OPC Model Generation Procedure for Different Reticle Vendors *
Andrew M. Jost ab, Nadya Belovaa, Neal P. Callana a LSI Logic, 23400 NE Glisan Street, Gresham, OR 97030-8411 b University of Oregon, Eugene OR 97403 ABSTRACT The challenge of delivering acceptable semiconductor products to customers in timely fashion becomes more difficult as design complexity increases. The requirements of current generation designs tax OPC engineers greater than ever before since the readiness of high-quality OPC models can delay new process qualifications or lead to respins, which add to the upward-spiraling costs of new reticle sets, extend time-to-market, and disappoint customers. In their efforts to extend the printability of new designs, OPC engineers generally focus on the data-to-wafer path, ignoring data-tomask effects almost entirely. However, it is unknown whether reticle makers’ disparate processes truly yield comparable reticles, even with identical tools. This approach raises the question of whether a single OPC model is applicable to all reticle vendors. LSI Logic has developed a methodology for quantifying vendor-to-vendor reticle manufacturing differences and adapting OPC models for use at several reticle vendors. This approach allows LSI Logic to easily adapt existing OPC models for use with several reticle vendors and obviates the generation of unnecessary models, allowing OPC engineers to focus their efforts on the most critical layers. Keywords: reticle, OPC, modeling, mask effects
1. INTRODUCTION The average turn-around-time for OPC model generation significantly increased at the 0.13µ technology node due to the necessity of model deployment on several critical layers and the difficulty encountered in generating and verifying models for 0.13µ designs. For new technologies, at least two learning cycles are required to generate a satisfactory OPC model, requiring approximately four to six weeks per cycle. In addition, each iteration requires a new, often expensive, test reticle. Under these demanding circumstances, OPC groups cannot afford to spend any more time than necessary to generate models and, if possible, must strive to reduce the number of new models required. Unfortunately, the need to reduce risk by qualifying multiple reticle suppliers often trumps these goals and OPC groups may be asked to develop models for several vendors. However, if several OPC models were generated from scratch for each layer, the OPC group would quickly become overwhelmed. Alternatively, if OPC models built on one vendor’s process are used with another vendor, serious risks are assumed since each vendor’s process can vary widely, even with identical tooling. It would be very beneficial, therefore, to have a methodology in place for adapting existing OPC models to several reticle vendors. In this way, the most tedious steps of OPC model generation, namely optimization and verification, can be performed only once for each OPC layer, while still producing many useable models.
2. EXPERIMENTAL METHOD 2.1 Materials and equipment Four reticles from two vendors were characterized for this investigation, each written from the same source data in different manufacturing facilities on ALTA3500 laser write tools. In this publication, the abbreviations A.1, A.2, B.1, and B.2 are used to distinguish each reticle according to its supplier. For example, the abbreviation A.2 refers to the second plate supplied to LSI Logic for this study from Vendor A.
