Using profilometer metrology to create a phase measurement standard
06/01/2005
While the National Institute of Standards and Technology (NIST) has critical dimension calibration standards for photomasks, the US agency has not yet developed a standard for phase measurements. To fill this void, a NIST-traceable phase-shift standard of varying wavelengths has been designed, fabricated, and tested.
Every metrology tool needs to be controlled, and, if possible, to a standard. Unfortunately, a phase standard for photomask measurements does not exist from NIST, but a joint research effort has developed a NIST-traceable phase-shift standard using the fundamentals of NIST-calibrated step height, quartz index, and an understanding of illumination optics in a phase-shift metrology tool. Researchers from Toppan Photomasks Inc., the Advanced Mask Technology Center (AMTC), and FEI Co. have demonstrated that a metrology tool (from Lasertec Corp.) can be calibrated with this standard for more accurate quality assurance of embedded and etch quartz phase-shift masks (PSM).
The measurement patterns on the phase-shift standard are compatible with recommended best practices for measuring step heights and phase on Lasertec tools. Multiple depths have been etched into the control mask, allowing for the calibration of phase tools to three NIST-traceable depth heights.
Figure 1 shows an example of a Lasertec MPM-248 phase-shift measurement system for 248nm-wavelength lithography in controlled vs. uncontrolled mode. In this case, the control is most needed when the source light is changed, even though the measurement tool is wavelength controlled. However, control does not mean that one tool will read the same value as another tool. Tool-to-tool variation can be reduced by sharing control masks between systems, but it does not mean that there is control between similar tools at different mask vendors. These variations are best addressed with a NIST calibration mask (as is done for CDs). Because a NIST phase standard does not exist, another vehicle for phase calibration is needed.
Phase path
Obtaining a calibrated phase shift from a known height difference is similar to calculating the phase of an alternating PSM. The phase shift is caused by the difference in the phase paths across the step. In each case, the phase path is the distance traveled (in waves: d/λ) times the index of refraction of the media. Thus, for quartz step height, the phase path difference is the phase path in quartz minus the phase path in air with an index of n = 1.
This equation works well for light at normal incidence, but when the light is coming from an angle, the path length is not d. Thus, the integrated path length of the illumination numerical aperture (NA) needs to be accounted for when this concept is used with a Lasertec phase metrology tool. This correction is m in the equation [1] in Fig. 2, which shows the use of this relationship on a mask with three step heights (nominally 120, 180, and 240nm) in quartz. The step heights were measured in depth and in phase with a Lasertec MPM-248 (248nm) and MPM-100 (365nm) tool. In each case, the phase was converted to a depth using the corrected relationship and solving for depth. The calculated depth agrees very well with the measured step height by the average difference in depth for each system.
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Percentage error
The traceable percentage error in the determination of the phase is the sum of the percentage errors of each of the terms in Eqn. 2. The dominant contribution to the error is the determination of the error in the NIST-traceable depth. Typically, this is about 1% of the measurement depth. The wavelength of the illumination is tuned in the Lasertec tools, and the index of quartz is well known. The error in the determination of m is based on a 10% error in the value of the illumination NA of the Lasertec systems.
| ΔΦ/Φ | = | Δd/d + Δλ/λ + Δn/n + Δm/m | (2) |
| = | 1% + 0.1% + 0.001% + 0.3% |
Calibration mask description
A phase-calibration standard mask has been designed as shown in Fig. 3. The standard format is that of a 6×0.25 in. chrome-on-quartz photomask. It consists of a five-chip array for evaluating phase in the four corners and center of the mask. Each array is composed of a labeled 10×10 array of calibration cells. The array allows metrologists the opportunity to change cells that may have been contaminated or damaged. Each cell is composed of an array of nine patterns. The rows have different widths to the quartz-etched area and the columns represent different depths. The varying pattern-width design allows for different shearing conditions on Lasertec tools. The multiple depths are designed to be approximately 180° for the 157, 193, and 248nm lithography cases. These depths also provide the opportunity to study the linearity of the metrology tools.
The calibration mask was fabricated using standard photomask processes. The etched-quartz areas were sequentially opened in a lithography process and were wet etched to achieve maximum uniformity and smoothness. The final step cleared the chrome from the reference areas and provided the labeling. This approach resulted in <0.5nm across-mask depth variation and no measurable across-chip depth variation. The depth and phase metrology both show approximately 0.5nm pattern-dependent depth variation (at the 2400Å depth), with the wider pattern having less depth. This mask can be used as a single standard for a phase tool, or utilized to cross-calibrate different depth metrology tools in the photomask industry, such as atomic force microscope or profilometer tools.
