20 nsec). Multiple offset exposure passes increase the final pattern accuracy by averaging out residual error sources. Four passes are typically used for the tightest mask requirements. The SLM-based writing principle and a field-programmable gate array (FPGA) based real-time data path provide mask throughput that is practically independent of pattern complexity, including OPC designs. The mask write time in four-pass mode is about three hours.
Because of the short wavelength, coupled with high NA and partially coherent imaging, the resolution and linearity are quite similar to what is obtained from 248 nm wafer lithography systems. The image log slope is enhanced with "negative black," a method analogous to attenuated phase-shifting masks (PSMs) but accomplished with SLM programming. Pattern data is rasterized during writing, facilitating real-time corrections. The mask writer described here is suited to a variety of mask applications, including binary masks, first-level patterning of attenuated PSM, and second-level patterning of advanced masks such as alternating PSM. 2?4
The optical proximity effect causes the printed width of a mask feature to depend on its nominal width, as well as the distance to adjacent features. Figure 1 illustrates the case of 200 nm equal lines and spaces on a photomask that would print at 50 nm at wafer scale due to the 4× reduction in wafer steppers. The range of the effect is fairly small ? only 300 nm for this DUV mask writer ? so only the linewidth of a feature and the gap to the adjacent feature are within the range of influence that must be considered in OPC. The impact on an uncorrected photomask is a difference in linewidth between isolated features and closely spaced features. Only the special case of 1:1 nested features is shown for simplicity.
Mask writer correction approaches
Because the DUV writer optical system operates very much like a wafer scanner or stepper, with the exception that the photomask is replaced by a SLM, it can be described with similar models, and enhancement techniques developed for conventional wafer lithography are also applicable. However, an important question in applying OPC to mask writers is whether to use rule-based or model-based correction. The selection of the correction approach is driven by several criteria:
- Accuracy requirements for patterns in the 180?250 nm range at mask scale (which is 4× the wafer scale)
- Containment of the computational effort
- Feasibility of generating a correction table based on direct measurements or with an optical model of the mask writer
Transposing mask process correction to work for ground rules of 65 nm at the wafer scale, we find ourselves in a mask feature space of roughly 250 nm at the 4× mask scale. At the 250 nm node, simple rule-based correction can be used to combat systematic proximity effects and deliver the requisite on-wafer CD control. For a 250 nm feature, the through-pitch proximity effect before correction is on the order of 10?15 nm, which can be addressed with just 2?4 correction "bins," suitable for rule-based correction. Each bin represents a unique local environment for an edge fragment ? the width of the shape on which it rests and the distance (space) to the edge of the nearest opposing shape. Rule-based OPC is relatively straightforward and can be accomplished with a suitable design rule checking (DRC) platform that provides access to a comprehensive geometry processing engine. Consequently, for the 65 and 45 nm non-critical masks discussed here, the chosen approach is rule-based correction.
Standalone vs. embedded OPC
A mask correction approach can be implemented in two ways ? either as a standalone pre-processing step prior to creating the final mask data under the responsibility of the mask house, or as an integrated part of the mask writing system.
A standalone correction module applies correction prior to data transfer to the mask writer. This approach provides flexibility for hardware selection and replacement, and allows easy sizing of the system to meet throughput requirements. However, it comes with an increased cost in data storage, handling and transfer. Furthermore, it requires integrating a new approach into the local job handling and queuing system. Correction parameter definition and maintenance reside with the mask house engineering team, and the recipient of the mask needs to be involved in decisions on changing the data flow to maintain the sign-off and data validation interfaces. The risk of operational error with such a standalone approach must also be considered.
An integrated, or "embedded," approach places the correction module into the mask writer, making it part of the operational flow for setup, monitoring, maintenance and writing. It provides a plug-and-play solution for the user because the input (mask write ready data fractured to the machine-specific format) is not changed. The user operates the system in a standard way, but with the benefit of achieving a mask with improved CD performance. All responsibilities related to the setup reside with the mask writer supplier who delivers the entire system, including control and setup procedures and an updated integrated workflow for the operator interface. Essentially, embedded OPC is transparent to the user and end customer, and leaves all data sign-off and validation procedures untouched.
