Figure 01a

(a) Simulated 1 MeV n_eq fluence predictions shown as a function of the radial and longitudinal distance from the geometric centre of the detector for a one-quarter slice (z>0 and above the beam) through the ATLAS FLUKA geometry. (b) Predictions for the lifetime fluence experienced by the four layers of the current ATLAS pixel detector as a function of time since the start of Run 2 (June 3, 2015) at z≈ 0 up to the end of 2017. For the IBL, the lifetime fluence is only due to Run 2 and for the other layers, the fluence includes all of Run 1. The IBL curve represents both the fluence on the IBL (left axis) as well as the delivered integrated luminosity in Run 2 (right axis).

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Figure 01b

(a) Simulated 1 MeV n_eq fluence predictions shown as a function of the radial and longitudinal distance from the geometric centre of the detector for a one-quarter slice (z>0 and above the beam) through the ATLAS FLUKA geometry. (b) Predictions for the lifetime fluence experienced by the four layers of the current ATLAS pixel detector as a function of time since the start of Run 2 (June 3, 2015) at z≈ 0 up to the end of 2017. For the IBL, the lifetime fluence is only due to Run 2 and for the other layers, the fluence includes all of Run 1. The IBL curve represents both the fluence on the IBL (left axis) as well as the delivered integrated luminosity in Run 2 (right axis).

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Figure 02

The measured (``Data") and predicted (``Sim.", fitting for Φ/L_int) leakage current for the four module groups of the IBL as a function of integrated luminosity since the start of the Run 2. The predicted leakage current is obtained from Eq. 1 and by fitting the data in the dashed region to determine the luminosity-to-fluence factor. The IBL pixel module groups M1, M2, M3 approximately span the ranges z in [-8,8] cm, |z|in[8,16] cm, and |z| in [16,24] cm, respectively. The M4 modules use 3D sensors and span the range |z| in [24,32] cm. Sharp drops correspond to periods without collisions.

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Figure 03

The fluence-to-luminosity conversion factors (extracted from leakage current fits) as a function of z, compared with the Pythia+FLUKA and Pythia+Geant4 predictions.

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Figure 04a

Calculated depletion voltage of (a) IBL and (b) B-layer according to the Hamburg model as a function of time from the date of their installation until the end of 2016. The calculations shown use the central values of the fitted introduction rates listed in Table 1. Circular points indicate measurements of the depletion voltage using the bias voltage scan method while square points display earlier measurements using cross-talk scans.

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Figure 04b

Calculated depletion voltage of (a) IBL and (b) B-layer according to the Hamburg model as a function of time from the date of their installation until the end of 2016. The calculations shown use the central values of the fitted introduction rates listed in Table 1. Circular points indicate measurements of the depletion voltage using the bias voltage scan method while square points display earlier measurements using cross-talk scans.

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Figure 05a

(a) A schematic diagram of the digitizer physics. As a MIP traverses the sensor, electrons and holes are created and transported to the electrodes under the influence of electric and magnetic fields. Electrons and holes may be trapped before reaching the electrodes, but still induce a charge on the primary and neighbour electrodes. (b) A flowchart illustrating the components of the digitizer model described in this article. The digitizer takes advantage of pre-computation to re-use as many calculations as possible. For example, many inputs are the same for a given condition (temperature, bias voltage, fluence). The Ramo potential [40,41] only depends on the sensor geometry and the quantities in dashed boxes further depend only on the condition information (see also Section 4.6). The output of the algorithm described in this paper is an induced charge on the primary electrode and the neighbours, which is then converted into a ToT by the existing software.

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Figure 05b

(a) A schematic diagram of the digitizer physics. As a MIP traverses the sensor, electrons and holes are created and transported to the electrodes under the influence of electric and magnetic fields. Electrons and holes may be trapped before reaching the electrodes, but still induce a charge on the primary and neighbour electrodes. (b) A flowchart illustrating the components of the digitizer model described in this article. The digitizer takes advantage of pre-computation to re-use as many calculations as possible. For example, many inputs are the same for a given condition (temperature, bias voltage, fluence). The Ramo potential [40,41] only depends on the sensor geometry and the quantities in dashed boxes further depend only on the condition information (see also Section 4.6). The output of the algorithm described in this paper is an induced charge on the primary electrode and the neighbours, which is then converted into a ToT by the existing software.

