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Basic Information for GPC2337_X_023_B_H2
Brief description of DB components associated to this Hybrid Assembly and associated tests
Shown below are results for the glue weight measurements
IService::UPLOADDB INFO Working on test code ASIC_GLUE_WEIGHT
GlueWeightSvc::uploadDB INFO Formatting database test for ASIC_GLUE_WEIGHT
IService::UPLOADDB INFO Working on test code VISUAL_INSPECTION
IService::log INFO Logging status 0111 for component GPC2337_X_023_B_H2
IService::install INFO Installing output directory to /home/data/modules/GPC2337_X_023_B_H2/GlueWeightHybridASIC_PROD_v2-1/
IService::install INFO Installed warningLog.txt...
IService::install INFO Installed errorLog.txt...
IService::install INFO Installed infoLog.txt...
IService::install INFO Installed 20USBHX2003105_image.jpg...
IService::install INFO Installed DB_COMMENTS.json...
IService::install INFO Installed DB_READY_HYBRID_ASSEMBLY_ASIC_GLUE_WEIGHT.json...
IService::install INFO Installed DB_READY_HYBRID_ASSEMBLY_VISUAL_INSPECTION.json...
IService::install INFO Installed GPC2337_X_023_B_H2.root...
IService::install INFO Installed status.json...
TopControl::monitor INFO Service with algoirthm name GlueWeightModule_LS_PPA ignored through users request!
TopControl::monitor INFO Service with algoirthm name GlueWeightModule_SS_PPA ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridBonding_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ModuleBonding_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridPullTest ignored through users request!
TopControl::monitor INFO Service with algoirthm name PullTestCicorelCard ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridFlexArray_PullTest_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name Powerboards_PullTest_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ABC_PullTest_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ABC_Wafer_PullTest_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HCC_PullTest_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name SensorBondingQC_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HVTabSheet_SheerTest_Before_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HVTabSheet_SheerTest_After_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name PhotoUpload ignored through users request!
TopControl::monitor INFO Service with algoirthm name PictureModule ignored through users request!
TopControl::monitor INFO Service with algoirthm name GeneralPictures ignored through users request!
TopControl::monitor INFO Service with algoirthm name PreHVTabIV ignored through users request!
TopControl::monitor INFO Service with algoirthm name SensorIV_PreTabIV_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name Module_postHVTabIV_LS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name SensorIV_PostTabIV_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ElectricalIV ignored through users request!
TopControl::monitor INFO Service with algoirthm name SensorIV_Module_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name SensorIV_AMACIV_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name SixWayJig_Y_slots ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridMetrology ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridPanelMetrology ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridPanelMetrology_v7 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridMetrology_v8 ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridMetrology_Y_v8 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_v10 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_v10-beta ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_Y_v0_thin ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_Y_v0_thin_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_X_v2 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_X_v2_thick ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_X_v2_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyHybrid_PROD_X_v2_thick_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name HybridToSensorMetrology_v2a ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_v8 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_v8a ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PPA_SS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PPB_SS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PPB_SS_wuerth_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PPB_LS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_LS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_SS_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_LS_v1_thin ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_LS_v1_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_LS_v1_thin_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_SS_v1_thin ignored through users request!
TopControl::monitor INFO Service with algoirthm name MetrologyModules_PROD_SS_v1_thin_interposer ignored through users request!
TopControl::monitor INFO Service with algoirthm name ModuleLS_Bow_PPA_v0 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ModuleSS_Bow_PPA_v0 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ElectricalHybrids ignored through users request!
TopControl::monitor INFO Service with algoirthm name ElectricalHybrids_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name BurnInHybrids_PPB_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name BurnInHybrids_PROD_v2 ignored through users request!
TopControl::monitor INFO Service with algoirthm name ElectricalModules_PPA_v1 ignored through users request!
TopControl::monitor INFO Service with algoirthm name TCModules_PROD_v0 ignored through users request!
