Inspecting Reticles Based on Yield and Cost

As mask-making processes become more complex, opportunities exist to improve mask manufacturing cost¹ and turnaround time by performing pattern inspections during intermediate process steps.² The question is where and when to add inspection steps. We recommend a data-driven decision method in determining whether an inspection process should be added, as well as when it can be removed as a process technology matures and yields increase.
 
The cost-based model derived in this work is "forward looking" in that sunk costs are not considered and only remaining process step costs are considered. That is, the cost of materials and process steps performed prior to the inspection point have no influence on whether additional value should be added. However, yield of the prior process step is required, since it attributes to overall process yield.

We chose a hypothetical tritone reticle manufacturing process (Fig. 1 ) for this model. This is a generic process in the sense that the same process steps would be performed in order to manufacture a simple or complex tritone reticle. In a simple tritone reticle, the chrome attenuator is usually restricted to the frame and scribe areas surrounding the primary die. An example of a complex tritone reticle is the case of a high-transmission (at the exposure wavelength) embedded attenuator film, where chrome attenuator is present within the primary die so as to prevent excessive background exposure of the wafer resist. That is, chrome attenuator is required within a few hundred nanometers of an embedded attenuator to the fused silica (i.e., quartz) geometric boundary and is also required for correct imaging. The difference between the simple and complex tritone processes is in second-write exposure tool registration, resolution and CD capability requirements.

1. Defects relevant at the first inspection step include extra/missing attenuator and CD/write errors. Since most of the non-repairable yield-limiting defects are present at this point, it may be a good time to perform sensitive defect inspection.

As shown, it is possible to perform pattern inspections after the first write and etch steps and after the second write and etch steps. Defects that would appear at the first inspection step include extra/missing attenuator (both chrome and embedded materials) and edge misplacements (CD and writer errors). At this point in the reticle manufacturing process, the reticle would resemble a binary chrome-on-quartz reticle. Optical complexity of the reticle is minimal at this point. Since all of the critical edge placements are defined by the first write and etch steps and most non-repairable, yield-limiting defects are likely present, it could be argued that the most sensitive defect inspection should be performed after the first write and etch steps.

Process yields and costs are the sole factors influencing the inspection-step decision in this model. Process yield is an estimate of the empirical probability that a process step, or a sequence of steps, will be successfully completed. We assume that defect-limited process yields are known or can be reasonably estimated for each process step. Defect-limited yield is used since it is pertinent to the defect inspection step. Other yield detractors from other metrology steps such as CD and registration measurements were excluded.

In general, the average cumulative cost to manufacture a reticle is equal to the sum of the material, equipment depreciation, and overhead costs to manufacture one reticle divided by the overall process yield. If we consider arbitrarily splitting the manufacturing process into two halves and assigning costs and yields to each half, the cumulative manufacturing cost is:

Equation 1

In Equation 1 , Yield₁ and Yield₂ equal the defect-limited yield caused by the first half (front end) and second half (back end) of the process, respectively. The quantity (Cost₁/Yield₁) equals a portion of the input material cost to the second half of the process and Cost₁ and Cost₂ represent the added material (i.e., resist and chemical costs), equipment depreciation and overhead costs of the front-end and back-end processes. Equation 1 simplifies to:

Equation 2

It should be noted for the purpose of this work that the optimum position to split the process in half is at a point where an inspection step can be inserted, such as the first inspection step. This in-process step refers to the fact that the reticle is not completed, and further writing and processing steps are necessary.

We would like to determine the cost breakeven point in terms of yield for performing the in-process inspection. First, we assume a cumulative cost with only one inspection performed after the second chrome etch step. To identify this set of values for this scenario, all values in Equation 2 will be primed.

Equation 3

Since only one inspection is performed, Yield₁'=1.0 and Yield₂'=Yield₁ × Yield₂. The Yield₁' defect-limited yield is 100% since we have no knowledge of the defect level. However, the yield at the second half of the process is now impacted by the first-half yield, hence the multiplication of the original defect-limited yields. To solve for the breakeven cost, we set the cumulative costs equal and solve for Cost₁-Cost₁'. Cost₂ and Cost₂' are assumed to be equal for both scenarios.

Equation 4

If Cost₁-Cost₁ ^' exceeds the actual cost of performing an in-process inspection, then a cost savings can be realized on average.

We first studied a 90 nm node simple frame-and-scribe tritone reticle, where the first-level write was performed using a vector-shaped beam (VSB) 50 kV e-beam writer and the second-level write was performed on an i-line raster laser writer. The second-level total write time was two hours. First and second inspections were performed on a TeraScan inspection system with a total setup, inspect and review time of two hours (reticle defect repair costs were not considered). The data is normalized to Cost₂, and is plotted as a function of the front-end defect-limited process yield, Yield₁ (Fig. 2 ).

2. At a front-end process yield of 50%, the in-line inspection neither adds nor decreases cost, known as the breakeven point.

