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VR Matching - Applications

Application 1: Single Wafer Self Analysis


Vector Raptor - Overlay & Double Pattern Modeling

VR Matching Brochure  

Advanced Setup & Fault Analysis using

Comparative & Difference Matching


Processes, Tools & Metrology.

(Imports any type or brand of metrology data)


This application example illustrates how the process variation across a wafer can be analyzed using the Difference Analysis. A particularly “noisy” metrology sample has been selected for the analysis to provide opportunities to illustrate methods for culling poor data. Reference data will be restricted to the center die on the wafer and this die will be subtracted from the remainder of the wafer data to see the full across-substrate variation.


Data Input:  A single overlay data file with some sites exhibiting poor metrology.

Analysis: Examine the variation field-to-field across the wafer. Illustrate methods of data culling so that metrology and setup errors are removed and the true process response can be examined.

Data fileNikon_raw_data-fullpgm49pt.XLS

Raw Data Input

Figure 1: Raw Data as input showing

Top:                       XY vector plot of raw data input.

Bottom Left:        X-reg vector plot of single variable

Bottom Right:     Y-reg vector plot of data

Raw Data Configuration

An overlay data set is shown in Figure 1. The vector plot in the top of the figure clearly shows some sites that exhibit poor metrology and the resulting large offset in the X-overlay values in the statistics. 

The bottom plots of Figure 1 show one-dimensional variable variation for the X-reg (left plot) and Y-reg (

right plot) data points. X-reg values exhibit a maximum value of 1.3 um, as reported on the “Scale” key on the bottom of the figure, with the majority of the data values ranging between 0.0 and -0.1 um as shown in the color bar-code key located in the lower right.

Y-reg values are more uniformly distributed as shown on the right-hand plot.

The analysis will require two levels of data culling:

  1. Both Reference and Match data must remove the large X-reg data metrology errors.

  2. The field in the center of the wafer is the exposure that is least subject to cross-wafer and wafer-edge process variation. The Reference data will therefore be culled to remove all but the data located on the center field.

Culling by X-reg Variable Range

Data culling histogram tool

Figure 2: Data Culling histogram tool
Upper: X-reg & Y-reg histogram of raw data
Lower:  Variable range culling setting that removes 29 data points

Use the left mouse-button to box-in the vector plot of Figure 1. Select a histogram plot from the pop-up menu to view the graphic of Figure 2.

The Histogram in the upper half of Figure 2 shows both X-reg and Y-reg variables with very similar major populations extending from -0.1 to approximately 0.0 um. The box-plot figures at the top and bottom of the histograms confirm this distribution. Some X-reg data extends as down below -0.4 um but the extreme points are not shown in the X-axis scale range.

Based on the histogram data, the Variable Range Cull settings are selected in the Variable Cull frame and entered as shown in the lower half of Figure 2. Subsequent plotting of the match or reference data shows that a total of 29 data sites are removed. Since the same data is loaded into both the reference and matching sections, these range cull values should be entered into both interfaces to remove the poor metrology points.

Culling User-Selected Sites Using the Mouse

Next we need to remove all but the data points associated with the center field on the wafer. Recall that this field will be the one that is least influenced by process and grid-alignment. If we remove this field, we can then see process variations across the wafer/substrate.  Two steps in the field-removal sequence are shown in Figure 3.

The general procedure is to drag the left mouse-button to box in all data points we want to remove and then select the “Cull selected data points” pop-up  menu option to remove all points in the box. The status bar at the left-bottom of the interface will indicate the number of points removed each time.

Figure 3:  Final Setup of Reference Data - selecting the center field exposure

Left:    After removing the data points above, the mouse is used to box-in the fields to the left.

Right:  Final Reference data field left after culling all fields but the center field.

Note: Any data points culled by this method can be easily restored by once again boxing in an area of the wafer and then selecting “Restore culled data in the selection” from the pop-up menu.

In our example we chose to first box-in and remove the fields located above the center-field. The 2nd step, shown on the left side of Figure 3, next removed the data points to the left of the center field. Finally, two box mouse selections, below and to the right of the field, resulted in all data being removed except for those data points on the reference  lots center field as shown in the right side graphic of Figure 3. 

Our reference lot is now ready and to be removed from the Match Lot as shown in Figure 4. The reference lot now contains 48 active data points in the center field and the Match Lot has had all poor metrology removed.

Figure 4: Reference & Match data now setup for Difference Calculation

Since both lots have the same field-site spacing, we can use the “Point-for-Point” difference calculation without Interpolation. An analysis similar to this could also have been performed without data culling by checking the “Average Field” control. Since we do not want our data to be influenced by larger edge-wafer excursions, we have instead decided to not use the site-averaging method.

Notice that the reference field in this case has one site removed by the range-cull feature. In a Point-for-Point difference, the final difference lot will there have only 48 points per field rather than the full 49 sites of the original layout.

