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

Hardware measurements of wafer distortions SCT barrel : NIM A 568 (2006) 642-671 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

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

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) 353-389 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)

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 :

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

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

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)

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

Simulation of Wafer Bowing MC sample : single muons from origin, p = 100 GeV/c simulated and reconstructed using 13.0.10 SCT_Digitisation-00-09-25 plus TOF bug fix perfectly aligned geometry ATLAS-CSC-02-00-00 50mm range cut, 50mm step limitation (results insensitive to this  treatment of secondary steps not critical) most plots for , 50k muons

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

Shift in local x of clusters due to bowing

Shift in local x of spacepoints due to bowing

Shift in local x of spacepoints due to bowing

Shift in local y of spacepoints due to bowing

Shift in local y of spacepoints due to bowing

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

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

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

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

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

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

Bias on track fit parameters vs rapidity

Average track fit pulls vs rapidity

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

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

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

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

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 …

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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