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Critical Dimension Sample Planning for 300 mm Wafer Fabs Sung Jin Lee, Raman K. Nurani, Ph.D., Viral Hazari, Mike Slessor, KLA-Tencor Corporation, J. George Shanthikumar, Ph.D., UC Berkeley

Critical dimension (CD) control is crucial in photolithography and etch processing steps, because of the relationship between gate length and device speed performance. To control the CD, values of lot average and/or lot variance are generally plot ted on SPC charts to detect mean and variance excursions that occur during these processes. An optimal sampling plan and control methodology must not only enable resolution of important (yield-impacting) excursions, but also minimize the time it takes to detect an excursion, thereby minimizing the number of lots exposed to an excursion.

A CD sampling plan specifies what CD measurements are performed, i.e., how many lots, how many wafers per lot, how many fields per wafer, and how many sites per field; as well as which wafers, fields, and sites are measured. The control methodology specifies how CD measurements are used to characterize normal variations and monitor and control deviations. This includes design of appropriate SPC charts and APC (automatic process control scheme with either closed or open loop feedback). A comprehensive methodology was previously presented2 to evaluate the effectiveness of different sampling plans by using the data from a 200 mm advanced logic fab. The effectiveness of a given sampling plan was evaluated by trading off the beta risk (probability of having material at risk) and the alpha risk (probability of having a false alarm). The current paper extends this methodology to the 300 mm domain, discusses potential issues for CD control of 300 mm patterning processes, as well as sampling recommendations for certain conditions.

The primary driving force for the 300 mm transition is the anticipated reduction in total production cost per square inch of silicon. The key to achieving this is to increase 60

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the productivity of the yielding die and wafers at minimum total cost. It is very important to note that the total cost includes not only the cost of producing the wafers but also the cost of controlling the process for minimizing the material at risk. While reducing the total cost of operations, it is critical to optimize the value of in-line defect and metrology inspection.

Otherwise, the cost of increased material-at-risk due to poorly optimized inspection methodology will outweigh the savings from reduced investment in process control.

A 300 mm wafer has 2.25 times more area than a 200 mm wafer. If all other parameters are held constant, it results in 2.25 times more die per wafer, with correspondingly more material exposed to process excursions.

Along with the 300 mm transition, the semiconductor industry is also transitioning from 248 nm to 193 nm lithography, from aluminum to copper interconnect metals, and from silicon dioxide to low-Îş interconnect dielectrics, all driven by ever-shrinking design rules.

Although a statistically determined sampling plan is essential in understanding and reducing material-at-risk, in practice, many sampling plans are still determined by historical precedent. Few papers present statistical approaches to determining the optimal sampling plan1.

In the current paper, issues and concerns regarding the importance of CD control in a 300 mm fab are presented.

A simulation study is presented, where 300 mm CD variations and excursions are simulated and compared

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to data from a 200 mm advanced logic fab1. Finally, CD sampling requirements for a 300 mm fab for excursion monitoring are evaluated. We will demonstrate that use of a sampling scheme optimized for 200 mm patterning processes will result in increased material at risk in a 300 mm fab, thus emphasizing the need for characterizing and optimizing the CD sampling plan for 300 mm fabs.

F i g u re 2. The area increas e in 8 to 12 inch wafer diameter transiti on

CD control for 300 mm

is much hig her than t hat of 6 to 8 inch wafer diamet er transition.

A primary requirement for designing an optimal CD control methodology is to characterize and understand baseline spatial CD distributions across the lot, wafer, and field. Below, we outline some anticipated characteristics of a 300 mm intra-wafer CD distribution based on variation signatures observed in 200 mm processes.

Stronger radial effects on baseline CD values Cross-wafer CD variations have a variety of sources, from direct causes such as etch-rate spatial non-uniformity, to those less direct, such as incoming film-reflectivity variation. These result in different baseline averages of the exposure fields on the wafer, as was reported in a case study 1. An example of a simple radial crosswafer CD variation is shown in Figure 1, with a typical (200 mm) 9-field intra-wafer sampling plan superimposed on the distribution. If such a variation signature were extended from a radius of 100 mm to 150 mm, the center-to-edge CD variation would be correspondingly amplified, resulting in a wider (and shifted) CD distribution.

Figure 2 graphically shows that the increase in the wafer area for the 8 inch to 12 inch transition is about 125 percent whereas the increase in the wafer area in the 6 inch to 8 inch transition is only about 69 percent.

Considering the fact that the device speed and performance are strongly influenced by CD, the amplified radial variation observed for 300 mm could cause significant deviations from specification near the wafer edge. Of course, these are the very die that are required to realize the potential benefit of the larger substrates.

It is important to characterize the spatial distribution of the baseline field averages by appropriate sampling plan and analysis for 300 mm processes; then, one can devise control and process improvement methodologies to reduce systematic variation signatures, such as the radial example presented here.