We now wish to create a “Vector” plot of the X-Y Vector (X-reg,Y-reg) difference and show the resulting statistics. To do this we allow the analysis to auto-scale by setting the Scale field value to “0” and checking the “Statistics” box.

Note that we have chosen not to save the resulting difference data by removing the “Save Results” check mark.

Press the “Calculate” command to create the difference plot of Figure 5. 

Figure 5:  Results of the Difference Calculation

Left Plot:              Whole wafer vector plot showing variation across the wafer.

Upper Right:        Collapsed field plot of vectors plotted at their field-site location.

Lower Right:       Histogram of X & Y overlay variation across the wafer.

 Results of the Difference Calculation

The wafer vector plot of Figure 5 illustrates the differences seen across the wafer. Notice that, even though it is partially hidden, the center field vectors are of zero length. We will address this with greater clarity below.

The actual data for the follow plots can be seen in spreadsheet format by selecting the “Data/View Data” menu command.

First observations suggest that the while some individual data points are seen as larger vectors approaching 0.05 um in size, most of the noise appears to be associated with across the field variation. There is very little suggestion of across-wafer systematic variation.

The field-vector plot in the upper right illustrates this across-exposure variation. Recall that the wafer-center field values were removed from every field on the wafer. Yet the variation across each row of the field-vector plot suggests a noise signature that is very systematic. The histogram of the figure also shows the near Gaussian or random distribution of the majority of the data points with excursions extending off to the positive values of overlay error.

This across field signature cannot be a lens or reticle related problem since the center field was removed. The variation is therefore represents the basic overlay capability limit of the exposure tool due to across reticle scan noise.

Notice that the full wafer overlay range of Figure 4 is (X,Y) = (0.187, 0.114) um. The across-wafer range of difference variation seen in Figure 5 is (0.175, 0.137) um suggesting the very little of the variation is due to lens/reticle problems. Scan noise, particularly at the extremities of the left side of the field, are the limiting the capability of this exposure tool.

Figure 6: Difference Data plot of variation across the center row of Field Sites

Examination of Reticle Stage Scan Noise

Variation across the center row of the field exhibits a base noise-signature for the reticle scan stage. The stage varies about zero with the extremities being greatest near the edges as shown in Figure 6. To generate this plot first plot the Difference Lot onto a Field-Vector plot as shown on the right side of Figure 6. Next use the left mouse-button to box in the center field row of data as outlined in the red box on the same plot. Finally choose the “Plot Selected Data/ XY Graph as Columns” menu selection from the pop-up menu.

We added two red lines that plot the path of each X-field-location’s median X & Y data population. To do this:

  • Right click the XY graph of Figure 6 and the Graph Editor interface will appear. 

  • Check the Box-Plot field on the “Chart Options” tab to generate a series of box plots.

  • After plotting, next select the “Contour Profiles” and “50% median” series check boxes and click the “Apply” button.

  • Turn off the box plots by un-checking the “Box-Plot” check box.

The two red lines plot the course of the median X and Y overlay error vales for each site on the field-row. This is essentially the amount of overlay scan noise present in the center of the field as the reticle is exposed in both scan directions and across the wafer. The X and Y axis overlay values closely track each other never varying by more than 10 nm except at the extreme left hand position on the slit where we see a split difference of close to 20 nm at -12 mm from field center.

Figure 7: Variation of slit overlay across wafer.

An X-axis stepping of 13.5 mm was used to show field center and edges for the 26.5 mm X die size.

Slit Scan Noise across the Wafer

We next examine the field noise variation across the full wafer as shown in Figure 7. To create this graph:

  • First plot a wafer-vector plot of the Difference Lot a portion of which is shown in the lower plot of Figure 7.

  • Use the left mouse-button to box in, as shown by the red box, the center row of data sites on the plot.

  • Select the  “Plot Selected Data/ XY Graph as Columns” menu selection from the pop-up menu.

  • Finally right-click the XY Graph and turn on the “Connect” check boxes for the X and Y series data and adjust the stepping and range of the graph axes.

First note that the sites of the center field, our “reference” field, are all set to zero because of the subtraction. The left-most die on the wafer has the greatest variation due to stage leveling. Every other field, starting with the left-most exposure on the wafer, exhibits a high tilt or slope across the slit. Conversely the 2nd and 6th fields show no tilt but a characteristic “W” pattern to the slit. The 4th field is represented by the reference die so we see it set to zero. This alternating variation suggests a scan direction dependence of the overlay errors that exaggerate the normal scan noise seen across the die.

Figure 8: Variation of X & Y overlay as a function of Radial Distance from Wafer Center

Radial Variation across the Substrate

Select the “Radial” entry from the “Graphic” combo control of the interface to generate the graph of Figure 8. The graph has been enhanced by setting the axes and adding two 2nd order fitted curves to the graph using the graph editor. Two observations can be quickly made from this plot:

  • The points located < 12 mm from the wafer center are all zero in value thus representing the reference field located at the center of the wafer.

  • The variation at the wafer edge position greater than 90 mm is significantly different than those of the interior dice.


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