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[email protected]; phone 503.618.5163
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The reticle layout was divided into 8.0 mm by 8.3 mm regions, each corresponding to a specific chrome load. Each region contains several redundant copies of the test features used for this study. This arrangement facilitates the collection of data at varying local chrome densities and at several points across the reticle, allowing a statistical analysis of each vendor’s process. All reticle measurements were performed with a Leica 250UV optical tool at 150X magnification using white light. Wafer measurements were performed with a KLA8100 series SEM. 2.2 Features investigated All measured features were dark field, indicating that on the reticle quartz spaces were the primary feature and that on the wafer trenches were the primary feature. Line ends, defined as a region of resist or chrome between two trenches or two projections of quartz, were measured at the exact center of the feature. Unless otherwise noted, all dimensions are reported at design level (1X). Twenty-two different features were used to characterize the reticle manufacturing process of each vendor, however, the following four suffice to illustrate the results (see Figure 1):
A. Isolated trenches (quartz spaces) ranging in size from 0.180 µm to 1.000 µm; B. Dense/semi-dense trenches (quartz spaces) with a 0.200 µm trench critical dimension (CD) and pitch ranging from 0.400 µm to 1.400 µm; C. Isolated line ends with a trench (quartz space) CD ranging from 0.180 µm to 0.400 µm and a constant line end space of 0.200 µm; D. Dense line ends (1:1) with a trench (quartz space) CD ranging from 0.180 µm to 0.400 µm and a constant line end space of 0.200 µm 2.3 Reticle characterization On each reticle, sixteen test pattern groups were measured corresponding to local chrome loads of 20% (4 identical test cells), 30% (4 identical test cells), 40% (4 identical test cells), and 50% (4 identical test cells). All reticle measurements were executed using an automation routine that facilitated in the collection of a large amount of consistent data. Lines were measured using a gate region extended as far a possible in the direction orthogonal to the measurement and wide enough to include the entire feature in the direction parallel to the measurement. Line ends were measured using a horizontal cut line approximately 10 nm thick positioned at the center of the feature and aligned using a built-in automated edge alignment routine with the y-direction tolerance set to ±25 nm. 2.4 Wafer characterization Wafers were exposed from each reticle using a condition set suitable for backend layers at the 0.13µ technology node. A KrF scanner was used with optimized NA and σ settings to minimize proximity curve swing and afford a >5% exposure latitude and at least 0.5 µm depth-of-focus. The target dose was selected using a 0.200 µm semi-dense trench at 0µm defocus (data not shown). Full sets of sample data, sufficient to generate independent OPC models, were collected from exposed wafers and selected features corresponding to those shown in Figure 1 were measured at the target conditions. All aspects of the SEM measurements were performed manually including measurement gate sizing and placement. Trenches were measured using a long gate as described in Section 2.3 to minimize the effects of line edge roughness. Line ends were measured using a polynomial fitting routine that approximates the curvature of
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opposing trenches as a 2nd order polynomial then calculates the minimum line end space. The measurement gates were sized manually to 50-80% of the trench width and placed at the center of the features. This method reduces measurement errors due to gate placement and allows the user to measure line end features with a relatively wide measurement gate, thereby minimizing noise induced by local imperfections or other anomalies at the trench ends. 2.5 OPC modeling Two independent Mentor Graphics Variable Threshold Resist Extended (VTR-E) models, designated α and β, were generated and tuned using wafer data corresponding to A.2 and B.1, respectively1. Model α was intended to compensate for the reticle processing effects of Vendor A and model β the effects of Vendor B. Model generation and tuning were performed in accordance with Mentor Graphics documentation and LSI Logic internal accepted practices for 0.13µ back end layers [1,2].
Table 1: Model Fitness Statistics Statistic
Possible Values
Optimum Value
real number
0
The mean of the error between measured and simulated edge placement errors (EPEs)
errRrms
real number
0
The weighted root-mean-square of EPE
m/s Corr
-1 to 1
1
The correlation coefficient between measured and simulated (EPEs). Percentage of points within the tolerance specification. The tolerance is 20 nm for line ends, 10 nm for lines.
Description
spec
0 to 100%
100%
errLE
positive number
0
The maximum error in line end predicted EPE in nm.
errNLE
positive number
0
The maximum error in line width predicted EPE in nm.
R2
0 to 1
1
The correlation statistic of the variable threshold fit, which describes how well threshold variance in the experimental data is reflected by the model.
rrms
positive number
0
The residual root mean square, a measure of discrepancy between empirical and simulated variable threshold.
0.01 to 0.6
First polynomial coefficient. Positive values indicate model stability
PolyCoef real number
Table 1: Adapted from Mentor Graphics Calibre WORKbench user's manual and Mentor Graphics LITHO Applicatrion Note #4 [1,2].
Model α*, an adapted version of model α, was generated by re-optimizing the resist model to Vendor B wafer data. Model β* was generated in similar fashion using Vendor A wafer measurements. All models were evaluated for fitness using the parameters listed in Table 1. 2.6 Chimeric model generation In addition to the models described above, a chimeric model, designated γ, was generated by combining the two data sets used for models α and β. Wafer measurements for Vendor B one-dimensional features were combined with complimentary measurements for Vendor A line ends to form a single, complete set of hybrid sample data without
1
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For model generation, rows 1 through 17 of a dark field Mentor Graphics 200 nm extended test cell, version 10, were used.
