Geometry and continuity
- Shape and layer coverage
- Voids and material connections
ViennaPS teaching example · updated
A simplified TSV traveler
Follow one simplified TSV cross-section from mask opening to polish. Saved ViennaPS simulations show what each step changes, what can fail, and what to measure.
This is a teaching model. Real TSV flows include more films, cleaning steps, and process controls.
What the current evidence says
The software can carry and measure geometry across the simplified traveler. It has not yet found or validated a complete TSV process window.
Improve the etchKeep the focused straight-wall region. Treat floor shape as the next separate objective.
Reduce copper void riskEstablish continuous deep seed and measured floor-faster-than-wall growth before adding more copper.
Finish the travelerResolve copper topology first. Then tune CMP using field clearance, plug loss, and stop loss together.
Practical next step: calibrate the model with split-wafer profile and growth measurements. Until then, the controls teach simulated mechanisms but do not define gas flow, plating current, or polish settings.
What we are modeling
A through-silicon via (TSV) is a vertical electrical connection through silicon. This model covers the steps that form its copper plug.
- 1. Open the mask
- 2. Etch the silicon
- 3. Coat the walls
- 4. Prepare for copper
- 5. Fill with copper
- 6. Polish the surface
Mask
Silicon
Liner
Barrier + seed
Copper
Inside this modelThe temporary mask is removed after etching. The liner is deposited next.
Later in fabricationWafer thinning exposes the bottom of the via. Wiring then completes the connection.
Fab settings and reliability
- Gas flow, plating current, and polish pressure
- Adhesion and stress; resistance and wafer behavior
PRESCRIBED GEOMETRY CONTROL · MEASUREMENT CHECK
How the measurement code checks a known geometry
The scripted control gives the measurement code one clear passing example: continuous layers, no resolved 2D void, and a connected plug after ideal planarization. This shows that the checks can recognize those simulated features. It does not show that a real fabrication tool would produce them.
Stress-test the void measurement
These prescribed shapes test whether the code distinguishes an open cavity, a trapped void, and a joined copper region.
This is not process tuning. The surface speed is deliberately prescribed to create two different geometric outcomes.
| Step | What happens | Purpose in fabrication |
|---|---|---|
| 1. Open the mask | A pattern marks where the hole will be made. | Sets the via's position and width. |
| 2. Etch the silicon | A deep hole is cut into the silicon. | Creates the via and shapes its walls. |
| 3. Coat the walls | An insulating liner covers the inside surface. | Keeps copper electrically isolated from silicon. |
| 4. Prepare for copper | A barrier and copper seed layer are added. | The barrier slows copper migration. The seed gives plating a conductive surface. |
| 5. Fill with copper | Copper fills the coated hole. | Creates the vertical electrical path. |
| 6. Polish the surface | Extra copper above the via is removed. | Leaves a flat surface and a copper plug. |
These known shapes test the geometry measurements. They do not show that a physical TSV recipe will produce the same result.
How the software works
ViennaPS is a process simulator. It calculates how material boundaries move under a chosen model. It does not emulate the control software of a specific fabrication tool.
ViennaPS stores each material interface as a level set. A process model supplies a local growth or removal speed. Some models use prescribed rates. Particle models instead trace many simulated paths, estimate where particles reach the surface, and use sticking or reflection rules to turn that arrival flux into surface motion.
The level-set solver advances the interfaces for the requested duration. The resulting geometry becomes the input to the next TSV step. Measurements such as depth, width, coating thickness, voids, and connectivity provide feedback for the next tested settings.
build_screening_traveler.py runs the steps in sequence and records the measurements.Geometry under declared rules
- Surface motion from the selected rate or particle-transport model.
- Material handoffs between simulated process steps.
- Geometry measurements at the chosen grid and sampling settings.
A real equipment recipe
- Gas flow, pressure, power, current, chemistry, or polishing settings.
- Coefficients matched to wafer measurements.
- Reactor-scale, electrical, thermal, stress, and full-wafer effects not included by the chosen models.
This tutorial uses a 2D trench-like surrogate. A cylindrical 3D via can change particle access and whether a void is truly connected.