Embedded OPC functionality
In general, rule-based OPC uses a set of standard DRC commands to analyze geometries and apply table-based corrections, with the values and complexity of the tables controlled by the user. A resulting derived layer may contain several types of corrections:
- Width- and space-dependent biasing to optimize CD linearity and proximity
- Serif and hammerhead addition to improve pattern fidelity
- Density-based biasing to reduce long-range CD variations
The embedded OPC application, also referred to as "LinearityEqualizer," provides CD linearity and proximity correction using the geometrical processing engine of the Mentor Graphics Calibre physical verification platform. The user defines a set of discrete "bins" and "move" values of the form:
Space >0.1 ?0.18 Width >0.1 ?0.13 Move 0.01
For example, this sample rule specifies that edges belonging to lines (polygons) with widths >0.1 ?m and =0.13 ?m, and with spaces to the next opposing feature >0.1 ?m but ?0.18 ?m, will be moved by 0.01 ?m. The user determines the values for the tables either by measurements of printed test patterns or with a system description model of the mask writer from the equipment manufacturer.
Figure 2a illustrates edge movement for the special case of two rectangular features within optical proximity. The end of each feature generates a new vertex in the opposing feature, and the correction rules are applied to the resulting edge segments. Figure 2b shows a general case where vertices on the opposite side of a polygonal feature create corresponding vertices on the edge being evaluated. Additional controls provide a smoothing function to suppress the creation of very small edges so that data is not overly complex in the downstream processing.
Hardware requirements
The goal is to perform mask writer correction without impacting mask throughput, so OPC time must be no longer than the average mask write time; this way, it can be "hidden" behind the writing operation. Throughput challenges are two-fold: flat input data with high figure counts, and a large number of rules to be processed. The challenge of processing large flat input data is addressed by applying massively parallel hardware in a highly scalable data processing mode for the correction and refracture.5
A typical embedded OPC software execution platform consists of commercial off-the-shelf cluster computer hardware based on the x86 architecture and running Linux. A rack cabinet contains a master computer with disks and multiple chassis, each containing a number of blade servers. Local data storage is an expandable RAID-5 configuration, typically providing around 1.8 TB of disk space. The interconnect fabric between master and blade chassis consists of gigabit Ethernet using link aggregate. Inside the blade chassis, single-gigabit Ethernet to each blade is used to form a tree topology with the master as the top node. The blade servers use multicore CPUs. A typical configuration for 65 nm mask designs needs about 200 cores running at 2.33 GHz and 2 GB of RAM per core.
Compensation rule setting
The preferred way to create correction tables is to use models of the writer system signature, although it is possible to produce correction tables manually based only on plate measurements. In either case, the input to embedded OPC will be CD data in the form of a matrix that describes the CD mean to nominal (MTN) as a function of linewidth and gap, where gap is the distance between the opposing edges of two neighboring lines. The modeling is performed in a function specifically designed for this purpose, the proximity matrix generator (PMG). The PMG produces a linewidth/gap matrix that maps the CD MTN as a function of linewidth and gap for all dimensions of interest.
Compared with producing correction tables based on only plate measurements, the PMG offers a faster solution that is more compatible with a production workflow. This is necessary because the writer may change somewhat over time (e.g., with a change of nominal dose). The PMG that models the behavior of the writer requires defined input data, including both system parameters and plate measurement data.
The Correction Map Manager parses the linewidth/gap reference and generates the corresponding rule commands, and a third molecule, Correction Prep, uses those commands to produce the DRC file used for execution of the embedded OPC software.
