Базова кінетична модель рентгенопровідності широкозонних напівпровідників
При реєстрацiї рентгенiвського кванта напiвпровiдниковим детектором вiдбувається генерацiя вiльних носiїв заряду в невеликому об’ємi (дiаметр < 0,5 мкм). Якщо до електродiв напiвпровiдника прикласти рiзницю потенцiалiв, то вiдбувається направлений рух згенерованих вiльних носiїв та вiдповiдний iм...
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Відділення фізики і астрономії НАН України
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Дегода, В.Я. Софієнко, А.О. 2010-11-05T14:01:47Z 2010-11-05T14:01:47Z 2010 Базова кінетична модель рентгенопровідності широкозонних напівпровідників / В.Я. Дегода, А.О. Софієнко // Укр. фіз. журн. — 2010. — Т. 55, № 2. — С. 201-207. — Бібліогр.: 21 назв. — укр. 2071-0194 PACS 72.20.Jv, 64.7 https://nasplib.isofts.kiev.ua/handle/123456789/13383 535.37 При реєстрацiї рентгенiвського кванта напiвпровiдниковим детектором вiдбувається генерацiя вiльних носiїв заряду в невеликому об’ємi (дiаметр < 0,5 мкм). Якщо до електродiв напiвпровiдника прикласти рiзницю потенцiалiв, то вiдбувається направлений рух згенерованих вiльних носiїв та вiдповiдний iмпульс струму в зовнiшньому колi. Запропоновано логiчну схему побудови базової кiнетичної моделi рентгенопровiдностi напiвпровiдникiв, яка застосовує послiдовний у часi розрахунок просторових розподiлiв вiльних носiїв заряду та використовує дифузiйно-дрейфову модель руху вiльних носiїв у твердому тiлi. Отримано базову форму iмпульсу струму у зовнiшньому колi в аналiтичному виглядi для випадку iдеального напiвпровiдника, тобто такого, що не мiстить глибоких пасток i центрiв рекомбiнацiї. Одержано основнi залежностi форми iмпульсу струму вiд мiсця поглинання рентгенiвського кванта та величини прикладеного електричного поля. При регистрации рентгеновского кванта полупроводниковым детектором происходит генерация свободных носителей заряда в небольшом объеме (диаметр < 0,5 мкм). Если к электродам полупроводника приложить разницу потенциалов, то происходит направленное движение сгенерированных свободных носителей и появляется соответствующий импульс тока во внешней цепи. Предложена логическая схема построения базовой кинетической теории рентгенопроводимости полупроводников, которая применяет последовательный во времени расчет пространственных распределений свободных носителей заряда и использует диффузионно-дрейфовую модель движения свободных носителей в твердом теле. Получена базовая форма импульса тока во внешней электрической цепи в аналитическом виде для случая идеального полупроводника, т.е. такого, который не содержит глубокие ловушки и центры рекомбинации. A logical scheme for the development of a basic kinetic theory of Xray conductivity in semiconductors has been proposed. It includes the calculation of spatial distributions of free charge carriers at successive time moments and uses the model of diffusion-driven drift motion of free charge carriers in a solid. An analytic expression for the basic shape of a current pulse in the external circuit has been obtained in the case of ideal semiconductor, i.e., when it does not contain deep traps and recombination centers. Basic dependences of the current pulse shape on the coordinate of an X-ray quantum absorption event and the strength of an applied electric field have been obtained. Роботу виконано при фiнансовiй пiдтримцi Державного фонду фундаментальних дослiджень України (проект Ф25.4/138). uk Відділення фізики і астрономії НАН України Тверде тіло Базова кінетична модель рентгенопровідності широкозонних напівпровідників Базовая кинетическая модель рентгенопроводимости широкозонных полупроводников Basic Kinetic Model for X-ray Conductivity in Wide-gap Semiconductors Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| spellingShingle |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників Дегода, В.Я. Софієнко, А.О. Тверде тіло |
| title_short |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| title_full |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| title_fullStr |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| title_full_unstemmed |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| title_sort |
базова кінетична модель рентгенопровідності широкозонних напівпровідників |
| author |