Follow the saved results in process order
Mask → dry etch → liner → barrier → seed → copper → polish.
Each panel replays saved simulation output. The controls select an existing case; the browser does not rerun ViennaPS or invent a shape. A deterministic control lineage exists, but these sensitivity panels are not one calibrated candidate recipe. Open the saved step data.
Current handoff status: improve the etch floor, deep film coverage, and copper model before running a new end-to-end candidate.
Choosing a ray count for faster experiments
More rays mean more sampled particle paths and more computation. They do not automatically make every measured result more stable.
This is a numerical-setting search, not etch-process tuning. It compares five ray counts while holding the grid and process inputs fixed.
Takeaway: increasing rays mainly increased runtime in these saved cases. It did not steadily reduce run-to-run variation. Grid spacing changed the etched geometry enough that it must be checked separately.
The plots report runtime, repeat-to-repeat spread, and movement between ray levels. No ray count is treated as the correct answer.
Five ray counts on three etched shapes
Each shape was run with three random streams at 250, 500, 750, 1,000, and 2,000 rays. The grid and process inputs stay fixed within each shape.
Choosing a grid spacing
Grid spacing controls how finely the profile is represented. Across a 0.30-wide opening, the four saved settings provide about 120, 60, 30, or 15 cells. More cells can resolve smaller shape changes, but they cost more time. This older study changes only the grid for one recipe; it does not identify a universally correct grid.
Read the two plots together: the left shows how the selected measurement moves; the right shows the runtime cost. Points are saved simulations from one research machine. Lines only connect tested settings.
What this study supports
The focused discovery data used grid spacing 0.0025 and 500 rays. These settings produced useful profiles quickly, but they are not approved as the general exploration setting. Phase B separately found categorical changes at 500 rays on a grid-0.005 panel. The two saved 500-to-1,000 comparisons below are observational; they do not confirm the published candidate.
Coarser gridGrid 0.0025 ran 3.6–5.0× faster than 0.00125 in two settings. Some measurements still moved, so this is local evidence only.
More rays1,000 rays took 2.0–2.3× longer than 500 in two pairs. It did not establish 1,000 as a confirmed setting.
Too coarseGrid 0.005 changed the selected width profile enough that this study stopped using it.
Next action: freeze and run a candidate-specific numerical check before choosing exploration and confirmation settings. These paired movements are not errors against ground truth. Open the focused observational review.
Equipment controls, model controls, and feedback
Geometry inputs define the starting shape. Model inputs control simulated surface motion. Neither is a calibrated machine recipe.
| Step | Equipment controls | Physical effect | ViennaPS representation | Measurement feedback |
|---|---|---|---|---|
| Mask | Focus and dose; bake and develop; resist coat | Changes opening size, height, and taper | Starting opening geometry | Top and bottom opening width; mask height |
| Silicon etch | Gas timing and flow; pressure; source power; bias; temperature | Changes removal, wall protection, and ion direction | Effective rates, sticking, directionality, and duration | Depth; top, middle, and bottom width; bow and scallop |
| Liner | Precursor exposure; pressure; temperature; plasma | Changes growth rate and transport into the via | Deposition amount, sticking, and source distribution | Field, wall, and floor thickness; continuity and opening |
| Barrier + seed | Target power; pressure; substrate bias; collimation; time | Changes arrival direction and deep coverage | Deposition amount and arrival-direction fraction | Regional thickness, continuity, and remaining opening |
| Copper fill | Current waveform; additives; chemistry; temperature; agitation | Changes suppression and floor-versus-wall growth | Candidate transport and kinetic rates | Open and sealed voids; seam history; copper above the surface |
| Polish | Pressure and speed; slurry; endpoint and overpolish | Changes removal rate and material selectivity | Removal amount and relative material rates | Field clearance; plug recess; stop loss; connectivity |
Numerical settings: grid spacing sets geometric resolution. Ray count controls Monte Carlo sampling noise. A random seed selects a reproducible ray sample. None is a fab knob.
Qualitative influence only: the two middle columns are not a conversion table. Equipment settings change the physical process. Mapping them to model inputs requires measurements from a specific tool.
