Insights: distributions and data

Lesson 06

Learn tsmap

Learn tsmap · 06 Insights: distributions and data

In this lesson

Yield tells you how many dies passed. The measurements behind it tell you how close to their limits the dies were. This lesson shows how test values spread, how groups of wafers compare, and where to find the numbers behind every chart.

  • Read how values spread, and where tests sit against their limits
  • Compare groups of wafers and see where on the wafer they differ
  • Export the numbers behind every chart
Learn tsmap · 06 Insights: distributions and data

Distributions

Learn tsmap · 06 Insights: distributions and data

The Distributions tab

This tab is about how values spread: process capability, a box plot per wafer, a histogram and the trend across wafers. It answers "are my tests healthy, or close to failing?"

The Distributions tab

Learn tsmap · 06 Insights: distributions and data

Tests by wafer

Which wafers behave differently from the rest? At the top of Distributions, Tests by wafer picks the tests whose wafers differ most and draws them as a grid. Each row is a test and each column is a wafer.

The Tests by wafer grid, six tests by twenty-five wafers

Learn tsmap · 06 Insights: distributions and data

Reading the colours of the grid

The colour of a cell shows how far that wafer's mean is from the mean of all the wafers: blue is below, orange is above, and a pale cell is close to average.

Learn tsmap · 06 Insights: distributions and data

Reading the grid in z-scores

Each cell needs a common scale, so that millivolts and megahertz can sit side by side.

  • Each test is rescaled on its own, so tests in different units share one colour scale
  • The number in a cell is a z-score: how many standard deviations the wafer's mean is from the mean of all wafers
  • A column that is dark in several rows is a wafer that moved several tests together
Learn tsmap · 06 Insights: distributions and data

Process capability

How much room does each test have before it fails? Each test is rescaled against its own limits: the low limit becomes 0 and the high limit becomes 1. That puts tests in different units on one scale, so you can compare their margins directly.

The Process capability card

Learn tsmap · 06 Insights: distributions and data

Reading the colours

Each test is a box showing where its values sit between the limits.

  • A box centred between 0 and 1, whiskers inside, has room; one against 0 or 1 does not
  • Lowest Ppk first: 1.33 or more is capable, under 1.0 poor
  • Ppk is the gap from the mean to the nearest limit, in units of 3σ
Learn tsmap · 06 Insights: distributions and data

Tests with no limits

A test without both limits still appears, drawn muted and dashed on its own range, with no Ppk. Its place says how its values spread, not how near a limit they are, because there is no limit to be near.

SWEEP-LOT-06 capability chart: tests without limits drawn muted and dashed

Learn tsmap · 06 Insights: distributions and data

One test for every card

Under the heading Test by test there is one Test menu. Changing it changes the box plot, the histogram, the trend and the scatter together, so every card is about the same test and you can read them as one story.

The Test menu in the Test by test row, listing every test

Learn tsmap · 06 Insights: distributions and data

Pin the tests you use

A lot can have hundreds of tests. Click the ☆ at the end of a row in any test menu, or press P on the focused row, to pin that test. Pinned tests are listed first, under Pinned, in every test menu in Insights, and tsmap remembers them for the next lot.

The Test menu with ioff_nA pinned at the top, under Pinned

Learn tsmap · 06 Insights: distributions and data

Other ways to change the test

Clicking a test in the capability chart does the same. A card shows a Test menu of its own only while you have expanded it.

Learn tsmap · 06 Insights: distributions and data

Axis controls

1 Axis includes limits widens the axis to the limits. 2 Clip outliers narrows it to the bulk of the data. 3 Log scale, on the box plot only, uses a log axis once every value is positive.

The box plot's three axis controls, outlined

Learn tsmap · 06 Insights: distributions and data

Clipping changes only the axis

Clipping does not remove data. The chart states how many values fall outside the axis, and every statistic still includes them.

The box plot with Clip outliers on

Learn tsmap · 06 Insights: distributions and data

Which limits are drawn

When a test has both kinds, a Limits choice appears on the box plot, histogram, trend and scatter: Test + spec (the default), Test limits, Spec limits or None. A limit off the edge of the axis is marked with an arrow.

The box plot with its Limits choice outlined

Learn tsmap · 06 Insights: distributions and data

One wafer or all

The histogram has a Wafer menu: all wafers pooled, or one wafer. Type to filter the list.

The Wafer menu on the value histogram

Learn tsmap · 06 Insights: distributions and data

Wafer-to-wafer trend

Is the process drifting from wafer to wafer? This chart shows each wafer's mean in slot order, with a band of ±1 standard deviation. There is no sort, because a drift only shows in sequence.

The wafer-to-wafer trend of ioff_nA

Learn tsmap · 06 Insights: distributions and data

Trend or control chart

Control chart shows the same wafers against control limits, with the points that break a rule marked.