Дегода, В.Я. Софієнко, А.О. |
| author_facet |
Дегода, В.Я. Софієнко, А.О. |
| topic |
Тверде тіло |
| topic_facet |
Тверде тіло |
| publishDate |
2010 |
| language |
Ukrainian |
| publisher |
Відділення фізики і астрономії НАН України |
| format |
Article |
| title_alt |
Базовая кинетическая модель рентгенопроводимости широкозонных полупроводников Basic Kinetic Model for X-ray Conductivity in Wide-gap Semiconductors |
| description |
При реєстрацiї рентгенiвського кванта напiвпровiдниковим детектором вiдбувається генерацiя вiльних носiїв заряду в невеликому об’ємi (дiаметр < 0,5 мкм). Якщо до електродiв напiвпровiдника прикласти рiзницю потенцiалiв, то вiдбувається направлений рух згенерованих вiльних носiїв та вiдповiдний iмпульс струму в зовнiшньому колi. Запропоновано логiчну схему побудови базової кiнетичної моделi рентгенопровiдностi напiвпровiдникiв, яка застосовує послiдовний у часi розрахунок просторових розподiлiв вiльних носiїв заряду та використовує дифузiйно-дрейфову модель руху вiльних носiїв у твердому тiлi. Отримано базову форму iмпульсу струму у зовнiшньому колi в аналiтичному виглядi для випадку iдеального напiвпровiдника, тобто такого, що не мiстить глибоких пасток i центрiв рекомбiнацiї. Одержано основнi залежностi форми iмпульсу струму вiд мiсця поглинання рентгенiвського кванта та величини прикладеного електричного поля.
При регистрации рентгеновского кванта полупроводниковым детектором происходит генерация свободных носителей заряда в небольшом объеме (диаметр < 0,5 мкм). Если к электродам полупроводника приложить разницу потенциалов, то происходит направленное движение сгенерированных свободных носителей и появляется соответствующий импульс тока во внешней цепи. Предложена логическая схема построения базовой кинетической теории рентгенопроводимости полупроводников, которая применяет последовательный во времени расчет пространственных распределений свободных носителей заряда и использует диффузионно-дрейфовую модель движения свободных носителей в твердом теле. Получена базовая форма импульса тока во внешней электрической цепи в аналитическом виде для случая идеального полупроводника, т.е. такого, который не содержит глубокие ловушки и центры рекомбинации.
A logical scheme for the development of a basic kinetic theory of Xray conductivity in semiconductors has been proposed. It includes the calculation of spatial distributions of free charge carriers at successive time moments and uses the model of diffusion-driven drift motion of free charge carriers in a solid. An analytic expression for the basic shape of a current pulse in the external circuit has been obtained in the case of ideal semiconductor, i.e., when it does not contain deep traps and recombination centers. Basic dependences of the current pulse shape on the coordinate of an X-ray quantum absorption event and the strength of an applied electric field have been obtained.
|
| issn |
2071-0194 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/13383 |
| citation_txt |
Базова кінетична модель рентгенопровідності широкозонних напівпровідників / В.Я. Дегода, А.О. Софієнко // Укр. фіз. журн. — 2010. — Т. 55, № 2. — С. 201-207. — Бібліогр.: 21 назв. — укр. |
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SOLID MATTER
200 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2
BASIC KINETIC MODEL FOR X-RAY CONDUCTIVITY
IN WIDE-GAP SEMICONDUCTORS
V.YA. DEGODA, A.O. SOFIENKO
Taras Shevchenko National University of Kyiv, Faculty of Physics
(2, Academician Glushkov Ave., Bld. 1, Kyiv 03127, Ukraine; e-mail: degoda@ univ. kiev. ua )
PACS 72.20.Jv, 64.70.Kq,
68.55.Ag, 07.77.Ka
c©2010
A logical scheme for the development of a basic kinetic theory of X-
ray conductivity in semiconductors has been proposed. It includes
the calculation of spatial distributions of free charge carriers at
successive time moments and uses the model of diffusion-driven
drift motion of free charge carriers in a solid. An analytic expres-
sion for the basic shape of a current pulse in the external circuit
has been obtained in the case of ideal semiconductor, i.e., when
it does not contain deep traps and recombination centers. Basic
dependences of the current pulse shape on the coordinate of an
X-ray quantum absorption event and the strength of an applied
electric field have been obtained.
