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Paste cannot occupy a ceramic hole without displacing the gas already there. If one entrance seals before gas escapes, the resulting via may contain a void yet show continuity through an annular wall film or connected surface caps. A model of entry pressure, vent state, and parallel conductance makes those ambiguities explicit. It does not assume a solid cylinder or translate surface smoothness into internal acceptance.
Key design decisions
- Model the time at which each opening remains available for gas escape.
- Separate core, annular, and surface contributions to measured conductance.
- Use section topology to constrain the electrical interpretation.
Convert the actual via into an entry-and-vent geometry
Record ceramic thickness, entrance and exit diameters, taper, wall roughness, edge damage, pitch, and surrounding pad openings. Declare paste-entry face and support condition. A tapered hole entered from its narrow side creates a different flow and sealing sequence from the same hole entered from its wide side.
Represent top and bottom paste reservoirs, screen or tooling contact, and any backing surface. Mark whether the exit is open, porous, covered, or already printed. Use measured extremes to create bounding geometries rather than relying on one nominal cylinder.
Track paste front and trapped gas qualitatively
Sketch the paste front as it enters, wets walls, and approaches the opposite face. Identify possible gas routes through the remaining opening, wall gaps, or tooling. A bridge across an entrance can trap a central pocket even while paste continues along the wall. Sequential printing can either complete the path or seal both ends.
The model need not claim paste viscosity or pressure values without evidence. It should identify which observable—fill mass, entrance image, exit transfer, section void, or resistance—would distinguish candidate flow sequences. Use transparent experiments only to generate hypotheses.
Represent continuity as parallel paths
Treat a central conductive core, annular wall coverage, and connected surface film as possible parallel contributors. The measured conductance is their sum. This explains why a hollow-looking section can still conduct and why a low resistance does not prove volumetric fill. The topology must still connect the selected measurement pads.
For illustration, contributions of 2, 3, and 1 siemens total 6 siemens, equivalent to about 0.167 ohm. The numbers are hypothetical. Actual partition cannot be solved from one total resistance; sectioning and isolated controls are required.
G_measured = G_core + G_annulus + G_surface
- G_measured: conductance between defined coupon terminals
- G_core: contribution from a continuous central path
- G_annulus: contribution from conductive wall coverage
- G_surface: contribution from connected face material
Candidate paths are electrically parallel between the same terminals. Real connectivity and effective cross-section require physical evidence.
Identify when entrance or exit becomes sealed
Record each print or fill action, squeegee or pressure direction, dwell, backing condition, drying step, flip, second-face action, and firing. Determine when the entrance can bridge and when the exit ceases to vent. The order can matter more than the final amount visible at either face.
Design witness groups with open vent, constrained vent, reversed entry, and relevant hole taper. Hold paste lot, geometry, drying, and firing constant. A controlled vent contrast can test the gas-displacement hypothesis without claiming a production recipe.
Design measurements that expose surface bypass
Route isolated pads on opposite faces so the test current must traverse the internal via. Add surface-only structures to measure any face routing included in the main coupon. Where possible, include annular or intentionally interrupted development controls that help interpret the equivalent circuit.
Use measurement current and duration appropriate to the reviewed structure. Check polarity, contact, and lead contribution. Map every resistance to the exact hole, entry condition, and later section. Avoid averaging a low-resistance surface bypass with an open internal path.
Translate sections into topology classes
Section through the axis and document preparation capable of smearing conductor into voids. Classify central core, annular wall film, isolated surface cap, trapped central void, side void, wall separation, and ceramic crack. One plane samples only part of the circumference.
Compare multiple planes or orthogonal evidence where the consequence justifies it. Register electrical and image data before destructive preparation. If a section contradicts resistance, reconsider pad routing, section plane, or additional parallel paths rather than choosing one result. Retain polished-section preparation controls to expose smearing or pullout that could create a false conductive bridge. Preserve that control image.
Use coupled signatures to select the next test
A single symptom remains ambiguous. Pair surface, electrical, and section signatures before assigning a mechanism.
| Observed combination | Candidate mechanism | Discriminator | Boundary |
|---|---|---|---|
| Smooth faces, low resistance, central void | Annular or surface path | Isolated pad routing and offset sections | Not solid-fill proof |
| Entry bridge, poor exit transfer | Early sealing | Reverse entry or open-vent control | Specific geometry |
| High resistance, continuous section | Constriction or contact | Thickness and terminal controls | Measurement boundary |
| Crack near entrance | Hole or thermal interaction | Pre-fill hole inspection and load map | Needs material review |
Choose cross sections that can distinguish fill topologies
A single polished plane can miss an off-center void or mistake a surface smear for a connected via. Define section orientation from the via entry, exit and printing direction, then select multiple depths or complementary views appropriate to the decision. Preserve before-section electrical measurements, top and bottom surface images and specimen identity. In the section, record paste continuity, wall contact, central void shape, entrance closure and exit formation without extrapolating beyond the observed plane. Where tomography or another nondestructive method is used, state its resolution and contrast limitations. Correlate structural observations with a measurement topology that suppresses surface bypass. The evidence set should answer whether current traverses the intended filled volume, not merely whether conductive material is visible near both openings.
Validate and release the via-entry model
Validate with independent coupons spanning hole and vent extremes. Require linked timestamps, face images, through resistance, and selected sections. Confirm that the model predicts which condition changes when entry direction or vent state changes. Keep unexplained contradictions open.
Control geometry, entry face, support, fill sequence, vent condition, drying, firing, pad topology, measurement, section method, classification, and disposition. Reopen after any of those changes. RFQ review needs the actual hole and electrical consequence; no fill percentage, resistance, or reliability is promised before validation.
Provide the via entry and vent boundary
Send the hole, paste route, and evidence needed to model gas displacement and conductive topology.
- Ceramic thickness, measured entrance and exit geometry, taper, wall condition, pitch, pad openings, and face names.
- Paste system, entry direction, tooling, backing, pressure or print actions, dwell, drying, flips, and firing.
- Terminal routing, resistance method, face images, section planes, topology classes, and specimen identity.
- Known void or continuity patterns, electrical consequence, geometry extremes, comparison plan, and change owner.
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