CIENCIAS NUCLEARES
Calculation
of the displacement cross sections and the DPA
distribution in hydrogenated amorphous silicon semiconductors detectors in medical
digital imaging applications
Cálculo
de la sección transversal de desplazamiento y la distribución
de los DPA
en detectores semiconductores de silicio amorfo hidrogenado en aplicaciones
de imagenología digital médica
Antonio Leyva Fabelo,
Ibrahin Piñera Hernández, Katerin Shtejer Díaz, Yamiel
Abreu Alfonso, Carlos Manuel Cruz Inclán
Centro de Aplicaciones
Tecnológicas y Desarrollo Nuclear (CEADEN)
Calle 30 No 502 e/ 5ta Ave. y 7ma. Playa, Ciudad de La Habana, Cuba
aleyva@ceaden.edu.cu
ABSTRACT
In present paper
the dependence of the displacement cross sections of the different species of
atoms in the a-Si:H structure, with the energy of the secondary electrons generated
by the X-rays of the typical energies using in medical imaging applications,
was calculated using the Mott-McKinley-Feshbach approach. It was verified that
for electron energies higher than 1.52 keV it is possible the occurrence of
hydrogen atoms displacements, while for the silicon atoms the threshold energy
is 126 keV. These results were compared with those obtained for similar detectors
but developed with crystalline silicon. With the use of the mathematical simulation
of the radiation transport in the matter, the energy spectrum of the secondary
electrons was calculated in order to estimate the number of atomic displacements,
which take place in the semiconducting amorphous device in working regime.
The spatial distribution of the dpa in the detectors volume, as well as its
behavior with the depth in the
work region are presented and discussed in the text.
RESUMEN
Utilizando la aproximación
de Mott-McKinley-Feshbach en el trabajo se calculó la dependencia de
la sección transversal de desplazamiento para cada especie de átomo
de la estructura del a-Si:H en los intervalos de energía típicos
de los electrones secundarios generados por los rayos X empleados en aplicaciones
de imagenología médica. Se observó que para energías
de los electrones superiores a 1,52 keV son posibles los desplazamientos de
átomos de hidrógeno, mientras que la energía umbral de
desplazamiento de los átomos de silicio resultó de 126 keV. Estos
resultados se compararon con los obtenidos para detectores similares pero fabricados
de silicio cristalino. Con el empleo de la simulación matemática
del transporte de la radiación en la materia se calculó el especto
energético de los electrones secundarios con el objetivo de estimar el
número de desplazamientos por átomos que tienen lugar en el dispositivo
amorfo semiconductor en régimen de trabajo. La distribución espacial
de
los dpa en el volumen del detector, así como su comportamiento con la
profundidad son presentados
y discutidos en el texto.
Key words:
cross sections, atomic displacements, semiconductor detectors, simulation, amorphous
states, silicon, x radiation, images
INTRODUCTION
The use of radiation
detectors manufactured with hydrogenated amorphous silicon extends quickly in
many fields of science and technology, because its low production cost, the
possibility to grow large areas, its appropriate sensibility operating at high
temperatures and the possibility to grown thin layers directly over the read-out
electronics.
Another of their
most important advantages over the crystalline detectors, is the existent compatibility
between the characteristics of their structure and the radiacional damage [1],
question of maximum importance when the application requires of high operation
stability, still after high exposition dose, like it happens in the experiments
of high energies physics and in the medical radiology.
The radiacional
damage can be characterized through the quantity of atomic displacements (dpa)
of certain atoms specie. For photons irradiation this type of damage can only
be produced in an indirect way by means of the secondary electrons that are
generated after the primary interactions of the radiation with the matter (photoeffect).
The range of energies
for most of the medical digital radiology applications is among some few eV
until the 150 keV, although in some applications like mammography and angiography
the maximum energy doesn’t exceed the 50 keV.
These relatively
low energies are the employees in this paper to determine the X rays effects
on the structure of the pin hydrogenated amorphous silicon (a-Si:H) detectors
in applications of radiological diagnosis.
Determination of the displacement cross section
The determination
of the displacement per atom (dpa) cross section is
an indispensable step to determine of the radiacional damage. Knowing
and the energies spectrum of the particles flow is possible to calculate the
total number of atoms that can be displaced of its positions per unit fluence
per a target atom. The approach of Mott-McKinley-Feshbach [2] has been used
for the
calculation. This approach supposes that the atom is bonded to the material
with an energy
,
and for electrons incident energies smaller than
,
= 0, while for the contrary case it is determined by:
where Z is the
atomic number of target atom,
- the Bohr radius,
- Rydberg energy,
= Z/137,
-
ratio of electron velocity to light velocity,
- maximum kinetic energy of recoil atom, M - mass of target atom, m - mass of
electron, and
- displacement energy.
This approach has
been considered exact with a margin of error of 1% for Z
40 [3].
In Ec. (1) all
the parameters are known, with the exception of the displacement threshold energy
of the target atom in the structure of the material,
.
For the case of
the a-Si:H the values of
appear in the literature with certain dispersion. For example, in [4] it is
reported that for the hydrogen,
Ed
H = 3.4 eV, in [5] Ed H = 3.3 eV and in [6]
=
3.6 eV. The authors of [7] assume that the displacement threshold energy of
Si is 20 eV, while in [8] they take
= 22 eV and in [9] they report that the energy required to remove a silicon
atom that is bonded with three other silicon atoms is approximately 25 eV.
We use
= 3.3 eV taking into account that this value is reported as the bonding energy
of H to the Si in the a-Si:H structure and for monovalent atoms the cohesive
energy coincides with the displacement threshold energy [10]. For the case of
the silicon we use
= 22 eV, an average of the reported values.
