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A polished cross-section observes a plane, not the complete volume around a via. A small discontinuity can lie between two inspected planes and disappear during the material removal that connects them. A useful location plan therefore records where observations occur, what material is destroyed without observation and how the suspected defect position relates to both. More section images improve coverage only when their positions are known.
Measurement purpose
Define spatial coverage and missed-region limits for serial cross-sections through a suspected ceramic-via feature.
Specimens and conditions
- Target range
- Location evidence and uncertainty tied to the original specimen datum
- Feature geometry
- Relevant extent along the chosen removal direction and required recognition conditions
Equipment and records required
- Controlled preparation: Suitable sectioning and polishing with actual plane-position evidence
- Observation: Imaging capable of resolving the specified feature with traceable plane and orientation records
Method sequence
- Planning
Map target range, initial removal and intended observation planes
Record: Coverage and unobserved-interval plan
- Serial preparation
Measure positions and inspect before further irreversible removal
Record: Ordered plane-image register
- Conclusion
Distinguish observed absence from unexamined material
Record: Bounded spatial finding and remaining evidence
Decision and uncertainty
A negative section result applies only to the supported observed planes and detection conditions; material removed between planes is not automatically inspected.
Target localization, actual removal, feature shape and image recognition limit both geometric and analytical coverage.
The failure-analysis owner approves the coverage and stop decisions; the product owner defines which feature would alter disposition.
Traceable outputs
| Record | Required contents |
|---|---|
| Coverage register | Target range, datum, initial kerf, measured planes and unobserved intervals |
| Investigation conclusion | Ordered images, observed features, recognition limits and remaining specimen locations |
Method review decisions
- Map inspected planes and unobserved removal intervals separately.
- Set section spacing from the defect extent and location uncertainty relevant to the question.
- Do not interpret a clean section as proof that the whole via volume is sound.
Locate the suspected feature before choosing a cutting direction
Combine drawing coordinates with the observations that motivate the investigation: a localized electrical change, visible edge anomaly or other suitable nondestructive evidence. Preserve the uncertainty of that localization. A point marked on a photograph is not an exact three-dimensional position inside a ceramic stack.
Choose a direction in which the planned planes can intersect the feature of interest. A long interfacial separation may be well represented by one orientation, while a small isolated pore requires a different coverage argument. Record the relevant size along the serial-removal direction rather than relying only on the defect size visible in a surface image.
Draw the observed planes and the material between them
Represent every finished inspected plane by its measured position along a specimen datum. The interval between consecutive planes is material that has been removed. Unless another validated measurement observed it, that interval is not part of the optical section evidence. A folder containing ten images does not state how much volume those images cover.
Include the initial saw kerf and the material removed before the first recorded plane. A target lying in either region may already be gone when microscopy begins. Retaining a remaining half can preserve additional evidence, but its saw-adjacent surface also needs an explicit relationship to the original target coordinates.
Use a geometric spacing condition before discussing detection probability
For ideal parallel section planes separated by distance d, a feature whose continuous extent along the removal direction is greater than d must intersect at least one plane if it lies fully within the covered span. A feature shorter than d can fit entirely between planes. This is a geometric intersection statement, not a validated probability of detecting the feature in an image.
At equality, a limiting intersection may touch only a boundary and be practically unresolvable. The plan therefore needs margin for position error, feature shape and required image visibility. A narrow crack can have a large in-plane length while presenting a very small extent along the selected removal direction.
Quantify a deliberately limited section-spacing example
Consider ideal planes spaced one hundred micrometres apart and a localized feature twenty micrometres long along the removal direction. Depending on its position, the entire feature can disappear between consecutive observations. Reducing spacing to ten micrometres changes the geometric intersection opportunity, but preparation damage and image contrast can still prevent recognition.
Under the additional assumption that the feature position is uniformly distributed relative to an indefinitely repeated plane pattern, the chance of at least one geometric intersection is twenty percent for the first example. This number is not an inspection detection rate. A localized target, finite covered interval, uncertain shape or nonuniform location distribution invalidates that simple probability interpretation.
Pintersection = min(1, ℓ/d)
- ℓ is continuous feature extent along the serial-section direction.
- d is uniform spacing between ideal observed planes.
Uniform unknown relative phase, periodic parallel planes, a contiguous feature and perfect recognition at any intersection; finite-span boundary effects are excluded. This is a geometric thought experiment, not a qualified probability-of-detection result.
Budget target and plane-position uncertainty separately
A target may be localized to a range rather than a point, while actual material removal also has uncertainty. Expand the planned start and finish positions to cover the supported target range, with appropriate margins. Then choose spacing within that range according to the feature dimensions the investigation must resolve.
Record actual plane locations using an appropriate physical measurement or validated preparation reference. Time spent grinding is not automatically a removed depth because removal rate can change with material, pressure and abrasive condition. A programmed increment is a command until the resulting plane displacement has been established.
| Finding | Coverage consequence | Appropriate response |
|---|---|---|
| Target lies before the first observed plane | Initial preparation may have removed the evidence | Preserve another specimen or use a revised approach direction |
| Potential feature fits between planes | A clean sequence can still miss it | Reduce supported spacing or use complementary volumetric evidence |
| Target range extends beyond the last plane | The investigation has not covered the full location range | Extend the justified plan or bound the conclusion |
| Actual removal depth is unknown | Image count cannot establish spatial coverage | Measure or recover plane positions before a coverage claim |
| Feature intersects but is not resolvable | Geometric coverage exceeds analytical detection capability | Improve the suitable imaging method or state the visibility limit |
| Preparation can create or erase the feature | Observed geometry may not represent the original state | Use controls and independently prepared evidence |
Make a stop decision before the target is polished away
Define what observation triggers a pause, additional imaging or a change in preparation method. Once a suspected discontinuity appears, capture its wider context and detailed boundary before removing more material. Continuing automatically to a nominal centre plane can erase the most informative location.
Track specimen orientation and image direction consistently throughout the sequence. A flipped mount or reversed image axis can make successive sections appear to move in the wrong direction. Preserve original files and link each to the physical plane, preparation stage and observations made before the next irreversible removal.
Write a negative result in terms of the inspected volume
A defensible negative result states that no qualifying feature was observed in the recorded planes under the stated resolution and preparation conditions. It also identifies unobserved intervals and any target region outside the covered span. It does not convert those missing regions into sound material.
If the decision requires a bound on missed defects, design and validate an inspection strategy appropriate to the feature population. Repeated planes from one specimen are correlated spatial observations, not independent production samples. They cannot be entered as separate defect-free parts in a lot-acceptance or reliability calculation.
Deliver a reproducible coverage record with the sections
The final package should include the target-location basis, specimen datum, cutting direction, initial removal, measured plane positions and an ordered image sequence. Record feature extent assumptions and the distinction between geometric intersection and actual recognition. Preserve the remaining material when it can support a different orientation or independent check.
ChipSimple can review the product coordinates and interfaces relevant to a project-specific failure investigation. The sectioning plan should answer a defined physical question while conserving evidence. Its value comes from knowing what was examined and what remains unobserved, not from the number of attractive microscope photographs produced.
Plan section locations around the failure question
Provide localization evidence before destructive preparation begins.
- Specimen coordinates and suspected buried interface
- Electrical or visual localization with uncertainty
- Feature dimensions that must be resolved
- Permitted sacrificial specimens and preservation needs
- Proposed plane spacing, initial removal and stop observations
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