SPIE Proceedings [SPIE Photomask Technology 2005 - Monterey, California (Monday 3 October 2005)]...

The effect of calibration feature weighting on OPC optical and resist models – investigating the influence on model

coefficients and on the overall model fitting

Amr Abdo,*1 Rami Fathy,2 Kareem Madkour,2 James Oberschmidt,1 Daniel Fischer,1 and Mohamed Talbi1

1 IBM Corporation, Microelectronic Division, 2070 Route 52, Hopewell Junction, NY 12533.

2 Mentor Graphics Corporation, Consulting Division, 51 Beirut St., Cairo, Egypt 11341.

ABSTRACT Performing model based optical proximity correction (MB-OPC) is an essential step in the production of advanced integrated circuits that are manufactured with optical lithography technology. The accuracy of these models depends highly on the experimental data used in the model development (model calibration) process. The calibration features are weighted relative to each other depending on many aspects, this weighting plays an important role in the accuracy of the developed models. In this paper, the effect of the feature weighting on OPC models is studied. Different weighting schemes are introduced and the effect on both the optical and resist models (specifically the resist model coefficients) is presented and compared. The effect of the weighting on the overall model fitting was also investigated. Keywords: model-based OPC, OPC model accuracy, OPC model fitting, variable threshold resist model

1. INTRODUCTION Model based optical proximity correction is an essential tool for the production of advanced integrated circuits (ICs). In MB-OPC, data is collected from optical lithography experiments on a wide range of features (calibration features) that are selected to be a representative set of the actual product pattern,1 this data is used as input to the model calibration tool (software) that fits the optical and resist behavior for the given process such that these models will later be able to predict the printed image resulting from the exposure of the actual product pattern. The OPC models developed in this work were generated using the technique of decoupling the optical and resist model effects in order to achieve better model accuracy, specifically through focus, that is similar to published techniques.2 The accuracy of these models depends on the accuracy of the calibration process. The accuracy of the calibration process in turn depends on the quality of the data collected and used as input to the calibration tool.3 The calibration feature weighting is used for relative weighting of the different calibration measurements depending on many factors such as, the measurement accuracy, the confidence level of the measurement, and the specific feature importance to the model. For example, as line-end features are difficult to measure and have higher associated noise level, compared to pitch structures, then the weight of the line-end structure must be lower than that of the pitch structure.3 How much to weight features is always a question for the OPC modelers that needs to be addressed and answered to develop more accurate OPC models. In this paper, we investigated the effect of the calibration feature weighting on both the optical and the resist models.

* Corresponding author electronic mail: [email protected]

25th Annual BACUS Symposium on Photomask Technology, edited by J. Tracy Weed, Patrick M. Martin,Proc. of SPIE Vol. 5992, 599253, (2005) · 0277-786X/05/$15 · doi: 10.1117/12.631817

Proc. of SPIE Vol. 5992 599253-1

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2. FEATURE WEIGHTING: EFFECT ON THE OPTICAL MODEL OPTIMIZATION For the optical model, eight different weighting schemes (shown in Table 1) were utilized to investigate the effect of the calibration feature weighting on the optimization of the optical model parameters. In this work, two optical model parameters were optimized for each weighting scheme, in order to investigating the effect of the feature weighting. Figure 1(a) shows a plot of the variation of the model error with respect of these two parameters. Figure 1(b) is the three-dimensional plot of the data plotted in Figure 1(a). Some of these weighting schemes used only the one-dimensional (1D) structures while most of the others used a mixed of both 1D and two-dimensional (2D) structures, but all the schemes have the 1D structures weighting higher than the 2D structures.

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Fig. 1. The optimization result of two of the optical model parameters (a) two-dimensional plot and (b) three-dimensional plot, showing the variation of the model error for different values of these two optical model parameters.

Table 1. Summary of the different feature weighting scheme used in the study.

