Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials
In the work, non-destructive testing the Si and Ge semiconductors by pulse X-ray sources is discussed. Mathematical simulation of the radiation generation in reflection and transmission anode tubes is performed. Details of energy spectrum formation in these pulse tubes are analyzed, and its transfor...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2006
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irk-123456789-1215952017-06-15T03:05:21Z Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials Denbnovetsky, S.V. Slobodyan, N.V. In the work, non-destructive testing the Si and Ge semiconductors by pulse X-ray sources is discussed. Mathematical simulation of the radiation generation in reflection and transmission anode tubes is performed. Details of energy spectrum formation in these pulse tubes are analyzed, and its transformation when passing through thin samples of semiconductor materials is discussed. The dependence of the amount of radiation absorbed by the samples on the amplitude of acceleration voltage is calculated. It is shown how the pulse operation regime and design features of pulse tubes influence the characteristics of the X-ray radiation. 2006 Article Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials / S.V. Denbnovetsky, N.V. Slobodyan // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 1. — С. 68-72. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 61.10.Nz http://dspace.nbuv.gov.ua/handle/123456789/121595 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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In the work, non-destructive testing the Si and Ge semiconductors by pulse X-ray sources is discussed. Mathematical simulation of the radiation generation in reflection and transmission anode tubes is performed. Details of energy spectrum formation in these pulse tubes are analyzed, and its transformation when passing through thin samples of semiconductor materials is discussed. The dependence of the amount of radiation absorbed by the samples on the amplitude of acceleration voltage is calculated. It is shown how the pulse operation regime and design features of pulse tubes influence the characteristics of the X-ray radiation. |
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Denbnovetsky, S.V. Slobodyan, N.V. |
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Denbnovetsky, S.V. Slobodyan, N.V. Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials Semiconductor Physics Quantum Electronics & Optoelectronics |
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Denbnovetsky, S.V. Slobodyan, N.V. |
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Denbnovetsky, S.V. |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials |
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simulation of radiation characteristics of pulse x-ray devices for non-destructive testing the semiconductor materials |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Simulation of radiation characteristics of pulse X-ray devices for non-destructive testing the semiconductor materials / S.V. Denbnovetsky, N.V. Slobodyan // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 1. — С. 68-72. — Бібліогр.: 10 назв. — англ. |
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AT denbnovetskysv simulationofradiationcharacteristicsofpulsexraydevicesfornondestructivetestingthesemiconductormaterials AT slobodyannv simulationofradiationcharacteristicsofpulsexraydevicesfornondestructivetestingthesemiconductormaterials |
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2025-07-08T20:11:29Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 68-72.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
68
PACS 61.10.Nz
Simulation of radiation characteristics of pulse X-ray devices
for non-destructive testing the semiconductor materials
S.V. Denbnovetsky, N.V. Slobodyan
National Technical University “KPI”, Electronics Department,
16, Politekhnichna str., 03056 Kyiv, Ukraine
Abstract. In the work, non-destructive testing the Si and Ge semiconductors by pulse X-
ray sources is discussed. Mathematical simulation of the radiation generation in
reflection and transmission anode tubes is performed. Details of energy spectrum
formation in these pulse tubes are analyzed, and its transformation when passing through
thin samples of semiconductor materials is discussed. The dependence of the amount of
radiation absorbed by the samples on the amplitude of acceleration voltage is calculated.
It is shown how the pulse operation regime and design features of pulse tubes influence
the characteristics of the X-ray radiation.
Keywords: non-destructive testing, pulse X-ray devices, X-ray radiation spectra,
radiation absorption.
Manuscript received 02.11.05; accepted for publication 15.12.05.
