Semiconductor Silicon Interposer Warpage Calculator
Subtract independently established local reference plane from actual silicon interposer survey before warp extraction; not raw extrema or geodesy/datum transformation.
Description
Interposer warpage depends on the reference plane removed from a height survey.
Interposer warpage depends on the reference plane removed from a height survey.1
A supplied plane separates local residual height variation from overall offset and tilt.
When to use Semiconductor Silicon Interposer Warpage Calculator
Use this tool when you need to reproduce the stated calculation from measured records or independently selected model inputs. Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
How to use Semiconductor Silicon Interposer Warpage Calculator and understand its results
- Prepare measured device or specimen records under independently matched branch, temperature, frame, and unit conventions.
- Enter observedInterposerReferencePlaneCoefficients, observedInterposerXyM, observedInterposerHeightsM, following the field table and rules below, then run the tool.
- Read referenceSubtractedInterposerHeightsM, observedReferenceSubtractedInterposerWarpM. Use the output meanings below to interpret units, signs, flags, and any nested result fields.
- Correct reported input issues and run again. For a successful result, check the stated evidence coverage and assumptions before using it in your review.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedInterposerReferencePlaneCoefficients | Observed interposer reference plane coefficients | list of number | Required |
| observedInterposerXyM | Observed interposer xy m | numeric matrix | Required |
| observedInterposerHeightsM | Observed interposer heights m | list of number | Required |
Use nonempty two-column x/y points in metres with aligned heights and exactly three finite plane coefficients [offset,xSlope,ySlope]. Subtract offset plus both slope terms at each point; return residuals and max minus min. The plane is not fitted here.
residual_i=z_i−a−bx_i−cy_i; warp=max(residual)−min(residual) Symbols follow the input and output meanings and the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| referenceSubtractedInterposerHeightsM | Reference subtracted interposer heights m | list of number |
| observedReferenceSubtractedInterposerWarpM | Observed reference subtracted interposer warp m | number |
{
"input": {
"observedInterposerReferencePlaneCoefficients": [
1,
2,
3
],
"observedInterposerXyM": [
[
0,
0
],
[
1,
0
],
[
0,
1
]
],
"observedInterposerHeightsM": [
1,
4,
4
]
},
"output": {
"referenceSubtractedInterposerHeightsM": [
0,
1,
0
],
"observedReferenceSubtractedInterposerWarpM": 1
}
}Limitations and assumptions
Matched measurement branch, material state, calibration, and conventions must be independently established. Results do not certify device performance or operating conditions.
Missing required fields, unknown fields, wrong types, and violated calculation rules are input issues. Numeric values must be finite; nonfinite results are rejected. Evidence arrays must be dense, with no missing cells. Numeric observation lists allow at most 10,000 entries, subject to any smaller bounds stated above. Numeric matrices are limited to 128 rows and 128 entries per row, with rectangularity required where stated.
Alternative or Complementary methods
For a related review, use Semiconductor Wlcsp Die Size To Package Ratio Calculator: A wafer-level chip-scale package footprint can be compared with its enclosed rectangular die. The die fraction and package overhang area describe footprint efficiency without evaluating the bump layout. For a complementary step, use Semiconductor Shallow Trench Isolation Stress Calculator: A reduced elastic stiffness matrix maps three strain components to three stress components in a declared local convention. Its component and shear conventions must match the supplied strain vector.
References
Similar or alternative tools
- Semiconductor Wlcsp Die Size To Package Ratio Calculator
A wafer-level chip-scale package footprint can be compared with its enclosed rectangular die. The die fraction and package overhang area describe footprint efficiency without evaluating the bump layout.
- Semiconductor Shallow Trench Isolation Stress Calculator
A reduced elastic stiffness matrix maps three strain components to three stress components in a declared local convention. Its component and shear conventions must match the supplied strain vector.