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Figure 06a

The simulated electric field magnitude in the z direction along the bulk depth, averaged over x and y for an ATLAS IBL sensor biased at: (a) 80 V and (b) 150 V for various fluences.

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Figure 06b

The simulated electric field magnitude in the z direction along the bulk depth, averaged over x and y for an ATLAS IBL sensor biased at: (a) 80 V and (b) 150 V for various fluences.

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Figure 07a

The z dependence of the electric field in an ATLAS IBL planar sensor, averaged over x and y, for a simulated fluence of Φ=1 x 10¹⁴ n_eq/cm², after varying parameters of the acceptor trap in the Chiochia model. (a) ± 10% variation in the fluence dependence (g^A_int) of the acceptor trap concentrations; (b) variation in the acceptor trap energy level by 0.4% (0.525 ± 0.002 eV from the conduction band level); (c) ± 10% variation in the electron capture cross section; (d) ± 10% variation in the hole capture cross section. The bias voltage was set to 80 V in all cases.

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Figure 07b

The z dependence of the electric field in an ATLAS IBL planar sensor, averaged over x and y, for a simulated fluence of Φ=1 x 10¹⁴ n_eq/cm², after varying parameters of the acceptor trap in the Chiochia model. (a) ± 10% variation in the fluence dependence (g^A_int) of the acceptor trap concentrations; (b) variation in the acceptor trap energy level by 0.4% (0.525 ± 0.002 eV from the conduction band level); (c) ± 10% variation in the electron capture cross section; (d) ± 10% variation in the hole capture cross section. The bias voltage was set to 80 V in all cases.

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Figure 07c

The z dependence of the electric field in an ATLAS IBL planar sensor, averaged over x and y, for a simulated fluence of Φ=1 x 10¹⁴ n_eq/cm², after varying parameters of the acceptor trap in the Chiochia model. (a) ± 10% variation in the fluence dependence (g^A_int) of the acceptor trap concentrations; (b) variation in the acceptor trap energy level by 0.4% (0.525 ± 0.002 eV from the conduction band level); (c) ± 10% variation in the electron capture cross section; (d) ± 10% variation in the hole capture cross section. The bias voltage was set to 80 V in all cases.

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Figure 07d

The z dependence of the electric field in an ATLAS IBL planar sensor, averaged over x and y, for a simulated fluence of Φ=1 x 10¹⁴ n_eq/cm², after varying parameters of the acceptor trap in the Chiochia model. (a) ± 10% variation in the fluence dependence (g^A_int) of the acceptor trap concentrations; (b) variation in the acceptor trap energy level by 0.4% (0.525 ± 0.002 eV from the conduction band level); (c) ± 10% variation in the electron capture cross section; (d) ± 10% variation in the hole capture cross section. The bias voltage was set to 80 V in all cases.

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Figure 08

The z dependence of the space-charge density ρ in a simulated ATLAS IBL planar sensor, averaged over x and y, for simulated fluences: 1 x 10¹⁴, 2 x 10¹⁴ and 5times10¹⁴ n_eq/cm². The bias voltage was set to 150 V in all cases. These are predictions based on the Chiochia model at temperature T=-10^circC.

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Figure 09a

The z dependence of the space-charge density in a simulated ATLAS IBL planar sensor, averaged over x and y, for simulated fluences of (a) Φ=1 x 10¹⁴ n_eq/cm² and (b) 2 x 10¹⁴ n_eq/cm². The bias voltage was set to 150 V in all cases. Three scenarios - Chiochia (no annealing), Hamburg and TCAD with effective annealing - to emulate annealing effects were simulated.

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Figure 09b

The z dependence of the space-charge density in a simulated ATLAS IBL planar sensor, averaged over x and y, for simulated fluences of (a) Φ=1 x 10¹⁴ n_eq/cm² and (b) 2 x 10¹⁴ n_eq/cm². The bias voltage was set to 150 V in all cases. Three scenarios - Chiochia (no annealing), Hamburg and TCAD with effective annealing - to emulate annealing effects were simulated.