1. Introduction
Nowadays, semiconductor materials are widely used in
ionizing radiation detectors. The advantage of semicon-
ductor detectors (SCDs) over other sensor systems (scin-
tillation and tracking ones) consists in a direct trans-
formation of the ionizing radiation energy into an elec-
tric current, which allows them to be successfully used
in spectrometry researches. In this case, an important
criterion of the detector quality is the charge collection
efficiency at the registration of an individual ionizing
particle or a quantum [1–5], because even small charge
losses of several percent at the charge drift make the line
shape in a detector response function much more com-
plicated [5–7]. Unfortunately, the modern approaches
to the calculation of the charge collection dynamics in
SCDs [5–8] do not consider the influence of the thermal
velocity of charge carriers on the kinetics of their drift,
although the thermal velocity still prevails over the drift
one even if the SCDs are cooled down to temperatures
of about 150 K. This circumstance has to be taken into
consideration in the theoretical analysis of the processes
of charge collection and current pulse formation in the
external electric circuit of a detector.
All physical processes that take place at the drift of
charge carriers in SCDs are known, but there is the lack
of a general kinetic model for their quantitative calcula-
tion. The construction of such a model should be started
from the consideration of the most simplified physical
scenario, which should be gradually—step by step—made
more and more complicated, approaching the real pic-
ture. The consideration should also be started from such
ionizing radiation that does not create new structural
defects in the detector material. Proceeding from those
conditions, the analysis should be started from the devel-
opment of a kinetic model for X-ray conductivity (XRC)
in an ideal semiconductor crystal without recombination
and trapping centers. Knowing the dependence of the
current pulse shape on the diffusion-drift parameters of
the charge carrier motion, the next step – the consider-
ation of the influence of shallow and deep traps on the
current pulse and the charge collection efficiency (and,
hence, on the detector response function) – can be done.
2. Model for X-ray Conductivity Kinetics
X-ray conductivity appears, when X-ray quanta are ab-
sorbed. The corresponding mechanisms of electron-hole
pair generation and the initial average distribution of
electron-hole pairs in space at the generation stage were
studied in detail in the framework of the kinetic theory
of X-ray luminescence (XRL) [9, 10]. It should be noted
that the trajectories of individual high-energy electrons,
which arise when X-ray quanta are absorbed, are not
identical but statistically random. Therefore, for the
consideration of XRL and XRC, the concept of “aver-
BASIC KINETIC MODEL FOR X-RAY CONDUCTIVITY
age spatial distribution of electron excitations” has been
introduced for charge carriers in space [10].
In experimental XRL and XRC researches, plenty of
exciting quanta (more than 106) absorbed non-uniformly
in the substance are always used. The absorption of X-
ray radiation is governed by the Bouguer–Lambert law.
Similarly to what happens at photoexcitation, X-ray ra-
diation creates macroscopically non-uniform electron ex-
citations in a crystal. However, unlike photoexcitation,
the absorption of X-ray quanta is accompanied by the
generation of hundreds of thousands of charge carriers.
That is why X-ray irradiation gives also rise to the ap-
pearance of a local microscopic non-uniformity of ex-
citation. The kinetics of luminescence and conductiv-
ity has to take such local microscopic non-uniformities
into account in this case. In work [11], the conductivity
and luminescence of wide-gap semiconductors were ex-
perimentally confirmed to depend substantially on the
excitation type. However, such differences cannot be ex-
plained in the framework of classical kinetic equations
[12, 13].
The physical aspects of motion of free charge carriers
were studied in detail in the kinetic theory of photocon-
ductivity (PC) and the semiconductor theory [12–16].
