1. Planar distortions for SCT Barrel Modules
Adrian Bevan
29th October 2013
Update of previous talk given on Oct 17th.
October 2013

2. Overview Recap of the problem Summary of my understanding Next steps
October 2013

3. Recap of the problem
The silicon sensors in each module of the SCT are non-planar, but the reconstruction code assumes that they are planar. The deviation between reality and REC scenarios is expected to lead to a bias on the reconstructed position of a space point in the SCT, hence may affect tracking performance.
Last week Anthony Morley made a few plots of the mean residual in the SCT, which shows a bias as a function of position in the detector.
Mean difference in residuals between sensors on the two sides of a module
Layer 0
Layer 1
October 2013

4. SCT Module deformation measurements
Plots taken from ATLAS-COM-INDET (Anna Mayne)
Along strips (CMM coords)
Perp. to strips (CMM coords)
Along strips (CMM coords)
Perp. to strips (CMM coords)
October 2013

5. SCT Module deformation measurements
Plots taken from ATLAS-COM-INDET (Anna Mayne)
October 2013

6. c.f. ATLAS Phase II upgrade sensors
c/o Bart Cam.
NOTE: These are not sensors used in the SCT
These sensors are 97 mm x 97 mm, so ~50% larger than the SCT ones. They do show similar bowing, but the direction of the bow is dependent on the sensor vendor.
"Ugly" looking plots are the result of flat sensors: the variation is consistent with the precision of the CMM.
"Nice" looking plots have a measureable bow. These sensors are convex: strips on top, corners bow up.
ATLAS 12 sensors from HPK are concave (corners down)
October 2013

7. Expected levels of bias on a reconstructed hit
Best case scenario (normal incidence).
For this scenario there is no issue.
Normal track incidence to module θ=0°.
Ideal (reconstruction) coordinates are overestimated by at most ~2.8μm (dominated by thermal contraction).
c.f. r−φ resolution of ~17μm, this bias is O(16%) of the design resolution, and 3.5% of the strip pitch.
c.f. z resolution of ~580μm this is completely negligible.
October 2013

8. Expected levels of bias on a reconstructed hit
45° angle of incidence relative to the plane of the module xm
true track trajectory
tmod = 1110μm
zm (ym)
ym (zm)
Δym=Δzm = 1110μm
In the vicinity of the centre of a sensor pair there is no expected bias on the reconstructed hit position, as the silicon is assumed to be flat about that point (epoxy used to glue silicon to baseboards via a vacuum jig).
This assumption can be tested later...
October 2013

9. Expected levels of bias on a reconstructed hit
45° angle of incidence relative to the plane of the module * xm
true track trajectory
tmod = 1110μm
zm (ym)
ym (zm) *
At the extremity of the sensor, there are biases in reconstructed in plane coordinates as noted before, but also a shift out of plane. The angle of incidence reconstructed will be smaller than the actual value.
October 2013

10. Expected levels of bias on a reconstructed hit
45° angle of incidence relative to the plane of the module * xm
true track trajectory
tmod = 1110μm
zm (ym)
ym (zm)
reconstructed track trajectory *
At the extremity of the sensor, there are biases in reconstructed in plane coordinates as noted before, but also a shift out of plane. The angle of incidence reconstructed will be smaller than the actual value.
There will be a bias in the xm, ym and zm coordinates as a result.
October 2013

11. Expected levels of bias on a reconstructed hit
It can be shown that
Halving/doubling the out of plane bias changes the bias in reconstructed angle by a factor of ~2 down/up.
~2° effect for θtrue= 11°
~4° effect for θtrue= 45°
This observable is almost independent of how thermal contraction is treated.
e.g. assume 80μm bow at edge
Worst case scenario, use the mid-point of the sensor to define the hit position in xm.
Best case scenario, assume the metal strip position defines the hit.
October 2013

12. Expected levels of bias on a reconstructed hit
So we can have biases on the reconstructed strip position in the SCT, but this is not what is important for tracking.
If the hit strip position is wrong by some amount as illustrated in the cartoon, then the associated "track stub" pivots about some point in the middle of the module, going from the true trajectory (solid) to the reconstructed trajectory (dashed).
This pivot point won't change much (<0.8μm at QA limit on bow), between the reconstructed and true locations, unless there is an asymmetry in the planar bowing of the sensors in a module.
Thermal contraction bias dominates at the extremities of the sensor: δthermal ~2μm, where
κ=3e-6/K (and there is no effect on the alignment offset coordinates for the centre of a sensor).
reconstructed track trajectory *
x=0
true track trajectory *
x=0
October 2013

13. Expected levels of bias on a reconstructed hit
So we can have biases on the reconstructed strip position in the SCT, but this is not what is important for tracking.
If the hit strip position is wrong by some amount as illustrated in the cartoon, then the associated "track stub" pivots about some point in the middle of the module, going from the true trajectory (solid) to the reconstructed trajectory (dashed).
This pivot point won't change much (<0.8μm at QA limit on bow), between the reconstructed and true locations, unless there is an asymmetry in the planar bowing of the sensors in a module.
Thermal contraction bias dominates at the extremities of the sensor: δthermal ~2μm, where
κ=3e-6/K (and there is no effect on the alignment offset coordinates for the centre of a sensor).
reconstructed track trajectory * *
true track trajectory * *
October 2013

14. Expected levels of bias on a reconstructed hit
So we can have biases on the reconstructed strip position in the SCT, but this is not what is important for tracking.
If the hit strip position is wrong by some amount as illustrated in the cartoon, then the associated "track stub" pivots about some point in the middle of the module, going from the true trajectory (solid) to the reconstructed trajectory (dashed).
This pivot point won't change much (<0.8μm at QA limit on bow), between the reconstructed and true locations, unless there is an asymmetry in the planar bowing of the sensors in a module.
Thermal contraction bias dominates at the extremities of the sensor: δthermal ~2μm, where
κ=3e-6/K (and there is no effect on the alignment offset coordinates for the centre of a sensor).
reconstructed track trajectory * *
true track trajectory
So: an 11 degree incident angle with an 80 [200] μm out of plane bow translates into a bias of 16 [38] μm on the reconstructed in-plane hit position.
Adding in thermal bias results in a 18 [40] μm bias on hit position. * *
October 2013

15. Expected levels of bias on a reconstructed hit
So we can have biases on the reconstructed strip position in the SCT, but this is not what is important for tracking.
Expect (at least) the following affects:
Thermal contraction shifts measured in-plane hits by ~2μm. This gives a small lateral translation to a reconstructed track trajectory.
The bias on the top and bottom side strip hits should cancel (to first order – assuming that there is an ideal assembly of SCT modules).
The track χ2 to be increased (using wrong residual hit coordinate to fit to in each module).
Alignment fit optimisation has to work harder to locate modules. More of a concern Re: local vs. global minimum determination.
By dfn. Incorrect covariance matrix V determined from fit which is input to matrix inversion.
Need to quantify effect on alignment constants
Asymmetric module construction is ignored here, but gives additional issues to be quantified.
True track
Reconstructed track * * * * * * * *
Cartoon exaggerating scale
October 2013

16. Summary/Next steps
The maximum bias on a hit strip position is at the extremity of a sensor:
Maximum effects at the level of 16-38μm [18-40μm] expected for tracks incident normal to SCT barrel cylinders.
Consistent with conclusion from previous study.
Consistent with the results from Anthony that show smaller results
The next logical step is to use the alignment software to explore this issue to correct for the effects noted in data by Anthony.
1) Evaluate the effect of the shift due to thermal contraction.
2) Once happy that this is accounted for then study deformation models wrt alignment.
October 2013