The Cost of Imperfect Wafer Environmental Control, Part 2

Devon Kinkead and Jim Mastrobuono Extraction Systems Inc., Franklin, Mass. Kim Dean and Walt Trybula International SEMATECH, Austin, Texas -- Semiconductor International, 7/1/2001

	At a Glance
In the second installment of this two-part article, we explore the implications of imperfect molecular base contamination control in advanced lithography and contemplate a number of return-on-investment scenarios for on-line contamination metrology equipment.

Chemical spills in adjacent bays, coolant leaks in step-and-scan systems, and inadequate tool pressurization can and do cause resist contamination. Contamination event probability studies demonstrate that the resist-coated wafer is exposed to greater than 5 ppb in the stepper 1% of the time and 5% of the time in the track. At ramp delay costs of $2.5M/day (see "The Cost of Imperfect Wafer Environmental Control," Semiconductor International, June 2001, p. 135), the cost of contamination can be characterized as the product of the event probability and the event cost, which is related to the percent of the total CD (critical dimension) budget consumed by contamination alone. The mean concentration of a contamination event, defined by a >5 ppb total molecular base measurement in the body of the track or stepper, is 6 ppb for the stepper and 8 ppb for the track. These measurements are typically taken sequentially every 20 min or 200 min between measurements based on 10 monitoring points. For the sake of conservative modeling, we will assume that a 7 ppb event lasts 5 hr — based on a 1457-count track data set with a contamination event probability of 1%. The Table, which models a 248 nm wavelength, 180 nm CD continuous process, demonstrates that, 1-5% of the time, 32% of the CD budget would be consumed by contamination for 5 hr in an otherwise continuous process.

Table. Typical Concentration of Contamination Eventin 248 nm, 180 nm CD Continuous Process (1)
Concentration (ppb)	CD shift (nm/ppb-min)	Exposure (min)	CD change (nm)	CD budget (nm)	% of CD budget
7	0.368	2	5.7	18	32%

The cost of this event during a new production ramp depends on the cost of a loss in CD control, which is related to device characteristics. Certain trends are evident. Figure 1 shows the general increase in contamination sensitivity for both dense and isolated features with smaller target CDs.¹ The cause of this trend may be, at a first-order level, the result of reduced film thickness over time. Figure 2 plots n-methylpyrolidone (NMP) concentrations over time in the resist films with progressively reduced thickness for the case of an ideal resist (lower line) that does not absorb NMP, and a chemically amplified resist that typically absorbs NMP (upper curve). The NMP adsorption data were derived from a report by Hinsberg et al (1993) of an NMP absorbance rate of ~10 ng/min within the first 15-20 min for all of the resist systems examined. Figure 2 assumes a 15 min delay, which yields a total mass of 150 ng NMP/wafer, which is then divided by the resist volume to create the upper curve. Viewed simplistically, one could argue that, over the next five years, the absolute molecular base concentration in a resist bulk — considering only the surface area to mass ratio of the resist increases — will increase.² Figure 3 shows the higher sensitivity of the top (air/contamination interface) of thinner resists than the thicker resist when comparing the change in top CDs at relatively low contaminant concentration, 5 ppb ammonia.³

1. Chemically amplified photoresist sensitivity trends.1

Further study revealed a more complex contamination mechanism. Under conditions identical to those used for Figure 3, however, the change in the bottom CDs was not very different, suggesting incomplete contaminant diffusion through the film. At higher levels of contamination (Fig. 4), the bottom of the thick resist was only affected by NH₃, possibly because the other contaminants were too large to diffuse efficiently through the film. The bottoms of the thin resist profiles were affected by all contaminants; perhaps all the contaminants could diffuse through the entire film thickness (150 nm). Irrespective of the exact contamination mechanism, all these scenarios were warnings of contamination in thin films.

Figure 5 shows the percentage of the total CD budget consumed by a 7 ppb molecular base spike in an otherwise continuous lithography process patterning dense features — assuming current trends in resist sensitivity continue.

2. Projected NMP concentration in the resist bulk for an ideal resist (lower line) and a more typical resist (upper curve) as a function of time and resist film thickness.

Here, the ramp costs are calculated for the 90 nm technology node, where 100% of the CD budget is consumed by a typical contamination event 1-5% of the time, at 1-5% of $2.5M/day, i.e., $25K-125K/day. The contamination ramp cost at the 130 and 150 nm technology nodes is then some proportional fraction of the $25K and $125K/day figure.

Cost of implementation

The value of a wafer depends on the quantity of acceptable product and the individual performance of these products. The distribution of products from a manufacturing lot follows a classical normal distribution, assuming that special causes of variation are not process-resident.

Market forces that reflect the scarcity of the higher-performance devices determine any additional value. While it is possible to observe trends across the industry, device-specific analysis can only be conducted by the device manufacturer. An initial analysis⁴ depicts potential areas of corporate benefit from an increased control of the CD of key levels in the manufacturing process. Figure 6 is a newer representation of this concept and is explained below.

3. Comparison of top and bottom CD changes in thick and thin resist films in response to a 5 ppb ammonia environment.

Several authors^5-7 have reported estimates of the cost of CD variation. The effect of a contamination event on CD variation is the product of the actual effect.

4. Comparison of top and bottom CD changes in thick and thin resist films in response to a ~30 ppb ammonia and mixed-base environment.

