Quantifying Focus-spot related Yield Loss

Garry Tuohy, GLOBALFOUNDRIES Inc., Dresden, Germany.

Abstract — Pressure to maximize yield has increased attention on backside wafer cleanliness. To perform adequate cost-benefit analysis for potential backside cleaning methods, the cost in terms of yield must be quantified. A method for quantifying the yield impact of focus-spots is presented. Attempts to predict die loss from the measured height of focus-spots proved to be of limited value for 65nm technologies but entirely practical for 28nm.

Key words — focus-spots, wafer backside defectivity, yield loss estimation

1. Introduction

The constant pressure to maximize yield as wafer processing costs and constraints on depth-of-focus increase have directed ever more attention towards backside wafer cleanliness and its subsequent affect upon focus-spot generation. In order to perform an adequate cost-benefit analysis for potential backside cleaning methods, the cost in terms of yield must be determined. A method is presented for quantifying the yield impact of focus-spots resulting from backside contamination.

2. The Challenge

Utilizing the Stage Distortion Map data from the Scanners/Steppers is a novel means of monitoring backside wafer cleanliness and has the added advantage of filtering out the least significant defects (nuisance, roughness). For the purpose of process control and monitoring it is sufficient to track the number and height of focus-spots. A stack map of focus-spots detected at a specific Mask Operation for more than 33000 wafers can be seen in Fig. 1.

It is also possible to convert these data to an equivalent defect map and perform a contingency analysis. However, this does not address a focus-spots ability to impact multiple adjacent die. This leads to the obvious questions; a) which focus-spots are yield relevant and b) what is the extent of their yield impact?

Fig.1: A focus-spot stack map from more than 33000 wafers at a specific Mask Operation with circle sizes representing the measured spot height.

3. Quantifying the focus-spot Loss

The method used to determine the area of influence of a given focus-spot is to calculate the vectors from the focus-spot to the corners of its resident die and to construct the perpendicular bisector that intersects at the focus-spot. Ordering the vectors according to their length identified the sequence of nearest neighbour die. Sorting through this sequence of die until a non-power related failing die (n) is encountered, identifies the maximum possible radius for the focus-spot and the number of die affected (n-1). The length of the previous vector can be considered as a minimum possible radius for the focus-spot. Figure 2 illustrates these relationships for a focus-spot that impacted two die — the die containing the center of the spot and the die immediately above it.

Fig. 2: Example of a focus-spot affecting two die and vectors to nearest eight neighbour die; identified by labels 2 to 9. The two failing die are indicated by the red background shading and with the labels 1 and 2.

There is a small risk of obtaining a “Hit” to a die with an unrelated power failure when none exists. This risk increases with larger die sizes, but is negligible for typical yield levels seen in volume production.

An ovular search pattern linked to the die size is employed for optimal overlay, in order to compensate for possible non-circularity of the defective regions. This does introduce a slight risk of erroneously including additional die and artificially increasing the loss estimate. This can be ignored for all but the most extreme outlier wafers.

Assessing the size and yield impact of focus-spots is less accurate for Edge Die due to the lack of neighboring die. Off-Die-Grid focus-spots should be aggregated separately due to the limitations of this method.

An example of a severe case can be seen in figure 3 where multiple die were affected, along with a subsequent defect inspection which revealed the same pattern.

(a)

(b)

Fig.3: Example of wafer backside defectivity resulting in (a) 14 failing die and (b) the front side defect map from a subsequent defect inspection.

Once these loss estimates exist on a wafer-mask level it is straightforward to aggregate these data in order to produce charts or stacked wafer maps for reporting purposes, to analyze the impact of experiments or monitor the result of process changes in terms of yield.

4. Focus Spot Loss Prediction

The possibility to predict die loss from focus-spot height was examined. It was clear that higher focus-spots are more likely to kill more die. However, the considerable overlap between the height distributions for each die loss value makes discrete prediction problematic.

This is also illustrated conversely in Figure 4 where the percentage of focus-spots generating a given number of failing die, within each focus-spot height bin is shown. Clearly a given spot height can result in a range of failing die numbers and this is driven by the location of the focus-spot. While it is rare to observe more than four failing die for typical die sizes, in the case of particularly small die sizes, this would not be expected to hold true.

Fig.4: Percentage of spots vs. focus-spot height, coloured by number of die lost. Layers A and B represent two upper BEoL layers with distinctly differing response. Layer C represents a typical BEoL layer while Layer D represents a FEoL step (the limited number of spots in the FEoL restrict the useful range of this chart to the first 6 bins).

This chart is not intended to generate a convenient model, but the percentages of focus-spots that generate zero failing die should be similar for products with similar critical-areas, irrespective of their die sizes. However, we would have to expect the percentages of focus-spots that generate higher numbers of failing die to be influenced by the size of the product’s die. This chart also helps to illustrate that you need focus-spot with considerable height to guarantee a failure and in some cases, a failure cannot be guaranteed within the range of typical focus-spots heights, which is a function of the critical-area at each mask layer. Additionally, it should also help to demonstrate that a focus-spot of a given height can generate a range of failing die numbers, depending upon its location within a die.

In an attempt to develop a model for focus-spot impact that can consider the influence of spot location as input to each loss prediction and which is independent of any specific product, we proceed to examine the data for a more fundamental relationship between the spot height and its impact radius.

Fig.5: Estimated focus-spot impact radius versus measured focus-spot height for a BEoL Mask Operation (Layer D from Fig. 4).

Fig 6: Estimated focus-spot impact radius versus measured focus-spot height for a upper BEoL Mask Operation (Layer A from Fig. 4), with logistic regression fit shown by the green dotted curve.

Examining the relationship between spot height and impact radius often shows linear relationships where sufficient data exists (see Fig. 5). The exposure window can influence the point at which this relationship starts. However, other layers clearly demonstrate a sigmoidal relationship (see green dotted curve in Fig. 6).

The form of the central tendency of the distribution is driven by the critical-area and mask layer’s exposure window, while the scatter around this tendency is a function of the die size and the location of the focus-spots — spots located near the corner of a die will have a much more precise estimates of their impact radius as compared with those that occur near the center of a die. Recognizing these differences allows for superior predictions of a focus-spots impact radius, the subsequent loss of die and allows affected die to potential be inked.

5. Conclusion

A method for determining the yield impact of focus-spots resulting from wafer backside defectivity, as measured by Lithographic Scanner’s stage distortion mapping capability was presented. This is not intended as a replacement for Wafer Backside Inspection, however the existence of these data for every wafer-mask operation makes their utilization compelling. This is particularly in relation to quantifying the effectiveness of wafer backside cleaning initiatives.

Attempts at predicting die loss from the measured height of the focus spot was determined to be only practical for the early FEoL mask operations, on 65nm technologies. For 28nm and below relationships can clearly be seen throughout the manufacturing process.

Acknowledgements

I would like to acknowledge Christian Hobert for identifying the existence of these data and initially suggesting its utilization.

References

[1] Saravanan C., et al., Investigating the impact of backside defect inspection on process development and yields. Micro Magazine, April 2004.

[2] Cheema L, et al., Yield Enhancement from Wafer Backside Inspection. Solid State Technology 46, pp 57–60, Sept. 2003.

[3] Carlson A., Le T., Microlithography International Symposium (31st), Feb. 2006.