Compensation for local proximity effects
04/01/2008
Executive OVERVIEW
Short range proximity effects in maskmaking processes require compensation over and above that presently applied to account for other effects such as electron backscattering. Model-based correction of these predictable effects markedly improves the CD distribution on MoSi attenuated-PSMs.
Achieving the mask CD control specified in the ITRS Roadmap for beyond the 45nm node will require attention to all factors that affect mask CD. This article is concerned with characterizing and compensating feature-scale proximity effects in an attenuated-PSM mask process using a vector shaped beam (VSB) writer. Feature-scale proximity effects, which contribute to nonlinearity and CD variability, are caused by forward scattering of electrons, molecular diffusion in resist during post-exposure-bake, shadowing during plasma etch, and possibly heating and charging during exposure and etch [1].
Figure 1a shows the flow of an experiment conducted to break down proximity effects by sub-processes. The test pattern includes many line-gratings, each with a different line and space width. Figure 1b shows the difference between measured resist width and database CD (the combined proximity effect of e-beam writing and resist processes) vs. line (MoSi) and space (glass) dimension.
Each small color square in the figure belongs to a line grating with a different combination of line and space widths. The colors in Fig. 1c show the difference between resist and chrome CDs (which is the proximity effect due to Cr-etch) again plotted vs. both opaque MoSi and clear (glass) widths. Evidently some error has appeared at small space widths! Figure 1d shows the difference between the MoSi and Cr CDs, which is the (negligible) proximity effect due to MoSi-etch. Figure 1e shows the overall proximity effect, the difference between MoSi CD and database. The color scales of Fig. 1b-e have the same range. The proximity effect is dominated by the Cr-etch for this particular process. Other mask processes have similar systematic proximity effects through the dominant contributor is not always Cr-etch.
VSB mask writers support a proximity effect correction (PEC) algorithm that changes the local exposure dose according to the density of the surrounding pattern. The goal of PEC is to compensate electron backscattering and fogging, and in some cases, etch-loading. PEC averages the pattern density over tens to hundreds of microns. Therefore, it doesn’t compensate feature-scale (nanometer) proximity effects.
Presently, feature-scale proximity effects in maskmaking are lumped into the OPC model of the wafer process. An inappropriate set of optical or wafer resist parameters attempts to account for these effects. Some OPC models account for mask corner rounding, but this is not the only infidelity in the mask processes.
 Figure 2. Mask process compensation (MPC) corrects systematic errors in the mask process delineated by the dotted box. |
The feature-scale proximity effect can be reduced either by process improvements or by software compensation as described in this article. Employing both approaches may become necessary to meet the CD control requirements of future nodes.
Mask process compensation
We investigated the use of a mask process compensation algorithm (MPC), which was inserted into the process flow, as shown in Fig. 2. MPC does not replace PEC but it corrects the systematic proximity error that is left over after the PEC algorithm. MPC, similar to model-based OPC, compensates feature-scale proximity effects by adjusting polygon edges according to a model of the maskmaking process (see Fig. 3). Since the incoming polygons have already been segmented by OPC, further segmentation of edges is usually not necessary.
 Figure 3. Input polygons and polygons corrected by MPC. Input polygons were further segmented in this example for illustration. |
When a mask process is compensated, it will become incompatible with previous OPC models that were calibrated using the uncompensated mask process. In the future, new OPC models will have to be calibrated using a test mask written by MPC.
Calibration data and model fit
Figure 4a shows an MPC calibration data set. The test patterns are many line gratings, each with a different combination of line and space width. The horizontal axis shows database-dimensions of glass features in the grating. The vertical axis shows database-dimensions of MoSi features. The color code indicates the observed CD error:
- ΔCDMEAS = (Measured MoSi CD) ??? (Database-dimension of MoSi feature)
which is the combined error of the mask writing process and the CD-SEM. Figure 4b shows ΔCDCALC predicted by a model. The model includes a local density effect and a plasma shadowing effect during etch. Adjustable parameters of the model were selected to minimize the sum of squares of the residual: ΔCDCALC ??? ΔCDMEAS. Figure 4c shows the residual. The residual is close to random and its standard deviation is significantly smaller than that of ΔCDMEAS. This indicates that the systematic error seen in Figs. 4a and 1e can be predicted and corrected by a model.
Evaluation of MPC
In order to test the efficacy of mask process compensation (MPC), we wrote a calibration mask, performed metrology, and fitted a model to ΔCDMEAS = CD(MoSi, Measured) ??? CD(MoSi, Database). We observed that the residual dispersion of the model was only 36% of the standard deviation of the measured CDs and that the residual range was only 46% of that of the measurements. Such statistics indicated that MPC may reduce mask writing error by more than a factor of 2.
The calibrated model was verified by simulating the two-dimensional patterns on the calibration mask. The structures that were used for verification were not used in model calibration. Figure 5 shows the contour predicted by the model superimposed on its corresponding SEM image.
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After the model was calibrated, we applied MPC to a test pattern according to the calibrated model. We wrote a second mask (evaluation mask), which included a set of compensated patterns and a set of uncompensated patterns for comparison. The time elapsed between writing the calibration mask and the evaluation mask was three months. Model-based MPC significantly reduced the range and 3σ of the observed error (see table on p. 51).
The test targets in this evaluation were clustered in a small area of the mask. Therefore, this table gives information only about compensation of the feature-scale proximity effects. Across-plate uniformity and global pattern density effects are not probed by such a short-range test and will require other methods to correct.
Conclusion
There are submicron-range, reproducible proximity effects in mask writing processes. Proximity effect correction algorithms, integrated with mask writers, do not correct such short-range effects. We have shown that the feature-scale proximity effects can be predicted by a 2D model, containing mask density and shadowing effects. Edges of the polygons in the incoming database can be compensated using this 2D model. We tested this concept and found that the range and 3σ of the mask writing error were halved by using a model-based mask process compensation algorithm.
Acknowledgment
The authors thank Yoshimitsu Okuda for his support, and G??khan Per??in, Jesus Carrero, Alan Zhu, and Anwei Liu for their contributions to this work.
Reference
- Kiyoshi Kageyama, Katsuyuki Miyoko, Michiel Kr??ger, Apo Sezginer, “Polygon-based Compensation of Proximity and Density Effects in Photomask Processes,” SPIE, Vol. 6730, 67302Y, 2007.
Contact Apo Sezginer, Distinguished Engineer, at Advanced Patterning Solutions, Cadence Design Systems, 2655 Seely Ave., San Jose, CA 95134; ph 408/944-7157, fax 408/944-7970, e-mail [email protected].