1. Introduction
The semiconductor materials and devices (electronic
industry production) as objects of the X-ray non-
destructive testing have a number of specific features. It
gives grounds to consider the X-ray testing the
semiconductor objects as a separate branch of
investigations. The semiconductor devices are
characterized by microscopic sizes of objects and
expected defects, by multilayer structure of different
density materials and by small absorption [1]. The
vulnerability of very sensitive semiconductor device
structures forces ones to limit the investigation with
moderate X-ray radiation energy range and use minimal
possible dose powers. The spectrum of X-ray radiation
after passing the thin semiconductor structure and
creating the shadow X-ray image contains almost all the
low-energy components of radiation emitted by the X-
ray source. At the same time, the ratio of the radiation
spectrum components intensities after passing through
the tested semiconductor sample strongly depends on the
sample thickness [2]. The necessity of taking into
account the real radiation spectrum and other
abovementioned factors complicates the mathematical
simulation of the radiation action on the X-ray-sensitive
elements of the equipment for semiconductor material
investigations.
The problem of computer simulation of the process
of shadow X-ray image formation by continuous
operating X-ray devices for thin samples of widely used
semiconductor materials (Si, Ge) was considered in [2].
There were found some features in the dependences of
the X-ray radiation absorption on the acceleration
voltage of an X-ray device and the sample thickness
when this radiation passes through thin semiconductor
samples.
However, side by side with the X-ray devices of
continuous operation, pulse X-ray devices are widely
used for non-destructive testing. The pulse X-ray devices
have a number of advantages. First, owing to
autoelectronic or explosive emission used in such
devices, a system of filament heating is not required.
Second, such devices can develop considerable power of
X-ray radiation during the pulse, while the average
consumed power is not large. This makes a cooling
system unnecessary and allows to considerably reduce
the dimensions and weight of the devices [3].
The characteristics of radiation from a pulse X-ray
device differ from those of a continuous operation
device. The characteristics are influenced by the constant
alternation of the acceleration voltage and anode current
during the pulse and their periodic cessation between
pulses [4, 5]. These factors together with design features
of pulse X-ray tubes considerably complicate the task to
mathematically simulate generation of X-ray radiation in
such sources.
In this article, we discuss the influence of the pulse
operation regime on the characteristics of the X-ray
radiation. We discuss the formation of the radiation
spectrum and its transformation when passing through
homogenous samples of different semiconductor
materials. We report qualitative differences between the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 68-72.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
69
Fig. 1. Typical shapes of anode voltage and current pulses (a).
Simplified forms of pulses (b).
pulse and continuous regimes of operation in testing
semiconductor devices and materials.
2. Pulse X-ray tube design
The majority of pulse X-ray tubes could be divided into
tubes with a reflection anode and those with a
transmission anode [4].
The reflection anode is a thin needle of a heavy metal
(tungsten, molybdenum, copper etc.) 2 to 6 mm in
diameter. It is sharpened at an angle α between 10 to
30°. In reflection anode tubes, radiation propagates in
the direction of the needle axis, passes through the
hollow of the cylindrical cathode and through the output
beryllium window.
The transmission anode is made of tantalum or
tungsten foil with the thickness Δ of 20 to 100 μm. In
transmission anode tubes, radiation passes through the
anode foil and propagates at right angle to its planar
surface.
3. Mathematical simulation
To simulate the pulse X-ray source, it is necessary to
take into account both the pulse character of operation
and the design features of the specific X-ray tube.
In [6], an approximation formula for the energy
spectrum of the quanta flux density for a realistic X-ray
tube of continuous operation was introduced.
Calculations by using this formula agree with
experimental spectra to within few percents.
This model can be taken as a basis for pulse X-ray
device simulation.
The device features of reflection and transmission
anode tubes must be taken into account in determining
the path length ),( maxEEy of X-ray quantum flow from
where they originate in the bulk of anode to its outside
surface. This path length defines the self-absorption of
radiation in anode material.