Number Weighting Scheme Description 1 Weighting scheme number 1 including 2D feature (x)

2 Weighting scheme number 1 NOT including 2D feature (x)

3 1D lines high weight and all others low weight

4 1D line and spaces high weight, and all others low weight

5 Critical pitches high weight (y value), 1D lines and space middle, 1 all others

6 Critical pitches high weight (z value), 1D lines and space middle, 1 all others

7 Critical pitches high weight, 1D lines middle, all others low

8 1D only: critical pitches, weighted higher than the others

By comparing the results, it was found that the values of the optimum optical model parameters in question are the same for the different weighting schemes (the 1D structure measurements were always weighted higher).3 For the cases studied, only minor changes were observed in the error curve which is basically the height and the depth of the peaks and valleys (respectively) shown in Figure 1(b). The reason that only minor changes were observed is believed to be the high accuracy of the measured data and the good filtering technique used to remove bad measurement point(s) from the data. The study was performed only with two of the optical model parameters.



3. FEATURE WEIGHTING: EFFECT ON THE RESIST MODEL DEVELOPMENT In this section, the effect of the calibration feature weighting on the resist model coefficient was investigated. The resist (or process) model is actually a polynomial that fits the image parameters with coefficients (called the model coefficients) as shown in Equation 1, which relates the variable threshold (VT) for each feature to its specific image parameters. A variable threshold resist model with 4 parameters (i.e., Imax, Imin, Slope, and Curvature) and a constant term was used in this study.4 The model form shown in Eqn. 1 was chosen only for the purpose of including all the four imaging parameters, for serving the purpose of the work conducted in this paper. The definition of the first three parameters is shown in Figure 2(a). The Curvature parameter exists only for the 2D structures.

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CrossTermCCrossTermCCrossTermCCrossTermCDensityCICICCurvatureCCurvatureCICICSlopeCSlopeCCVT

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(1) To investigate the effect of the weighting on the resist model, a script was generated to produce different weighting schemes for the calibration data and then generate a resist model for each scheme. In the first experiment, the feature weighting of all the 1D features was varied (increased from 1 to 600) while the weighting of the 2D features was kept constant at 1.0. In the second experiment, the process is reversed to change similarly the weighting of all the 2D features while keeping the weighting of all the 1D features constant at 1.0. The values of the resist model coefficients are calculated and recorded for each case. Referring to Eqn. 1, in order to obtain a stable model, the first coefficient C0 must be the largest term in Eqn. 1, but also, the rest of the coefficients must have a non zero small value as shown in Figure 2(b).5

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Fig. 2. (a) Schematic illustrating the definition of three of the image parameters, i.e., Slope, Imax, and Imin and (b) an example showing the values of the resist polynomial coefficients for a resist model.

The constant term coefficient C0 is an important coefficient in the threshold polynomial as this value determines the average threshold value where the resist would develop. Thus, studying the weighting effect on this coefficient is important. The normalized variation of the values for the first coefficient with the 1D structures weight is shown in Figure 3(a), while it is shown with the 2D structures weight in Figure 3(b). To better interpret the results, we suggest making the reference point where the weighting is 1.0 for all features. The trends of the curves in both figures show that weighting all the 1D structures high, increases the first coefficient on the other hand, as the 2D structures weight increases, the first coefficient slightly decreases then levels off.



Increasing the weight of the 1D structures to 10 while reducing the weight of the 2D structures to 0.5, for example, will result in a larger constant term compared with the case where all weights are 1.0. The optimum weighting could be determined such that the value of the constant term nearly matches the best threshold value extracted from the measurement data. The data showed a continues increase in the constant term with the increase of the 1D structures weight in Figure 3(a) till a saturation point. To counter balance that effect and keeping a reasonable variable threshold value, it appears that other coefficients are getting smaller (or larger in negative magnitude) as the weight of the 1D structures increase, as it will be shown later.

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Fig. 3. The variation of the first coefficient C0 (the constant term) of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.