Metadata
Value
Component type
Operator
KA
Date
2025-07-16T22:06:48.893+00:00
Program
ASIC-X.SRC
Field
Weight/Volume
Assummed density of glue
1.077
Total volume of ASIC glue [uL]
41.697
Volume per glue dot [nL]
801.869
Weight of glue under ASICs [mg]
44.900
Weights of bare hybrid [g]
3.314
Weights of stuffed hybrid [g]
3.359
Metrology results
Shown below are the results of the module metrology scans
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_0] Height in z : 437.701000 +/- 3.165250 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_0] Height in z : 66.519750 +/- 12.887728 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 371.181250
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 71.181250 +/- 14.181408 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 372.181250 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_1] Height in z : 428.183750 +/- 2.091250 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_1] Height in z : 66.820889 +/- 5.650333 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 361.362861
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 61.362861 +/- 7.829406 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 362.362861 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_2] Height in z : 421.509250 +/- 3.008750 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_2] Height in z : 54.443889 +/- 8.013167 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 367.065361
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 67.065361 +/- 9.912791 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 368.065361 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_3] Height in z : 414.607500 +/- 3.488500 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_3] Height in z : 49.301444 +/- 6.835500 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 365.306056
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 65.306056 +/- 9.159350 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 366.306056 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_4] Height in z : 410.295250 +/- 3.433250 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_4] Height in z : 52.262667 +/- 6.978667 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 358.032583
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 58.032583 +/- 9.246026 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 359.032583 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_5] Height in z : 405.568750 +/- 2.328000 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_5] Height in z : 53.940111 +/- 6.387667 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 351.628639
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 51.628639 +/- 8.439305 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 352.628639 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_6] Height in z : 403.078000 +/- 2.568250 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_6] Height in z : 43.442667 +/- 5.743000 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 359.635333
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 59.635333 +/- 8.036041 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 360.635333 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_7] Height in z : 401.189750 +/- 2.598500 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_7] Height in z : 42.883778 +/- 6.095167 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 358.305972
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 58.305972 +/- 8.300799 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 359.305972 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_8] Height in z : 401.548750 +/- 2.896250 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_8] Height in z : 44.869111 +/- 7.585000 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 356.679639
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 56.679639 +/- 9.535224 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 357.679639 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_9] Height in z : 404.089250 +/- 3.022000 um
MetrologySvc::analyzeGlueHeights INFO ----> [ABC_X_9] Height in z : 37.881625 +/- 13.533493 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 366.207625
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 66.207625 +/- 14.740690 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 367.207625 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeGlueHeights INFO Printing associated surfaces...
MetrologySvc::analyzeGlueHeights INFO ----> [HCC_X_0] Height in z : 413.147250 +/- 0.984750 um
MetrologySvc::analyzeGlueHeights INFO ----> [HCC_X_0] Height in z : 37.785375 +/- 5.125464 um
MetrologySvc::analyzeGlueHeights INFO ----> Difference in heights : 375.361875
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue assuming 300.000000 +/- 5.000000 extra material : 75.361875 +/- 7.227732 um
MetrologySvc::analyzeGlueHeights INFO ----> Thickeness of glue using derived value -1.000000 from hybrid measurements : 376.361875 um
MetrologySvc::analyzeGlueHeights INFO ---------------------------------------------------------------------------------
MetrologySvc::analyzeHybridThickness INFO Total stack up 1005.528500, chip thickness 300.000000 and glue 71.181250, giving hybrid 634.347250 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 999.773330, chip thickness 300.000000 and glue 61.362861, giving hybrid 638.410469 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 996.086071, chip thickness 300.000000 and glue 67.065361, giving hybrid 629.020710 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 991.878927, chip thickness 300.000000 and glue 65.306056, giving hybrid 626.572871 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 990.848657, chip thickness 300.000000 and glue 58.032583, giving hybrid 632.816073 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 989.086925, chip thickness 300.000000 and glue 51.628639, giving hybrid 637.458286 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 988.015379, chip thickness 300.000000 and glue 59.635333, giving hybrid 628.380046 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 985.965464, chip thickness 300.000000 and glue 58.305972, giving hybrid 627.659492 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 985.939921, chip thickness 300.000000 and glue 56.679639, giving hybrid 629.260282 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 989.357693, chip thickness 300.000000 and glue 66.207625, giving hybrid 623.150068 thickness
MetrologySvc::analyzeHybridThickness INFO Total stack up 994.510250, chip thickness 300.000000 and glue 75.361875, giving hybrid 619.148375 thickness
IService::UPLOADDB INFO Working on test code ASIC_METROLOGY
MetrologySvc::uploadDB INFO Doing DB upload...
