Neutron irradiation influence on the silicon voltage limiter parameters
The influence of neutron irradiation on breakdown voltage (Ubd) and limitation voltage (Ulim) is investigated in silicon voltage limiter. The coefficient Kρ is basic radiation parameter, forming dependences Ubd = f (F) and Ulim = f (F), which determines the dependence of basic charge carriers concen...
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| Zitieren: | Neutron irradiation influence on the silicon voltage limiter parameters / A.Z. Rakhmatov, M.Yu. Tashmetov, L.S. Sandler // Вопросы атомной науки и техники. — 2012. — № 5. — С. 81-87. — Бібліогр.: 17 назв. — англ. |
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Rakhmatov, A.Z. Tashmetov, M.Yu. Sandler, L.S. 2016-11-18T21:07:15Z 2016-11-18T21:07:15Z 2012 Neutron irradiation influence on the silicon voltage limiter parameters / A.Z. Rakhmatov, M.Yu. Tashmetov, L.S. Sandler // Вопросы атомной науки и техники. — 2012. — № 5. — С. 81-87. — Бібліогр.: 17 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/109026 621.315.592 The influence of neutron irradiation on breakdown voltage (Ubd) and limitation voltage (Ulim) is investigated in silicon voltage limiter. The coefficient Kρ is basic radiation parameter, forming dependences Ubd = f (F) and Ulim = f (F), which determines the dependence of basic charge carriers concentration in silicon from neutron fluencies. The mechanisms, which form the Ulim value after neutron irradiation are determined. On basis of obtained results analysis is proposed the model, which makes it possible to forecast changes in the breakdown voltage and limitation voltage, which occur as a result the neutron irradiation of voltage limiter. Влияние нейтронного облучения на напряжение пробоя (Uпроб) и напряжение ограничения (Uогр) исследовано в кремниевых ограничителях напряжения. Коэффициент Kρ является основным радиационным параметром, формирующим зависимости Uпрб = f(Ф) и Uогр = f(Ф) и определяющим зависимость концентрации основных носителей заряда в кремнии от флюенса нейтронов. Определены механизмы, формирующие величину Uогр после нейтронного облучения. На основе анализа полученных результатов предложена модель, позволяющая прогнозировать изменения напряжения пробоя и напряжения ограничения, которые происходят в результате нейтронного облучения ограничителя напряжения. Вплив нейтронного опромінення на напругу пробою (Uпроб) і напругу обмеження (Uобм) досліджено в кремнієвих обмежувачах напруги. Коефіцієнт Kρ є основним радіаційним параметром, що формує залежності Uпрб = f(Ф) і Uогр = f(Ф) і визначає залежність концентрації основних носіїв заряду в кремнії від флюенса нейтронів. Визначені механізми, що формують величину Uобм після нейтронного опромінення. На основі аналізу отриманих результатів запропонована модель, що дозволяє прогнозувати зміни напруги пробою і напруги обмеження, які відбуваються в результаті нейтронного опромінення обмежувача напруг The authors are grateful to Prof. Karimov M, Dr. Tursunov N. and Mr. Ismatov N. to work results discussion. Work is executed within the framework of F2-FA-0- 11372 grant of Committees on Coordination of Development Sciences and Technology. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Материалы реакторов на тепловых нейтронах Neutron irradiation influence on the silicon voltage limiter parameters Влияние нейтронного облучения на параметры кремниевых ограничителей напряжения Вплив нейтронного опромінення на параметри кремнієвих обмежувачів напруги Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Neutron irradiation influence on the silicon voltage limiter parameters |
| spellingShingle |
Neutron irradiation influence on the silicon voltage limiter parameters Rakhmatov, A.Z. Tashmetov, M.Yu. Sandler, L.S. Материалы реакторов на тепловых нейтронах |
| title_short |
Neutron irradiation influence on the silicon voltage limiter parameters |
| title_full |
Neutron irradiation influence on the silicon voltage limiter parameters |
| title_fullStr |
Neutron irradiation influence on the silicon voltage limiter parameters |
| title_full_unstemmed |
Neutron irradiation influence on the silicon voltage limiter parameters |
| title_sort |
neutron irradiation influence on the silicon voltage limiter parameters |
| author |
Rakhmatov, A.Z. Tashmetov, M.Yu. Sandler, L.S. |
| author_facet |
Rakhmatov, A.Z. Tashmetov, M.Yu. Sandler, L.S. |
| topic |
Материалы реакторов на тепловых нейтронах |
| topic_facet |
Материалы реакторов на тепловых нейтронах |
| publishDate |
2012 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Влияние нейтронного облучения на параметры кремниевых ограничителей напряжения Вплив нейтронного опромінення на параметри кремнієвих обмежувачів напруги |
| description |
The influence of neutron irradiation on breakdown voltage (Ubd) and limitation voltage (Ulim) is investigated in silicon voltage limiter. The coefficient Kρ is basic radiation parameter, forming dependences Ubd = f (F) and Ulim = f (F), which determines the dependence of basic charge carriers concentration in silicon from neutron fluencies. The mechanisms, which form the Ulim value after neutron irradiation are determined. On basis of obtained results analysis is proposed the model, which makes it possible to forecast changes in the breakdown voltage and limitation voltage, which occur as a result the neutron irradiation of voltage limiter.
