ELECTRONIC CONFIGURATIONS OF THE LEVELS OF DIVACANCIES
IN GERMANIUM
A.P. Dolgolenko
Institute of nuclear researches NАN of Ukraine,
E-mail: [email protected]
High-resistance samples p - Si (p0 = 1.63·1011 cm-3), grown up by the floating-zone melting after irradiation by
fast neutron of the reactor at 320 K after isochronal annealing were studied. The energy levels of a divacancy in
germanium in two charge states, depending on its configuration in silicon are determined. Experiments which can be
explained as configuration transitions of a divacancy from a bigger distortion in smaller and vice versa in silicon and
germanium are considered. The energy levels values of the divacancies and E – centers are resulted. It is shown that
radiations defects in Ge no donor levels and by Hubbard energy have the same defects as in Si. Divacancy (V2) level
(-/0) Ev+0.085 eV in Q1 configuration determines the concentration of holes 2.2·1017 cm-3 in the valence band p-Ge
and the position of the Fermi level Ev+0.125 eV in clusters of defects produced by fast neutron in Ge. The
concentration of ~2·1018 cm-3 defects in clusters form the impurity zone near the valence band of width 0.08 eV.
PACS 61.72.Cc, Ji; 61.80.Fe, 61.82.Fk
INTRODUCTION
The irradiation by nuclear particles is an effective
method of research in solid state physics. To date, it
became obvious need for clarification of the electronic
levels of divacancy in the band gap not just in silicon,
but also in germanium. The calculation by molecular
orbital method [1] fully confirmed the idea of the twopit potential of divacancy in silicon in the neutral and
charged states. It is known that the irradiation by high
doses of fast-pile neutrons the Fermi level is near with
the middle of the band gap of silicon, and is located at a
neutral level of divacancy in the first configuration with
strong distortion [2]. Irradiation by large doses either
60
Co by γ-rays or fast neutrons of reactor spectrum of
single-crystal germanium of p - type showed that the
limit position of Fermi level is changed from Ev + 0.24
eV to Ev + 0.125 eV, respectively [3]. The obtaining of
thick relaxed crystals Si1-xGex [4] made it possible to
determine the energy levels of divacancy and other
defects in the band gap as a function of the Ge
concentration in n-, p - type Si. In work [4, 5] is
experimentally shown that an increase of the
germanium concentration in silicon the levels of
radiation-induced defects as the acceptor and donor
reduce their energy in band gap. The Hubbard energy
between levels of divacancy V2 (= / -) and V2 (-/ 0) with
increasing concentration of germanium in silicon
remains ≈ 0.2 eV. A divacancies in negatively-charged
state in the upper half of the band gap Si1-xGex with (x
<0.25) are attractive for electron capture, and in the
lower half of band gap (x > 0.25) are attractive for
seizure of the hole. There was a lack of the continuity ~
0.07 eV at position of V2 (- / 0) divacancy level, when
he crosses the middle of gap. By now become evident
the need to clarify experimentally electronic levels of
divacancy, A, E - centers, in the germanium band gap.
EXPERIMENTAL RESULTS
Samples of p - Si (p00 = (1.63-7.09)⋅1011 cm-3) grown
by the floating-zone melting were irradiated the fluency
of (5.0 1012 ÷ 3⋅1013) no⋅cm-2 fast-pile neutron at a
temperature of 320 K. The irradiation was performed in
the horizontal channel of the WWR – M reactor. Flow
(1⋅1010 no⋅cm-2⋅s-1) of fast neutrons was determined 32S
threshold detector with an accuracy of 10% and led to
energy of neutrons starting from ~ 100 keV. The
measurement of conductivity and Hall coefficient were
carried out with an accuracy of 3% by the Van der Pauw
method on square samples of size 10 × 10 × 1 mm
compensatory manner. Contacts were formed by the
rubbing of aluminum into the silicon polished surface.
On fig. 1a, b are presented the temperature dependence
of the effective holes concentration in the valence band
of p - Si, irradiated with different doses of fast-pile
neutrons after isochronous annealing at different
temperatures under 30 - minutes duration. The results of
calculations are presented in tables (1 ÷ 3). On fig. 2a, b
is shown the enthalpy of ionization of the divacancy in
different charge states relative to the conduction band of
Si1-xGex as a function of the Ge concentration (x) in
silicon [4].
