Reconstruction and Analysis

The collected data are reconstructed with EUTelescope. No hardware configuration, i.e.

FE parameter, is used to limit the accepted LV1 windows. Hence, 16 subsequent LV1 windows are read out. Data are collected with a MIO3 board and a BIC adapter card.

The default, newly implemented, STcontrol producer, as described in Section 6.2, is used for DAQ.

Prior to clustering, noisy pixels are removed. A newly introduced processor allows the selection of pixel hits with a specified LV1 value for a given DUT. Furthermore, the possibility to set a cut on the charge, i.e. ToT, was implemented. A flow diagram of the

Data5Conversion

Noisy5Pixel5Removal

Clustering5EAllf Temporal5Cut5ELV1:54f

ELV1:55f ELV1:56f ELV1:57f

Clustering5ELV1:58f Clustering5ELV1:54f

Temporal5Cut5ELV1:58f

Hit5Derivation5EAllf Hit5Derivation5ELV1:58f

Hit5Derivation5ELV1:54f

Alignment5EAllf

Track5Fit5EAllf

Efficiency5EGlobalf Efficiency5ELV1:58f

Efficiency5ELV1:54f

''5FF5'' ''5FF5'' ''5FF5''

''5FF5'' ''5FF5'' ''5FF5''

''5FF5'' ''5FF5'' ''5FF5''

''5FF5'' ''5FF5'' ''5FF5''

Figure 9.10.: The strategy used in the reconstruction and analysis of the in-time effi-ciency measurements. On the left, the same reconstruction steps are per-formed for the various LV1 bins.

analysis is shown in Figure 9.10, where the mentioned initial steps are the same for all the following reconstruction branches.

In order to only look at data from a single LV1 bin, raw data collections for the various LV1 windows are created and processed. This is done by using the LV1 information and cloning entries with an appropriate LV1 value into the new collection. To obtain a precise alignment, also a collection without any cuts is processed and used (the branch on the right in Fig. 9.10). This is done to not reduce statistics or to bias the hits because of time-walk effects.

Every raw data collection is processed in the clustering and hit position derivation step. The unmodified collections are used for pre-alignment and alignment. Alignment constants are obtained in an iterative two-step alignment approach.

In order to validate the track fit, every run was analysed and a fit to the residual distribution was performed. This is exemplarily shown for the first run used in the analysis, run 4009 in Figure 9.11.

The parameters for the residual fit in x-directions are the following, whereH(x)is the unit step function and erf() the (Gauss) error function:

−0.2 −0.1 0 0.1 0.2

(a) Fit with Eq. 9.1 of the residual distribution in x-direction. The obtained fit results are given in the box.

(b) The same histogram and fit for the residual distribution in y-direction. The σ parame-ter is derived from the x-direction fit.

Figure 9.11.: Residual distribution after the fitter step used to validate the data. Shown is run 4009.

The obtainedσ from the residual fit in x-direction is used as a fixed parameter in the y-direction fit. This is done because the residual distribution contains multiple sized clusters and hence the y-direction distribution is assumed to have a more pronounced peak in the centre due to the smaller pixel pitch in that direction. The σ however is merely dominated by the tracking resolution of the telescope and charge sharing properties in the pixel sensors. Assuming similar charge sharing along both pixel edges and the tracking resolution being isotropic, theσfrom the x-direction residual fit is used to obtain a better estimate of the y-distribution’s width.

The distance between the falling edge and rising edge, as given by x_fall and x_rise in the fit, are used to extract the width. For all runs used in the analysis, the width in both directions as well as the σ parameter are fitted and plotted in Figure 9.12. The deviations from the nominal pixel pitch of250µm in x-direction and50µm in y-direction are approximately 3.5 µm in both directions. The smaller residual width is expected due to charge sharing between adjacent pixels. No difference of the absolute deviation between expected and measured residual width in x- and y-direction is anticipated, i.e.

the same value is expected in both directions. This is reflected in the observed result.

The σ parameter is a measure of the intrinsic tracking resolution convolved with the turn on behaviour of the pixel, governed by the charge collection properties. The fit result of σ = 14.5 µm are slightly higher than the previously reported 10 µm we

242 244 246 248 250 252 µm]

box-fit width in x-direction [ 0

(a) The obtained box-width in x-direction.

The mean width is at(246±0.9)µm.

40 42 44 46 48 50 52 54

µm]

box-fit width in y-direction [ 0

(b) The obtained box-width in y-direction.

The mean width is at (46.4±1.6)µm.

Figure 9.12.: The box widths andσfrom the fit for runs used in the subsequent analysis.

All the processed runs are well centred with no significant outliers.

obtained during the HV-CMOS measurements with a similar set-up [97]. However, the HV-CMOS test beam investigated sub-pixel encoding and the set-up was optimised for in-pixel studies and the beam energy was at 5 GeV compared to the 4 GeV. The 4 GeV were used to increase the trigger rate which is already decreased by a factor of five due to the gating window. The tracking resolution is sufficient for any global in-time studies.

9.3.1. Efficiency Definition

The analysed runs all have at least10⁵ triggers with 1-2 tracks per trigger in the active time window of the FE-I4, which all contribute to the global efficiency. The statistical uncertainty in the case of non-extreme efficiencies, i.e. away from 1 and 0 with a sufficient number of events, should be estimated as a binomial uncertainty. This yields δε =

1/Np

Nε(1ˆ −ε)ˆ where the measured efficiency as given by the number of observed tracks divided by the expected tracks is used as a best estimator for ε. Assumingˆ N ≈ 10⁵ the statistical uncertainties are in the order of 0.04% and thus neglected as they are a magnitude smaller than the assumed systematical uncertainty. The above definition is used as the estimator for the efficiency, the number of observed tracks in the fiducial region divided by the number of expected tracks in that region:

ε= #observed tracks|fiducial region

#expected tracks|fiducial region (9.2) The expected tracks are determined by the reference sample. This poses a possible bias and would be true if an inefficiency of the reference sample is correlated to an inefficiency on the DUT. For example, if the FE-I4 suffered from an inefficient lower left corner region and this were the case for the reference sample as well as the DUT, the measurement of the overall efficiency would be biased as the sensors’ inefficiency is spatially correlated. Another bias could arise if the FE-I4 were inefficient in a temporal fashion as the FE clocks are completely correlated by the DAQ system.

No such behaviour of the FE-I4 has been reported. Assuming no hidden correlated inefficiencies, the determined efficiency is not biased by the reference sample.