Влияние нейтронного облучения на напряжение пробоя (Uпроб) и напряжение ограничения (Uогр) исследовано в кремниевых ограничителях напряжения. Коэффициент Kρ является основным радиационным параметром, формирующим зависимости Uпрб = f(Ф) и Uогр = f(Ф) и определяющим зависимость концентрации основных носителей заряда в кремнии от флюенса нейтронов. Определены механизмы, формирующие величину Uогр после нейтронного облучения. На основе анализа полученных результатов предложена модель, позволяющая прогнозировать изменения напряжения пробоя и напряжения ограничения, которые происходят в результате нейтронного облучения ограничителя напряжения.
Вплив нейтронного опромінення на напругу пробою (Uпроб) і напругу обмеження (Uобм) досліджено в кремнієвих обмежувачах напруги. Коефіцієнт Kρ є основним радіаційним параметром, що формує залежності Uпрб = f(Ф) і Uогр = f(Ф) і визначає залежність концентрації основних носіїв заряду в кремнії від флюенса нейтронів. Визначені механізми, що формують величину Uобм після нейтронного опромінення. На основі аналізу отриманих результатів запропонована модель, що дозволяє прогнозувати зміни напруги пробою і напруги обмеження, які відбуваються в результаті нейтронного опромінення обмежувача напруг
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/109026 |
| citation_txt |
Neutron irradiation influence on the silicon voltage limiter parameters / A.Z. Rakhmatov, M.Yu. Tashmetov, L.S. Sandler // Вопросы атомной науки и техники. — 2012. — № 5. — С. 81-87. — Бібліогр.: 17 назв. — англ. |
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2025-11-26T01:42:41Z |
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2025-11-26T01:42:41Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2012. №5(81) 81
Раздел третий
КОНСТРУКЦИОННЫЕ МАТЕРИАЛЫ РЕАКТОРОВ НОВЫХ
ПОКОЛЕНИЙ, РЕАКТОРОВ НА БЫСТРЫХ НЕЙТРОНАХ
И ТЕРМОЯДЕРНЫХ УСТАНОВОК
UDC 621.315.592
NEUTRON IRRADIATION INFLUENCE ON THE SILICON VOLTAGE
LIMITER PARAMETERS
A.Z. Rakhmatov1, M.Yu. Tashmetov2, L.S. Sandler1
1JSC Photon, 100047, Tashkent;
2Institute of Nuclear Physics of the AS of RUz, 100214, Tashkent, s. Ulugbek
The influence of neutron irradiation on breakdown voltage (Ubd) and limitation voltage (Ulim) is investigated in
silicon voltage limiter. The coefficient Kρ is basic radiation parameter, forming dependences Ubd = f (F) and
Ulim = f (F), which determines the dependence of basic charge carriers concentration in silicon from neutron
fluencies. The mechanisms, which form the Ulim value after neutron irradiation are determined. On basis of obtained
results analysis is proposed the model, which makes it possible to forecast changes in the breakdown voltage and
limitation voltage, which occur as a result the neutron irradiation of voltage limiter.
INTRODUCTION
In view of continuous enhancement of radio-
electronic equipment (REE), increase in the number of
carried out functions and decided tasks, the
requirements for its reliability and failure-free operation
sharply grew. One of the basic factors which decreases
reliability and failure-free performance of REE is the
influence of unregulated electric pulses such as
atmospheric electricity, powerful switching noise, etc.