INFILLING STATISTIC OF STATES OF
THE DONOR AND ACCEPTOR DEFECTS
IN THE p – SI
Let us consider a semiconductor (p – Si) borondoped with net Na concentration and the average-degree
compensation by donor (phosphorus) over the range
from room temperature up to liquid nitrogen. Let fastpile neutrons evenly create the point donor-type defects
(except for disorder regions) with a concentration of
Nd <Na, as well as introduce the acceptor defects. We
assume p - Si as non-degenerate (Na <1014 cm-3). Then
as is increased the temperature of a p - Si sample from
77 K we will have some concentration of holes in the
valence band due to the thermal excitation of level Ed
both in the conducting matrix p1(T, Φ) and in the space
charge region of defect clusters P3(T, Φ). From the
solutions of the quadratic equation one may to obtain
ISSN 1562-6016. PASТ. 2013. №5(87), p. 37
the temperature dependence of the holes concentration
in the sample:
N (Φ)
1⎛
⎞
p1 (T, Φ, Ed ) = ⎜ Na − d
− p11(Ed ) ⎟x
2⎝
λ
⎠
⎛
⎞
⎜
⎟
⎜
⎟
4Na p11(Ed )
+1⎟
⎜ 1+
2
N (Φ)
⎛
⎞
⎜
⎟
− p11(Ed )⎟
⎜ Na − d
⎜
⎟
λ
⎝
⎠
⎝
⎠
⎛
Ed
p11 ( E d ) = g N V (T ) exp ⎜⎜ −
⎝ λ kT
defects, the carrier concentration in the conducting
matrix of p - Si can be determined by the calculating of
the total holes concentration ∑ p i (T , Φ , E i ) , which
i
will be delivered into the valence band by the ionization
of acceptor and donor levels:
p(T , Φ) = ∑ pi (T , Φ, Ei ) − p00 + N D (Φ) , (3)
i
⎞
⎟⎟ ,
⎠
(1)
where g = 2 – is the degeneracy factor of donor levels in
p - Si; Nd(Φ) - is the concentration of donor defects
introduced by neutrons after irradiation by the fluency
Φ; p11(Ed) - is the concentration of holes in the valence
band of p - Si, when the Fermi level coincides with the
Ed level in the conducting matrix or with the Ed /λ
effective level in the space-charge region of a defect
clusters. Equation (1) obtained from the solutions of a
quadratic equation it follows from the condition of
electrical neutrality [6]. Similarly, when the temperature
of the p – Si sample increases from 77 K we will have
some concentration of holes in the valence band due to
the thermal excitation of the acceptor level Ea both in
the conducting matrix p0(T,Φ) and in the space charge
region of defect clusters P4 (T,Φ).
⎛
1
4 N (Φ) ⎞⎟
p0 (T , Φ, Ea ) = p11(Ea ) ⎜⎜ 1+ a
− 1⎟ ,
2
(
)
p
E
11
a
⎝
⎠
⎛ E ⎞
p11 (Ea ) = g1 NV (T ) exp ⎜⎜ − a ⎟⎟ ,
(2)
⎝ λ kT ⎠
Where g1 = 0.5 – is the degeneracy factor of acceptor
levels in p - Si; Na(Φ) - is the concentration of radiationintroduced acceptor defects after the irradiation by the
fluency Φ.
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 region of a defect clusters, then λ=1.2.
The analysis of the temperature dependences peff(T,Φ)
showed that we get the best description of them,
depending on T and Φ, if we assume the existence in the
space-charge region of defect clusters a point defects
with an Ea/λ effective level, which compensates the
screening effect of a shallow acceptors (boron). Here Ea
- is the energy position of the same defect in the
conducting matrix of p - Si. Then the additional holes
concentration in the valence band of the conducting
matrix of p – Si samples is equal to p = p0 + p1, and the
additional concentration of the screening centers in the
space-charge regions of defect clusters - P2 = P4 + P3.