NIST-traceable depth measurements
Two calibration masks have been fabricated and measured. Two cells on each mask were measured (E5 and G7 of the center array), including each of the nine patterns and depths. These measurements were made multiple times to determine the repeatability of the depth metrology. The depth was measured using an FEI Surface NanoProfilometer (SNP) metrology tool. The average repeatability across tools and samples was 0.3nm (3σ).
Each mask was measured on two separate depth tools against three independent NIST standard sets. Each standard set used to calibrate the SNP tool consists of three depth standards around 25, 100, and 500nm. The range associated with the three different sets of NIST samples averaged 0.7% of the depth reading (i.e., about 0.7nm for the 130nm depth and 1.9nm for the 240nm depths). Note that the depth data from tool to tool do not agree within the tool’s repeatability, but do fall within the NIST-traceable standard error (1% of the reading), thus pointing out that the depth calibration is only as good as the NIST-traceable standard depth. For this reason, we chose to use the average of the three depth readings for our calculation of phase.
Phase data
From the calibrated depths for each mask we can calculate the phase that a Lasertec tool should read for each depth. Note that the mask can be used for calibrating a Lasertec tool of any wavelength. Figure 4 shows a plot of the Lasertec phase minus the calibrated phase value vs. the phase determined from the average quartz depth values. This plot contains data from the two masks and three Lasertec tools of different wavelengths (one MPM-193 and two MPM-248s). The MPM-248 data is flat with different mean offsets vs. the calibrated depth; however, the MPM-193 tool data shows a slight slope response.
When using these masks to calibrate a Lasertec tool, the recommended approach is to find a best-fit slope for the phase data at 180°. This slope can then be used directly with the tool as a linear correction factor. This approach is good for all tools and for phase values around 180°. The average 3σ of the residuals from the calibration mask was 0.34° and the 3σ of the control masks were all <0.7°. This approach is valid for the typical maskmaker’s use of the tool, where the target phase is 180°. The linear correction factor is also compatible with the Lasertec software.
Conclusion
Both phase tool control and control to a standard are needed so that IC manufacturers can receive masks referenced to a standard. With the proper corrections for illumination NA, a NIST-traceable phase can be obtained from NIST-traceable depth standards. The uncertainty of the phase is dominated by the uncertainty in the depth standard (about 1%). The FEI SNP is calibrated to three depth standards and shows that three different standard groups agree to within 0.7% of each other (1.3° at 180°).
Moreover, when a quartz-depth phase standard is used in a linear fit, the 3σ residuals of a quartz control mask are <0.7°. This value represents the variation in the metrologies and not the NIST calibration, which still remains at the 1% value due to the depth calibration standards. In practice, this method has great benefit for manufacturing embedded and etched quartz phase-shift masks consistently over time under tightly controlled conditions.
Reference
- H. Fujita, H. Sano, H. Kusunose, H. Takizawa, K. Miyazaki, et al., “Performance of i and g-line Phase-shift Measurement System MPM-100,” Proc. SPIE Photomask and X-ray Mask Technology III, Vol. 2793, pp. 497-512, 1996.
Gregory P. Hughes received his PhD in physics from Dartmouth College, and is a member of the advanced photomask development team at Toppan Photomasks Inc. (formerly DuPont Photomasks Inc.), 400 Texas Ave., Round Rock, TX 78664; ph 512/310-6000, fax 512/244-9469, e-mail [email protected].
Cindy Goodman received her BSIE from the U. of Pittsburgh, and she is a metrology engineer at Toppan Photomasks.
Gunter Antesberger received his PhD from the Max Planck Institüt for Quantum Optics. He is a process engineer in metrology at the Advanced Mask Technology Center GmbH & Co. KG.
Stefan Burges received his degree in electrical engineering from the U. of Siegen, Germany, and is a process engineer in metrology at the Advanced Mask Technology Center.
Troy Morrison received his MS from MIT. He is a senior product manager in the Circuit Edit and Mask Repair Division at FEI Co.
Alex Buxbaum received his PhD from the Technion Israel Institute of Technology. He is a senior applications development engineer in the Circuit Edit and Mask Repair Division at FEI Co.