Study of the intrinsic spatial resolution

The intrinsic spatial resolution of the DEPFET prototypes is measured by comparing the center of gravity of clusters to the reference hit position provided by the telescope. The distribution of these track residuals

column

Figure 5.8.: Profile of the mean seed charge for individual columns (left) and rows (right) of Module A exposed to120GeV pions at CERN. The global mean seed charge averaged over all pixel columns or rows is equal to3130signal electrons. The variations of the mean seed signal per column (row) is sensitive to variations of pixel gains(g_q)and channel by channel variations on the ADC chip (DCDB). The observed variation of the mean seed signal is smaller than

±100electrons.

Figure 5.9.: Cluster signal (left) as a function of the incident angle θ = arctant_v of the incoming particle. The incident angle in the other directionarctant_u is close to zero. The cluster signal (left) and cluster size (right) increases with the incident angle as expected. Histograms are normalized to unit area.

µm

Figure 5.10.: Measured residual distribution for the case of 120GeV pions at perpendicular incidence for Module A. The width of the residuals is9.6µm (RMS99) and17.8µm (RMS99). The simulated detector resolution function is smeared with a Gaussian error in order to simulate the estimated telescope pointing resolution of1.5µm.

allows to estimate the spatial resolution after subtracting the pointing resolution of the telescope. The method to infer the spatial resolution from track residuals was introduced and tested in section 4.4.2.1.

The key point is an accurate estimation of the pointing resolution of the telescope using a Kalman Filter based track fitting which takes into account multiple scattering and telescope alignment corrections.

In the case of the detector simulation, the distribution of position measurement errors can be obtained directly by comparing the center of gravity of the cluster to the true intersection coordinates of the particle as described in section 3.4.

The residual distribution for the measurements of the intersection coordinates perpendicular to and along the columns are shown in Fig. 5.10. The residual distribution is obtained for Module A during a test beam at CERN with 120GeV pions at perpendicular incidence. The pointing resolution of the EUDET telescope estimated by the track fitter is1.5µm. This is significantly better than the expected intrinsic spatial resolution of the DEPFET module. The measured residuals are compared to the sim-ulated distribution of true position measurement errors smeared with the estimated telescope pointing resolution of1.5µm. The detector simulation describes the shape of the residuals well in theudirection.

The width of the residuals is taken as the root mean square of the central99 %of data points (RMS99).

The width of the residuals in the u direction is9.6µm for Module A and 9.5µm for the simulation.

However, the measured residual distribution in the vdirection shows two shoulders which are not re-produced in the simulation. The appearance of shoulders causes a discrepancy between the width of the residuals from simulation (17.0µm) and test beam data (17.7µm). The origin of these shoulders is still under investigation.

In Fig. 5.11 (left) the effect of the non-perpendicular incident particles on the cluster size is shown.

The average cluster size grows and the spatial resolution improves while rotating the DEPFET module to tilt angles θranging from 0^◦ to46^◦. The data is obtained from a test beam at DESY with3GeV electrons and agrees well with the results from the detector simulation. The intrinsic spatial resolution

[degree]

Figure 5.11.: Mean cluster size (left) as a function of the incident angleθ= arctant_v of the incoming particle. The incident angle in the other directionarctantu is close to zero. The mean number of rows in a cluster increases from1.2 to 1.6 for the largest measured incident angle of46^◦. The positive effect of having larger clusters is visible on the spatial resolution (right). The resolutionσv in thev direction is obtained after quadratic subtraction of the telescope pointing resolution and drops from17.7µm to9.9µm for46^◦.

of Module A with 50×75µm² pixels is measured to be 9.6µm (17.8µm) in the short (long) pixel direction in the case of perpendicular incidence. The simulation shows that a minimum resolution of 6.7µm could be achieved in the long pitch direction for even larger tilts of55^◦. At this rotation angle, the average number of hit rows in clusters is1.8and the center of gravity is able to interpolate an improved hit position from the signals of the two rows. At even larger angles, the cluster size quickly increases and the signal interpolation is less beneficial. In theudirection, the mild increase in the mean number of hit columns is a secondary effect caused by the overall increase of signal charge in clusters. The quoted error on the measured spatial resolution quickly grows with the tilt angle. The origin of this effect is the increased spacing between the two arms of the EUDET telescope which is needed to accommodate the tilted DEPFET module in the center of the telescope. The pointing resolution at the central DEPFET module depends on the spacing between the arms and degrades from5.7µm at perpendicular incidence to16.4µm for a rotation angle of46^◦. The error on the measured spatial resolution is dominated by the assumption of an5 %uncertainty on the estimated telescope pointing resolution.

The spatial resolution of the DEPFET modules operated in Belle II depends on the incidence angle of tracks, the pitch of pixels in theuandvdirection and the sensor thickness. For this reason, the spatial resolution reported here can not be applied immediately in the Belle II environment. The detector simulation provides a good model for the data obtained from test beams. Moreover, it contains enough detector physics to extrapolate the estimated spatial resolution from the test beam environment to the Belle II case.