On Fig. 1 the calculated according to the equations (1 ÷
3) the temperature dependences of an effective holes
concentration in the valence band of p - Si sample after
irradiation by various fluencies of fast-pile neutrons at
certain temperatures of isochronous annealing are
presented. It was assumed that in the case of the absence
of a statistical interaction between the levels of radiation
Where i = 3 - are present in the conducting matrix of
one acceptor and two donor defect levels; p00 – is the
holes concentration in the p - Si before irradiation;
ND(Φ) – is the concentration of the deepest donor level.
If the samples after irradiation were completely
annealing, the clusters of defects are absent or in the
conducting matrix of p - Si already are not the spacecharge regions after the annealing at 200 °C. Therefore,
the fraction of non-conductive volume in the samples
does not make sense take into account. Good
temperature dependence of holes concentration in the
silicon after irradiation and subsequent-isochronous
annealing of samples was performed under λ = 1 for
according to the equations (1÷3). The energy positions
in the band gap (BG) silicon of radiation-induced
defects and their concentrations are presented in Table1.
DISCUSSION
Table 1 shows the levels Ev + 0.21 and Ev + 0.365
observed in equal concentrations, suggesting that this
defect is located in one and the same charge condition.
Since Ev + 0.21 (0 / +) - this is the position in the band
gap silicon of positively charged divacancy, then Ev +
0.365 and Ev +0.20 - this provision V2 (0 / +) in the first
and second configurations, respectively. The divacancy
changes the configuration in the temperature range (230
÷ 300) K: experimental values of the concentration of
holes in the valence band are above the theoretical
curve. With increasing of the temperature of sample the
holes, freed from the level Ev +0.21 eV have insufficient
energy to be captured at the level Ev + 0.365 eV. Under
these fluency of irradiation in high-resistively silicon a
divacancies after isochronous annealing (200-325) oC
are moving from the first to the second configuration,
even at room temperature (Fig. 1). In [2] it is shown that
the neutral level of divacancy Ev +0.45 eV, according to
theoretical calculations [1] should differ by 0.07 eV
from the neutral level of divacancy Ev +0.53 eV in the
first configuration. In our case, this energy difference is
0.08 eV. Neutral divacancies in the first and second
configuration pit is exposed to normal exchange
reaction V20 → V2+ + V2−. She (V2) act as like
recombination centers, which higher than the room
temperature captured an electrons, and below 292 K - a
holes so that their energy in the capture of holes are
increased at (0.01 ÷ 0.02) eV. The slow trapping centers
of electrons in the temperature recharge of E0.17 - centre
(Ec-0.17 eV) were investigated in detail in [7]. It is
shown that the rate of their introduction is not
dependent on the energy of electron irradiation, but
b
a
Fig. 1. The temperature dependence of the carrier concentration in the p - Si (P00 =2.62·1011 cm-3, p00 =
7.09·1011 cm-3) irradiated by fast-pile neutron (Φa = 5·1012 no·cm-2, Φb =3.0·1013 no·cm-2), respectively, after the
isochronous annealing temperature: a) 1 – 200 °C; 2 – 225 oC; 3 – 250 oC;. b) 1 – 250 °C; 2 – 275 oC; 3 – 300 oC;
4 – 325 oC. • - experiment —- calculation; during – 30 min
these defects are annealed at 277 °C. Divacancies are
annealed in the same temperature range, but the rate of
their introduction depends on the energy of electron
irradiation. The slow trapping centers in the samples Si
(Fz) with Schottky barrier have activation energy (0.08
± 0.015) eV of the electron capture cross section for the
acceptor level with thermal activation energy 0.17 eV.
Then later-radiation defect with the enthalpy of
ionization (0.09 eV) and the position of Ec–0.09 eV
exists in the silicon band gap relative to the bottom of
the conduction band. In the case of annealing at 277 ºC
for 4.5 hours this defect disappeared. As and the A center, the concentration of this defect does not depend
on the energy of electron irradiation (in contrast
divacancy). It is shown that the Ec-0.09 eV in the
oxygen silicon and p-i-n diode without oxygen showed
a relatively low concentration with respect to the A center.
