Diamond degradation in hadron fields1


S.Lazanua, I.Lazanub, and E.Borchic


a Institute of Physics and Technology of Materials, POBox MG-7, Bucharest-Magurele, Romania
b University of Bucharest, POBox MG-11, Bucharest-Magurele, Romania
c Universit di Firenze, Via S.Marta 3, 50139 - Florence, Italy




The energy dependence of the concentration of primary displacements induced by protons and pions
in diamond has been calculated in the energy range 50 MeV - 50 GeV, in the frame of the Lindhard
theory. The concentrations of primary displacements induced by protons and pions have completely
different energy dependencies: the proton degradation is very important at low energies, and is higher
than the pion one in the whole energy range investigated, with the exception of the 33 resonance region.
Diamond has been found, theoretically, to be one order of magnitude more resistant to proton and pion
irradiation in respect to silicon.





1. INTRODUCTION Its resistivity, higher than 1014 cm, eliminated
the need of any form of junction, conducing, this
way, to the reduction of parallel shot noise in the
The possible use of diamond detectors in high readout electronics, in respect to silicon and GaAs.
energy physics is due to its more appropriate
 15 Apr 1999 material properties, in respect to, especially, silicon. Its low dielectric constant causes a small bulk
and surface (interstrip) capacitance, which in turn
Diamond is, conceptually, a much simpler reduces the series noise at the first stage of the
material to make detectors, as a result of its lack of signal amplifier. This is particularly important in
p-n junction. A diamond detector works in an high rate applications.
analogue way to an ionisation chamber: an electric
field is applied between the 2 electrodes (sandwich However, due to the high band gap of diamond,
configuration), and free carriers are generated at the the energy to create an e-h pair is greater than for
passage of ionising radiation. The formed carriers other semiconductor materials. So, for a 300 m
induce signals to the electrodes. device, in the ideal situation, at the passage of a
particle at minimum ionisation, the average signal
is 13200 e-h pairs, (in comparison with 32400 in


1 presented at the 6-th Int. Conf. "Advanced Technology and Particle Physics"; Como, Italy, Oct. 1998,
in press to Nuclear Physics B (Proc. Supplement).





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silicon), while the most probable signal is about As we shown before [1], the relevant quantity
10800 e-h pairs in diamond (and 21600 in Si). In for the evaluation of radiation effects is the
reality, diamond detectors available today are far concentration of primary defects, produced by the
from ideal, and even a worse detected signal is unit particle fluence. This is calculated as the sum
obtained (about 40% of that generated). of the concentrations of defects resulting from all
Diamond is intrinsically very fast, particularly interaction processes, and all characteristic
suitable for high rate operation. It is also an mechanisms corresponding to each interaction
excellent thermal conductor, quality that offers process.
advantage for large heat dissipation from the read- The concentration of primary radiation induced
out electronics, and has excellent mechanical defects (CPD) has been calculated as:
strength, that, coupled with low atomic number can
reduce multiple Coulomb scattering. (
n E )
It is its expected extreme radiation hardness that CPD = (
E)
is the primary reason for considering diamond as a
material for vertex detectors. Its outstanding
properties (fast read-out with negligible noise, very with:
good thermal management, reduction of multiple
scattering) are shadowed by its (even in the ideal
case) reduced signal. ( N d
n E ) = (
E)d i