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changing the number of data points included. The resultant data set was used to generate a new model, γ. As above, the resist model was re-optimized with Vendor A data to generate γ*, which was evaluated for fitness. 2.7 OPC model application OPC was applied to several structures for verification and comparison. General settings such as aggressiveness parameters and iteration count were set according to LSI Logic internal practices for 0.13µ metal-x layers. The OPC correction grid was set to 5 nm. Constraints were not used, allowing each model to correct the input GDS as fully as the model predicted. All setup parameters were the same for every OPC run.
3. RESULTS 3.1 Reticle characterization data A summary of the reticle measurement data is shown in Figure 2. Each data point represents the arithmetic mean of 16 independent measurements of the indicated feature through variations in chrome loading density and across the reticle (see Section 2.3). Data for identical features from regions of differing chrome load were grouped together for analysis based on the data in Section 3.3. Figure 2 indicates there were no significant differences between the two vendors for the isolated line or pitch features. For these features, both vendors were within 5% of target and exhibited similar signatures for every pitch and CD. For Figure 2: Reticle Measurements
Figure 2: Reticle process characterization data. For each point, the mean of 16 measurements is plotted. Four reticles from vendors A and B were investigated to characterize the effects of reticle manufacturing variation between the vendors. See Figure 1 and Section 2.2 for a description of the features used. Error bars denote the observed maximum and minimum measurement for the indicated feature.
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Figure 3: Wafer Measurements
Figure 3: Wafer characterization data. The reticles characterized in Figure 2 were exposed using a condition set suitable for 130 nm backend layers. The dose was adjusted to target the 0.400 µm pitch features to within ±5% of target CD at 0 µm defocus. For pitch structures, each point is the mean of 4 measurements. For line ends, each point is the mean of 4 measurements for reticle B.2, and 16 measurements for all others. The observed standard deviations for the lines ends at trench CD = 0.180 µm were 10.6 nm (A.1), 5.1 nm (A.2), 12.2 nm (B.1), and 10.3 nm (B.2).
line ends, the data indicate each vendor had a distinct, consistent process signature through quartz line CD that was not dependent on the multiplicity of lines. For Vendor A, the maximum deviation from target for isolated line ends was +9.5%; for Vendor B, the maximum deviation was +24.1%. The manufacturing location was not observed to play a significant role in the reticle signature. 3.2 Wafer characterization data Wafer measurements for select features are plotted in Figure 3. Proximity effects resulted in a 15-25 nm CD swing from 0.400 µm pitch to 0.600 µm pitch for 0.200 µm trenches. The CD remained approximately constant at pitches greater than 0.600 µm. For line ends, lithographic effects dominated over mask effects, yet variations in the mask remained a discernible secondary factor. At trench CD = 0.180µm, 0.200 µm line ends pulled back at least 0.187 µm (94%) in all cases. For these features, the worst-case vendor-to-vendor discrepancy was 55 nm. 3.3 Chrome load effects The effects of variations in chrome load on wafer line end CDs are shown in Figure 4. Wafer data from two reticles is shown for the smallest isolated line end feature. The data for each feature are decomposed into constituent measurements that are represented in terms of the distance from the mean expressed in standard deviations. The linear regression of each data set was used to calculate the rate of change of the wafer CD with respect to changes in the regional chrome load on the reticle. For A.2, the measured CD increased by approximately 1 nm per 10% increase in the chrome load with R2 = 0.048; for B.1, the measured CD decreased by approximately 4.4 nm per 10% increase in the chrome load with R2 = 0.175. The effect of chrome load on reticle CDs was also investigated. As above, the change in reticle CD with respect to chrome density was estimated using the linear regression. Isolated 0.720 µm (4X) quartz lines and dense 0.800 µm (4X) quartz lines were investigated on each reticle. In all cases, these data indicate the change in reticle CD per a 10% change in chrome load was ≤ 3.0 nm (4X) with a correlation (R2) no greater than 0.26 (data not shown).
