rameter K = µ
Á
/µ|| is determined for the inter-valley re-
distribution of electrons for the n-Ge (XºJ º[111]), as
well as for the n-Si (XºJ º[100]), by the relation (3), the
essential decrease of the ρ
ì
/ρ
0
value (Fig. 6, curves 1-4)
cannot be connected, as it was noted earlier [21], with the
increase of scattering anisotropy at single-charged radi-
ation centers [31, 40], because at exposure dose
1.1⋅1017 quanta/cm2 their concentration is relatively low
(∼1013 cm-3).
Let us note, that the compensated semiconductors are
characterized by the presence of the current carriers scat-
tering on the potential relief, amplitude σ of which is de-
termined as it was found in [41]:
σ
χ
=
e N
n
t
scr
2 2 3
1 3
/
/ (4)
where χ is a dielectric constant, n
scr
and N
t
are concentra-
Fig. 5. Dependencies ρ
x
/ρ
0
= f(X) for neutron-doped n-Si(P)
(N
p
= 3.15⋅1014 cm-3) obtained at different doses of γ-irradia-
tion, Φ, 1017 quanta /cm2: 1, 1' � 0; 2, 2' � 1.36; 3, 3' � 1.76; 4, 4' �
2.1; 5, 5' � 8. Solid and dash lines are obtained for samples
orientated in equivalent crystallographic directions [001] (along
the growth direction) and [100] (perpendicularly to the direc-
tion of crystal growth). The curves 1, 1' � 4, 4' are obtained at
T = 78 K, and the curves 5, 5' at T = 300 K.
Fig. 6. Dependencies ρ
x
/ρ
0
= f(X) are obtained for n-Ge(Sb)
crystals at T = 78 K and different doses of γ-irradiation, Φ,
1016 quanta /cm2: I, I� and 1, 1' � 0; 2, 2' � 6.4; 3, 3' � 8.8; 4, 4' � 11.
Concentrations of doping Sb-impurity in Ge - crystals are as
follows: I, I� � N
Sb ≈ 1⋅1012 cm-3; 1, 1'�
4, 4' � N
Sb ≈ 2.7⋅1013 cm-3.
X, 103 kG⋅cm2X, 103 kG⋅cm2
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
5 2 SQO, 2(1), 1999
tions of screening charge carriers and charged defects,
respectively.
The change of the scattering mechanism in compen-
sated crystals leads apparently to the significant decrease
of the ρ
ì
/ρ
0
value with the increase of the compensation
degree also in n-Si crystals (Fig. 3, curves 1-4).
The data on the dose dependencies of the electrons
mobility and ρ
ì
/ρ
0
value of tensoresistive effect [21], which
are presented in Fig. 7 also argues convincingly in favor
of that. Not only the electron mobility, but also and the
ρ
ì
/ρ
0
value are essentially decreased for the samples in
which the layers with the maximum compensation de-
gree are included in series with the layers with minimal
compensation degree (samples were prepared in the di-
rection of crystal growth, see Fig. 7, curves 1,2). At the
same time, the decrease of the electron mobility and
ρ
ì
/ρ
0
value for the samples with the parallel inclusion of
layers with minimal and maximal compensation degrees
(samples were prepared in the direction perpendicular
to the axis of crystal growth) is essentially smaller (Fig. 7,
curves 1´, 2´). Let us notice, that tensoresistive effect, which
is measured in n-Si and n-Ge crystals in the equivalent
directions ( {100} � for n-Si and {111} for n-Ge) has small
anisotropy also in unexposed samples, curves 1, 1´ in Fig. 1,
5, 6 and curves I, I´ in Fig. 6 were obtained by us for high-
ly pure samples of n-Ge with insignificant doping level of
antimony impurity (≈1012 cm-3).
We associate the presence of this difference in ρ
ì
/ρ
0
value obtained in the region of tensoresistive effect satu-
ration with residual deformations in crystals caused by
the defect structure in the form of growth layers.
4. Characteristics of the energy levels for the defects
of radiation origin in γγγγγ-exposed Si and Ge crystals
Due to the radiation influence the defects of structure
originate in semiconductors, which create the series of
complexes to which correspond different energy levels.
Because the electrophysics properties of materials are di-
rectly connected with the characteristics of energy lev-
els, identification of the level type and determination of
the model for the respective radiation center are devoted
by a number of works [15,18, 20, 24, 25, 40, 42-59]. On
the base of analysis of electrophysics properties investi-
gations of γ-exposed Si and Ge crystals it was established
that in silicon, due to the creation of radiation centers
(so called A-centers), the deep energy level E
c
- 0.17 eV
arises in the forbidden gap [15, 24].