(LERi)
The radiation resistance of diamond detectors 2E
i d
d k
has been experimentally confirmed for photons and
electrons, and the tests for other particles are in
progress.
where: E is the kinetic energy of the incident
In the present paper, the behaviour of diamond hadron; N - atomic density of the target material; E
in hadron fields is presented, as the concentration of d
- threshold energy for displacements in the lattice;
primary defects (CPD) induced by irradiation.
Proton and pion degradations are calculated and (E) - the pion fluence in the primary beam; ERi -
compared, in the energy range 50 MeV - 50 GeV. recoil energy of the residual nucleus in the
interaction k (k= elastic, absorption and inelastic if
the hadron is a pion, and k = elastic, inelastic if it is
a nucleon, respectively), in the interaction
mechanism i, having a d / d - differential cross
2. MECHANISMS OF DAMAGE AND i
RELEVANT QUANTITIES section; L(ERi) - Lindhard factor describing the
partition between ionisation and displacements.
This factor describing the energy partition has been
In the projectile energies considered in this calculated in [2].
work, the hadron interacts dominantly with the The contribution of each channel to the total
nucleus, essentially unscreened, producing concentration of defects depends on the probability
displacement defects in the diamond lattice. In the of interaction and on the kinematics of the process,
interaction process, one or more light energetic reflected in the recoil energy of the residual nucleus.
particles are produced. The light particles are For monoatomic materials, the CPD is
supposed to escape from the diamond material, proportional to the non-ionisation energy loss
considered as a thin layer, without undergoing a (NIEL) [3], a physical quantity historically used for
second collision, while recoil nuclei loose all their the characterisation of lattice degradation in particle
energy in the lattice, by ionisation and atomic fields.
motion. They produce this way bulk damage, by
subsequent collisions with other atoms.





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3. HADRON INTERACTIONS For the concrete calculations, the available
experimental data have been used, and also different
phenomenological approximations for their
The interaction between a hadron and a nucleus interpolations / extrapolation.
can be either an elastic or an inelastic event. Rutherford and nuclear elastic scattering of
In an elastic scattering process of interaction, hadrons on nuclei cannot be treated separately due
symbolically represented by: to the strong interference mechanisms [4]. The data
h + Nucleus h + Nucleus from reference [5] and [6-9] have been used
respectively for pion and proton carbon differential
cross sections, and they have been extended at other
the hadron does not excite the target nucleus. energies in the frame of a simple optical model,
The inelastic hadron - nucleus scattering both for pions and for protons.
includes all reactions of the type:



h + Nucleus a1 + a2 + ... + an+ Residual
Nucleus



where the reaction products a1, a2, an can be proton,
neutron, deuteron, other particles or light nuclei.

When the kinetic energy of the incident particle
exceeds the threshold energy of 140 MeV,
secondary pions could also be produced.

If the inelastic process is produced by nucleons,
the identity of the incoming projectile is lost, and
the creation of the secondary particles is associated
with energy exchanges which are of the order of
MeV or larger.
Figure 1. Energy dependence of proton - carbon
For pion - nucleus processes, a characteristic cross sections: total, elastic and inelastic. The lines
interaction is possible: the pion can disappear as a represent parametrisations of the data.
real particle within the nucleus, by absorption. In
these calculations, the absorption process is
considered separately. Absorption on a single
nucleon is kinematically prohibited, and the In Figures 1 and 2, the energy dependencies of
simplest process is on two nucleons. Absorption on the proton - carbon and pion - carbon cross sections
more nucleons is also possible. are shown, respectively.
The interaction of pions with nucleons and For proton - carbon interactions, the elastic cross
nuclei at kinetic energies comparable to the pion sections are from [10], the inelastic ones (data) from
rest mass is dominated by the delta resonance [11], and the continuous curve represent the
production, with spin and isospin 3/2. At higher parametrisation from reference [12].
energies, other nucleons and resonances could be
produced, but with much less importance. For positive pions - carbon interactions, the data
are from [5] for the elastic cross sections, from [11,
Since the inelastic and absorption collisions are 13-14] for reaction, and from [13,15] for absorption
considerably more complex than elastic scattering, respectively. The continuous lines are best fits of the
special reaction models must be developed for their data, and have been used to extrapolate / interpolate
analysis. the values of the cross sections at energies of





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interest. The inelastic cross sections are obtained as From the point of view of the isospin, the proton
differences between reaction and absorption ones, and the neutron are states of the nucleon, and + , -
and are represented as dashed lines in Fig. 2. and 0 are different charge states of an unique
The energy dependence of these cross sections, system. The isospin symmetry is exact only for the
for proton and pion interactions with the carbon strong interaction. In reality, this symmetry is
nucleus present very different behaviours: the broken by the electromagnetic interaction, which is
proton - nucleus cross section decreases with the manifested in the difference in mass between these
increase of the projectile energy, and has a particles, and in the different interaction
minimum at low energies, while the pion - nucleus probabilities of each particle with other systems.
cross sections present for all processes a large For nucleon - nucleus interaction, above 100
maximum, at about 160 MeV, which reflects the MeV, the Coulomb interaction is not important, and
resonance structure of the interaction. the characteristics of proton - nucleus and neutron -
nucleus reactions are very similar. Below 100 MeV,
the cross sections for neutrons are somewhat larger
that the corresponding proton cross sections, while
the isotopic distributions of the residual nuclei from
proton and neutron interactions are very similar. At
around 20 MeV or below, the proton reaction cross
section decreases rapidly because of the proton
nucleus Coulomb barrier. This barrier does not
apply to neutrons.

