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Find the pattern across the wafer.

Investigate yield variation, compare process conditions and connect test measurements to wafer position. l supplies the column operations and numerical expressions for moving from a lot-level summary to the devices behind it.

01 / The workload

Connect the measurement to its context.

  • Device measurements
  • Process observations
  • Wafer coordinates

A yield number is the beginning of the investigation.

A shift can appear across lots, process steps, test bins or regions of a wafer. Understanding it means retaining both the measurement and its manufacturing context. The useful question changes as the investigation moves from a broad trend to one device population.

Yield and test-bin analysis

Group device outcomes by lot, wafer and test classification. Calculate counts and proportions, compare populations and extract the measurements behind a change.

  • Compare bin distributions across lots
  • Drill from wafer totals to device results

Wafer and spatial patterns

Use die coordinates and recorded measurements to compare regions. Prepare the coordinate-level aggregates needed by your wafer-map visualization and engineering analysis.

  • Compare edge and center populations
  • Inspect neighboring device measurements

Process and equipment variation

Analyze datasets that associate test outcomes with process steps and equipment conditions. Compare measurements across tools, recipes and operating periods.

  • Compare distributions by tool or recipe
  • Investigate changes across process steps

Parametric test characterization

Calculate statistics across numerical test columns and study relationships between measurements. Isolate outliers or populations for further review in your engineering tools.

  • Study correlations between test parameters
  • Compare distributions before and after a change

02 / From data to analysis

Follow a yield shift to a device population.

Use the same identifiers and coordinate fields from the manufacturing record through to the focused engineering extract.

  1. 01Source data

    Bring the test context

    Start with flat measurement tables and associated lot, wafer, die, recipe and equipment identifiers.

    • Device measurements
    • Wafer coordinates
    • Process identifiers
  2. l>Compute with l

    Compare the populations

    Filter test conditions, group outcomes and calculate distributions or numerical relationships across the selected devices.

    • Lot & bin groups
    • Spatial filters
    • Parameter statistics
  3. 03Analytical result

    Inspect the contributing devices

    Return comparison tables, coordinate-level aggregates and individual device rows to your quality and engineering applications.

    • Yield comparison tables
    • Wafer-map aggregates
    • Device-level extracts
Count devices by wafer
/ Count devices by wafer

l>t:([]wafer:1 1 1 2 2 2;ok:110101b)

l>select sum ok by wafer from t
wafer| ok
-----|---
1    | 2
2    | 2

l>exec avg ok from t
0.6666667

l>exec wafer from t where not ok
1 2

l>

03 / Why l

The expression stays simple.
The layout does the work.

You write q/k. The runtime considers the physical representation of the data, choosing encoding-aware operations where supported and materializing values when needed.

A natural fit for repeated column operations
Counts, grouping, masks and numerical reductions are array operations. l can choose encoding-aware paths based on a column’s physical representation.
Connect the analysis to the engineering tools
Use Python for application integration and the native Arrow library for columnar data exchange. Retain the identifiers needed to connect results back to the manufacturing record.
Read the research

04 / Your first evaluation

Start with a result
you can verify.

Choose several lots with a known test shift, consistent die coordinates and measurement tables that include both passing and failing populations.

Available as a research preview for local evaluation.

Questions to answer with your sample

  1. Do device counts, test-bin proportions and null handling reconcile?
  2. Can the same population be selected by lot, wafer and coordinate?
  3. What is the cost of regrouping the sample across tools and recipes?

Your data. Your next question.

What is hiding between your test results?

Let’s talk