Experimental results
The ability of embedded OPC to improve mask writer operation was evaluated by comparing plates printed with and without corrections applied. A calibration pattern having programmed linewidths (CDs) and duty cycles was first printed and used to calculate the rule tables, including rules based on the system description model. The pattern was then printed again with embedded OPC corrections applied and the results were compared.6
Figure 3 shows the measured CD linearity for clear and dark features in the calibration pattern, comparing the uncorrected performance (Fig. 1) to the performance with embedded OPC applied with a PMG-generated linewidth/gap matrix. The linearity of 1:1 nested features is improved to the point of essentially eliminating the proximity effect for this pattern. The CD range is reduced to under 4 nm at a feature size of 200 nm, which is smaller than the 220 nm specified primary feature size of the mask writer evaluated here. The CD range is reduced to 9 nm at the minimum feature size in the pattern design (140 nm), compared with a 45 nm CD range in the uncorrected case.
Another benefit of embedded OPC is that the practical resolution of the mask writer is extended. This results from the automatic biasing of features so that they print at the designed dimension, rather than falling off at the low end of the linearity curves as seen for uncorrected features. Figure 4 shows SEM images of a test pattern with a 260 nm central feature straddled on either side by two 120 nm assist features. In the uncorrected pattern, the central feature prints somewhat undersize, but the assist features are not even resolved. With embedded OPC, all features are corrected so that they print on size.
Summary
An embedded OPC application, consisting of Calibre table-driven OPC and mask data preparation software embedded in the Sigma7500 DUV mask writer system data processing flow, can be used to significantly enhance the CD linearity and proximity performance on photomasks by applying pre-patterning CD corrections to the mask pattern data. Experimental results indicate an improvement in the CD linearity and proximity range from over 20 nm down to 5 nm for the test patterns evaluated. Using an optical system model as the basis for correction table/rules gives comparable performance to tables/rules based on plate measurements, allowing for easier calibration and tracking of the embedded OPC application. An embedded OPC implementation using a single cabinet blade computer cluster can apply correction without compromising mask writer throughput. This makes it possible to use an optical mask writer on sub-critical 65 and 45 nm photomasks that previously could only be printed by variable shaped e-beam systems.
Anders Österberg, an engineering program manager at Micronic Laser Systems AB, received his Masters degree in electrical engineering from the Royal Institute Technology in Sweden. He has been with Micronic for seven years, and is currently working on projects combining datapath technology with mask patterning enhancements.
Steffen Schulze is the Marketing Director for Calibre Mask Data Preparation and platform applications at Mentor Graphics. He received his Masters degree in material science from the Lomonossov Institute for chemical engineering in Moscow, Russia. He holds a Ph.D. in electrical engineering from the University of Bremen, Germany, and an MBA from the University of Oregon. He has been with Mentor Graphics for six years, and is currently focused on projects improving post tapeout data preparation flows in semiconductor manufacturing.
References:References
- H. Sjöberg et al., "Sigma7500: An Improved DUV Laser Pattern Generator Addressing Sub-100 nm Photomask Accuracy and Productivity Requirements," Proc. SPIE, 2006, Vol. 6283.
- T. Öström, A. Beyerl, H. Sjöberg, T. Newman and P. Högfeldt, "Second Level Exposure for Advanced Phase Shift Mask Applications Using the SLM-Based Sigma7300 DUV Mask Writer," Proc. SPIE, 2005, Vol. 5835, p. 155.
- M. Chandramouli et al., "Second Level Exposure for Phase Shift Mask Applications Using an SLM-Based DUV Mask Writer," Proc. SPIE, 2005, Vol. 5853, p. 398.
- B. Olshausen, M. Chandramouli, D. Wall, B. Auches and D. Cole, "Production Performance of a Sigma7300 DUV Mask Writer," Proc. SPIE, 2005, Vol. 5992.
- W. Zhang, E. Sahouria and S. Schulze, "Distributed Computing in Mask Data Preparation for 45-nm Node and Below," Proc. SPIE, 2007, Vol. 6349.
- A. Österberg et al., "Embedded Optical Proximity Correction for the Sigma7500 DUV Mask Writer," Photomask Japan, 2007.
author: Anders Österberg, Micronic Laser Systems AB, Täby, Sweden, www.micronic.se, Steffen Schulze, Mentor Graphics Corp., Wilsonville, Ore., www.mentor.com
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