Table 1
Parameters to calculate the concentration and energy position of the levels in the band gap of silicon after irradiation
and isochronal annealing of the sample p-Si (P00=2.62·1011 cm-3, p00=7.09·1011 cm-3).
o
2
EV+Ed, eV
Na, cm-3
Nd, cm-3
Tann,oC
Р00, cm-3
Φ, n /cm
5·1012
3·1013
2.62·1011
7.09·1011
0.367
0.283
0.365
0.283
0.200
0.365
0.280
0.200
0.365
0.280
0.365
0.283
0.365
0.280
0.365
0.280
Let us remember that these defects with the slow
electron capture are observed on samples with a barrier
Schottky. In such structures should take into account the
large number of defects near the surface of the silicon
(especially vacancies). Because of the high
concentration of vacancies near the surface, the
probability of a radiation vacancy form divacancy,
united with a vacancy near the surface. Therefore, the
rate of introduction of a divacancies in samples with
5.4·1012
6.0·1011
8.2·1012
2.2·1012
6.0·1011
1.4·1013
7.0·1012
4.0·1012
1.4·1013
2.0·1012
2.0·1013
5.0·1012
2.85·1013
7.00·1012
3.60·1013
6.00·1012
4.8·1012
4.8·1012
6.0·1012
1.6·1012
6.0·1012
7.0·1012
3.0·1012
7.0·1012
1.2·1013
3.0·1012
1.5·1013
3.0·1013
2.15·1013
1.20·1013
3.00·1013
7.00·1012
200
225
250
250
275
300
325
Schottky barrier will not depend on the energy of the
electron irradiation. Then we can assume that the Ec0.09 eV is divacancy in a thrice negatively charged state
in the first configuration. In the single negative and
double negative charge state the positions of divacancy
levels in silicon in the second configuration are (Ec0.42 eV) and (Ec-0.17) eV, respectively. It was assumed
that the energy of Hubbard does not depend on the
number of electrons trapped on the radiation defect.
b
a
Fig.2. The ionization enthalpy of divacancy in different charge states: neutral (left) and the negatively and
positively charged state (right) with respect to the conduction band of Si1-xGex as a function of the Ge concentration
(x) in silicon [4]
In [4] it is shown that in the Si1-xGex (0 <x <0.5) n-type
conductivity a divacancy reduces the energy position of
the acceptor levels relative to the bottom of the
conduction band, and in p - type – of the donor levels
relative to the valence band as a result increasing energy
of the valence band. This rule also applies to other
radiation defects, such as E - centers [5]. On Fig. 2 it is
shown the results of such behavior of acceptor and
donor levels of divacancies obtained in [4]. There was a
lack of the continuity in position of V2 (- / 0) divacancy
level ~ 0.07 eV, when is crossing the center of the
forbidden band as can be seen in Fig. 2. After crossing
the middle of the forbidden zone Si1-xGex as well as
negatively and positively charged divacancy relative to
the bottom of the conduction band does not change its
position by increasing of the germanium concentration
in silicon. All above said allows definitely confirming
that the observed breakup ∼0.07 is precisely related to
the configuration transition of divacancy from Q1 to Q2
configuration. The width (Eg) of the band gap Si1-xGex
depends on the concentration of germanium in silicon
can be determined according to the expression [4]:
Eg ( x) = Eg ( Si ) − 0.43 ⋅ x + 0.206 ⋅ x 2 ,
(x<0.85),
Eg ( Si ) = 1.169 − α ⋅ T 2 /( β + T ) ,
(α = 4.9⋅10-4 eV/K; β = 655).
At T = 300 K, x = 0.5, Eg(x) = 0.9565 eV.
Determining the positions in the Si1-xGex of a divacancy
levels relative to the valence band at x = 0.5 and taking
into account the increase in the energy of the valence
band in the transition to germanium, the position of the
divacancy levels in the band gap in Q1 and Q2
configurations in single-crystal Ge was obtained. The
levels of the different charge states of the divacancy in
silicon and germanium, depending on the configuration
the Q1 or Q2 are presented in table 2.