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Figure 10a

The z dependence of the electric field in a simulated ATLAS IBL planar sensor, averaged over x and y, for simulated fluences of (a) Φ=1 x 10¹⁴ n_eq/cm² and (b) 2 x 10¹⁴ n_eq/cm². The bias voltage was set to 150 V in all cases. Three scenarios - Chiochia (no annealing), Hamburg and TCAD with effective annealing - to emulate annealing effects were simulated.

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Figure 10b

The z dependence of the electric field in a simulated ATLAS IBL planar sensor, averaged over x and y, for simulated fluences of (a) Φ=1 x 10¹⁴ n_eq/cm² and (b) 2 x 10¹⁴ n_eq/cm². The bias voltage was set to 150 V in all cases. Three scenarios - Chiochia (no annealing), Hamburg and TCAD with effective annealing - to emulate annealing effects were simulated.

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Figure 11

The projected time (in the absence of trapping) for an electron or hole to drift all the way from their point of generation to the collecting electrode (electrons) or back plane (holes) in an ATLAS IBL planar sensor biased at 80 V as a function of the depth (z) using the averaged E fields predicted by Chiochia model through TCAD simulation (Figure 6). The n⁺ electrode is located at the left (z=0) and the back plane at z= 200 upmum.

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Figure 12a

The z position of trapped (a) electrons and (b) holes as a function of their starting position and the time travelled for Φ=10¹⁴ n_eq/cm². The n⁺ electrode is located at the left (z=0) and the back plane at z= 200 upmum.

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Figure 12b

The z position of trapped (a) electrons and (b) holes as a function of their starting position and the time travelled for Φ=10¹⁴ n_eq/cm². The n⁺ electrode is located at the left (z=0) and the back plane at z= 200 upmum.

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Figure 13a

(a) The depth dependence of the Lorentz angle for electrons and holes for four fluences in an ATLAS IBL planar sensor biased at 80 V. (b) The integrated Lorentz angle for electrons (see Eq. (11)) as a function of the starting and ending position for a fluence of Φ=2 x 10¹⁴ n_eq/cm². The collecting electrode is at a z position of 0.

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Figure 13b

(a) The depth dependence of the Lorentz angle for electrons and holes for four fluences in an ATLAS IBL planar sensor biased at 80 V. (b) The integrated Lorentz angle for electrons (see Eq. (11)) as a function of the starting and ending position for a fluence of Φ=2 x 10¹⁴ n_eq/cm². The collecting electrode is at a z position of 0.

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Figure 14

A slice of the full three-dimensional ATLAS IBL planar sensor Ramo potential as computed with TCAD at y=0. The dashed vertical line (at 25 μm) indicates the edge of the primary pixel.

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Figure 15a

The average fraction of charge collected as a function of the starting location and the time to be trapped for (a) the same pixel as the electron--hole pair generation, (b) the neighbour pixel in the short-pitch (50 μm) direction and (c) the neighbour pixel in the long-pitch (250 μm) direction. For illustration, in this figure only, the electric field is simulated without radiation damage and the vertical axis is the time to trap. The induced charge includes the contribution from electrons and holes, while the electron time to trap is used for the vertical axis.

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Figure 15b

The average fraction of charge collected as a function of the starting location and the time to be trapped for (a) the same pixel as the electron--hole pair generation, (b) the neighbour pixel in the short-pitch (50 μm) direction and (c) the neighbour pixel in the long-pitch (250 μm) direction. For illustration, in this figure only, the electric field is simulated without radiation damage and the vertical axis is the time to trap. The induced charge includes the contribution from electrons and holes, while the electron time to trap is used for the vertical axis.

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Figure 15c

The average fraction of charge collected as a function of the starting location and the time to be trapped for (a) the same pixel as the electron--hole pair generation, (b) the neighbour pixel in the short-pitch (50 textmu m) direction and (c) the neighbour pixel in the long-pitch (250 textmu m) direction. For illustration, in this figure only, the electric field is simulated without radiation damage and the vertical axis is the time to trap. The induced charge includes the contribution from electrons and holes, while the electron time to trap is used for the vertical axis.

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Figure 16

A schematic set-up of the geometry for the TCAD simulation of 3D sensors. The dashed box shows the unit cell that is simulated and tessellated to produce an entire pixel.

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Figure 17a

Simulated magnitude of the electric field as a function of local x and y in an ATLAS IBL 3D sensor with a bias voltage at V_bias = -40 V for (a) an unirradiated sensor and (b) for a fluence of 5 x 10¹⁴ n_eq/cm². The doping type of the columns is indicated.