Therefore the guaranteed protection of radio-electronic
equipment (or its separate elements) of the influence of
such pulses is one of the basic ways of its reliability
growth. The overwhelming majority of known
protection ways is that at the moment of action of
“dangerous” electric pulse the protective element "cut
away” the peaks of voltage pulses up to a safe level, and
so the excess electrical energy is dissipated on
protective element. One of perspective protective
elements is the semiconductor voltage limiter (VL); it is
the semiconductor diode, where the most important
parameter is limiting voltage (Ulim). The voltage is the
maximum voltage which provides overpowers
protection of the REE [1]. If Ulim > 20 V one can
consider that the avalanche breakdown of p-n junction
[2] is the basic mechanism forming the Ulim value. In
this case one of the parameters characterizing VL
should be also avalanche breakdown voltage (Ubd). Ubd
is the voltage since which voltage limiting at protected
REE (or its element) begins. Limiting voltage (Ulim) and
avalanche breakdown voltage are connected by the
relation:
lim lim ( ) , (1)bd dif serU U I R R= + +
where Ilim is the current passing through VL when the
overvoltage pulse appears; Rdif and Rser - differential and
series resistances of VL, respectively.
This current value characterizes of the excess
electrical energy dissipated on VL in the “limitation”
regime which does not lead of VL parameters to
destruction or degradation. VL is in so-called “waiting”
mode in the absence of an overvoltage pulse. The
reverse voltage (Urev) is fed to VL which equal to
working voltage of the protected REE (or its element).
Apriori Urev <Ubd, and reverse current (Irev) of VL at this
voltage characterizes power losses in VL when working
in "waiting" mode.
It is evident that the dependence of the VL
parameters on the external influencing factors (EIF) (the
most important of which are ambient temperatures [2, 3,
4] and radiation) defines its efficiency as an element of
electrical circuit under the actual conditions of REE
operation.
Radiation influence on Ubd and Irev of rectifier diode
and stabilitron is described in variety of works (for
example [5-8]). At the same time radiation influence on
Ulim and connection of this parameter with Ubd are not
investigated practically. First of all it concerns neutron
radiation which is the strongest factor influencing on
semiconductors and semiconductor devices parameters.
The present work is dedicated to study of neutron
irradiation influence on limiting voltage and its
connection with breakdown voltage under radiation
influence.
INVESTIGATED SAMPLES
AND EXPERIMENTAL TECHNIGUE
The VL were studied with voltage limitation
Ulim = 50 V. The construction of the investigated VL is
schematically shown in Fig. 1 (two-layered protection
of crystal surface by organic materials is not shown).
The schematic construction of the active part of the
voltage limiter crystals used in the experiment, some of
its geometric dimensions (in millimeters) are presented
in Fig. 2.
Detail description of crystal making technology
basic principles for the VL is given in [2]. The most
important physical characteristics of the VL structure
and technological regimes fabrication will be given.
82 ISSN 1562-6016. ВАНТ. 2012. №5(81)
Fig. 1. VL construction (schematic)
They are the following:
– the area of p-n junction is ~ 9.3·10-2 cm2;
– for crystal VL making n- type silicon with specific
resistance of 0.3 Ohm·cm was used;
– p+ and n+ layers were created by the boron and
phosphorus diffusion, respectively;
– diffusion was carried out by the package method
[2] at (1250 ± 5) ºC during 1 h. At this diffusion method
the distribution of the diffusing admixture is obeyed to
the errors addition function [2].
Fig. 2. VL crystal construction (schematic)
The calculations carried by formulas [9] and initial
data [2, 9] (diffusion coefficients, surface
concentrations) showed that:
– p-n junction occurrence depth Xj (boron diffusion
depth) is ~ (37±1) μm;
– concentration gradient of impurity which crea-tes
p-n junction at x= Xj is ~ (1.0±0.2)·1020 cm-4;
– n-n junction occurrence depth (phosphorus
diffusion depth) is ~ 45 μm.
Neutron irradiation of samples was carried out at the
research reactor. Neutron fluence dosimetry was
realized by the sulfuric indicators 32S (E > 3 MeV)
followed by reduction (using reactor spectrum) to the
neutrons fluence with the E ≥ 100 keV energy. The
average neutrons energy was ~ 1.5 MeV and dosimetry
error − ± 20 %.