The examination of the geometric scheme of genera-
tion and emission of X-ray quanta in pulse tubes of dif-
ferent designs enables us to express the path length as:
)(
)(
)2/(ctg),( 22
max
max
max EE
Ec
EEy
m
r −=
ρ
α (1)
and
)(
)(
),(
max
22
max
max Ec
EE
EEy
m
tr ρ
−
−Δ= (2)
for the tubes with reflection and transmission anodes. In
these formulae, E is the quantum energy in keV, maxE is
the maximal quantum energy, mρ is the anode material
density in g/cm3, and )( maxEc is the Thomson-
Widington constant.
To take into consideration the pulse character of the
regime, the value of the maximal quantum energy maxE
(which corresponds to the accelerating anode voltage in
kV) and the value of the anode current i must be
changed to time dependent functions of these parameters
(i.e., functions describing current and voltage pulse
profiles) – )(max tE and )(ti . This determines the instan-
taneous energy distribution of X-ray quanta at a given
time point t . The integral of this time dependent
function over the time interval of the pulse duration
gives the energy distribution of X-ray quanta for one
pulse. The integral of this distribution over the energy
yields the total number of quanta emitted by the source
per pulse.
The functions )(max tE and )(ti represent current
and voltage pulses profiles. They depend on electrical
feed circuit and physical processes in the X-ray diode.
Typical shapes of anode voltage and current pulses are
shown in Fig. 1a [4]. In the present work, to facilitate the
calculations, we used simplified forms of pulses as
shown in Fig. 1b.
The regime parameters of pulse X-ray devices are
determined by the characteristics of the discharge loop,
but the dependence is rather complicated. It has been
shown in [4] that the dependence of the maximal value
of the anode current maxI (in А) on the maximal
quantum energy maxE (in keV) for X-ray tubes with
explosive emission may be approximated as:
4/3
max
2/16
maxmax )/(1012.1)( EdCEI ⋅= , (3)
where C is the condenser capacity of the pulse X-ray
tube in farads; d is the cathode-anode spacing in centi-
meters.
The averaged radiation energy distribution per pulse
)(~ EN for a pulse X-ray device is a sum of the two
integrals over time – 1D and 2D divided by the pulse
duration τ . They correspond to two time intervals of the
pulse: from 0 to 1τ (when the voltage is constant and the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 68-72.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
70
Fig. 2. The normalized spectra of radiation for X-ray devices
of various types.
current linearly increases); and from 1τ to τ (when the
voltage and the current linearly decrease to zero value).
Thus,
τ
),(),(
)( max2max1~ EEDEED
EN
+
= . (4)
The corresponding expressions for 1D and 2D are:
dt
t
EIEENEED E∫=
1
0 1
maxmaxmax1 )(),(),(
τ
τ
(5)
and
∫
−
−
×
−
=
1
max
1)( 1
maxmax2 ),(),(
ττ
ττ ττ
E
E
E E
t
ENEED
dttEI
1
max )(
ττ −
× . (6)
The lower limit of the integral in expression (6) is
made variable to prevent the situation when the
expression )( max EE − becomes negative for certain
relations between t and E . In expressions (5), (6)
)( maxEI is defined by (3); and ),( max EENE is defined
as:
×
−⋅
=
Er
EEZk
EEN E 2
max1
max
)(
),(
[ ]00max )(),()(exp HEEEyEm μμ −−× , (7)
where 12
1 101.1 ⋅=k s·quantum/A·kV; Z is the atomic
number of the anode material; r is the distance to the
tested object in centimeters; 0H is the output X-ray tube
window thickness in centimeters; )(Emμ and )(0 Eμ
are the linear coefficients of X-ray radiation absorption
of anode and output window materials in cm−1; the path
length ),( maxEEy of X-ray quantum flow defined by
the formulae (1) and (2) for tubes with reflection and
transmission anodes, respectively. To define the pulse
X-ray radiation spectrum after passing the testing object,
the expression (7) must be multiplied on ])(exp[ HEμ− ,
where )(Eμ is the linear coefficient of X-ray radiation
absorption by the sample material in cm−1; H is its
thickness in centimeters.