Shown in the tutorialMask geometry; six etch controls; liner dose and sticking; barrier/seed dose and directionality; reduced copper transport; CMP amount and selectivity.
Implemented but not fully shownMask erosion, breakthrough etch, reflection angle, model-family choices, additional copper coefficients, and height-dependent CMP.
Needs tool calibrationGas flow, pressure, power, bath chemistry, current waveform, pad conditions, and their mapping into model coefficients.
Coverage: the page teaches the main wired controls, not every ViennaPS input. Omitted controls need their own evidence before they become tutorial sliders.
How a model becomes useful for a real tool
The conversion is learned from wafer data. It is not read from the ViennaPS input value.
1. Split recipesVary a small set of pressure, power, gas, timing, or temperature controls.
2. Measure profilesRecord depth, widths, sidewall shape, floor shape, and repeat variation.
3. Fit model controlsFind the ViennaPS inputs that reproduce those measured profiles.
4. Test unseen recipesCheck the fitted mapping on wafer recipes that were not used for fitting.
5. Use within rangeOptimize only inside the calibrated recipe and geometry range.
Smart calibration: screen many candidate controls first. Fit only the influential ones. Use repeated measurements and hold back some recipes for validation. Report prediction error instead of calling the fit exact. This ViennaPS project has not yet received the wafer data needed to perform that calibration.
What a good etch result must report
A clean-looking outline is not enough. Keep the required measurements separate so one good number cannot hide another failure.
| Question | Measurements | Status here |
|---|---|---|
| Did it reach the intended depth? | Depth | Compared with an assumed teaching target |
| Did the width stay controlled? | Top, middle, bottom, and minimum width | Measured on both walls |
| Are the walls straight and balanced? | Taper, bow, necking, scallop, and left/right symmetry | Measured; not calibrated fab limits |
| Is the base acceptable? | Floor peak-to-valley, center relief, symmetry, and unresolved extrema | Diagnostic only; still needs qualification |
| Can the result be trusted numerically? | Measurement availability, repeats, grid check, and higher-ray movement | Scoped to the tested region |
Important: the dashed rectangle is a teaching reference, not a fabrication specification. The current focused result has good depth and walls, but its rounded or uneven floor remains open work.
Where the etch measurements come from
The lines below are drawn over one saved ViennaPS profile. They show what depth and top, middle, and bottom width mean.
Viewer scope: each sensitivity panel below uses its own controlled starting shape. Changing one panel does not change the next. No continuous passing traveler is claimed.
Step 1: Screen six dry-etch controls
Each line is one saved run in which six model controls changed together.
This 18-run design samples combinations efficiently instead of testing every possible combination. Select a line or scrub through the runs. The browser shows the exact saved profile; it does not interpolate or rerun ViennaPS.
The purpose is broad screening: identify which controls move depth, width, wall shape, and floor shape enough to deserve a smaller follow-up study. Initial etch time, passivation sticking, and ion reflection angle were held fixed. Cycle count, mask geometry, and mask erosion remain separate studies.
Action: inspect the nominated control pairs below. These rankings are descriptive because each combination has one random stream. Add repeats before treating a ranking as stable.
Open all 18 profiles, measurements, model settings, and source-row citations.
Step 2: Inspect four corners of a selected control pair
Saved sensitivity · one stream per case · not DOE · model units
Choose a factor pair, then inspect the four saved simulated profiles.
Choose two controls nominated for follow-up. Their four corners are low × low, low × high, high × low, and high × high. This makes the pair easier to interpret than the six-control screen. Each corner has one random stream, so it is visual sensitivity evidence, not a confirmed interaction estimate.
Equipment controlsPlasma and surface stateViennaPS model controlsSimulated profileGeometry measurements
Action: if a pair brackets a useful profile, add centre points and repeats inside that box. Then tune the smaller region and confirm the promoted setting independently.
Open the exported profiles and citations. The browser does not interpolate between the four sampled combinations.
Watch the via deepen over repeated etch cycles
Scrub through seven replayed checkpoints from one 500-ray run with a fixed random seed. Each frame shows the profile after a complete etch/passivation cycle.
Step 3: Tune and repeat the promising region
Ion arrival direction and directional removal were changed together across nine saved settings.