Ubd, Ulim, Irev and voltage dependence of barrier
capacity (volt-farad characteristics) were measured at
VL before and after radiation. Ubd was measured in
accordance with the State Standard 18986.2 by the bend
of voltage-current characteristic (under sharp decrease
of differential resistance and the reverse currents which
exceed Irev not less than 10 times over the prebreakdown
region). Ulim was measured in accordance with the
procedure described in [1] by compensation method
with the error not more than 5 %; the current Ilim was
50 A. Irev was measured according to the State Standard
18986.1 under the assigned reverse voltage with the
error not exceed 5 %. The barrier capacity from voltage
dependence (volt-farad characteristics) at investigated
VL was measured by bridge method at the 1 MHz
frequency according to the State Standard 18986.4 with
the error not more than 5 %. The samples (selection
consisted of 20 VL) were irradiated and the mentioned
parameters were measured. For reactor time economy
and reduction of the reactor startup number the sample
selection were divided into 5…6 groups (by 3…4 VL).
Each sample group was irradiated into two stages (by
two neutron fluxes) followed by measurement of
parameters after each irradiation stage. For the analysis
of parameters dependence from neutron fluence (Φ) the
average values of the parameters were used. The VL
experimental parameters values were processed by the
least-squares method. Obtained graphic dependences,
their analytic equations (y = f (x)), quantity coefficient
of approximation (R2) and experimental points are given
in all subsequent figures.
BASIC RESULTS AND DISCUSSION
The ln [Ubd(Φ / Ubd(0)] = f(Φ) and
ln [Ulim(Φ) / Ulim(0)] = f (Φ) dependences are presented
in Fig. 3.
Fig. 3. Neutron fluence dependences
of avalanche breakdown voltage and limiting
voltage: 1 – ln[Ubd(Φ / Ubd(0)] = f (Φ);
2 – ln[Ulim(Φ)/Ulim(0)] = f (Φ)
From the figure one can see that the dependences are
straight lines with sufficiently high (R2 ≥ 0.9) reliability
of approximation and, therefore, for investigated VL the
relations Ubd(Φ) / Ubd(0) and Ulim(Φ) / Ulim(0)
exponentially depend on the neutron fluence:
1( ) (0 ) ( ), ( 2 )b d b dU Ф U ехр К Ф=
lim lim 2( ) (0) ( ), (3)U Ф U ехр К Ф=
where K1 and K2 – coefficients which are determined by
slope of lines in Fig. 3 are represented in table1.
Table 1
K1, cm2 K2, cm2
6.3·10-17 7.1·10-17
So, K1 and K2 values are near each other and are
distinguished less than 10 %. Themselves the values of
breakdown voltage change on ~ 12…13 % and of
limiting voltage on ~ 20…23 % even at the maximum
neutron flux (~ 2·1015 cm-2). In Fig. 4 the
ln [Ubd(Φ)/Ubd(0)] = f (Φ) dependence, built according
to experimental data, is presented. Fig. 4 shows that the
Ubd dependence on neutron fluence Φ is exponential
y = 7.1·10-17x
R2 = 0.96
ln
[U
bd
(Ф
)/
U
bd
(0
)
ln
[U
lim
(Ф
)/
U
lim
(0
)
Ф, 1015 cm-2
y = 6.3·10-17x
R2 = 0.94
ISSN 1562-6016. ВАНТ. 2012. №5(81) 83
nature which is typical [6, 7]. K1 coefficient value in
exponent and its independence of specific resistance of
silicon which is used for creation of p-n junction, and
from the structure is novel (within certain degree):
according to [6, 7] this coefficient is K1 = 0.75 Kρ,
where Kρ is a constant of the specific resistance change
of semiconductor under radiation influence.
Fig. 4. The dependence of ln [Ubd(Φ) / Ubd(0)] = f (Φ)
It is known [5, 6, 10] that if neutron irradiation
weakly influences on carriers mobility the relation
occurs:
0
/ ,dn dФK
nρ = (4)
where dn/dΦ – carriers removal rate; n0 – initial
concentration of equilibrium basic current carriers.
In accordance with [6], for the initial silicon specific
resistance of ρ0 ~ 2 Ohm·cm (n0 ~ 2.5·1015 cm-3) dn/dΦ
can be within the limits of 1.5…4 cm-1. In this case the
coefficient Kρ must be ~ (1.1±0.5)·10-15 cm2 and,
therefore, according to [6,7] the coefficient K1 must be
~ (0.8±0.4)·10-15 cm2. But for the investigated VL
samples this value is approximately by an order less and
is ~ 6.6·10-17 cm2 (Fig. 5). It is the most probable that
such discrepancy in the K1 value is related to the fact
that in the works [6, 7] the sharp p-n junctions were
investigated but in the present work the p-n junctions
with the linear distribution of impurity in the base
(Fig. 5, curve 1) are examined.