Table 2 shows that if the electron is capture to the level
of the divacancy in Si and Ge in the first configuration,
the energy level is increased by 0.165 eV, and the
second configuration to 0.250 eV. In [8], it was shown
the original scheme of their own levels for intrinsic
radiation defects, which is based not only both on
published data and the original experiment, was
proposed. It is necessary the following positions to take
into account: (j) radiation defects creates additional
energy levels of electrons in the gap, and the intrinsic
defects in silicon are amphoteric; (jj) under capture of
one or the second electron on the acceptor levels of a
divacancy or a di-interstitial, the their position in the
silicon band gap is changed by ΔE0 = 0.165 ± 0.005 eV,
and in the case of vacancies or interstitials the
mentioned value is doubled; (jjj) the connection of
carbon to the divacancy increases the energy position of
the acceptor levels of divacancies on ΔE1 = 0.035 eV
and lowers the energy of the donor levels, whereas the
addition of oxygen to a divacancy decreases the energy
of the acceptor levels and increases the energy position
of the divacancy donor-levels on the value ΔE2 =
0.06 eV. It should make some more updates to the
model modification of radiation defects, such as
divacancy and A - centers. Joining the interstitial silicon
atoms reduces the energy position of the acceptor level
of the A - center on 0.03 eV and increases the energy of
the donor level on 0.03 eV. In the case of accession to A
- center of di-interstitial the energy position of the
acceptor level has changed on 0.06 eV similarly a
divacancy modified by oxygen atom. Carbon modifies
A - centre, as well as the divacancy. The Hubbard
energy (EH) in the configurations Q1 and Q2 of
divacancy the same as Si and Ge can be assumed that
the background impurities will modify the radiation
defects as Ge and Si similarity. When you modify the
radiation-induced defects by the background impurity
the position their neutral levels in the band gap does not
change.
Table 2
The energy levels positions in various charge state of divacancy in silicon and germanium, depending on its atomic
configuration
Atomic
Charge state
EH,
ΔE,
configuration
eV
eV
eV
Si
Ge
3-/22-/-/0
0/0
0/+
Q1
Ec-0.09
Ec-0.261
Ec-0.426
Ev+0.53
Ev+0.365
0.165
Q2
Ec+0.08
Ec-0.17
Ec-0.42
Ev+0.45
Ev+0.20
0.25
Q1
Ec-0.25
Ev+0.25
Ev+0.085
Ev-0.08
0.165
0.16
Q2
Ec-0.05
Ec-0.30
Ev+0.11
Ev-0.14
0.25
0.13
The position of the E - center Ev + 0.30 in Ge was
first defined Fage-Pedersen et al. in [9]. A further study
VP − centers in Ge is showed that the second acceptor
level of E − center Ec − 0.37 eV can be in the doublenegative charged state [10, 11].
Table 3
V2(Q1) eV
The modification of radiation-induced defects by the background impurities in germanium
V2(Q2) eV PV eV
VOi eV
VOiIGe eV IGe eV
I2Ge eV
V eV
Ev+0.25
Ev+0.085
0.16
0.165
Ec−0.30
Ev+0.11
0.13
0.25
Ec−0.37
Ev+0.10
0.105
0.195
Ec−0.20
0.025
Ec−0.23
0.025
Ec–0.19
Ev+0.14
0.15*
0.33
Ec−0.25
Ev+0.25
0.10*
0.165
Ec−0.28
Ev+0.05
0.19*
0.33
Charge
state
=/−
−/0
ΔE eV
EH eV
* - There are no reliable values of ΔE-displacement levels. The charge of levels IGe conditionally understated by one.
This means that there must exist in silicon also doublecharged state of E - center in the forbidden zone: Ec −
0.265 eV (=/−). According to [4], the negatively
charged E - centers with increasing Ge concentration in
the silicon decreases the energy position in the band
gap. Therefore, in the germanium band gap relative to
the Ec -zone the energy of the acceptor levels E - centers
will be reduced on 0.105 eV about the Ec -zone in
silicon. The appearance in Ge, irradiated 2 MeV
electrons, some time after irradiation, and the
disappearance of levels Ec − 0.13 eV and Ec − 0.19 eV
in ten days can be explained as the release of the
interstitial atom Ge (IGe) from the trap and a partial
capture on the atom phosphorus in order to run off in
the future on vacancy sink. In silicon has been observed
that A - center increases energy on 0.17 - 0.105 =
0.065 eV near dopant (phosphorus) at VOiP. [12].