The majority of the rest of the coefficients follow a similar trend, increasing the weight of the 1D structures decreases the other coefficients (a desirable trend), while when the weight of the 2D structures is increased, the values of these coefficients slightly increase (an undesirable trend). As it is not possible to show the variation of all the coefficients with the weighting experiments in the space available for this article, we decided to show the most important coefficients. Table 2 shows an example of the values of the imaging parameters for some random 1D and 2D structures. Based on these parameter values, the coefficients of Slope, Slope2, Imax, Curvature, and Imin (i.e., C1, C2, C3, C5, and C7, respectively) were picked and plotted in the following graphs to show the effect of the weighting on the resist model coefficients.

Table 2. Example of the imaging parameters values for a random 1D and 2D structures.

Slope Imax Curvature Imin 1D Structure 2.59 0.25 0 0.06 2D Structure 2.68 0.45 -1.04 0.02

Figures 4(a) and 4(b) show the coefficient C1 of Slope, while Figures 5(a) and 5(b) show the coefficient C2 of Slope2, for the 1D and 2D structures weighting, respectively. These two normalized coefficients are relatively important because the value of the Slope (and consequently Slope2) parameter is considerably larger than the other parameters, which results in a higher impact of these coefficients on the overall polynomial. By examining the graphs, as the 1D structures weighting increase, C1 decreases (increase in negative magnitude) while C2 increases. On the other hand similar trends (but smaller in the magnitude) is observed when increasing the weight of the 2D structures.



Although it is hard to extract a conclusion in this case, counter affecting the increase of the constant term seems to be a good explanation for the increase with negative magnitude for the coefficient C1. While the increase of the coefficient C2 maybe related, as the two coefficients are somehow dependant on each other, since they are for the same parameter (Slope), but with a different exponent.

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Fig. 4. The variation of the second coefficient C1 of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.

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Fig. 5. The variation of the third coefficient C2 of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.

Figures 6(a) and 6(b) show the coefficients of Imax, Figures 7(a) and 7(b) show the coefficients of Curvature, and Figures 8(a) and 8(b) show the coefficients of Imin, for the 1D and 2D structures weighting, respectively. All the coefficients are normalized. These graphs show that by increasing the weighting of the 1D structures, the values of the coefficient examined decrease, as in Figures 6(a), 7(a), and 8(a). On the other hand, when the weighting of the 2D structures increases, different effects took place for the coefficients: decrease then slight increase in the value of C3, as shown in Figure 6(b), and almost no effect on C5 and C7, as shown in Figures 7(b) and 8(b). Increasing the weight of the 2D structures, in general, shows small effects on C3, C5, and on C7.



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Fig. 6. The variation of the forth coefficient C3 of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.

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Fig. 7. The variation of the sixth coefficient C5 of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.

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Fig. 8. The variation of the eighth coefficient C7 of the resist model polynomial for (a) increasing the weight of the 1D structures while the 2D structures weighting is kept constant, and (b) increasing the weight of the 2D structures while the 1D structures weighting is kept constant.



Although there are some coefficient behavior that was not clear how to interpret, it appears that in order to end-up with a stable model the weight of the 1D structures must be higher than that of the 2D structures, as shown by the trend of most of the coefficient curves. To determine the best weighting scheme, not only must all the coefficients be smaller than the constant term, but the variation of the coefficients also needs to be small relative to each other.5

4. FEATURE WEIGHTING: EFFECT ON THE OVERAL MODEL FITNESS In order to investigating the effect of the calibration features weighting on the overall model fitting, several weighting schemes were used to generate the model, then the error RMS of the model fitting was recorded. Table 3 shows the effect of the 1D structures weighting on the model fitness error (all the 2D structures weighting was kept constant at 1.0). The error in this table was normalized with respect to the error obtained when the weight of all the features is 1.0. It is shown from the summarized result in Table 3 that as the weighting of the 1D structures increases, the overall model fitting improves. Table 4 shows the effect of varying the weighting of the 2D structures on the overall model fitting. The result shows that as the weight of the 2D structures increases, the model fitting error increases. If the 2D structure weighting is further increased more than 5, a random behavior was observed.