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Figure 4: Chrome Load Effects (Wafer Data)
Figure 4: Effects of regional variations in chrome load on trench CD. Data from wafers exposed with reticles A.2, and B.1 are shown. A single feature (0.200 µm line end, 0.180 µm trench) was measured at several regions of varied chrome load. Within each region, 4 separate instances of the feature were measured, each exactly once. The results are plotted in terms of the deviation from mean (expressed in standard deviations), through chrome load. The slope of the linear regression (dashed) gives the observed dependence of CD on chrome load for each reticle. The standard deviations for these features equal 5.1 nm and 12.2 nm for Vendor A and Vendor B, respectively.
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3.4 OPC model fitness Table 2 presents the OPC model fitness results for models α, α*, β, β*, and γ*. Models α and β (bold) represent “direct fitness,” where a model was generated, optimized, and tested for fitness in the normal way, that is, using only one set of data from a single reticle. Models α* and β* represent “cross-fitness,” where the optical model was generated and optimized from one vendor’s data, then adapted for second vendor’s process and tested for fitness against the second vendor’s data (see Section 2.5). Model γ* is a special case where data from both vendors was used to generate and optimize the model (see Section 2.6). Table 2: Fitness Results Model Fitness Statistics Model α α* β β*
0.0 -0.1 0.0 0.0
errRrms 4.9 4.9 5.1 5.3
m/s Corr 0.988 0.986 0.986 0.986
spec 98.8% 92.7% 92.7% 97.5%
errLE 19.0 16.1 17.1 21.8
errNLE 11.1 17.5 15.9 11.8
R2 0.860 0.907 0.904 0.851
rrms 0.021 0.020 0.021 0.023
PolyCoef 0.20 0.44 0.74 0.82
γ∗
0.0
5.0
0.987
98.8%
19.4
10.9
0.845
0.021
0.24
Table 2: Models α and β were generated and tuned using wafer data from a Vendor A and a Vendor B reticle, respectively. The models were then tested for fitness against the wafer data from each vendor to yield "direct fitness" statistics (bold) and "cross-fitness" statistics (non-bold). For the cross-fitness evaluations, the resist models were re-optimized (1 iteration) to generate models α* and β*. Model γ* was generated using a hybrid data set (see Section 2.6). The fitness statistics are explained in Table 1.
Table 2 shows that the parameters , errRrms, m/s Corr, and rrms do not serve to differentiate the models. The statistics R2, spec, errLE, and errNLE primarily depend on the wafer data used for resist optimization rather than on the optical model. In general, models adjusted for Vendor A exhibit a lower correlation, but higher percentage of in-spec points. Fitness results for the chimeric model, γ*, indicate it is most similar to model α. 3.5 OPC model application results Each of the OPC model combinations shown in Table 2 was used to apply OPC to five verification structures. The results are shown in Table 3. For each structure, the post-OPC drawn CDs are reported to allow a direct comparison of the behavior of each model. The intent is to see whether all models tuned to Vendor A give the same result (and vice versa), even though the correction may differ from one vendor to the next. Table 3 shows all models intended for Vendor A give the same correction to within 5 nm (one snap of the OPC correction grid) for all measurement sites investigated. The models intended for Vendor B exhibit a maximum discrepancy of 10 nm (one snap per edge). The OPC models shown in Table 3 were applied to a sample of 0.13µ SRAM. Each non-standard model (non-bold in Table 3) was compared with the corresponding standard model (bold in Table 3) using the Boolean XOR operator to generate an error layer containing the discrepancies between each model pair. The number of polygons on each XOR layer is reported in Table 3. The XOR layers were run through an automated check to look for the maximum feature size. A single discrepancy of 10 nm was noted at a non-critical feature (α vs. β*), but all other polygons were of width 5 nm. Models α and β were compared using XOR (data not shown). The resulting layer contained 578 error polygons, with a maximum polygon width of 15 nm.