MetrologySvc::writeOutput INFO Writing common output file /home/data/output//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H2/1//Data__GPC2337_X_023_B_H2.txt
MetrologySvc::writeOutput INFO Writing results output file /home/data/output//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H2/1//Results__GPC2337_X_023_B_H2.txt
MetrologySvc::writeOutput INFO Writing common output file /home/data/output//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H2/1//Data__GPC2337_X_023_B_H2.txt
MetrologySvc::writeOutput INFO Writing results output file /home/data/output//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H2/1//Results__GPC2337_X_023_B_H2.txt
IService::log INFO Logging status 0111 for component GPC2337_X_023_B_H2
IService::install INFO Installing output directory to /home/data/modules/GPC2337_X_023_B_H2/MetrologyHybrid_PROD_X_v2_thick_interposer-1/
IService::install INFO Installed warningLog.txt...
IService::install INFO Installed errorLog.txt...
IService::install INFO Installed infoLog.txt...
IService::install INFO Installed Summary.pdf...
IService::install INFO Installed TotalStackUp.pdf...
IService::install INFO Installed HybridThickness.pdf...
IService::install INFO Installed Positions.pdf...
IService::install INFO Installed Tilt.pdf...
IService::install INFO Installed Data__GPC2337_X_023_B_H2.txt...
IService::install INFO Installed Results__GPC2337_X_023_B_H2.txt...
IService::install INFO Installed Results.json...
IService::install INFO Installed DB_READY_HYBRID_ASSEMBLY_ASIC_METROLOGY.json...
IService::install INFO Installed GPC2337_X_023_B_H2.root...
IService::install INFO Installed status.json...
MetaData::readField INFO Reading file /home/data/upload//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H3-1.config
IService::next INFO Scheduling GPCGPC2337-X-023-B0-2-3-4-5-6.txt file to run...
IService::next INFO Writing results to /home/data/output//MetrologyHybrid_PROD_X_v2_thick_interposer//GPC2337_X_023_B_H3/1/
MetaData::getLocalName WARNING Could not find a local name for identifier 20USBHN0005670
Measurement::addPoint ERROR Unknown type ?! Ignoring!
The thickness of the glue \(t_{glue}\) is calculated as:
$$t_{glue} = \frac{1}{N_{c}}\sum_{c=1}^{N_{c}} z_{c} - \frac{1}{N_{b}}\sum_{b=1}^{N_{b}} z_{b} - t_{chip} $$
where \(t_{chip}\) is the thickness of the chip
\(z_{i}\) is the z-height measurement,
\(N_{i}\) is the number of measurements on a given surface,
and \(c\) and \(b\) run over measurements taken on the chip and base, respectively.
The assumed thickness of the chip is \(t_{chip} = 300\mu m\).
Uncertainties on the glue height measurement are estimated from the spread in z-height measurements on a given surface.
On a given surface, the height uncertainty \(\sigma_{i}\) is calculated as:
$$\sigma_{i} = \frac{\Delta z}{2\sqrt{N_{i}}}$$
where \(\Delta z = z_{max} - z_{min}\) and \(z_{max}\) and \(z_{min}\) are the maximum and minimum z-height measurements, respectively.
In addition, a conservative \(\sigma_{chip} = 10\mu m\) uncertainty on the chip thickeness is assumed.
The total uncertainty is calculated as:
$$\sigma_{glue} = \sqrt{ \sigma_{c}^2 + \sigma_{b}^2 + \sigma_{chip} }$$
The glue thickness measurements for each ASIC are shown in the figure and table below.
The thickness total stack up is measured from the top of the each chip to the jig,
and accounts for the combined thickness of hybrid flex, glue, and ABC/HCC chips in the case of hybrid.
The positions of the ASICs are measured on the 95x95 \(\mu m^2\) square pads on the opposite side of the sensor wire bonds.
These measured positions are compared against the technical drawns to calculated the relative ASIC position.
In some cases, the SmartScope incorrectly measures a different object than these square pads,
and using properties (such as the perimeter), the position is corrected.
The positions are shown in the figure below. If any corrections are applied, they are shown as transparent points.
The hybrid thickness is plotted below. It is calculated from the total stack up height minus the assembed chip thickness and measured glue thickness.
The tilt of a chip can be calculated in either the direction along the surface of a chip. We define
the x-direction to be any points whose difference is much larger along x, and similarly for y. The tilt in both cases is defined to be:
$$tilt = \frac{|\Delta z|}{\sqrt{\Delta x^{2} + \Delta y^{2}}} $$