Table 3. Model fitness error as a function of the 1D structures weighting.

Weight ErrRMS Weight ErrRMS 1 1.000 50 0.796 2 0.973 60 0.792 5 0.919 70 0.787 10 0.878 80 0.783 20 0.842 90 0.778 30 0.819 100 0.774 40 0.805 250 0.756

Table 4. Model fitness error as a function of the 2D structures weighting.

Weight ErrRMS 0 0.738

0.25 0.932 0.5 0.973 1 1.000 5 1.041

5. SUMMARY AND CONCLUSIONS

Performing accurate MB-OPC is essential to meeting the tight requirements for IC manufacturing. The accuracy of the OPC models depends on the accuracy of the model calibration process. Feature weighting is an important aspect of the model calibration process and it affects the model precision, so it must be performed as accurately as possible. In this work, the effect of the calibration feature weighting on the optical model optimization, resist (process) model development, and the overall model fitness, was investigated. A data set containing 1D and 2D structures was used to perform this work.



To study the effect on the optical model optimization, several weighting schemes were utilized to optimize two of the optical parameters. It was found that the optimum value of these parameters did not change by varying the weighting. It must be mentioned that for all the weighting schemes used, the 1D structures were always weighted higher than the 2D structures. It is believed that this result was due to the high accuracy of the 1D measurement as well as the good filtering technique used for eliminating the measurement errors. For the resist model development, other weighting schemes were utilized such that different weighting was applied to all the 1D structures while keeping the weighting of the 2D structures constant and vise versa. For each weighting, the resist model coefficients were calculated and recorded. Although the variation of the coefficients was not completely clear and need further investigation in future work but, in general the comparison of the results showed that, in order to obtain a stable model, the 1D structures weighting must be higher than the 2D structures. Finally, the effect of the calibration feature weighting on the overall mode fitness was investigated. It was shown that increasing the weighting of the 1D structure reduced the model fitness error while increasing the weighting of the 2D structure increased the model fit error. Based on this case study it was proved that the weighting of the 1D calibration structures must be higher relative to that of the 2D structures in order to obtain better OPC models.

ACKNOWLEDGMENTS This work has been supported by IBM Microelectronic Division and it is the result of the productive collaboration with IBM Corporation and Mentor Graphics Corporation. The authors would like to thank the members of the IBM OPC Integration team and the IBM Advanced RET team and specially Dr. Scott Mansfield for their useful input to this work.

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and S. Baron, “Improving Model-Based OPC Performance for the 65nm Node Through Calibration Set Optimization,” Proceedings of the 2005 SPIE Symposium on Design and Process Integration for Microelectronic Manufacturing III, Vol. 5756, pp. 294-301, 2005.

2. J. Schacht, K. Herold, R. Zimmermann, J. Torres, W. Maurer, Y. Granik, C. Chang, G. Hung, and B. Lin,

“Calibration of OPC Models for Multiple Focus Conditions,” Proceedings of the 2004 SPIE Symposium on Optical Microlithography XVII, Vol. 5377, pp. 691-702, 2004.

3. R. Schlief, “Effect of Data Selection and Noise on Goodness of OPC Model Fit,” Proceedings of the 2004 SPIE

Symposium on Optical Microlithography XVIII, Vol. 5754, pp. 1147-1158, 2004. 4. Y. Granik, N. Cobb, and T. Do, “Universal Process Models with VTRE for OPC,” Proceedings of the 2002

SPIE Symposium on Optical Microlithography XV, Vol. 4691, pp. 377-394, 2002. 5. J. Torres, G. Bailey, J. Word, P. LaCour, T. Do, S. Shang, T. Brist, W. Maurer, S. Kyohei, and J. Sturtevant,

“VT5 and TCCcalc Model Calibration,” Mentor Graphics Corporation, Application Note 0342.



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