Select a setting to view the exact simulated profile. The center was run three times. Other cells have one run, so they show direction but not repeatability.
Result: the repeated center stays near the target depth and its walls remain close to vertical.
Next action: optimize and repeat the floor-shape measurement separately. The saved floors remain rounded or uneven, so this is not yet the final etch profile.
Explore copper filling
Copper can trap a void when the opening closes before the center fills.
Advanced: failure modes and tuning details
Mask opening
Explore saved results ↓Potential failureAn opening that is too wide, too narrow, or tapered.
Machine controlsFocus and dose; bake and develop; resist coat.
ViennaPS controlsOpening width, mask height, and taper.
Possible downsideThe opening must expose enough silicon while protecting the surrounding surface.
Silicon etch
Explore saved results ↓Potential failureWrong depth, bowed walls, or a narrow neck.
Machine controlsSF6/C4F8 timing and flow; pressure; source power; bias; cycles.
ViennaPS controlsCycle count; phase times; effective rates; sticking; directionality.
Possible downsideFaster removal can deepen the via but make its walls harder to control.
Potential failureA thin floor coating or a narrowed opening.
Machine controlsPrecursor exposure; purge; pressure; temperature; plasma.
ViennaPS controlsDeposition amount and particle sticking.
Possible downsideMore coating improves thickness but leaves less room for copper.
Potential failureA thin or disconnected coating near the floor.
Machine controlsTarget power; pressure; substrate bias; collimation; time.
ViennaPS controlsDeposition amount and arrival-direction fraction.
Possible downsideBetter deep coverage can also narrow the copper opening.
Copper fill
Explore saved results ↓Potential failureA center seam, trapped void, or early mouth closure.
Machine controlsCurrent waveform; additives; chloride; temperature; agitation.
ViennaPS controlsCandidate suppressor transport and floor-versus-wall growth.
Possible downsideMore wall growth closes the mouth sooner.
Polish
Explore saved results ↓Potential failureCopper left on top or a recessed plug.
Machine controlsPressure and speed; slurry; endpoint; polish time.
ViennaPS controlsRemoval amount and relative material rates.
Possible downsideMore removal clears the surface but can cut into the plug.
What the saved experiments show
These are measured boundary examples. They are not yet full process-margin maps.
What the transport-based copper run shows
The coarse grid reports 97.4% copper by area and an opening-connected cavity. The last merger is only about two grid cells wide, so that topology is not accepted as converged.
All layers and model controls stay fixed. Scrub through eleven saved checkpoints.
Decision: nearly full by area, but not a confirmed fill. No resolved sealed void is detected at this checkpoint.
How to resolve it: rerun the same case with smaller grid cells and more checkpoints near closure. Call it void-free only if the cavity disappears without an unresolved merger and the result agrees at the two finest settings. Call it a void only if a sealed region persists with several cells across its smallest dimension.
Next process study: measure floor and wall growth across additive, current-waveform, and seed splits. Use those data to calibrate the growth model before extending copper time.
Core ViennaPS call used by this candidate model
params = ps.CopperSuppressionFillParams()
params.suppressorStickingProbability = sticking
params.suppressorSourcePower = source_power
model = ps.CopperSuppressionFill(params)
ps.Process(geometry, model, checkpoint_interval).apply()What the sampled copper settings show
Bottom-up fill needs less suppressor and faster copper growth at the floor.
Choose a depth and measurement. Then select one of the 21 saved transport samples. This is not a fitted response surface or a fill simulation.
Takeaway: every sampled suppressor ratio is at least 1.021. Bottom-up filling needs the floor to receive less suppressor than the lower wall, which means a ratio below 1.
Action: stop expanding this same two-control path. Calibrate a broader model using additive, current-waveform, and seed experiments.
Coupled inputs: adsorption strength was set to 0.25 divided by sticking in every case. The map therefore tests a held-product path, not two independent copper controls.
Lower is better for suppressor transport. A ratio of 1.00 means equal flux at the floor and lower wall.
Advanced research notes
CURRENT
What the new experiments indicate
On the ideal protected geometry tested, the Cu law does not create enough bottom-up growth. Real etched-shape, liner/seed, and selective-CMP handoffs remain open.