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Table 3: OPC Application Results Site 1
Site 2
Site 3
Model Trench α 190 Vendor A β* 190
Vendor B
Site 5
180 nm
180 nm 200 nm
180 nm
Site 4
200 nm
Gap N/A N/A
Trench 220 220
Gap 90 90
Trench 200 200
Gap 70 70
Trench 280 280
Gap 170 170
Trench 320 320
Gap 150 150
γ*
190
N/A
220
90
200
70
280
165
320
150
β α*
190 190
N/A N/A
230 220
80 70
230 220
80 80
285 285
165 160
320 320
130 130
XOR: # of Polygons
295 54
183
Table 3: Results of OPC model application to various test patterns. Post-OPC database CDs are reported for each feature to allow direct comparison of the models. Pre-OPC CDs are shown for some features. Models α and β were each adapted for the manufacturing process of the other vendor to generate models α* and β* (see Section 2.5). The chimeric model, γ*, was generated using a hybrid data and is adapted for Vendor A. The models were applied with an OPC correction grid of 5 nm. The post-OPC line CDs (at the line end) and line end CDs were measured as indicated by cut lines in each picture. The models were run on a section of SRAM, then compared with the Boolean XOR operator to generate three error layers. The number of polygons on each error layer is reported.
4. DISCUSSION The first step in the process of adapting an OPC model is to fully characterize the manufacturing process of each vendor. To do this, several thousand reticle measurements were collected on an optical measurement tool with the aid of an automated program (see Figure 2). The effort required to generate an automated program was justified in this case for two reasons. First, large amounts of data were required to generate statistically valid results for several features and, second, an automated program reduced the chances of user error on features where gate placement was critical (such as line ends). From an OPC standpoint, it is not necessary that each vendor be precisely on-target for all features. Rather, each vendor must display a consistent signature for each feature that can be accounted for by the OPC software since there is no way OPC can apply a correction to compensate for an erratic reticle process. If there exist process signature differences from one vendor to the next they must be accounted for by the process of adapting the OPC model to a new vendor. The reticle measurements show that Vendor A and Vendor B have virtually identical signatures for one-dimensional features but have different process signatures for line ends. Multiple masks from each vendor were examined to confirm that the differences in CD signature were truly a result of the manufacturing process and not some other artifact. These results support the claim that both vendors have unique, repeatable signatures meaning it is in theory possible to adapt an OPC model from one process to the next.
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Corresponding features were examined on exposed wafers to determine whether the differences seen on the reticle are detectible on the wafer. The data shown in Figure 3 indicate the differences between the two vendors are discernible in the line end measurements. It is therefore very probable that an OPC model built for one vendor will need to be adapted in some way for use with another vendor. Since measurements were collected from regions of differing chrome load, it was necessary to determine the effects of chrome load on reticle and wafer CDs. To do this, the measurements for each feature were arranged in a scatter plot, showing the distance from each measurement to the mean, expressed in standard deviations (see Figure 4). Any relationship between chrome load and CD would cause the plot to skew in one direction. The scatter plots, however, show the data points scattered around the mean in an almost perfectly random arrangement. As expected for a normal distribution, the great majority of measurements are within two standard deviations of the mean, with a few measurements between two and three standard deviations from the mean. The calculated linear dependence of CD on chrome load was quite small in all cases (see Section 3.3) and the correlation coefficient (R2) was very low in all cases. From these data, it was concluded that the local chrome load did not significantly affect the measured value for trenches or line ends, so data from regions of differing chrome density were grouped into the same statistical set. Two OPC models, α and β, were generated from a Vendor A reticle and a Vendor B reticle, respectively. These models were generated and tuned in the usual way and were treated as golden standards for each vendor. In other words, model α was taken to be a suitable OPC model for use at Vendor A, so any other model that behaves like model α will be considered useable with Vendor A. The model fitness results for these models are shown in bold in Table 2. To determine if the models could be used directly at either vendor, model