The dependences of the linear coefficients of X-ray
radiation absorption )(Emμ , )(0 Eμ and )(Eμ were
obtained in this study by using cubic spline
approximation of the reference-book table data of the
mass coefficients of X-ray radiation absorption [7] and
their multiplication on the material densities.
4. Simulation of the spectra
In the present calculations, typical parameters of the
pulse X-ray devices “MIRA” and “ARINA” are
used [3, 4]. The parameters of pulses of the current and
voltage are: 25=τ ns, 101 =τ ns; the parameters in the
formula (3) are: 40=C pF, 2.0=d cm.
The normalized spectra of radiation for X-ray
devices of different types are shown in Fig. 2 for
comparison. These results were obtained for tungsten
anodes; 120max =E keV; 30=r cm. In the plot, the
curve 1 is the spectrum of a continuously operating
device. It is calculated by the method introduced in [6].
The anode tilt angle is 19°; the anode current is 10 mA;
the output beryllium window thickness is 40 =H mm.
The curves 2 to 5 are the energy quantum distribution
per pulse of pulse X-ray devices. They are calculated
using the formula (4). The curves 2 and 3 are related to
the reflection anode tube spectrum. For both tubes the
thickness of output beryllium windows is 40 =H mm,
and half angles of anode sharpening are °= 62/α and
°= 192/α , respectively. The curves 4 and 5 are
transmission anode tube spectra. The anode thickness is
20=Δ μm and 70=Δ μm, respectively.
The analysis of the plotted relations allows us to
understand the influence of pulse operation and of
design features on the radiation spectrum.
To see the influence of the pulse operation regime,
let us compare the curves 1 and 2. The design dependent
parameters used to calculate the curves 1 and 2 were the
same: the reflection anode half-angle of the pulse tube is
equal to the anode tilt angle of the continuous operating
device (19°). Thus, the only difference is that in a pulse
device the anode current and voltage change in time. It is
seen that compared to the spectrum of the continuously
operating device (curve 1) in the pulse device (curve 2)
the hump is shifted to lower energies (~ 39 keV and ~ 36
keV, respectively). This effect agrees with experimental
results for the spectrum of a pulse device [4, 8]. The
effect is explained by the fact that during a considerable
part of the pulse the voltage on the pulse tube anode is
lower than its amplitude value. It weakens the high-
energy part of the spectrum of a single pulse. Since the
low-energy part is absorbed more efficiently, the
radiation absorbed by the test object must increase.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 68-72.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
71
Fig. 3. The dependence of the average absorbed quantum flux
per pulse on the anode voltage amplitude for the tubes with
tungsten, molybdenum and copper reflection anodes: a –
silicon sample, b – germanium sample.
Fig. 4. The dependence of the average absorbed quantum flux
per pulse on the anode voltage amplitude for the tube with a
tungsten transmission anode: a – silicon sample, b –
germanium sample.
To determine the influence of the design on the
spectra, we performed similar calculations for a tube
with the reflection anode half-angle of °= 62/α
(curve 3). The hump of this spectrum (~ 53 keV) is
strongly shifted to higher energies. This is related to the
fact that the distance from the point where the quanta
originate to the point where they are emitted increases
when the anode angle decreases (formula (1)). In this
case, the design factor is stronger then the factor of the
pulse operation, which acts in the opposite direction and
weakens the high-energy part of the spectrum.
In the case of the transmission anode, as the foil
thickness increases the hump of the spectrum shifts to
higher energies: from ~ 30 keV (curve 4, 20=Δ μm) to
~ 50 keV (curve 5; 70=Δ μm). When the anode is thin,
the hump shifts to the left because the low-energy quanta
that originate deeper in the bulk must pass a shorter
distance to the outer surface then the high energy quanta.