Research status: foundation auditMeasurements and controlled failure tests come before another large recipe search.
Evidence is counted by reviewed casesCurrent case counts and limits are recorded in the evidence map.
No recipe recommendation yetThe tested 2D expansion has stopped; a matched 3D check is next.
FOUNDATION CHECK COMPLETE
Use the verified full-width setup before the broad Bosch screen
- Observation
- All 24 cases are independently valid. Pattern gates pass 24/24. Etch mask and width pass 24/24 and 23/24. Depth and bow both pass 22/24.
- Interpretation
- The quarter-width shortcut changes depth and top CD; the coarse grid changes six outputs. Mask loss is monotonic, but every tested erosion arm survives.
- Process move
- Keep the full-width fine grid and qualify the lower ray count. Extend erosion until failure appears. Save selected shapes natively.
GEOMETRY CHECKS EXERCISED
The baseline films are continuous, but not functional
- Observation
- All 12 layer runs remain continuous and leave the aperture open. The baseline still passes 0/4 liner gates and 0/4 barrier/seed gates at the fine setting.
- Interpretation
- The liner has enough local thickness but poor deep coverage: lower-wall/field is 0.859 against a 0.995 target. Barrier plus seed is too thin and highly directional: stack minimum is 0.00480 against 0.012.
- Process move
- Screen lower liner sticking for deeper coverage. For barrier and seed, test more conformal transport and additional dose while protecting the Cu-fill aperture.
SCRIPTED FILL CONTROL
A prescribed control produces a void-free plug in this geometry
- Observation
- The candidate rate law pinches laterally and fails at both tested grids. A prescribed bottom-up control fills the same protected stack at both grids with positive overburden.
- Interpretation
- The checks can register a void-free control, but this does not establish physical fillability. The tested law starts with nearly equal floor and wall velocity; the geometric criterion calls for about 10× at the floor.
- Process move
- Establish bottom selectivity before sweeping total Cu thickness. More conformal growth alone closes the sidewalls and traps a void.
TESTED 2D EXPANSION STOPPED
Lower sticking helps, but the gain is flattening
- Observation
- At sticking 0.00625, all 24 new runs are valid. Results at 1,600 and 3,200 reflections are identical. Suppressor transport improves in all eight paired streams, but the combined gate still passes 0/8.
- Interpretation
- The worst flux gain is 0.0041, below the 0.0167 numerical envelope. Floor/wall growth reaches 1.004–1.011 versus required ratios of 10.46 and 25.10.
- Process move
- Run the same transport question in a cylindrical 3D via. If 3D also misses, replace or extend the growth law before spending compute on Cu morphology or a large recipe sweep.
CMP METRIC CHECKED ON CONTROLS
The CMP metric distinguishes connected from cut layers in the tested controls
- Observation
- The new metric checks whether each material region connects the via floor to both mouth sides. Controlled planarization preserves the SiO2 stop and barrier at two grids. Seed and Cu also remain intact.
- Interpretation
- We can distinguish a connected layer from a cut layer. The removal model is still height and material dependent only; it has no pad-pressure physics.
- Process move
- Declare allowable stop and Cu-plug loss. Then screen material selectivity, endpoint, and overpolish. Do not optimize surface recess alone.
PROCESS MOVES
What to tune next
These are directions for the next simulation blocks. The coefficients are not calibrated to tool recipes. The page therefore gives no gas flows, currents, or polish pressures.
