The high rate at which particles are produced in the proton-proton collisions at LHC result in a large amount of radiation inside the detector, leading to radiation damage of detector elements and the electronics, and to the activation of detector material. All parts of the detector, including the optical link, are affected by radiation damages.
According to NIEL scaling, any particle fluence can be reduced to an equivalent 1 MeV neutron fluence producing the same bulk damage in a specific semiconductor. The scaling is based on the hypothesis, that generation of bulk damage is due to non-ionising energy transfers to the lattice.
Given an arbitrary particle field with a spectral distribution f(E) and of fluence F, the 1 MeV equivalent neutron fluence is:
k
is called the hardness parameter and is defined as:
where f is the differential flux, and
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with 
the displacement KERMA or the damage function for the energy E of the incident particle,
the cross-section for reaction k,
the probability of the incident particle to produce a recoil of energy ER in reaction k
and the partition function (the part of the recoil energy deposited in displacements) [1].
EDK(1MeV)=95MeVmb [2]. The integration is done over the whole energy range. Figure 1 shows the displacement damage functions in silicon recommended by Angela Vasilescue in [3]. The damage function can be converted into NIEL values with following conversion:
For silicon A=28.086 g/mol and consequently 100 MeV mb = keV cm^2/g .
Figure 1: Recommended displacement damage functions for NIEL scaling in Silicon [3].
The damage functions of high energy particles in GaAs are not as well experimentally determined as for silicon. In [4] the NIEL for fast neutrons, protons and pions in GaAs has been deduced from published calculations. There is a strong correlation between the observed reduction of charge collection efficiency with radiation dose from NIEL. The results are summarised in Figure 2 and Figure 3.
Figure 2: Calculations for the NIEL stopping power for neutrons in GaAs as a function of the kinetic energy [4].
Figure 3: Calculations of the NIEL stopping power for neutrons in GaAs as a function of kinetic energy [4].
The calculated and experimentally established results indicate, that GaAs has a greater radiation hardness to neutron irradiation than Silicon. This is due to the fact that the 1 MeV neutron cross sections are similar for the two materials whilst the number of atoms in GaAs per unit mass is lower due to the larger atomic weight. On the other hand the NIEL for fast protons and pions is larger in GaAs than in Silicon. This can be understood from the Lindhard factors for the two materials. The Lindhard factors give the total fraction of the energy which appears as ionisation energy [5]. Figure 4 shows the Lindhard factors as a function of the energy for Silicon and GaAs. The threshold energy above which the ionisation becomes dominant is about 7 times higher in GaAs than in Silicon due to the lower velocities of the heavier ions in the former. As a result the average NIEL deposited by a fast recoil in GaAs is higher than that in silicon [4].
Figure 4: The total fraction of the energy appearing as ionisation energy due to interactions with atomic electrons for GaAs ions in GaAs and Si ions in Si calculated according to the formulae of Lindhard et al. [4].
The simulations of the expected radiation levels for the ATLAS Inner Detector were performed by A. Ferrari [6], constructing a detector model which produces the location and quantity of the material in the Inner Detector and calorimeter regions, including the supports and services. A Monte Carlo program for hadronic multiparticle production has been used to generate minimum bias particles. This DTUJET code is based on the two-component dual parton model which includes the dual topological unitarisation of soft and hard cross sections. The geenrated particle have been passed through the detector simulation and their subsequent decays or interactions were treated with the FLUKA transport code. At the radii of the Inner Detector, the dominant source of radiation is the direct proton-proton interaction, with typically 23 interactions per BCO (every 25 ns) at the full luminosity of 1034 1/cm2s [7]. The cross sections used by the DTUJET program for the particle flux are sInelastic=81mb and sNSD=67mb. The ATLAS assumption is sNSD= 70mb. Therefore this number has to be corrected for this difference in the cross section sNSD. The total number of interactions per LHC year (107sec) is calculated for all layers:
The expected flux and fluence numbers of charged and neutral particles quoted in this report are calculated for different positions in the Inner Detector, using the FLUKA output as input. For all calculations the so-called ATLAS luminosity scenario is assumed: For the first and the second pixel layer and all SCT layers this means three years of low luminosity operation1033 cm-2s-1 for 107 s/year) followed by seven years of high luminosity operation 1034 cm-2s-1 for 107 s/year). For the Pixel B-layer three years of low luminosity operation followed by two years of high luminosity operation are assumed.
The fluxes are also necessary to define the fluxes needed during single event effect studies at test beams. The particle flux f, the number of particles per second and cm2, is needed to estimate the behaviour of the device under test in such an environment. At high fluxes single event effects are expected. The output of the FLUKA code is the number of particles per cm2, interaction and energy bin. From this output the flux in the the ATLAS Inner Detector was calculated using:
The radii of all Pixel layers have changed since the TDR [7]. In order to calculate the fluxes for the new radii, the calculated fluxes for the old radii were plotted versus the radii and fits were applied. The charged particles were fitted with an inverse quadratic function, the neutrons with an ansatz with a free but negative exponent. The fit parameter were also used to determine the flux for the PP0 area at a radius of 18cm, which was not included in the original simulation. Table 1 lists the results for the patch panel PP0, the position for the Pixel optical link, and the SCT 1 Layer.
|
|
Pions |
Neutrons |
Total |
PP0 |
2.01*10^6 |
3.08*105 |
2.32*106 |
|
SCT 1 |
9.88*10^5 |
1.90*105 |
1.18*106 |
Particle fluence F is defined as the number of particles traversing a unit area in a certain point in space for a given period of time weighted with a particle- and material-specific damaging factor. Most frequently, it is measured in cm-2. In particular, neutron fluence in high-energy physics applications is of interest in the context of the radiation environment around the interaction regions of colliders; it serves as a measure for potential radiation damage for the detector systems to be used. It is common practice to express charged and neutral particle contributions to radiation in terms of dose and 1MeV neutron equivalent fluence (also NIEL scaling), respectively. The annual fluences at high luminosity were calculated as following:
Fneq gives the fluence of neutral particles whereas Fpeq is used for the calculation of the charged particles. By assuming that the damages in Silicon and in GaAs scales with the NIEL, the NIEL values for Silicon and GaAs were taken from Figure 1, 2, and 3 respectively. For particle energies between the given values, the NIEL value was interpolated. Commonly the total fluence is given in 1MeV equivalent neutrons. Therefore the fluence calculated for the charged particles has to be converted with a conversion factor, i.e. for GaAs:
The annual fluences for the new radii, including PP0, were also calculated by applying the same fitting strategy as for the flux. The total fluence was calculated by adding the 1MeV annual fluences for charged particle and neutrons and scaling to the full LHC lifetime. A +50% safety margin has been added to allow for the uncertainties; this is a common procedure agreed on within the ATLAS collaboration. Table 2 and 3 list the total fluences for PP0 and SCT1 in 1MeV neutrons and converted for 24GeV protons and 30MeV protons for Silicon and GaAs respectively.
|
Silicon |
1 MeV neutrons |
24 GeV protons |
30 MeV protons |
PP0 |
3.7*1014 |
6.3*1014 |
1.6*1014 |
|
SCT1 |
2.3*1014 |
3.9*1014 |
9.7*1013 |
|
GaAs |
1 MeV neutrons |
24 GeV protons |
30 MeV protons |
|
PP0 |
2.0*1015 |
3.8*1014 |
2.7*1014 |
|
SCT1 |
9.9*1014 |
1.9*1014 |
1.4*1014 |