They can be applied to studying the XRC as well. For
the construction of a kinetic model of XRC, it is neces-
sary to firstly consider, in detail, the kinetics of motion of
free charge carriers generated at the absorption of one
X-ray quantum. To build a basic XRC model, let us
consider only the main processes. We use the following
assumptions:
1. The energy of an X-ray quantum is insufficient for
the creation of new structural defects in the detector
material.
2. Free charge carriers are generated in a very small vol-
ume of a semiconductor [10]. The number of generated
pairs N0 is determined by the energy of an X-ray quan-
tum, hνX , and the energy gap width in the semiconduc-
tor, Eg [17]: N0 = hνX
3Eg
.
3. The initial spatial distributions of electrons and holes
are identical.
4. The electric field in a semiconductor is uniform. It
is determined by the potential difference applied to the
electric contacts and the specimen thickness.
5. The local region of free carrier generation at the ab-
sorption of an X-ray quantum is cooled down within sev-
eral tens of picoseconds in almost all semiconductors [9].
This allows the local heating at the absorption of an
X-ray quantum to be neglected.
Since the rates of various XRC processes are different,
the general XRC kinetics can be actually separated in
time into three basic stages:
1. The generation stage (t = 0÷ 10−12 s), during which
an X-ray quantum is absorbed, and a high-energy pho-
toelectron emerges. The photoelectron generates, at the
thermalization, an initial average spatial distribution of
N0 free electrons and P0 free holes (N0 = P0).
2. The migration stage (t = 10−12 ÷ 10−7 s), when the
spatial distribution of free charge carriers changes owing
to their diffusion-drift motion (localization of carriers at
probable recombination centers and traps; delocalization
of carriers from shallow traps, followed by the charge col-
lection at electrodes). The complete calculation of this
stage allows the amplitude and the shape of a current
pulse in the external circuit at the absorption of one X-
ray quantum to be determined.
3. The relaxation stage (t > 1 s) includes the delocaliza-
tion of charge carriers from deep traps. The carriers can
be localized again at the recombination centers or traps.
Alternatively, under the action of an external field, they
reach contacts with a large time lag. In other words, they
can create a practically constant background current.
The time boundaries between stages are rather rela-
tive, so that the stage periods can vary even by several
orders of magnitude, depending on the semiconductor
substance, electric field strength, and specimen thick-
ness. Such a classification of stages allows the calcula-
tions to be simplified considerably, because only a few
processes dominate at each stage.
The following logic scheme can be used to construct
the kinetics of X-ray conductivity. First, it is necessary
to determine the shape of a current pulse in the exter-
nal circuit at the absorption of one X-ray quantum in
an ideal semiconductor, i.e. when the latter does not
contain traps and recombination centers. Such a pulse
shape will serve a reference point for the further account
of centers of various types which will change this pulse.
Then, it is necessary to take the Coulomb interaction
between free carriers with opposite charge signs into ac-
count. Afterwards, point defects may be introduced into
the consideration: first, shallow traps; then deep traps
and recombination centers. The introduction of point
defects into the calculation scheme will allow the vari-
ation kinetics of free carrier spatial distributions to be
established and, accordingly, a variation of the current
pulse shape to be found. Knowing the shape of a current
pulse that arises in the external circuit, when an X-ray
quantum is absorbed, one can calculate the charge col-
lection efficiency as well. The summation of separate
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2 201
V.YA. DEGODA, A.O. SOFIENKO
pulses will allow the total current of X-ray conductivity
to be determined.
3. Generation of Free Charge Carriers and
Their Motion
When an X-ray quantum with an energy of 1 to 50 keV
interacts with a solid, the main process is the photoab-
sorption of the quantum, resulting in the emergence of
both an ion in the solid and a high-energy photoelectron.
The photoelectron, due to ionization losses of its kinetic
energy in the course of thermalization (10−13−10−12 s),
creates N0 electron-hole pairs, on the average, in a lo-
cal volume. Using the diffusion model for the photo-
electron thermalization process [10], one can obtain the
average spatial distribution of the concentration of gen-
erated free charge carriers N0(r), which is well described
by the Gaussian distribution:
N0 (r) =
N0
(2π)3/2 r3g
exp
(
− r2
2r2g
)
, (1)
where rg is the generation stage parameter which is de-
termined unambiguously in terms of the substance pa-
rameters and the energy of X-ray quantum [10]. Such
a spatial distribution of free electrons and holes can
be accepted as initial for the following migration stage.