| Process step | Next useful knob | Expected benefit and tradeoff | Evidence |
|---|---|---|---|
| Photolithography / mask opening | Opening width and mask height; taper; later 3D placement error | Controls etch aperture and downstream access. Treat width and mask height as product inputs until a lithography model is added. | Registry complete; screen pending |
| Bosch DRIE | Geometry representation, ray count, and mask erosion | Use full-width geometry. Complete a candidate-specific numerical check before choosing the exploration setting. Then locate the mask-survival boundary without losing depth, width, or bow. | No exploration ray count is approved |
| SiO2 liner | Lower sticking, then adjust total dose | Lower sticking may improve floor and lower-wall coverage. Extra dose can narrow the aperture, so both coverage and remaining opening stay gated. | Geometry trends only; passing boundary not bracketed |
| Barrier and seed | More conformal transport, dose, and directionality | Raise lower-wall thickness without closing the fill opening. If directional deposition remains near 0.23 wall/field coverage, test a more conformal model family. | Baseline fails 0/4 |
| Cu electrofill | Matched 3D transport check; then chemistry-dependent bottom-up kinetics if it also misses | Test whether cylindrical transport changes the floor advantage. Total thickness is secondary until the bottom grows faster than the walls. | 320 reviewed transport cells; tested 2D expansion stopped |
| CMP | Material rates and endpoint; selectivity and controlled overpolish | Clear field Cu while retaining the stop layer and connected Cu plug. Dish, erosion, and material loss must be read together. | Metric ready; DOE blocked on loss limits |
EXPERIMENT LOGIC
Why the large DOE is waiting
A broad response surface is useful only after the measurements and model can recognize both success and failure. Each block below removes one reason a large sweep could mislead us.
- Verify measurementsWidth, thickness, and topology checks exist. Physical limits and downstream material-survival checks remain incomplete.
- Reproduce failureMake the centerline void and destructive CMP behavior repeat on controlled geometries.
- Check a known geometryUse a prescribed geometry example to verify that the measurements can register the intended state.
- Screen the mechanismTest whether suppressor transport points in the direction required for bottom-up Cu growth.
- Expand one justified edgeThe next halving improves the response only slightly and survives the reflection check, but still fails every stream.
- Check the cylindrical viaUse matched 3D transport to decide whether this law earns morphology work or must be replaced.
Decision rule: a completed batch is not progress by itself. A block advances only after its required measurements and numerical checks are usable. Assumed bands are reported separately.
CU RESPONSE
What the copper map shows
The criterion requires less suppressor and faster Cu growth at the floor than at the lower wall. Compare the 1.25-deep target with a 3.0-deep stress case. Each cell shows the worst of four paired streams.
Lower sticking was checked at three finer settings after the 21-point surface. The response improved slightly but still missed the target. A matched 3D check is next.
TUTORIAL
Explore the repository
The published guide and its derived JSON can be inspected after cloning the public repository.
git clone https://github.com/haomingkoo/ViennaPS-HBM.git
cd ViennaPS-HBM
python3 -m http.server 8000Then open http://localhost:8000/explainer.html.
Read tsv_process.py on GitHub to see the process functions.
Reproduction: the public repository includes the tutorial data and selected native checkpoints. Rebuilding every historical campaign still requires external native artifacts identified by recorded hashes.
DATA
See the saved simulation output
The guide is built from checked-in JSON. Use it to inspect the values behind the plots and claims.
The phase-one download is retained only to audit withdrawn measurements and conclusions. Selected current checkpoints are public. Some large historical artifacts remain hash-referenced only.
Archived first campaign: withdrawn measurements and conclusions
KNOBS
tuning knobs connected to the earlier DOE
The original runner varied these 17 factors. Other ViennaPS controls remain excluded until validated.
| Step | Tuning knobs | What they control |
|---|---|---|
| Mask opening | mask taper | Mouth geometry, dry-etch transport, downstream aperture |
| Silicon DRIE | cycles; etch time; initial etch time; neutral rate/sticking; passivation thickness/sticking; ion exponent; theta minimum | Depth and width; bulge and stochastic geometry |
| SiO2 liner | thickness; sticking | Functional coverage versus aperture closure |
| Barrier/seed | thickness; isotropic ratio | Floor coverage versus fill aperture |
| Cu fill | thickness; isotropic ratio | Deposited volume and centerline tip gap |
| CMP | overburden multiplier | Modeled dish and mask survival |
ViennaPS also exposes direction vectors and material rates. Angular distributions and numerical settings are available too. They need separate validation before counting as recipe knobs.
EARLIER METHOD
How the first campaign chose experiments
Current automation limit: the runner records and resumes frozen cases, but a human-reviewed step still chooses each follow-up batch. It does not yet fit a model and propose new cases by itself.
Each result chose the next experiment. Random runs were repeated, downstream recipes shared the same etched shape, and edge results triggered a wider range.