The figures 1 and 2 show the founded dependences for the displacement cross-sections for hydrogen and silicon atoms respectively, with the electrons and positrons energy.
The analysis of
both figures show that, in our experimental conditions (<
50 keV, typical maximum energy in the most of medical radiographic applications)
the probability of H atoms of being displaced from their position is nonzero
only for energies higher than 1.52 keV, while the Si atoms are insensitive to
the displacement effects because to achieve its displacement from the bonded
position there are required electrons with
126
keV. This result allows concluding that in the a-Si:H detector the structural
displacement defects are only possible for the hydrogen atoms that passivate
the dangling silicon bonds.
For c-Si the
was also calculated using the same code and
= 25 eV reported in [11,12]. Figure 3 shows the
behaviour with the electron energy in this crystalline material. As is observed,
the differences between the calculated results for a-Si:H and c-Si are very
small, because of the similar displacement threshold energy. For example, in
[13] was reported that the d s for silicon in c-Si irradiated with 1 MeV electrons
is 68 barn, while for identical energy our results were 70.3 barn for the same
material and 67.2 barn for hydrogenated amorphous silicon. Also, the displacement
threshold energies for silicon in c-Si reported in the literature, 133 keV [14]
and 150 keV [15], are very close to our results, 126 keV for a-Si:H and 141
keV for c-Si.
Hydrogen dpa
determination
Having the values
of
as a function of the secondary electrons energy, to calculate the dpa, it is
required to determine the energy spectrum of the secondary electrons in the
volume of interest.
To calculate this flow spectrum the code system MCNP-4C [16] based on Monte Carlo method was employed. MCNP-4C simulates the transport of photons and electrons in matter.
In the simulation were taken into account all material and geometric details of both detectors (simple pin detector and matrix detector based in pin diode with pixelated electrode, figures 4(a) and 4(b) [17]).
As X-rays source, a parallel photons beam generator with the Mo emission spectrum (17.6 keV and 19.7 keV) was modeled.
The distance between
the source and the detector was selected l = 60 cm. The histories numbers for
each experiment was selected according to the required statistic. In all the
cases the relative error of the calculated values was lower than 10%. The results
of simulation were obtained using the tally F4, which deliver the values of
the differential energy flow in ().
This spectrum is multiplied by the corresponding cross sections and integrated
in the interesting energies interval, determining by this way the total number
of dpa that take place as consequence of the transport in the device of each
incident photon.
When irradiating
the detector with photons coming from the Mo source (
photons) it is observed that the distribution of the calculated atomic displacements
in the intrinsic layer as a function of the depth presents a behavior, just
as it is shown in figure 5.
The obtained distribution
is characterized by very high values of dpa in the adjacent regions to the Cr
electrodes, as a consequence of the higher Z of Cr with respect to the Z of
the intrinsic material, which lead to the increment of the number of generated
secondary photoelectrons particles
with the ability to provoke atomic displacement on the hydrogen atoms.
The highest value of dpa is reached near the front surface, 1.56 x ,
while in the center of the active intrinsic volume the number of dpa is 6.65
x 10-21. It means that for each
-
photons that impact in the sensor of 70x70x30
only will take place between 1 and 7 hydrogen atomic displacements.
This number of
structural defects is very small and completely negligible keeping in mind that
the average number of photons incident in a similar detector working in conditions
of clinical operation in one year is ~ 1 x .
This annual number of photons was calculated using the data of deposited dose
(2 x
Gy) reported in [18] in a similar detector.
By the same way,
using in the calculation the dose data reported [19], the maximum number of
photons that impact in our detector under real diagnostic exploitation in one
year doesn’t exceed the
photons, still smaller value.
Besides this, some authors, as example [20, 21], demonstrate experimentally
that in a-Si:H the recombination processes of defects are very improved thanks
to the characteristics of the own structure. This natural process contributes,
as these authors report, to the reversion of the generated defects by the recombination
simply by a 5-10 h room temperature annealing.
Previous experimental
studies [18, 22] demonstrated that these low dose levels do not have a significant
effect in the values of the carrier mobility, linearity and other noise properties
in a-Si:H detectors or FET. This way they conclude that the devices based on
the a-Si:H has the appropriate and necessary resistance to the radiacional damages
indispensable for these applications.
In the case of
the a-Si:H matrix detector, given their large dimensions, the calculation shows
a higher dispersion of the results although 2.5 x
histories were run. Nevertheless the relative error stayed inferior to 10%.
The figure 6 shows the obtained results for the dpa distribution in the intrinsic volume of three different pixels (lateral, corner and a center) as a function of the depth. Observe the same behavior that in the figure 5 with very little difference relative to the position that occupies the pixel in the matrix arrangement.
CONCLUSIONS
Using the Mott-McKinley-Feshbach
approach the displacement cross sections of H and Si in a-Si:H were calculated
as a function of the secondary electrons energy. It was determined that the
probability of occurrence of hydrogen atoms displacements from the structure
is possible for energy superiors to the 1.52 keV, while for the silicon atoms
it is possible for energies that surpass the 126 keV.
The number of defects
generated as consequence of the H atoms displacements, according to the calculation,
is totally negligible in order to affect the efficient work of the device under
operation conditions.
These results,
supported by the reports about the amplified defects recombination properties
of this material and the effective and fast restoration of the radioinduced
damages after the device annealing at room temperature, contribute to support
the idea that the devices based on the a-Si:H have the appropriate and necessary
resistance to the radiacional damages, indispensable for the applications of
digital medical radiology.
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Recidido: 14 de abril de 2007
Aceptado: 28 de mayo de 2007