The charge carriers generated within the time interval of
about 10−12 − 10−11 s become thermalized [16] due to
their interaction with crystal lattice phonons.
4. Spatial Distribution of Charge Carriers at
Their Drift
An external electric field and the concentration gradient
of generated charge carriers in the crystal invoke the drift
and diffusion currents, the density of which is determined
in the general case by the relation
J± = eN±(x, y, z, t) · µ±E∓ eD±∇N±(x, y, z, t). (2)
The sign “+” in Eq. (2) corresponds to holes, and the sign
“−” to electrons, N+(x, y, z, t) and N−(x, y, z, t) are the
spatial concentration distributions of generated free car-
riers with the corresponding sign, E is the electric field
vector, D± are the diffusion coefficients of charge car-
riers, and µ± are their mobilities. To be unambiguous
in the choice of a charge carrier drift direction, consider
a Cartesian coordinate system, in which the OX axis
is normal to the detector electrodes and opposed to the
electric field direction. Relation (2) in the accepted co-
ordinate system should be appended by the continuity
equation for the time-variation of the charge carrier con-
centration. Together, they allow one to obtain a system
of kinetic equations for the diffusion-drift motion of elec-
trons and holes:
∂N−
∂t
= D−ΔN− − µ−E ∇N− ,
∂N+
∂t
= D+ ΔN+ + µ+ E ∇N+ .
(3)
We suppose the dimensions of a local region, where free
charge carriers are generated, to be much less than the
detector thickness d, and the transverse dimensions of
the detector (along the directions OY and OZ) to be
much larger than its thickness. This allows the delta-
function approximation to be used as the initial dis-
tribution of charge carriers, because the parameter rg
in Eq. (1) is much smaller than the dimensions of the
drift region in SCDs. Having achieved the electrodes,
the charge carriers disappear from the total distribution.
Therefore, the following boundary conditions must be
applied, when solving the system of equations (3):{
N+(0, y, z, t) = N−(0, y, z, t) = 0,
N+(d, y, z, t) = N−(d, y, z, t) = 0. (4)
The solution of Eqs. (3) determines the spatial concen-
tration distribution of charge carriers at their drift. It
can be obtained using the variable separation method:
N±(x, y, z, t) =
N0
4πD± t
exp
[
− (y − y0)2 + (z − z0)2
4D± t
±
±µ
±E (x− x0)
2D±
− (µ±E)2t
4D±
]
× 2
d
∞∑
n=1
{
sin
(πnx
d
)
×
× sin
(πnx0
d
)
exp
[
−
(πn
d
)2
D± t
]}
, (5)
where x0 is the coordinate of an X-ray quantum absorp-
tion event in a semiconductor. In Fig. 1, the calculated
distribution functions for the concentration of free elec-
trons along the OX direction in a silicon detector at
various time moments are depicted. At calculations, we
used the data on the mobility of charge carriers in Si
taken from work [17].