Higher baseline field-to-field variation: Need for Generalized ANOVA As discussed above for a 200 mm to 300 mm transition, one might expect an increased cross-wafer range of CDs, resulting in increases in both systematic (different field means) and random field-to-field variances. When a traditional nested ANOVA analysis technique is employed, higher systematic field-to-field variation has a greater chance of providing negative numbers for random wafer-to-wafer variation, as was shown in1.

Thus, for reliable estimates of 300 mm variance components, it is necessary to use the Generalized ANOVA presented in 1 for separating the systematic variations from random variation.

Impact of wafer level excursion on 300mm Y/mm X/mm

F i g u r e 1. Baselin e CD values across the di e showing stro ng radial e ff e c t s .

A previous paper1 discussed several CD mean and variance excursion types based on data from a 200 mm wafer fab. Some of those types are re-presented in Figure 3a and 3b under different groups. Observe that the occurrence of the first type affects CD deviations on all the fields on a wafer, either uniformly or with a certain pattern. Some of these examples include wafer Spring 2001

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F i g u r e 3a. Di ff e rent types of wafer level excursions.

wedge excursion and all-fields-down (where the CD values of all the fields on the wafer are far below the lower process control limit). The occurrence of the second type affects CD variation only on single field or on smaller subset of fields on a wafer. Some of these examples include one-feature-up excursion, and one-featuredown excursion in a field (see Figure 3b). Also, note that this type of excursion could occur randomly in any set of fields on the wafer. Excursions in both categories will become major issues in 300 mm fab. More area on 300 mm wafers can cause higher variation than in 200 mm wafers. The impact of these two groups of excursion types on a 300 mm wafer will be different and need to be studied.

Consider the case of wafer wedge excursion. There can be higher CD variation on the 300 mm edge fields as compared to 200 mm edge fields. This tells us that the excursions in the first category can cause more para-

F i g u re 3b. Dif f e rent types of field level excursions.

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metric yield problems in 300 mm fab than in 200 mm fab. Therefore, it is critical to minimize risk for 300 mm wafers.

Impact of field level excursion on 300 mm Because of the increase in the number of fields for a 300 mm wafer (see Figure 1), a given wafer has a greater chance of exposure to field level excursions before detection. Also, several lots may be at risk if there is a significant delay in detecting such an excursion. In a later section, we present the impact of using the 200 mm sampling plan in such scenarios and recommend a new 300 mm sampling plan. To detect field level excursions on 300 mm wafers, it may be important to control CDs at the wafer level or even within the wafer level, suggesting evaluation of lot-level SPC charts.

In summary, both baseline characterization and excursion detection should be examined more thoroughly in

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a 300 mm fab because of the greater material-at-risk in each wafer. The higher field-to-field variation expected across a 300 mm wafer will necessitate a baseline sampling plan that effectively resolves all significant variation signatures, as well as separates systematic (meanshift) from random variations.

A simulation study: Optimal 300 mm sampling plan for excursion detection

As discussed in the previous section, it is essential to have optimal sampling plans for both baseline characterization and excursion detection. In this section, we focus on the sampling plan for excursion detection.

First, we investigate application of the optimal 200 mm sampling plan for monitoring excursions in a 300 mm patterning process, and show that this direct transfer could cause significant increase in material-at-risk. We then propose and evaluate an improved 300 mm sampling plan that matches material-at-risk levels of the 200 mm sampling plan.

Assumptions

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8*2.25=18, and 18 respectively. This will lead to an excursion occurring every 30.8 (=50*32/52) lots on the average in an equivalent 300 mm fab, essentially doubling the excursion frequency Baseline averages and CD shifts during mean and variance excursions were extrapolated from the 200 mm fab data. Extrapolation was done by assuming that the CD values on a wafer follow a smooth radial pattern.

The most natural definition of a 200 mm sampling plan in 300 mm fab is to assume that the same measurement tool capacity is used by both of the fabs. To ensure this, the number of fields sampled in a 300 mm fab should be equal to the number of fields sampled in a 200 mm fab multiplied by the ratio between the arrival rate at a measurement tool for the two fabs. In this analysis, the underlying assumption was that the ratio was equal to one.

Results

200 mm wafer fab with 200 mm sampling plan and 300 mm fab with the same 200 mm sampling plan

Data from a 200 mm fab case study data is used for this evaluation1. As part of this case study, the optimal sampling plan in 200 mm fab was found through KLA-Tencor CD Sample Planner software. We denote the optimal 200 mm sampling plan as X wafers per lot, Y fields per wafer, and Z sites per field. It is assumed that the die size of a wafer is 1.3 x 1.1cm, and 6 die are in a field.

This assumption gives 138 die (23 fields) on a 200 mm wafer, and 366 die (61 fields) on a 300 mm wafer.

Baseline statistics and excursion statistics of CD values from the 200 mm fab case study was used. Because of the increase in wafer area, field-level excursion frequency (see the previous section, “Excursion Detection� and Figure 2) will increase by 2.25 times. However, we assume that excursion frequency in the first category remains same. Then, the mean time to an excursion in 300 mm fab, when expressed in terms of number of wafers or lots, will be much less than the mean time to an excursion in 200 mm fab. For example, suppose an excursion was seen in every 50 lots on the average in a 200 mm fab. Also, suppose that there are two types of wafer-level excursions, wafer wedge and all-up excursions, and that there are two types of field-level excursions, say feature-A-up and feature-B-down excursions.