The control chart view of the wafer-to-wafer card

Learn tsmap · 06 Insights: distributions and data

Which view to use

The two views answer different questions. The trend shows how the dies within each wafer spread. The control chart shows whether a wafer's mean stands out from the others, and it needs at least three wafers.

Learn tsmap · 06 Insights: distributions and data

The histogram when grouped

With Group by on, each group's bars are a share of its own dies, so groups of different sizes compare by shape rather than by size. Counts shows the number of dies instead.

The value histogram with one series per split, as shares

Learn tsmap · 06 Insights: distributions and data

Histogram or cumulative

Cumulative draws the same values as a curve instead of bars. Each die sits at the share of dies at or below its value, on a scale where a normal distribution falls on a straight line. A group whose curve is further right has higher values, and a steeper curve is a tighter spread.

The same values drawn as a cumulative curve, one line per split

Learn tsmap · 06 Insights: distributions and data

The box plot when grouped

With Group by on, the box plot also offers Split, then wafer: each split's wafers sit inside it, coloured by split, so you see the spread between splits and within each.

The box plot with each split's wafers inside it

Learn tsmap · 06 Insights: distributions and data

By wafer or by radius

The box plot can show one box for each wafer (By wafer) or one for each ring, from the centre of the wafer out to the edge (By radius). By radius is the one to use when you suspect a value changes with distance from the centre: the boxes then step up or down from Ring 1 to Ring 4.

The box plot drawn by radius, with By radius outlined

Learn tsmap · 06 Insights: distributions and data

Why each wafer counts once

Comparing groups raises a fair question: why not use every die? Because the dies are not independent.

  • Dies on one wafer went through the same processing, so they are not independent
  • Counted die by die, thousands of dies make a tiny difference between two wafers look certain
  • So a comparison of groups takes each wafer's mean as one value: n is wafers
Learn tsmap · 06 Insights: distributions and data

Comparing groups

When you compare groups, the table gives you three things to read.

  • Welch p, Rank p: how likely a difference this large is by chance
  • q corrects p for many tests: read q
  • Largest shift is the size; Control compares each group with one

The Comparison by split table

Learn tsmap · 06 Insights: distributions and data

Tests by group

With Group by on, Tests by wafer becomes Tests by split: one column for each group instead of each wafer, in z-scores again. A group that is dark across several rows differs on several tests at once, which suggests one cause.

Tests by split, six tests by five splits

Learn tsmap · 06 Insights: distributions and data

Group by temperature

Grouped by Temperature, the card compares the six wafers tested at 85 °C with the nineteen at 25 °C. At 85 °C leakage (ioff_nA) is high, while the thresholds and both idsat_n_uA and fmax_MHz are lower.

Tests by temperature: the 85 group against the 25 group

Learn tsmap · 06 Insights: distributions and data

Other fields

Tester, program revision and burn-in time each pick out a different set of wafers. Group by each in turn to see which tests it moves.

Learn tsmap · 06 Insights: distributions and data

Where on the wafer

Once you know two groups differ, the next question is where. The difference map shows where on the wafer two groups differ, not whether the difference is significant. Use the comparison table for that.

The difference map: FF minus FS on ioff_nA

Learn tsmap · 06 Insights: distributions and data

The numbers behind it

Learn tsmap · 06 Insights: distributions and data

The Data tab

Every chart is drawn from numbers, and you can have them. Data, the tab after Correlation, holds every number behind the charts as tables. The foot of the Overview links to it too.

The link to the Data tab at the foot of the Overview, outlined

Learn tsmap · 06 Insights: distributions and data

Statistics

The Data tab holds the same numbers as tables, in three sub-tabs: Statistics, Wafers and Dies. Statistics has two tables, each with its own CSV button: 1 Test values CSV and 2 Functional CSV.

The Statistics table with its two CSV buttons outlined

Learn tsmap · 06 Insights: distributions and data

Wafers

The Wafers table has one row per wafer: its lot fields, die counts, yield and the mean of each test.

The Wafers table

Learn tsmap · 06 Insights: distributions and data

Dies

The Dies table has one row per die: position, ring, quadrant, site, bins, every test and the PAT verdict. Copy puts it on the clipboard and Export CSV saves a file; Wide has a column per test, Long a row per die and test.

The Dies table

Learn tsmap · 06 Insights: distributions and data

Try it yourself

  1. In the web app, Load sample data, then switch to Insights
  2. On Distributions, pick ioff_nA and turn on Clip outliers
  3. On Data → Dies, export the table
Learn tsmap · 06 Insights: distributions and data

Recap

  • Distributions shows how values spread and where tests sit against their limits
  • With Group by on, the same tab compares groups of wafers
  • Data holds every number as a table you can export

You can now say how a test behaves and whether groups differ. Next: which tests move together.

More in the wafer map guide

Learn tsmap · 06 Insights: distributions and data

Next lesson

07 · Correlation →

Which tests move together.

Learn tsmap · 06 Insights: distributions and data