5. Current Pulse Shape at X-ray Conductivity
To calculate the current i(t) created by generated free
charge carriers (q− and q+) in the external electric cir-
cuit at their drift to electrodes under the action of an
202 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2
BASIC KINETIC MODEL FOR X-RAY CONDUCTIVITY
Fig. 1. Spatial distributions of electrons along the OX direction in
a flat Si crystal at various time moments t = 125 (1 ), 100 (2 ), and
50 ns (3 ). Calculation parameters are d = 300 µm, x0 = 150 µm,
E = 100 V/cm, and T = 300 K
electric field E = U/d, it is necessary to apply the Ramo–
Shockley theorem for point-like charges [20, 21]. Since
the work done by the electric field to move all free charge
carriers is defined as a sum of works done to move every
carrier, the current in the external circuit is determined
as a sum of currents created by every free charge carrier:
i(t) =
q−(t)µ−E
d
+
q+(t)µ+E
d
=
=
eN0E
d
[
E(t)µ− + P (t)µ+
]
, (6)
where E(t) and P (t) are the fractions of those generated
electrons and holes, respectively, which remain free at
the time moment t and continue to drift. This relation is
valid for a uniform electric field and in the case where the
resistance of the external electric circuit of a detector can
be neglected (the corresponding scheme of XRC current
measurement is shown in Fig. 2). Using relation (5), one
can obtain the relative numbers of free charge carriers of
each sign, E(t) and P (t), at every time moment:
E(t) =
1
N0
∞∫
−∞
∞∫
−∞
d∫
0
N−(x, y, z, t) dx dy dz ,
P (t) =
1
N0
∞∫
−∞
∞∫
−∞
d∫
0
N+(x, y, z, t) dx dy dz . (7)
In Fig. 3, the calculated dependences of relative val-
ues of a charge collected at Si-detector electrodes in the
−
+
e
p
nAx
0
x0
d
Fig. 2. Measurement scheme for the X-ray conductivity current in
a semiconductor detector
Fig. 3. Kinetics of the relative charge collection on Si-detector
electrodes at the charge carrier drift calculated for various regis-
tration coordinates: 150 (1 ), 100 (2 ), and 50 µm (3 ). Calculation
parameters are d = 200 µm, E = 140 V/cm, and T = 300 K
cases where charge carriers are generated at various de-
tector points are depicted. They testify to a considerable
influence of free carrier mobilities on the current pulse
duration. In Fig. 4, the results of calculations of the cur-
rent pulse shape in a Si-detector at various electric field
strengths are shown. The prolonged damping of the cal-
culated current pulse amplitudes results just from the
diffusion-driven expansion of the spatial distribution of
carriers at their drift.
The solution of Eqs. (7) becomes considerably com-
plicated due to the fact that expression (5) includes
an infinite series. The calculations can be simplified to
some extent, if one takes into account that the relation
µ±Ed
2D± � 1 is practically always satisfied. Then Eqs. (7),
after integration, can be expressed in the following sim-
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2 203
V.YA. DEGODA, A.O. SOFIENKO
Fig. 4. Current pulse shapes in a Si-detector at various electric field
strengths E = 140 (1 ), 100 (2 ), and 60 V/cm (3 ). Calculation
parameters are d = 200 µm, x0 = 100 µm, and T = 300 K
plified form:
E(t) =
2
π
exp
[
µ−E
4D−
(2x0 − µ−E t)
]
×
×
∞∑
n=1
n exp
[
−
(
πn
d
)2
D−t
]
sin
(
πnx0
d
)
(
µ−E d
2πD−
)2
+ n2
,
P (t) =
2
π
exp
{
µ+E
4D+ [2(d− x0)− µ+E t]
}
×
×
∞∑
n=1
(−1)n n exp
[
−
(
πn
d
)2
D+t
]
sin
(
πnx0
d
)
(
µ+E d
2πD+
)2
+ n2
. (8)
But even simplifications do not allow the system of equa-
tions (8) to be obtained in the analytical form because
of the difficulties faced at the summation of the corre-
sponding infinite series. However, the detailed analysis
of relations (8) makes it possible to find the analytical
functions, to which they best correspond. In turn, this
allows one to propose simple analytical dependences for
their approximation:
E(t) =
1 + exp
µ−E t− x0√
1
2 D
− t
−1
,
Fig. 5. Exact theoretical function E(t) (solid curves) and its ap-
proximation (dash-dotted curves) for various registration coordi-
nates x0 and electric fields E in a ZnSe-based detector: (1 ) x0 =
50 µm, E = 120 V/cm; (2 ) x0 = 125 µm, E = 180 V/cm;
(3 ) x0 = 200 µm, E = 180 V/cm; and (4 ) x0 = 200 µm,
E = 120 V/cm. Calculation parameters are d = 250 µm and
µ− = 700 cm2/(V × s)
P (t) =
1 + exp
µ+E t− (d− x0)√
1
2 D
+ t
−1
. (9)
The use of approximating relations in the forms of ex-
pressions (9) allows, first, the calculations to be made
considerably simplified by avoiding the evaluation of the
sums of infinite series in Eqs. (8) and, second, allows the
current pulse function, which preserves its dependence
on the main kinetic parameters of the charge carrier mo-
tion, to be described analytically.