The mentioned reason for discrepancy is probable
sufficient because the authors [5] showed that for the
diffusion p-n junctions Ubd practically does not change
under irradiation, and they explained this effect by fact
that at the large reverse voltages the quasi Fermi level in
the space charge region of p-n junction falls below
energy of the deep acceptor levels injected by
irradiation. As a result the ionization degree of these
deep levels becomes negligible and the properties of the
space charge region are determined only by ionized
initial donors and acceptors. However in the mentioned
work the quantitative data were not given which
confirm both the explanation and statement about the
Ubd (Φ) weak dependence of diffusion diodes. Therefore
the mechanisms will be considered in more detail which
form the dependences described by formulas (2) and
(3).
According to [3, 11, 12], the avalanche breakdown
voltage of p-n junction is directly related to the width of
space charge region (SCR) of the p-n junction:
[ ]~ ( ) ,m
bd bdU Uω (5)
where ω (Ubd) – VCR width at the reverse voltage equal
to Ubd; m – exponent equal to ~ 0.84 [11, 12].
Dependence (5), given in the literature, relates to the
p-n junctions which were not being exposed to
irradiation. It is very interesting to determine possibility
of existence of similar dependence in the p-n junctions
which were neutron irradiated. Note that the
characteristics of the space charge region can undergo
sufficiently noticeable changes as a result of radiation
exposure. It is illustrated by Fig. 5: in this figure the
typical volt-farad characteristics (VFCh) of the VL
before and after irradiation are presented on the log-log
scale [13]:
2 2
0
2 ln(( ) / 8 ) ,
3d i
kT kTU a qn
q q
εε= (6)
where Ud – gradient potential; k – Boltzmann constant;
T – absolute temperature; q – electron charge;
a – impurity gradient which creates p-n junction;
ε – silicon dielectric constant; ni – intrinsic
concentration of carriers in silicon. Fig. 5 shows that
before irradiation the barrier capacitance of p-n
junctions in VL is proportional to ~ U-0.33 (where U –
reverse voltage), which is typical for linear p-n junction
[13].
Fig. 5. Volt-farad characteristics of VL:
1 – before and 2, 3 – after irradiation with neutron
fluence of 7·1014 and 2·1015 cm-2, accordingly
But after irradiation exponent has a tendency to
decreasing. At increasing reverse voltage the slope
angle of the lg [C (Φ)] - lg (U+Ud) dependences after
irradiation approximates to the slope angle of these
dependences before irradiation.
ln[ω(Ф)/ω(0)] = f(Ф) (if Urev ≈ Ubd) dependence is
presented in Fig. 6.
Fig. 6. Dependence of ω(Ф)/ω(0) ratio
on neutron fluence
y = 6.3·10-17x
R2 = 0.94
ln
[U
bd
(Ф
)/
U
bd
(0
)]
y = 6.6·10-17x
R2 = 0.91
Ф, 1015 cm-
y =-0.33x+3.1
R2 = 1.0
Ф, 1015 cm-2
y=7.1·10-17x
R2 = 0.98
ln
[ω
(Ф
)/ω
(0
)]
84 ISSN 1562-6016. ВАНТ. 2012. №5(81)
It is possible to see that for the studied VL the next
relation is carried out with quite large reliability
(R2 ≈ 1):
( ) (0 ) ( ),Ф ехр КФω ω= (7)
where K – the coefficient equal to 7.1·10-17 cm2
(Urev ≈ Ubd).
Dependence (7) is general for the studied type of VL
and the obtained graph is described well by formula:
-17( ) (0) (7,1·10 ).Ф ехр Фω ω= (8)
Using data given in Fig. 4 and 6 it is possible to
build the dependence Ubd(Ф)/Ubd (0) = f(ω(Ф)/ω(0))
(if Urev≈ Ubd) which on the log-log scale is given in
Fig. 7. It follows from this figure that after irradiation,
in spite of a change in the structure of diffusion p-n
junction, the avalanche breakdown voltage also obey of
the universal dependence (5) with the quite large
reliability (R2 = 0.91), and therefore this formula may
be used for calculating Ubd after irradiation.
It is of certain interest to confirm the experimental
dependence (8) by calculations.
Fig. 7. Dependence of ratio Ubd(Φ)/Ubd(0)
on ratio ω(Ф)/ω(0)
At that let us assume that both before irradiation, in
entire range of reverse voltages, and after irradiation at
the rather high reverse voltages (U ~ Ubd) of the SCR
width can be calculated by the known formula for the
graded p-n junction [13]:
1
3
012 ( )
,dU U
qa
εε
ω
+⎛ ⎞
= ⎜ ⎟
⎝ ⎠
(9)
where a − impurity gradient which creates p-n junction.