α was tested for fitness against Vendor B data, and model β was tested for fitness against Vendor A data. The results (not shown) indicate a very poor fit in both cases, with R2 less than 0.65. Therefore, the models must be adapted in some way for use with another vendor. To accomplish this, the resist models were optimized to new data from the other vendor’s reticle. For example, data from Vendor B was used to re-optimize the resist model of α, generating α*. The fitness results for the adapted models, shown in Table 2, indicate α* and β* are comparable to α and β in terms of the fitness statistics and could, therefore, potentially be used as substitutes. To verify that the adapted models, α* and β*, could be used as substitutes for β and α, all of the models were applied to several test structures (see Table 3). By comparing the post-OPC results of each adapted model to the results of the standard models, it was possible to see the impact of substituting one model for another. OPC results were analyzed by performing a Boolean XOR comparison between layer pairs. The results show that the impact of substituting models is minimal in these cases. Although the number of error polygons on each layer varies from model to model, it is noteworthy that virtually all discrepancies were equal to the OPC correction grid size, namely 5 nm. Based on the XOR comparison of models α and β, one can conclude that each vendor does require a different OPC model (see Section 3.5). The error layer from that comparison has the greatest number of polygons and several errors as large as 15 nm. Therefore, model α is not a suitable substitute for model β or vice versa. The use of hybrid data was explored to test whether an OPC model could be adapted for another vendor using only a partial set of wafer measurements. Based on the reticle measurements, it was known that the two vendor’s process signatures differed only for line ends. Therefore, a useable OPC model could possibly be generated by combining the line end measurements from one vendor with the line measurements from another vendor. This would shorten the process of adapting an OPC model since data that is unlikely to differ from one vendor to the next would not need to be recollected. The line end measurements accounted for approximately 30% of the total measurements used for model generation. The hybrid data set described in Section 2.6 was used to re-optimize the resist model for β in an attempt to adapt β to Vendor A. The fitness results (not shown) indicated the approach failed, so the hybrid data was used to generate a new model, γ. The fitness results (not shown) indicated model γ did not accurately fit the data from either vendor, so the resist model was re-optimized using the complete data from Vendor A to generate γ*. The XOR results for γ*, shown in
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Table 3, indicate that γ* matched α closer than α* did, however, it must be noted that γ* required considerably more work since it was ultimately generated and optimized as a new model. To adapt an existing OPC model to a second vendor, the only material required is a test reticle from the second vendor, requiring one week. Importantly, the same layout library used for the model generation reticle can be reused for the model adaptation reticle. To acquire the necessary data, the new reticle must be exposed, the wafer targeted, and a single test cell measured, requiring two days. A verification reticle is not necessary since the adapted model is only a small perturbation of the original model. The time required to adapt the model and verify its fitness is 3 days, thus, the entire process of adapting an OPC model can be accomplished in 2 weeks. In addition, since only one reticle is required, the process is cheaper than generating a new model, which requires two cycles of learning (8-12 weeks total).
5. CONCLUSIONS A procedure for characterizing the process signature of reticle vendors successfully predicted qualitative wafer-level differences. The procedure is based on an automated system and could therefore be used for in-line process monitoring of incoming reticles. Two OPC models were successfully adapted for use at different vendors. The process of adapting an existing OPC model for use at a new reticle vendor is faster, easier, and less expensive than generating, tuning, and verifying a new model, requiring approximately two weeks.
ACKNOWLEDGEMENTS The authors wish to thank Kunal Taravade for his immense help with the editing and layout of this document. Also, John Jensen, Aftab Ahmed, and the Reticle Engineering Group for their help in data preparation and Mark Simmons for his help in programming the reticle measurement tool.
REFERENCES 1. Calibre WORKbench User’s Manual, ver 2002.08, Mentor Graphics Corp., 2002 2. LITHO Application Note #4, Rev 2.4, Mentor Graphics Corp., 2001
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