The results of calculations of the function E(t) and
its approximations by relation (9) made for various val-
ues of the charge carrier generation coordinate and the
electric field strength are depicted in Figs. 5 and 6 for Si
and ZnSe crystals, respectively. It should be noted that,
depending on the choice of a semiconductor detector ma-
terial, the influence on its spectrometric characteristics is
mainly determined by three factors: the material purity,
efficiency of ionizing radiation registration, and mobility
of free charge carriers. Wide-band-gap semiconductors
have been considered lately as rather promising in this
respect. The same purity degree as for, e.g., silicon, has
not been reached for them yet. However, they are char-
acterized by extremely small dark currents (at a level of
1 pA for ZnSe single crystals at a temperature of 300 K
and an electric field strength of 500 V/cm) and a high
efficiency of ionizing radiation absorption.
204 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2
BASIC KINETIC MODEL FOR X-RAY CONDUCTIVITY
Fig. 6. The same as in Fig. 5, but for a Si-based detector. The
curve notation is the same. Calculation parameters are d = 250 µm
and µ− = 1400 cm2/(V × s)
6. Conclusions
A basic model for the kinetics of X-ray conductivity in
semiconductors has been proposed. It allows the cur-
rent pulse shape at the absorption of an X-ray quan-
tum in an ideal semiconductor to be obtained in the
first approximation, and the influence of key material
parameters and the electric field on the pulse shape to
be analyzed. An analytical relation for the current pulse,
which arises in the external electric circuit at the absorp-
tion of an X-ray quantum, has been proposed, which
considerably simplifies the subsequent development of a
kinetic model of X-ray conductivity in semiconductors.
The next step should consist in determining the influ-
ence of the Coulomb interaction between generated free
charge carriers and point defects (traps and recombi-
nation centers), which always exist in real substances,
on the amplitude and the shape of a current pulse that
arises at the absorption of an X-ray quantum.
The work was financially supported by the State Foun-
dation for Fundamental Researches of Ukraine (project
F25.4/138).
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Received 08.04.09.
Translated from Ukrainian by O.I. Voitenko
БАЗОВА КIНЕТИЧНА
МОДЕЛЬ РЕНТГЕНОПРОВIДНОСТI
ШИРОКОЗОННИХ НАПIВПРОВIДНИКIВ
В.Я. Дегода, А.О. Софiєнко
Р е з ю м е
При реєстрацiї рентгенiвського кванта напiвпровiдниковим де-
тектором вiдбувається генерацiя вiльних носiїв заряду в не-
ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2 205
V.YA. DEGODA, A.O. SOFIENKO
великому об’ємi (дiаметр < 0,5мкм). Якщо до електродiв на-
пiвпровiдника прикласти рiзницю потенцiалiв, то вiдбувається
направлений рух згенерованих вiльних носiїв та вiдповiдний
iмпульс струму в зовнiшньому колi. Запропоновано логiчну
схему побудови базової кiнетичної моделi рентгенопровiдностi
напiвпровiдникiв, яка застосовує послiдовний у часi розраху-
нок просторових розподiлiв вiльних носiїв заряду та викори-
стовує дифузiйно-дрейфову модель руху вiльних носiїв у твер-
дому тiлi. Отримано базову форму iмпульсу струму у зовнi-
шньому колi в аналiтичному виглядi для випадку iдеального
напiвпровiдника, тобто такого, що не мiстить глибоких пасток i
центрiв рекомбiнацiї. Одержано основнi залежностi форми iм-
пульсу струму вiд мiсця поглинання рентгенiвського кванта та
величини прикладеного електричного поля.
206 ISSN 2071-0194. Ukr. J. Phys. 2010. Vol. 55, No. 2
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