If to consider that the p-n junction is formed by
linear distribution of impurity: N0(x) = ax, then after
irradiation, according to [5, 6, 10], this dependence is:
0( , ) ( )exp( ),N x Ф N x K Фρ= −
(10)
where Кρ – coefficient determined for the linear
junction; x – depth of impurity arrangement (depth of
the p-n junction position);
0,77
1( ) ,
( )
K x
k axρ =
(11)
where k – number which for n- type silicon varies from
387 to 3300 depending on the specific resistance and
neutron spectrum [10].
Differentiating (10) by the «х» coordinate we obtain:
( , ) (1 0.77 )exp( ).dN x Ф a K Ф K Ф
dx ρ ρ= + −
(12)
If 0,77КρФ < 1 (it is not difficult to see that this
condition is carried out practically for entire range of
neutron fluences used in the experiment), then:
( , ) exp( 0.23 ).dN x Ф a K Ф
dx ρ= −
(13)
Using (13) and (7), it is easy to obtain:
( ) exp(0.077 )
(0)
Ф K Фρ
ω
ω
= (14)
at that Urev≈ Ubd.
By comparing (8) and (14) one can see that these
exponential dependences are identical and experimental
value of the coefficient is Кρ ≈ 0.9·10-15 см2. In this case
the question arises: to what initial (before the
irradiation) carriers concentration can be related this
coefficient value. In our opinion, it should be related to
the average carrier concentration that forms of VCR
width of in n-region (ωn). In the first approximation the
average carriers concentration is equal to ~n(ωn)/2,
where ωn is VCR width in the n- region. The results of
ω, ωn, n(ωn) and Кρ calculation are presented in table 2.
Table 2
Name of
calculated value
Calculation
result for VL
with Urev ≈ 50 V
Calculation
procedure
Total width of
VCR (ω), cm 2.5·10-4 [14]
Width of VCR in
n-region (ωn), cm 1.36·10-4 [14]
Carriers
concentration
(ωn), cm-3
8.2·1015 [12]
Average
concentration of
main carriers in
ωn, cm-3
4.1·1015 nav = n(ωn)/2
Carriers removal
rate, cm-1 3.7
By formula (4)
at carriers
removal rate
of 2.5 cm-1
As can be seen from the calculation results (table 2),
the values of the carriers removal rate, obtained from
the experimental dependence ω (Ф) (Fig. 6 and formula
(8)) and also from its design model expressed by the
formula (14), it is very close to the value Кρ given at [5]
for the value of the carriers removal rate of 1…4 cm-1.
This value lies inside the interval of its possible values.
So, formula (14) may be used in practice for calculating
the ω(Ф) dependence and its following application for
calculation and predicting the dependence Ubd = f(Ф)
according to formula (5).
Let us consider in more detail the dependence of
limiting voltage (Ulv) upon neutron fluence. In
accordance with formula (1) the value of this parameter
is related by linear dependence with breakdown voltage,
lg
[U
bd
(Ф
)/
U
bd
(0
)]
lg [ω(Ф)/ω(0)]
y=0.85x
R2 = 0.91
ISSN 1562-6016. ВАНТ. 2012. №5(81) 85
differential resistance of p-n junction in limitation
regime and series resistance of semiconductor structure
in this regime. As already mentioned, the limitation
regime is characterized by the current of Ilim = 50 А for
VL. Аpriori one can state that in this case the p-n
junction is located in “deep” breakdown, and in
accordance with the Miller formula [9]:
1
lim 1 ,
C
R bd
I UM
I U
−
⎛ ⎞⎛ ⎞
⎜ ⎟= = − ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(15)
where M − coefficient of carriers multiplication; C = 5
for the silicon p-n junction; IR − reverse current of p-n
junction if U << Ubd .
We will obtain from (15) that:
1
lim
lim lim lim
.