The model of A-center in silicon was proposed by au-
thors [15] with taking into account the data on paramag-
netic resonance investigations in the directly deformed
crystals. It is determined that due to the γ-exposure the
association of the vacancy with the oxygen atom arises,
which under that is shifted from the lattice site in the
direction of (100) plane. As follows from the results of
theoretical calculations [42], an oxygen atom is stabilized
in the site displaced along [100] direction. Closer shifted
to it are also enclosing atoms of silicon, whereupon the
crystal lattice in the place of A-center localization must
have both hydrostatic and directed deformation com-
ponent. It is established hereby, that A-center is charac-
terized by the determined in the space axis (defect axis)
which coincides with the crystallographic orientation
[100] and belongs to such non-cubic centers the symme-
try of which is lower than the crystal point symmetry
and is determined by the point group C
2V
.
The results of the tensoresistive effect investigation
also testify that the rate of the energy shift of the level,
which belongs to A-center, is maximal when the defor-
mation coincides with [100] direction.
Values of coefficient for the change of an energy gap
between the silicon conoluetive band bottom and the A-
center energy level were estimated for the different ori-
entations of the deformation axis. Thus, for Xº [100] the
value of such coefficient is α = 3.9 × 10-6 eV cm2/kG ; at
the same time for the Xº [111] and Xº [110] this coeffi-
cient α ≈ 1.4 × 10-6 eV cm2/kG [21].
The values of the respective parameters, obtained in
the work [30] on the base of analysis of the electrophys-
ics properties of the γ-exposed neutron-doped n-Si(P)
crystals, are: the ionization energy of the A-center � E
c
-
0.14 eV, and the energy level change with the pressure
for the Xº [100] orientation is characterized by the coef-
ficient α = 4.5⋅10-6 eV cm2/kG. Obtained were the pa-
rameters of the mobility anisotropy K and scattering
anisotropy Kτ as were as values of deformation poten-
tial constant Ξ
u
which were the same as for the n-Si doped
Fig. 7. Dose dependencies of the Hall mobility values for cur-
rent carriers and for ρ∞/ρ
0
ratio in n-Ge crystals with the impu-
rity concentration N
Sb
≈ 2.7⋅1013 cm-3 obtained at T = 78 K for
samples of the group I (curves 1, 2) and the group II (curves 1′,
2′), respectively.
µ
H
, 1
04
cm
2 V
-1
s-1
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
53SQO, 2(1), 1999
by phosphor during the course of growth. These results
testify that the values of the elastic constant C
11
and C
12
for the silicon crystals doped by phosphor by different
methods also coincide within the experimental accuracy
limit values.
The essential anisotropy of the shift with pressure
for the energy level E
c
- 0.2 eV of radiation center (com-
plex: donor-divacancy [18,40]) was also observed in γ-
exposed n-Ge crystals. Thus for the directions of the
uniaxial pressure Xº [111] and Xº [110] the energy level
E
c
- 0.2 eV shifts down relative to its position at X = 0,
respectively, with the coefficients 5.6⋅10-6 eV cm2/kG and
1 × 10-6 eV cm2/kG, while for the orientation Xº [100]
this level shifts upwards in accord to the factor
4⋅10-6 eV cm2/kG [19].
Creation and annealing of the radiation defects in
the grown by Chochralsky method and doped by ger-
manium neutral impurity p-Si(B), with the oxygen con-
centration ≈ 8⋅1017 cm-3 and the carbonone ≈ 5⋅1017 cm-3,
were investigated in the work [46] at doses of crystals γ-
exposure which reach 5⋅1017 - 5⋅1018 quanta/cm2 . Identi-
fied were two types of the radiation defects with the
close values of energy levels E
v
+ 0.31 eV and E
v
+ 0.35 eV,
which previously have been associated with one type of
defect, namely, the so called K-center. It is established
that the correlation between concentrations of radiation
defects which are created during the course of γ-expo-
sure and to which the said energy levels correspond, de-
pends on the presence of germanium impurity. It is also
established that the rate of creation of the C
O
V
2
and C
i
O
i
complexes depends on the state of oxygen and carbon
impurities, which can be in isolated form as well as in
the form of associations.
On the base of the analysis of the investigation re-
sults concerning the influence of the exposure and con-
sequent annealing on the semiconductor properties, it
was ascertained that the most active impurities which
take part in the defects formation are oxygen and car-
bon. Stability of silicon devices are mainly determined
be stability of radiation defects and connected with them
deep energy levels of radiation origin, particularly, after
the radiation treatment. It was determined, for exam-
ple, that deep radiation centers which have carbon are
not stable [49, 50].