Therefore, the level Ec − 0.19 eV in germanium belongs
interstitial atom Ge (IGe3-/2-) and the level Ec − 0.13 eV
IGeP=/− - defect. A similar value of energy in the BG germanium can have di-interstitial I2Ge. It is possible
that at room temperature a Frenkel pair is split and a
vacancy and interstitial atom of germanium in equal
concentration were born. A vacancy near the interstitial
oxygen atom will have a level Ec-0.13 eV (3-/2-) and
interstitial atom germanium - Ec-0.19 eV (3-/2-). The
level of divacancy V2 (-/0) (E (V2) = Ev + 0.085 eV)
specifies a limit on the Fermi level position in
germanium irradiated with fast neutrons of reactor
spectrum: Ef = Ev +0.125 eV and the concentration of
holes in the valence band: P = 2.2·1017 cm-3.⋅Then the
concentration of V2 in clusters easy is calculated:⋅
E f − E (V2 )
⎡
⎤
N (V2 ) = P ⎢2 ⋅ exp(
) + 1⎥
kT
⎣
⎦
At T = 300 K, N (V2) = 2.0·1018 cm-3.
Under such a high concentration of divacancies in
clusters near the valence band an impurity band of
width equal (ΔE) [13] is created:
ΔE = 8 ln 2 ⋅ B
B=
e 2 ( Na + Nd ) 2 / 3
,
χχ 0 ( Na − Nd )1 / 3
Where e - is the electron charge; Na, Nd - concentration
of acceptors and donors; χ = 70, χ0 = 8.85·10-12 f/m.
When Na = 2·1018 cm-3 (ΔE = 0.08 eV), which agrees
with the experimental value of the concentration of
holes in the valence band n0-irradiated Ge p =
2.2·1017 cm-3:
P = Nv ⋅ exp(
E f − ΔE / 2
kT
)
The density of states in the valence band:⋅
Nv (T ) = 4.82 ⋅ 1015 T 3 / 2 (mdp / m0 ) 3 / 2 ,
Where mdp/m0 = 0.39, Nv (300 K) = 6.04·1018 cm-3
CONCLUSIONS
In silicon and germanium is determined the values
of the energy levels of the divacancy in different
configurations. It is shown that in forbidden zone of Ge
there is not the donor levels of radiation-induced defect,
and Hubbard energy of defects the same as in silicon.
The V2 (-/0) level of divacancy Ev + 0.085 eV in Q1
configuration determines the concentration of holes
2.2·1017 cm-3 in the valence band of p − Ge and the
position of the Fermi level Ev + 0.125 eV in clusters of
defects produced by fast neutrons in germanium. The
concentration of defects ~ 2·1018 cm-3 creates in the
clusters an impurity band near the valence band width
of 0.08 eV.
REFERENCES
1. С.С. Моливер. Метод открытой оболочки для
электронной структуры дивакансии кремния // ФТТ.
1999, том. 44, в. 3, с. 404−410.
2. А.П. Долголенко. Электронные уровни
конфигураций дивакансий в кремнии// Вопросы
атомной науки и техники. Серия “Физика
радиационных повреждений и радиационное
материаловедение”. 2012, 5(81), с.13-20.
3. J.H. Crawford, Jr., and J.W. Cleland. Nature of
Bombardment and Energy Levels in Semiconductors //
J.of Appl. Phys. 1959, vol. 30, №8, p.1204−1213.
4. A.Nylandsted Larsen, A.Bro Hansen, A. Mesli.
Irradiation−induced defects in SiGe // Mater. Sce. Eng.
B. 2008, vol. 154-155, p.85-89.
5. Arne Nylandsted Larsen, Abdelmadjid Mesli.
The hidden secrets of the E−center in Si and Ge //
Physica B. 2007, vol. 401-402, p.85-90.
6. A.P. Dolgolenko, I.I. Fishchuk. A-centres build–
up kinetics in the conductive matrix of pulled n-type
silicon with calculation of their recharges at defect
clusters // Phys. Stat. Sol. (a). 1981, vol. 67, № 8, p.407.
7. S.D. Brotherton
and
P. Bradley.
Defect
production and lifetime control in electron and γ -
irradiation silicon // J. Appl. Phys. 1982, vol. 53, №8,
p.5720.
