Correlation

Lesson 07

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In this lesson

When one test moves, does another move with it? Knowing which tests travel together helps you find a shared cause, and spot a number that only looks like a link. This lesson shows how to read the matrix, and how to check a relationship before you trust it.

  • Read the correlation matrix and open a pair as a scatter
  • Check a relationship wafer by wafer and group by group
  • Chart just the dies you drag a box around
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The matrix and the scatter

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The Correlation tab

The matrix on the left shows the correlation between every pair of tests. The scatter on the right shows one pair, with a point for each die. Use the matrix to find a pair worth looking at, then the scatter to see it.

The Correlation tab: the matrix and the test scatter

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The matrix

Each cell is r for two tests. Blue: they rise together; orange: one falls as the other rises. Stronger colour, stronger link. A link is not a cause, but it tells you where to look. 1 sets how many tests; 2 saves a table.

The matrix, with Max tests and Correlation CSV outlined

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Fewer tests

A matrix of many tests gets hard to read. You can set Max tests between 5 and 100 (default 20). The card counts pairs with |r| of 0.7 or more as strong and 0.4 to 0.7 as moderate. With five tests it finds 2 strong and 4 moderate.

The matrix limited to five tests

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Values or fails together

Values colours each cell by r, how two tests' values move together. Fails together asks a different question: of the dies that fail either of two tests, what share fail both?

The matrix drawn as Fails together: each cell is the share of failing dies that fail both tests

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Reading fails together

Read this view when you want to know which failures go together.

  • A high cell means the two tests tend to fail on the same dies, which often means one cause
  • A low cell means they fail on different dies
  • The card names the pair that shares the most failures, and clicking a cell shows that pair in the scatter
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Open a pair

Click a cell and the scatter shows that pair, with r and n, the number of dies, above it. Here idsat_p_uA falls as vth_p_mV rises, r = −0.81, a strong link. Click a point to open its wafer's map.

The scatter after clicking the idsat_p_uA, vth_p_mV cell

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Log axes

Log X and Log Y draw an axis on a log scale, which helps when values run over several orders of magnitude, such as leakage. Each is offered only while every value on that axis is above zero, because a log scale cannot show zero or a negative number.

The scatter with Log X and Log Y both on

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Is it real?

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Bin buttons

The Bin 1, Bin 2 and Bin 3 buttons above the plot show or hide the dies of each bin. Click one to switch it off or on. This shows whether failing dies sit at one end of the relationship, which tells you whether the link has anything to do with yield.

The scatter with only bin 1 shown, the Bin 1 button outlined

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The Mixed Split warning

A strong r is not always real. Pooling splits can make a trend that is only the groups sitting at different levels, not a link inside each group (Simpson's paradox). The card warns when the dies mix a field, so you know to check.

The Mixed Split warning above the matrix

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One wafer at a time

The first check is to look at one wafer. The Wafer menu narrows the scatter to one wafer. The X and Y menus pick the tests, as the matrix cells do.

The Wafer menu on the scatter

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Inside one wafer

Looking at W07 alone, r is −0.564, not −0.81. Part of the pooled figure may come from the splits sitting at different levels. The warning is gone because only one wafer is left. The link is still there, but weaker than the pooled figure suggested.

The scatter for W07 · TT only

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A line for each group

The second check is to look at each group. With Group by on, the scatter colours the dies by group and draws a fitted line through each. If the lines sit apart but run parallel, the groups differ in level; if they run in different directions, the pair does not move together in the same way in every group.

The test scatter coloured by Split, with a fitted line for each split

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Within groups

You can run the same check on the whole matrix. With Group by on, it offers Pooled | Within Split. Pooled is the matrix you have seen. Within takes each group's own mean off every test first.

The matrix drawn Within Split, with Within outlined

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Pooled or within

Compare the two views pair by pair.

  • Taking the group means off means a difference in level between groups is not read as a link between tests
  • A pair that is strong pooled but weak within is the groups sitting at different levels, not the tests moving together
  • A pair that stays strong within is a link inside every group
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Group by

You can also look at one group on its own. Group by → Split, then Show → TT: the matrix and scatter use only TT's dies. idsat_p_uA against vth_p_mV reads r = −0.41 inside TT, not −0.81 pooled. The link holds, but part of the pooled figure was the splits sitting at different levels.

The Correlation tab with Show set to TT

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Dies from the scatter

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Drag a box

To find out which dies sit at an extreme of the relationship, drag a rectangle over the scatter. The dies inside it, on any wafer, open the menu of charts and tables for just those dies.

A box dragged over the scatter, with the menu of charts and tables

(The same menu is the subject of lesson 08.)

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Try it yourself

  1. In the web app, Load sample data, then Insights → Correlation
  2. Click the cell for idsat_p_uA and vth_p_mV: what is r?
  3. Pick W07 · TT in the Wafer menu: how does r change?
  4. Group by → Split, then Show → TT, and pick the same two tests again in X and Y: does it still hold?
  5. Drag a box over the scatter: how many dies does the menu say you have selected?
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Check your results

  1. idsat_p_uA against vth_p_mV reads r = −0.81: when one rises the other falls. (vth_n_mV against idsat_n_uA reads −0.81 as well.)
  2. On W07 · TT alone r is −0.564, weaker than the pooled −0.81. The warning has gone, because one wafer is not a mix of splits.
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Check your results, continued

  1. Inside TT, r is −0.41: still clearly negative, but weaker than pooled. Some of the pooled figure came from the splits sitting at different levels.
  2. The menu names how many dies you selected; it depends on the box you drag.
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Recap

  • The matrix shows every pair; a cell opens that pair as a scatter
  • r says two tests move together, not why
  • Check it wafer by wafer and group by group before trusting a pooled figure

Next you will learn to filter and chart exactly the dies you care about.

More in the wafer map guide

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Next lesson

08 · Drilling into any population →

Filter, select and chart just the dies you care about.

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