Assuming a conservative value of a 6 nm/min CD shift upon exposure to a TMB concentration of 15 ppb for 1 min, and the probability that an event will occur at about 1%, the contamination effect on CD variation is 0.06 nm in added variation (6 nm CD shift × 1% = 0.06 nm). The cost of monitoring is $0.12/wafer, and with this we can begin to discuss when monitoring does, and does not, make economic sense.

Figure 6 describes the relationship between three parameters: the economic penalty for increased CD variation, the number of die per wafer, and the cost of monitoring divided by the cost of variation. Much like an investment in a smoke detector to protect a home from fire, the cost of in situ real-time monitoring cannot exceed the possible return it offers. In short, the solution cannot be more costly than the problem, the problem being defined as the probability that the problem will occur multiplied by the cost of the problem when it does occur.⁸

5. Percentage of CD budget consumed as a function of target CD.

Figure 6, then, demonstrates the following:

• Monitoring does not make economic sense when the penalty for increased CD variation is less than $0.20/nm/die and the number of die per wafer is less than 20.

• Assuming that measuring a process-limiting parameter enables at least a 10% reduction in process variation, a return on investment in monitoring would yield a return in all cases where metrology cost/CD variation cost ratio is less than 0.10.

• The return-on-investment argument is very sound for cases where both the CD variation penalty and the number of die per wafer are high.

Using the $9/nm/die figure,⁵ the return-on-investment arguments are compelling because the metrology cost/CD variation cost for all cases of 150-500 die/wafer is less than 0.001. That is, a 10% reduction in CD variation would be possible with a monitoring cost of 1/100 that amount (0.1/0.001) = 100× return-on-investment opportunity.

Conclusions

6. Return on metrology investment depends upon the cost of process variation, the number of die/wafer, and the perceived benefit that can be obtained through data-driven process control.

Molecular contamination control will become more critical as we march forward, and is likely to consume an increasingly larger portion of the total CD budget. On-line contamination monitoring is perhaps the only way to systematically improve control over time. Having said that, many questions remain unanswered in the area of managing work in process contamination risk and disposition decision logic using real-time contamination data streams. These questions will prompt us to the further work and solution codification needed to keep the semiconductor industry on the productivity curve.

Devon Kinkead, a founder of Extraction, has several years of experience as project manager of AMC control projects on process tools and cleanrooms in fabs, as well as many other industrial applications worldwide. He has a bachelor's degree in biology/chemistry from The Claremont Colleges.
Phone: 1-508-553-3900
e-mail: dkinkead@extractionsystemsinc.com

James Mastrobuono recently joined Extraction as the corporate quality director. He holds a B.S. in chemistry from Gannon University and an M.A. in environmental studies from Brown University.
Phone: 1-508-553-3900
e-mail: jmastrobuono@extractionsystemsinc.com

Kim R. Dean is project manager of the 157 nm resist development group at International SEMATECH. She received her Ph.D. in physical chemistry from the University of Texas in 1990 for her research in the photophysical properties of polymers.
Phone: 1-512-356-3500
e-mail: kim.dean@sematech.org

Walt Trybula is an International SEMATECH Senior Fellow in the lithography division. He has a Ph.D. in information science from the University of Texas, an M.B.A. from James Madison University and a B.S. in physics from the Illinois Institute of Technology.
Phone: 1-512-356-3500
e-mail: walt.trybula@sematech.org

---

REFERENCES

1. M. Ercken, D. Ruede, "Molecular Base Sensitivity Studies of Various DUV Resists Used in Semiconductor Fabrication," SPIE 2001, February 2001.
   
2. Simple geometry says that the concentration of leaves (leaves/gallon of water) in a 1 meter deep open swimming pool after a storm is higher than for an adjacent pool of the same size but 10 meters deep. Employing Ockam's razor — an axiomatic principle credited to 14th century scholastic William of Ockham, which states, pluralitas non est ponenda sine necessitate, or "plurality should not be posited without necessity" — all else being equal, the shallow swimming pool explanation may be a first order effect.
   
3. K.R. Dean, O. Kishkovich, "Environmental Stability of Chemically Amplified Resists: Proposing an Industry Standard Methodology for Testing," SPIE Advances on Resist Technology and Processing XVII, Vol. 3999, 2000, p. 284.
   
4. D.A. Kinkead, K. Turnquest, W. Goodwin, "Modeling and Controlling the Effects of Base Contamination in DUV Lithography Resists," Micro, October 2000.
   
5. Cost of CD variation = $9/nm. Sturtevant, "Manufacturing Implementation of a Feedback Controller for CD and Overlay," Microlithography World, Summer 1994.
   
6. A gate CD of 225 nm yields a 200 MHz device with an average selling price of $x while a 195 nm device yields a 300 MHz device with an average selling price of $4.6x. H. de Haas, "Proportional relationships between gate CD and die average selling price," ASML.
   
7. +3% of linewidth yields an average selling price of $x, < target - 3% yields a $2x average selling price, and > target + 3% yields $0.5x average selling price. Preil, Levinson, "Yield Limiting Issues in Deep UV Lithography," Microlithography World, Spring 1998.
   
8. These concepts of chance, which are foundational to the modern insurance industry with its actuarial mathematics, were originally described in the early 18th century by Bayes and de Moivre in The Doctrine of Chances. Bayes defined the probability of any event as the ratio between the value of an expected event and the value of the event actually occurring.
   

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