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Figure 17b

Simulated magnitude of the electric field as a function of local x and y in an ATLAS IBL 3D sensor with a bias voltage at V_bias = -40 V for (a) an unirradiated sensor and (b) for a fluence of 5 x 10¹⁴ n_eq/cm². The doping type of the columns is indicated.

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Figure 18a

The projected (in the absence of trapping) time for electrons and holes to drift from their point of generation to the corresponding collecting electrode for an ATLAS IBL 3D sensor. (a) and (c) are computed for unirradiated sensors, respectively, for electrons and holes; (b) and (d) show the ratio of the time for a fluence of 5× 10¹⁴ n_eq/cm² to the time for no radiation damage for electrons and holes, respectively.

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Figure 18b

The projected (in the absence of trapping) time for electrons and holes to drift from their point of generation to the corresponding collecting electrode for an ATLAS IBL 3D sensor. (a) and (c) are computed for unirradiated sensors, respectively, for electrons and holes; (b) and (d) show the ratio of the time for a fluence of 5× 10¹⁴ n_eq/cm² to the time for no radiation damage for electrons and holes, respectively.

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Figure 18c

The projected (in the absence of trapping) time for electrons and holes to drift from their point of generation to the corresponding collecting electrode for an ATLAS IBL 3D sensor. (a) and (c) are computed for unirradiated sensors, respectively, for electrons and holes; (b) and (d) show the ratio of the time for a fluence of 5× 10¹⁴ n_eq/cm² to the time for no radiation damage for electrons and holes, respectively.

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Figure 18d

The projected (in the absence of trapping) time for electrons and holes to drift from their point of generation to the corresponding collecting electrode for an ATLAS IBL 3D sensor. (a) and (c) are computed for unirradiated sensors, respectively, for electrons and holes; (b) and (d) show the ratio of the time for a fluence of 5× 10¹⁴ n_eq/cm² to the time for no radiation damage for electrons and holes, respectively.

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Figure 19

The Ramo potential for an ATLAS 3D sensor as computed with TCAD. The two n⁺ electrodes of the centre pixel are electrically connected and therefore both are held at unit potential in the calculation of the Ramo potential. The circular holes are due to the p⁺ electrodes. White numbers indicate the maximum induced charge (normalized to one electron charge) in that pixel considering all starting positions and trapping times in the central pixel. A red dashed rectangle shows which pixels are included in the simulation.

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Figure 20

An illustration of charge trapping and the Ramo potential in one-half of a 3D sensor. The initial electrons originate from the top right corner of the plot (indicated by a star). Under the influence of the electric field, they drift toward the n⁺ electrode in the centre. As they drift, there is a chance that they get trapped. Markers indicate the location of trapped charges and the colour shows the induced charge. The process is repeated many times, with diffusion. The simulated bias voltage was -20 V.

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Figure 21

The charge collection efficiency as a function of integrated luminosity for 80 V, 150 V, and 350 V bias voltage. A linear trendline is added to the simulation to guide the eye. The bias voltage was increased during data-taking, so the data points are only available at increasing high-voltage values. The points are normalized to unity for a run near the beginning of Run 2. The uncertainty on the simulation includes variations in the radiation damage model parameters as well as the uncertainty in the luminosity-to-fluence conversion. Vertical uncertainty bars on the data are due to the charge calibration drift. Horizontal error bars on the data points due to the luminosity uncertainty are smaller than the markers.

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Figure 22a

(a) The mean transverse cluster size versus transverse incidence angle near the end of the 2016 run (about 2× 10¹⁴ n_eq/cm²) with a bias voltage of 80 V. (b) The change in the Lorentz angle (θ_L) from the unirradiated case as a function of the integrated luminosity in 2015-2016. Two TCAD radiation damage models are considered, Chiochia and Petasecca.

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Figure 22b

(a) The mean transverse cluster size versus transverse incidence angle near the end of the 2016 run (about 2× 10¹⁴ n_eq/cm²) with a bias voltage of 80 V. (b) The change in the Lorentz angle (θ_L) from the unirradiated case as a function of the integrated luminosity in 2015-2016. Two TCAD radiation damage models are considered, Chiochia and Petasecca.

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