Assume that the average number of occurrences of these excursions is 8, 8, 8, and 8 respectively. Extending this from 200 mm to 300 mm, the expected number of occurrences of these excursions will become 8, 8,

F i g u re 4. Usi ng 200 mm sam pling scheme for C D contr ol on 300 mm waf ers results in hi gher mater ial-at-risk.

Figure 4 presents the results of a 200 mm and 300 mm wafer fab with the 200 mm sampling plan. The vertical axis represents the average fraction of material-at-risk, i.e., the average fraction of lots that will be exposed to undetected process excursions. This is a function of the excursion types, their frequency of occurrence, their magnitude and the effectiveness of the sampling plan and control methodology in detecting process excursions. For this analysis, we assumed that the lot average and lot standard deviation of the CD values were used on SPC charts to monitor the CD variations. The horiSpring 2001

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zontal axis represents the average fraction of false alarms, which happens when the SPC chart provides a signal while the process is in control.

It can be observed from Figure 4 that for a false-alarm fraction of two percent, the fraction of material-at-risk increases by almost 50 percent from using the 200 mm sampling plan in 300 mm fabs. It is clear from this result that the 200 mm sampling plan can lead to very high material-at-risk in the 300 mm fab. Thus, an entirely new sampling plan is required to reduce the material-at-risk in the 300 mm fab.

It is important to emphasize that a one percent saving in material-at-risk could result in significant financial returns in a 300 mm fab. For example, assume that a fab has 5,000 wafer starts per week, 200 die per wafer on a 200 mm wafer and an equivalent 450 (=2.25*200) die per wafer on a 300 mm wafer, and $100 selling price per die. Then, one percent material-at-risk has a revenue potential of $1 million a week for the 200 mm wafer, whereas the 300 mm wafer has a revenue potential of $2.25 million a week, which translates into $117 million a year. Assume a very conservative yield benefit estimate of 10 percent, which is the difference between the baseline and excursion yield, and a baseline yield of 50 percent. Saving one percent materialat-risk will result in a net benefit of $2.6 million a year for the 200 mm fab, and $5.85 million a year for the 300 mm fab. Note that the excursion yield is generally much lower than the baseline yield. Also, the selling price for lower performance chips can be much lower. Hence the yield benefit of reducing material-atrisk by one percent can be much higher. This additional dollar saving needs to be weighed against the cost of any increase in capacity of CD measurements.

300 mm fab with 200 mm sampling plan, and a recommended 300 mm sampling plan KLA-Tencor’s CD Sample Planner was implemented to determine a sampling plan that would reduce the fraction of materials-at-risk close to that of a 200 mm fab.

Since 2.6Y number of fields gave the desired fraction of materials-at-risk, the CD Sample Planner suggested using X wafers, (2.6)Y fields, and Z sites, as a 300 mm sampling plan. Figure 5 displays the results.

Conclusions

Optimal CD control should be a primary concern for 300 mm fabs. To achieve this, the most appropriate sampling plan and control methodology must be deter64

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F i g u re 5. New 300 mm sa mpling p lan wit h mo re fields on the wafer reduces t he material-at-risk to the level of 200 mm waf er.

mined using quantitative statistical methods, such as KLA-Tencor’s CD Sample Planner. More frequent occurrence of certain excursions, a stronger spatial impact of these excursions, and higher field-to-field variation within a wafer are all expected for 300 mm patterning processes. These concerns will reinforce the necessity of more accurate characterization of baseline and excursion statistics through appropriately selecting the sampling plans and control methodology.

The utility of carrying an optimal 200 mm sampling plan into the 300 mm fab was evaluated under certain conditions. It was shown that there could be almost 50 percent increase in the fraction of material-at-risk when the fraction of false alarm is held fixed at two percent, by simply implementing the 200 mm sampling plan for a 300 mm fab. Considering the more severe effects of certain types of excursions in 300 mm wafers, this 50 percent increase may cause significant yield loss.

Clearly, a careful examination of 300 mm sampling plans is warranted to ensure realization of all the benefit of the larger wafer size.

References: 1 . R . E l l i o t t, R. N u r a n i , S . Le e , L . O r ti z, M . P r e i l, G. Shanthikumar, T. Riley, and G. Goodwin, “Sampling plan optimization for detection of lithography and etch CD process excursions,” In Proceedings of SPIE Metrology, Inspection, and Process Control for Microlithography XIV, vol.

3998 (2000) pages 527-536.

2 . B. Charles et. al., “Current state of 300 mm lithography in a pilot line environment,” SPIE conference on Pro c e s s , Equipment, Materials and Contro l, vol. 3882,140-153.

3 . A. J. Maltabes et. al., “ Integrated Metrology: The next logical step for increasing fab pro d u c t i v i t y. ”