С
С
bd R
dif
R
U I I
R
C I I I I
−
⎛ ⎞⎛ ⎞⎛ ⎞
= ⎜ ⎟⎜ ⎟⎜ ⎟−⎝ ⎠⎝ ⎠⎝ ⎠
(16)
For the considered regime of limitation and for real
values of reverse currents in the waiting regime
(IR ≤ 5·10-5 A) we obtain that Rdif ≈ 10-5 Ohm and so in
the formula (1) the Rdif value can be neglected. As
regards the value of series resistance (Rser) (in formula
(1)), it consists of two parts [16]. The first part is
resistance the part of SCR in which impact ionization
does not occur. This part is named “transit-time region”
and, in accordance with [15], its resistance (Rttr) is
determined by the relation:
2
0
( )
,
2
m
ttr
sat
R
SV
ω ω
εε
−
= (17)
where ωm – width of the part of VCR in which impact
ionization occurs, S-area of p-n junction; Vsat –
saturation rate of carriers in silicon, which, in
accordance with [14], is 107 cm/s. The second part is the
ohmic resistance of neutral base of VL:
,nb
base nb
d
R
S
ω
ρ
−
=
(18)
where ρnb – specific resistance and dnb – width of neutral
base.
Note that ωm value calculating for the diffusion p-n
junctions is realized by various expressions for each
concrete case but the results of ωm calculating are
single-valued for the sharp p-n junctions [16].
At the same time taking into account that Rdif and,
therefore, voltage drop across the ωm section is
negligibly little, it follows from formula (1):
lim lim ( ) ,bd base ttrU U I R R− = +
(19)
where Rbase and Rttr are determined by formulas (17) and
(18), respectively.
According to formulas (17–19), using initial (before
irradiation) experimental values of Ulim – Ubd, the values
of SCR width ω (for U≈Ubd]) calculated by formula (9),
the neutral base width (dnb) and its specific resistance
(ρbase), one can calculate the ωm value. Calculation gave
ωm≈1.3·10-4 cm. It is interest to note that in [16] for
sharp p-n junctions it is obtained ωm≈ 0.5·10-4; at that
the p-n junctions have been prepared using silicon with
the same initial specific resistance (~0.3 Ohm·cm) that
the investigated VL. The fact that the length of
avalanche multiplication region in the smooth p-n
junctions is larger than in the sharp ones is completely
regular, and it, in our opinion, confirms reliability of the
obtained values of ωm for the VL structures under study.
Subsequently we will consider that the ωm value
does not depend upon irradiation. In this case Rttr (17)
depends on irradiation only because during irradiation,
in accordance with formula (14), value ω changes. In
the table 3 the results of the voltage drop calculation at
the transit-time part of SCR in dependence on neutron
flux (Φ) at the current Ilim are presented.
Table 3
Neutron flux (Φ),
сm-2
Voltage drop at the
transit-time part (Uttr),V
0 0.7
1.0·1014 0.72
3.5·1014 –
7.3·1014 0.85
1.3·1015 0,93
1.6·1015 –
2.0·1015 1.1
2.5·1015 1.2
Using calculation data given in table 3 and
experimental dependences Ubd(Ф) and Ulim(Ф) (Fig. 3)
it is possible to find the dependence of voltage drop at
neutral base (Ubase) on neutron fluence:
lim
lim
( ) ( )
( ) ( ) ( ).
base base
bd ttr
U Ф I R Ф
U Ф U Ф U Ф
= =
= − −
(20)
The dependence ln[Ubase(Ф)/Ubase(0)] on neutron fluence
(Ф) is presented in Fig. 8. The similar method of the
dependence representation permits to exclude the poorly
controlled values of dnb and ω and to bring them to the
dependence ρbase(Ф)/ρbase(0) by (18). Fig. 8 shows that
for the investigated VL the relation Ubase(Ф)/Ubase(0)
and consequently the relation ρbase(Ф)/ρbase(0)
exponentially depend on neutron flux.
ln
[U
ba
se
(Ф
)/
U
ba
se
(0
)]
y=3.8·10-16x
R2 = 0.96
Ф, 1015 cm-2
86 ISSN 1562-6016. ВАНТ. 2012. №5(81)
Fig. 8. Dependence Ubase(Ф)/Ubase(0) on neutron fluence
At that, for the VL Kρ = 3.8·10-16 cm2. This value of
the coefficient Kρ corresponds to the carriers removal
rate under neutron irradiation (4) which is 7.6 cm-1 for
n-type silicon used when making VL with
ρbase ≈ 0.3 Ohm·cm. This carriers removal rate value is
sufficiently near literature data [17]: dn/dФ ≈ 9 cm-1 for
silicon with ρ ≈ 0.3 Ohm·cm, and it permits to consider
that the proposed calculation procedure can be used for
predicting of the radiation resistance Ulim – the most
important parameter of VL. It is reasonable that for the
similar prediction it is necessary the knowledge of the
structure of p-n junction of VL, the electro physical
properties of silicon on which it is prepared and also the
Kρ value of used silicon (or the carriers removal rate
under irradiation).
