1. SCT Wafer Distortions (Bowing)
SCT Offline Software Meeting
24th April 2008
Richard Batley
(Cambridge)
Summary of SCT wafer distortion measurements
Estimate of possible effects using single muon MC
try to assess whether SCT wafer bowing needs to be included in simulation, or corrected for in reconstruction

2. Hardware measurements of wafer distortions
SCT barrel :
NIM A 568 (2006)
wafer surface heights were measured on a 10 x 5 grid for axial and stereo sides of all modules
use the height at each grid point averaged over all barrel wafers to derive a “common profile” :
Y values (mm)
-0.1
-0.08
-0.06
-0.04
-0.02
0.02
0.04
-80.0
-60.0
-40.0
-20.0
0.0
20.0
40.0
60.0
80.0
X mm
-31.5
-15.8
15.8
31.5
X values (mm)
-0.1
-0.08
-0.06
-0.04
-0.02
0.02
0.04
-40.0
-20.0
0.0
20.0
40.0
Y mm
-63.8
-48.0
-32.1
-16.2
-0.3
0.3
16.2
32.1
48.0
63.8

3. Bowing has opposite sign on axial and stereo sides
 axial and stereo wafer corners bow towards each other
(axial-stereo separation at wafer corners is ~150 mm less than separation at wafer centre)
Fluctuations around common profile :
rms = 10 mm
maximum deviation from common profile for upper surface of each barrel module

4. Temperature dependence :
(measurements were made at room temperature)
studied with four dummy modules
temperatures T = -17, -6, +7, +21, +39 oC
find movements ~ 1.3 mm / oC at corners
(in which direction ?)
SCT endcaps :
NIM A 575 (2007)
endcap wafer surface heights were measured over a grid of points, similarly to barrel
no real discussion of wafer distortions in paper
but anyway expect negligible impact from bowing in endcaps (since endcap modules are not tilted)

5. Effect of wafer distortions
For an SCT barrel module, viewed transverse to strips :
track
nominal mid-plane position, side 0
mid-plane positions after bowing
nominal mid-plane position, side 1
Estimate average cluster shift :

6. Similarly, for an SCT barrel module viewed longitudinally :
track
side 0
side 1
Expect negligible effect on reconstructed cluster position

7. Effect of wafer distortions on spacepoints
Layers 0, 2
15 mm
15 mm
~ 750 mm
Layers 1, 3
15 mm
15 mm
Dx to alternate in sign
for spacepoints, expect
Dz < 0 for all layers

8. Simulation of Wafer Bowing
Parameterise the barrel common profile using a simple piecewise-linear approximation, separately for xloc, yloc :
-0.08
-0.06
-0.04
-0.02
0.02
-80.0
-40.0
0.0
40.0
80.0
X mm
-0.02
-0.01
-40.0
-20.0
0.0
20.0
40.0
Y mm
Apply this bowing profile identically to every SCT wafer
(including endcaps)

9. Simulation of Wafer Bowing
“Simulate” bowing by modifying SCT_Digitisation :
shift effective position of each G4 step to mimic effects of wafer bowing :
(neglect slope of bowed surface)
(primary G4 steps only – exclude secondaries)
original track
effective position of track including bowing

10. Simulation of Wafer Bowing
MC sample :
single muons from origin, p = 100 GeV/c
simulated and reconstructed using
SCT_Digitisation plus TOF bug fix
perfectly aligned geometry ATLAS-CSC
50mm range cut, 50mm step limitation
(results insensitive to this 
treatment of secondary steps not critical)
most plots for , 50k muons

11. Clusters and Spacepoints
For clusters, consider
true local x of G4 hit for nominal wafer position (same with or without bowing)
Similarly, for spacepoints, consider
Plot with and without bowing applied …
Note that :
the average track angle to the wafer surface is smaller for xlocal > 0 than for xlocal < 0
even without bowing, already have due to an intrinsic position bias induced by the SCT digitisation model

12. Shift in local x of clusters due to bowing

13. Shift in local x of spacepoints due to bowing

14. Shift in local x of spacepoints due to bowing

15. Shift in local y of spacepoints due to bowing

16. Shift in local y of spacepoints due to bowing

17. Track fit residuals
Look at average “semi-unbiased” track fit residuals
as a function of (xloc,yloc) position on wafer
Find qualitatively similar shifts in average residuals to those seen already for clusters and spacepoints …
A correction for the cluster position bias has been applied in SCT_ClusterOnTrackTool 
average residual without bowing is close to zero

18. Average residuals vs local x, side 0
(stereo)
(axial)

19. Average residuals vs local x, side 1
(axial)
(stereo)

20. Average residuals vs local y, side 0
(stereo)
(axial)

21. Average residuals vs local y, side 1
(axial)
(stereo)

22. Effect of bowing on track fit parameters
For example, for the impact parameters d0 and z0 :
Find that bowing gives
- significant shift in average z0 and q in barrel region
- negligible shift in average d0, f0, p
- negligible effect on all track parameter resolutions

23. Bias on track fit parameters vs rapidity

24. Average track fit pulls vs rapidity

25. Average z0, q pulls vs rapidity
same as previous slide, but with finer binning in rapidity :
(making fine structure visible)

26. Track parameter resolutions vs rapidity
negligible effect on resolution from SCT bowing

27. SCT Pixels  Origin of bias on longitudinal track parameters
track reconstructed after bowing
true track
Pixels 

28. Effect of SCT bowing on pixel residual pulls
residuals in each pixel layer are biased as per diagram on previous slide

29. Summary  Wafer bowing in SCT barrel produces :
significant shifts in longitudinal track parameters
negligible effect on track resolution
visible effects in track residuals
(in an ideal, perfectly-aligned world, at least) 
SCT bowing cannot obviously be neglected …

30. confirm / discuss hardware measurements with detector experts
Possible next steps :
confirm / discuss hardware measurements with detector experts
would be straightforward to add a “common profile” bowing option to SCT_Digitisation
also straightforward to add a “common profile” bowing correction to SCT_ClusterOnTrackTool
apply individual distortion measurements for each wafer via CondDB ?
study interaction with detector alignment : -
do realistic wafer misalignments wash out the effects of bowing ? -
does bowing affect the alignment precision ?

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