1. List the settingsFind every input the current workflow can change.
2. Search broadlyTry many combinations across wide ranges, with four repeats each.
3. Compare fairlyGive downstream recipes the same etched via so random shape differences do not bias the result.
4. Test the edgesExpand a range when its best result sits at the minimum or maximum.
5. Repeat the bestUse fresh stochastic etched shapes before recommending a recipe; phase one did not control simulator seeds.
Select an experiment to see the question it answered. The internal loss chart was removed because scores from different search ranges were not directly comparable.
LEGACY RESULT
The phase-one pass conclusion has been withdrawn
saved full-process simulations are retained as research history. The table shows what the old scorer reported. Those labels are not accepted as current physical validation.
| Step | Old target | Old scorer output |
|---|
Why the Cu conclusion is suspended
The legacy scalar tracked center height above the floor, not sealed-void topology. A raw 3D topology metric and a coverage/transport fill model are required.
Why the CMP conclusion is suspended
The old one-rate removal could erase Cu and oxide. It could also erase silicon and mask. The new study measures endpoint, overpolish, and selectivity separately. It also measures dish, erosion, and material survival.
No fab recipe is recommended. The selected screening geometry is a test fixture for later 3D transport, physical-model, and process-window work.
EARLIER SEARCH
The old 81-recipe search
Historical grid: four settings with three values each. This is not the current process window. Lower and farther left is better; amber means the old CMP step removed the mask.
Chance that a simulated liner particle sticks on contact. Higher values make deep, even coverage harder.
Total modeled Cu deposition amount. Larger is not automatically better because the centerline void can grow.
Zero is mostly vertical growth. Larger values add more growth in every direction.
Multiple of the Cu above the target surface. Too much removal consumes the mask.
Result: 48 recipes preserve the mask in all four repeats. None closes the Cu gap or produces a flat CMP surface.
LEGACY CHECK
Sixteen fresh stochastic repetitions
Phase one compared two recipes on 16 new DRIE geometries, reusing each geometry for fairness. RNG seeds were uncontrolled, so this is not reproducible confirmation.
LEGACY SHAPES
Why the old fill and CMP steps failed
These cross-sections explain the old model failures. They remain useful failure reproductions, not current recipe candidates.
The persistent void and bowl-like CMP retreat match the numerical failures and the missing fill-chemistry and pad-pressure physics.
HISTORY
What the earlier studies changed
Earlier studies found three mistakes: comparing different depths, trusting one random run, and calling an edge setting optimal before widening the range. The nine experiments above apply those corrections.
WORKFLOW
A measure-run-update workflow
Every step needs a target and a measurement before its output moves downstream.
1. Define successChoose the target and the measurement that can detect failure.
2. Measure each stepCheck opening width and etch depth. Then check layer coverage, fill voids, and polish clearance.
3. Test both outcomesUse one known failure and one prescribed passing control.
4. Carry geometry forwardGive downstream comparisons the same upstream shape.
5. Repeat and mapControl random seeds. Then map where results change from pass to fail.
6. Update the modelChange the model when more tuning cannot represent the needed physics.
CD means critical dimension. Measure the etched via at three locations: top, middle, bottom.
SOURCES
How the sources shaped this lesson
Each source answers a different teaching question.
- ViennaPS process API
- Explains how this simulation changes a surface over time.
- ViennaPS simulation domain
- Explains how material geometry and interfaces are represented.
- NIST TSV metrology
- Explains why via shape, coating coverage, and copper voids must be checked.
- NIST bottom-up Cu model
- Explains why copper must grow in the right order to avoid a trapped void.
- TU Wien Bosch simulation paper
- Shows how Monte Carlo ray transport and level sets can evolve an etched profile.
- IEEE TSV scallop study
- Explains why etched-wall roughness can matter to later dielectric and barrier behavior.
- ECS copper superfilling review
- Explains accelerator-driven bottom-up copper growth and why simple conformal filling can pinch off.
- Constrained search method
- Motivates learning from expensive simulations while keeping pass/fail requirements separate.
The sources guide the lesson. They do not turn this simulation into a fab recipe.