8. A.P. Dolgolenko,
P.G. Litovchenko,
M.D. Varentsov,
G.P. Gaidar,
A.P. Litovchenko.
Particularities of the formation of radiation defects in
silicon with low and high concentration of oxygen //
Phys. Stat. Sol. (b). 2006, vol. 243, №8, p.1842.
9. J. FagePedersen,
A.N. Larsen,
A. Mesli.
Irradiation-induced defects in studied by transient
spectroscopies // Phys. Rev. B. 2000-1, vol. 62, №15,
p.10116-10125.
10. V.P. Markevich, A.R. Peaker, V.V. Litvinov,
V.V. Emtsev, L.I. Murin. // J. Appl. Phys. 2004, vol. 95,
p.4078.
11. V.P. Markevich, I.D. Hawkins, A.R. Peaker,
K.V. Emtsev, V.V. Emtsev, V.V. Litvinov, L.I. Murin,
L. Dobaczewski // Phys. Rev. 2004, vol. 70, p.235213.
12. G.E. Jellison, Jr. Transient capacitance studies of
an electron trap at Ec−ET = 0.105 eV in phosphorus
doped silicon // J. Appl. Phys. 1982, vol. 53, №8,
p. 5715−5719.
13. Я. Партыка, П.В. Жуковский, П. Венгерэк,
А. Родзик,
Ю.В. Сидоренко,
Ю.А. Шостак.
Температурная зависимость ширины зоны глубоких
уровней в сильно дефектном кремнии // ФТП. 2002,
т. 36, №12, с.1412.
Article received 22.03.2013
ЭЛЕКТРОННЫЕ УРОВНИ КОНФИГУРАЦИЙ ДИВАКАНСИИ
В ГЕРМАНИИ
А.П. Долголенко
Исследованы высокоомные образцы p-Si (p00=(1,63…7,09)·1011 см-3), выращенные методом бестигельной
зонной плавки, после облучения быстрыми нейтронами реактора при 320 К. Определены энергетические
уровни дивакансии в германии в трех зарядовых состояниях в зависимости от её конфигурации в кремнии.
Рассмотрены эксперименты, которые можно объяснить как конфигурационные переходы дивакансии с
большей дисторсии в меньшую и наоборот в кремнии и германии. Приведены значения энергетических
уровней дивакансии в кремнии и германии в разных конфигурациях. Показано, что у радиационных
дефектов в Ge отсутствуют донорные уровни, а энергия Hubbard у дефектов такая же, как и в Si. Уровень
дивакансии V2(−/0) в Q1-конфигурации Ev+0,085 эВ определяет концентрацию дырок в валентной зоне p-Ge
2,2·1017 см-3 и положение уровня Ферми Ev+0,125 эВ в кластерах дефектов, созданных быстрыми
нейтронами в Ge. Концентрация дефектов ~2·1018 см-3 в кластерах образует примесную зону около
валентной зоны шириной 0,08 эВ.
ЕЛЕКТРОННІ РІВНІ КОНФІГУРАЦІЙ ДИВАКАНСІЇ В ГЕРМАНІЇ
А.П. Долголенко
Досліджені високоомні зразки p-Si (p00 = (1,63…7,09)·1011 см-3), вирощені методом безтигельної зонної
плавки, після опромінення швидкими нейтронами реактора при 320 К до і після ізохронного відпалу.
Визначено у германії енергетичні рівні дивакансії в трьох зарядових станах у залежності від її конфігурації в
кремнії і приведено значення енергетичних рівнів дивакансії та Е-центра. Показано, що в радіаційних
дефектів у Ge немає донорних рівнів, а енергія Hubbard у дефектів така ж, як і в Si. Рівень дивакансії V2(−/0)
у Q1-конфігурації Ev+0,085 еВ визначає концентрацію дірок у валентній зоні p-Ge 2,2·1017 см-3 і положення
рівня Фермі Ev+0,125 еВ у кластерах дефектів, створених швидкими нейтронами у Ge. Концентрація
дефектів ~ 2·1018 см-3 у кластерах утворює домішкову зону біля валентної зони шириною 0,08 эВ.