In a thick anode the pass length for quanta of all energies
increases considerably and the hump in the spectrum
shifts to high energies.
The simulation results are compared to the
experimental spectrum of a reflection anode tube
published in [8]. The characteristics of the tube were
described in [9]. They correspond to the parameters of
the tube, the calculated spectrum of which is shown by
the curve 3 in Fig. 2. The present simulation agree with
the measurements to within 12 %, whereas the
calculation of [8] deviate from the experimental data by
44 %. This is because the method used in [8] does not
take into account the radiation self-absorption in the
target. Improved simulations introduced in these work
may replace experimental investigations, which are
extremely complicated in the case of pulse devices and
may themselves have large errors.
5. Pulse radiation absorption
in the semiconductor samples
As it was mentioned in the introduction, the results of
simulation of the irradiation of semiconductors by the
continuous X-ray radiation were presented in [2]. The
tubes with tungsten and molybdenum anodes were used
at a constant anode current value. The investigations
show that for silicon and germanium samples of 0.03 –
0.06 cm thickness range at certain values of anode
voltage, peaks in absorption of radiation are observed.
The conclusion was made that such simulations can help
to determine efficient operation regimes to obtain a high-
quality shadow image of the defects in semiconductor
structure formation.
The possibility of the efficient absorption of pulse X-
ray radiation in thin samples of semiconductor materials
(silicon and germanium) is investigated below. The
calculations were made for the parallel-sided plates of
the crystalline silicon and germanium with homogenous
density. The silicon and germanium sample densities
used for determination of the coefficients )(Eμ for
these materials are 2.33 and 5.32 g/cm3, respectively
[10].
The results of calculations are shown in Figs 3 and 4
for the samples with 400 μm thickness of silicon (Figs
3a and 4a) and of germanium (Figs 3b and 4b). Shown is
the dependence of the average quantum flux absorbed by
the semiconductor sample per pulse )( maxER on the
anode voltage amplitude. For the tubes with tungsten,
molybdenum and copper reflection anodes
corresponding dependences are shown in Fig. 3. (The
anode half-angle was °= 62/α ). For the tubes with a
tungsten transmission anode the results are shown in
Fig. 4. (The anode thicknesses were 20, 30, 50, 70,
100 μm).
It can be seen that in contrast to continuously
operating devices [2], for pulse X-ray sources and thin
semiconductor samples there are no clear absorption
maxima. Nevertheless, for the reflection anode tube in
the case of silicon sample (Fig. 3a) for the Mo target the
curve saturates (from 60 to 160 keV) and there is the
evident knee in the neighborhood of 50 keV for the W
and Cu targets. In the case of germanium sample, there
is a peak of absorption at 260max =E keV for the
tungsten target (Fig. 3b).
For transmission anode tubes, the absorbed radiation
part increases with the amplitude of anode voltage, and
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 1. P. 68-72.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
72
there are no singularities in the corresponding plots for
the samples of silicon and germanium (Fig. 4). The
thinner the target, the steeper the curves.
6. Conclusions
1. The developed mathematical simulation of the
radiation characteristics of pulse X-ray devices agrees
with experimental results.
2. The pulse regime of operation and design features
of the pulse X-ray device (the electrode configuration
and the discharge gap geometry) strongly influence the
energy distribution of X-ray quanta.
3. The pulse regime of operation leads to a shift of
the spectrum hump to lower energies compared to the
spectrum of a continuously operating device.
4. In pulse X-ray devices, a decrease of the reflection
anode angle or an increase of the thickness of a
transmission anode lead to a shift of the energy spectrum
hump to higher energies.
5. In pulse X-ray devices with reflection anode tubes,
the anode voltage dependence of the radiation absorption
in thin semiconductor samples has under certain
conditions some structures, but they are not as
pronounced as those in continuously operating devices.
6. For transmission anode tubes, the absorption in
silicon and germanium steadily increases with the pulse
voltage amplitude.
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