CONCLUSIONS
As a result of study of neutron irradiation influence
on the breakdown voltage (Ubd) and the limiting voltage
(Ulim) of the silicon voltage limiters the following is
established:
– the experimental dependences Ubd = f(Ф) and
Ulim = f(Ф) for VL with the 50 V limiting voltage before
irradiation are obtained;
– it is shown that the relation Ubd(Ф)/Ubd(0)
practically does not depend on the breakdown voltage
value of VL before irradiation;
– it is shown that in the relation
Ubd(Ф)/Ubd(0) ≈ [ω (Ф) / ω (0)]m (if Urev ~ Ubd) the
exponent “m” does not change after irradiation and is
equal to ~ 0.84;
– it is shown that the coefficient Kρ is the basic
radiation parameter which forms the dependences
Ubd = f(Ф) and Ulim = f(Ф) which determines the
dependence of the concentration of basic charge carriers
in silicon on neutron fluence;
– mechanisms which form the Ulim value after
irradiation are determined;
– the model is suggested and is calculated which
takes into account “smoothness” of the investigated p-n
junctions and which makes it possible to predict
changes in the breakdown voltage and limiting voltage
which occur as a result of neutron irradiation of VL.
The authors are grateful to Prof. Karimov M,
Dr. Tursunov N. and Mr. Ismatov N. to work results
discussion.
Work is executed within the framework of F2-FA-0-
11372 grant of Committees on Coordination of
Development Sciences and Technology.
REFERENCES
1. Certificate СМО.012.018 for a method of limiting
voltage measurement. Novosibirsk, 1989, р. 19.
2. A.Z. Rahmatov. Development of physics-technical
bases of obtaining the silicon voltage limiters: Authors
abstract of dissertation on competition of a scientific
degree of a Cand. Tech. Sci. Tashkent, 2008, р. 31 (in
Russian).
3. N.V. Grekhov, Yu.N. Seryozhkin. Avalanche
breakdown of p-n junction in semiconductors // Energy.
1980, р. 57-60 (in Russian).
4. P.V. Akimov, N.V. Grekhov, Yu.N. Seryozhkin.
Temperature dependence of avalanche breakdown
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G.V. Melnik, N.A. Spiridonova. Radiation influence to
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Статья поступила в редакцию 28.05.2012 г.
ISSN 1562-6016. ВАНТ. 2012. №5(81) 87
ВЛИЯНИЕ НЕЙТРОННОГО ОБЛУЧЕНИЯ НА ПАРАМЕТРЫ КРЕМНИЕВЫХ
ОГРАНИЧИТЕЛЕЙ НАПРЯЖЕНИЯ
А.З. Рахматов, М.Ю. Ташметов, Л.С. Сандлер
Влияние нейтронного облучения на напряжение пробоя (Uпроб) и напряжение ограничения (Uогр)
исследовано в кремниевых ограничителях напряжения. Коэффициент Kρ является основным радиационным
параметром, формирующим зависимости Uпрб = f(Ф) и Uогр = f(Ф) и определяющим зависимость
концентрации основных носителей заряда в кремнии от флюенса нейтронов. Определены механизмы,
формирующие величину Uогр после нейтронного облучения. На основе анализа полученных результатов
предложена модель, позволяющая прогнозировать изменения напряжения пробоя и напряжения
ограничения, которые происходят в результате нейтронного облучения ограничителя напряжения.
ВПЛИВ НЕЙТРОННОГО ОПРОМІНЕННЯ НА ПАРАМЕТРИ КРЕМНІЄВИХ
ОБМЕЖУВАЧІВ НАПРУГИ
А.З. Рахматов, М.Ю. Ташметов, Л.С. Сандлер
Вплив нейтронного опромінення на напругу пробою (Uпроб) і напругу обмеження (Uобм) досліджено в
кремнієвих обмежувачах напруги. Коефіцієнт Kρ є основним радіаційним параметром, що формує
залежності Uпрб = f(Ф) і Uогр = f(Ф) і визначає залежність концентрації основних носіїв заряду в кремнії від
флюенса нейтронів. Визначені механізми, що формують величину Uобм після нейтронного опромінення. На
основі аналізу отриманих результатів запропонована модель, що дозволяє прогнозувати зміни напруги
пробою і напруги обмеження, які відбуваються в результаті нейтронного опромінення обмежувача напруги.
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