In connection with the fact that both creation and
structural transformation of radiation defects are directly
associated with the initial defect structure of real crys-
tals (background impurities, associations of background
and doping impurities; enclosed by impurity atmosphere
growth dislocations, etc.) the influence of background
oxygen and carbon impurities on the above mentioned
processes in silicon was studied [15-18, 24, 40, 46-54]; as
well as doping (apart shallow impurities): Ge [46, 60], Pt
[55, 56], Yb [57]; and doping by compensating impuri-
ties [45, 61], etc.
The properties of defects in n-silicon after exposure
by γ- quanta and particles which are created during the
decomposition process of 252Cf and consequent thermal
annealing at temperatures up to ≈ 450 0C were investi-
gated in the work [47]. It was found, that annealing at
T = 300 0C during 30 minutes leads to the creation of the
defects (B-centers), which are responsible for the activa-
tion energy of electrons transiting into conduction band.
This energy equals to (E
c
- 0.23) eV. It is assumed that
B-centers arise due to thermal activation of the defects
of interstitial type as the concentration of B-centers is
proportional to the exposure dose and does not depend
on the type of exposure and doping level.
Transformation of the defects of vacancy type, which
arises in the conditions of exposure by α-particles at tem-
perature T = 77 K and annealed at temperature increase
was studied in the work [60], when using the samples of
single-crystal silicon grown by Chochralsky method and
doped by phosphor and germanium impurities.
The parameters of the deep levels of radiation defects
which arise during the process of the cyclic exposure of
high-resistance silicon by α-particles and its annealing
at temperatures close to the room one and in the region
250-400 0C were determined in work [48]. Data obtained
are important for predicting characteristics of detectors
fabricated on the base of structures using high-resistance
silicon, because the analysis of the results testify about
the direct connection of the transformation reguliarities
of radiation defects with the characteristics of the initial
material and technology of structure fabrication. It is as-
certained that the transformation of the radiation defects
in p+-n-n+ structures from high-resistance silicon after cy-
clic exposure by α-particles and consequent annealing is
connected with the activation of the formation of com-
plexes on the carbon base in crystals with the increased
oxygen content.
Influence of γ-radiation on the properties of porous
silicon was studied in works [62, 63].
It is necessary to notice that wide technological pos-
sibilities of ion implantation determine the intensive de-
velopment of the reguliarities investigations of exposure
influence by different elements ions on the formations
and change of the defect structure of a subsurface semi-
conductor layer and its electrophysical properties.
5. Conclusions
Presented investigation data of the electrophysical prop-
erties of γ-exposed n-Si and n-Ge crystals testify about
considerable increase of gradients in crystal resistivity
with the increase of exposure dose. Increase of resistivity
gradients is connected with the increase of compensation
degree of donor impurity by radiation defects with ac-
ceptor properties. Thus, at significant exposure doses
when the compensation degree approaches to unit, the
crystal resistance increases, so that the measurements of
electrophysical characteristics are noticeably complicat-
ed [21, 30], because the concentration of free charge car-
riers considerable decreases.
It is found also, that the neutron-doped n-Si(P) crys-
tals are more stable in relation to the γ-radiation in com-
Yu. P. Dotsenko al.: Electro-physical properties of γγγγγ-exposed crystals ...
5 4 SQO, 2(1), 1999
parison with silicon doped by phosphor in the course of
growing. Other characteristics of the mentioned materi-
als, such as : constants of deformation potential, elastic
constants, parameter of electron mobility anisotropy, co-
efficients which determine the shift rate of energy levels
caused by radiation with pressure change for the defor-
mation axis orientation along the main crystallographic
directions, etc., within the limits of accuracy of the meth-
ods for their determination coincide.
Analysis of the tensoresistive effect investigations in
strongly deformed γ-exposed crystals enables on the base
of the determination of the shift rate of radiation defect
energy level for different crystallographic directions of
pressure to obtain certain conclusions about the micro-
structure of defect.
It is necessary to notice, that the defects of crystalline
structure of semiconductors, which create deep energy
levels in the forbidden gap (in particular, defects of radi-
ation origin) determine, as useful consequences of their
presence, impurity photoconductivity, high tenso- and
thermal sensitivity, centers of high-speed recombination,
etc., as weel as appearance of the undesirable consequenc-
es, namely: capture effects, oscillations, negative resis-
tance, gradients increase, which are connected with the
non-uniformities of the structure, etc.
Therefore, the investigations of the properties of semi-
conductors, determined by the peculiarities of the defect
structure of actual crystals remain actual both from the
scientific and the practical point of view, in particular,
in the field of materials science, which investigates the
change of physical properties under the influence of ra-
diation.
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