For this case study, the first inspection breakeven point occurs at a 50% defect-limited yield attributed to the front-end process only. The way Figure 2 should be interpreted is that, at a front-end process yield of 100%, none of the back-end process costs are saved and all of the first inspection cost is added to the manufacturing cost of the reticle, since the front-end process never contributes a defect that would cause a reticle to be rejected. At a front-end process yield of zero, 100% of the back-end process costs are saved and at a cost savings of 50% of the back-end process costs (however, a zero front-end process yield has its own cost issues).

At a front-end process yield of 50%, the added first inspection neither adds nor decreases costs and is called the "breakeven point" for this particular case. Note that the exact back-end cost estimates have a very strong influence on the breakeven point.

The second case studied was for a complex tritone reticle, where the only change from the previous case was that the second-level write was performed on a VSB e-beam writer with a total write time of four hours. The change in second-level write tool was necessitated by requirements for improved level-to-level registration and small feature resolution. Figure 3 shows the relative cost savings plotted as a function of the front-end defect-limited process yield. This change in second writing tool has increased the first inspection breakeven point from 50 to 72% front-end process yield.

3. A change to a back-end e-beam writer instead of laser raster scanner significantly shifts the breakeven point.

Since the second-level write time could be a variable dependent upon the amount of data to be written, and because of the e-beam writer's apparent large impact on breakeven cost, a set of calculations were performed varying second-level write time to determine the front-end process yield breakeven point (Fig. 4 ). The second-level write time is observed to have a large effect on the front-end yield breakeven point. This can be expected since writing-system depreciation is a major component of back-end manufacturing costs.

4. Second-level write time was varied to determine the front-end process yield breakeven point.

This cost model provides a good framework for determining the cost of an in-process inspection step in terms of process yield preceding the in-process inspection point and the subsequent manufacturing costs. However, a number of other factors need to be considered in deciding whether to add or remove an in-process inspection step.

The maturity of the manufacturing process in terms of yield stability and understanding of defect sources needs to be considered. We assumed relatively stable yields and that the Pareto distribution of defect sources were well understood — at least, attributable to the front or back-end processes. The addition of an in-process inspection can accelerate the cycles of learning in order to improve yield. In the first case studied, a 50% front-end yield was the breakeven point for the in-process inspection cost. However, additional cycle time would be added before the defects are detected if the in-process inspection were removed. This has the effect of lengthening the cycle of learning and slowing down the rate of yield ramping. Ultimately, this results in much higher cost.

Assuming that a process is running at a high front-end yield, changes in the back-end process or equipment set should trigger a re-evaluation of the costs involved. As shown in the second case studied, a change in the second-level writing tool made a large change in the breakeven point. Use of a high-end VSB writer instead of a laser raster writer drove more cost into the back-end process. More complex reticle-based resolution enhancement techniques (RETs) will likely drive the industry in this direction.

One also needs to consider the second-level write tool capacity and availability in making the in-process inspection decision. In the case of low availability or capacity of the second-level exposure tool, performing an in-process inspection in order to screen out defective reticles would help optimize the second-level write tool's productivity.

The cost model should be evaluated on a case-by-case basis. The reticle front-end yield may be influenced by a number of parameters, including the technology node that the reticles are being manufactured for and the wafer process level for which the reticle is being built (i.e., gate, contact, metal or via). The reticle-based RET used is related to these two parameters, and an appropriate inspection methodology for each RET is required. Each requires its own cost model evaluation based on its respective front-end process yield and back-end manufacturing cost.

Repair capability or difficulty should also be considered in making in-process inspection decisions. For reticle manufacturing processes that involve quartz etching, it would be easier to repair a chrome defect than a quartz-phase bump defect that is detected after the quartz etch step.

Although not considered in this study, the second inspection could be optimized to detect defects that are produced in the back-end process. For the simple tritone case, these would consist of extra and missing chrome on top of halftone (embedded attenuator) material. The defect detection requirements are typically less stringent for this class of defects than for CD and edge-misplacement defects on the halftone-to-quartz edges.

One overlooked factor when considering in-process inspections is the impact on inspection system evaluation, namely test masks. Test masks are typically representative of the completed reticle RETs. However, test mask design should consider including sections that are representative of intermediate process steps where an in-process inspection is performed.

Additional in-process inspections can be used to decrease reticle manufacturing costs, and their benefit can be determined from a knowledge of front-end process yield and back-end process costs. This needs to be considered on a case-by-case basis since yields and costs may be influenced by reticle RET choice and back-end writing strategy.

Changes in back-end process costs can greatly impact the in-process inspection breakeven point and should be re-evaluated when back-end process changes are made. The primary focus of this study was cost. However, cycle time could be substituted in place of cost to determine potential gains in cycle time by performing an in-process inspection.

This article is based on a paper that was originally presented at Photomask Japan 2004 (SPIE Proc. Vol. 5446, Photomask and NGL Mask Technology XI). Reprinted with permission from SPIE.