The interaction of 0 with nuclei do not present
interest for these studies. For + and -, the
differences in the interactions are due to the
Coulomb barrier. Two aspects are relevant: the
differences in the values of the cross sections, effect
more important at low energies, and an energy shift
of the maximum cross section in the region of the
33 resonance region. At high energies, far from the
Figure 2. Energy dependence of pion - carbon cross resonance, these effects decrease, and than become
sections: up to down the curves represent total, unimportant. The behaviour of the pion - nucleus
inelastic, elastic and absorption cross sections. The interaction do not differ significantly for that of
lines are the best fits of the data. other hadrons.




Both the pions and the nucleons interact 4. MODEL CALCULATIONS, RESULTS
strongly with the nucleus. It is important to AND DISCUSSIONS
compare nucleon - nucleus and pion - nucleus
reactions. The dominant excitation modes directly
affect the distribution of secondary fragments, Elastic and Rutherford contributions to the CPD
which deposit ionisation energies in the host have been treated together, as specified before.
material. In reference [16], this study was been The main difficulty is related to the inelastic
done. It can be seen that far from the delta interaction, due to the multitude of open channels,
resonance, the behaviour of pions and protons is corresponding to possible final states. In order to
somehow similar, and a scaling procedure could be obtain an estimation of the average recoil energies,
applied from one particle to another, while in the
some simplifying assumptions concerning this
33 energy range this is not possible. interactions have been made, starting from the





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available experimental data.. Both for pions and The recoil energy partition between ionisation
protons, the knock-out interaction has been and displacements has been considered in the frame
considered separately, using the data from [13, 17- of the Lindhard theory.
18] for pions, and from [10] for protons The results obtained for the energy dependence
respectively. The rest of the channels have been of the CPD and NIEL produced by protons and
considered as equivalent to the interaction on an pions are represented on the same graph in Figure
effective number of nucleons. 3. The CPD for protons present an abrupt decrease
Particle generation has been neglected. at low energies, followed by a minimum and at
In the case of pions, an important contribution is higher energies, by a plateau. For pions, there exists
given by absorption, in the energy range of the delta a large maximum in the region of the 33
resonance, while above 1 GeV we considered it as resonance. The minimum for proton degradation
negligible. The simplest absorption mechanism and respectively the maximum for pion one are in
involves two nucleons. We supposed that the the same energetic range.
absorption on quasideuteron is the dominant two Comparing the present results for the protons
nucleon mechanism. The experimental data show and pions degradation in diamond with the
that in carbon the contribution of three-body corresponding ones in silicon (for protons, see
absorption is also important, but the absorption on reference [3], for pions, reference [19]), the
four or more nucleons is negligible [15]. The rest diamond proves to be one order of magnitude more
can be attributed to other mechanisms, especially to resistant to radiation.
final state interactions, and has been treated
statistically. Details could be found in [2].
5. SUMMARY
Both for protons and pions, the energy
dependence of the CPD follows the energy
dependence of the cross sections. The energy dependence of the CPD and NIEL
produced by protons and pions in diamond have
been calculated, in the energy range 50 MeV - 50
GeV.

Pions produce a higher degradation in diamond,
in respect to protons, only in the 33 resonance
energy range.

Diamond has been found one order of magnitude
more resistant to proton and pion irradiation in
respect to silicon.

Experimental measurements are necessary to
validate the present calculations.




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(continuous line), in diamond. 2. I.Lazanu et al., Nucl. Instr. Meth. Phys. Res. A
406 (1998) 259.





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