The successful implementation of extreme ultraviolet lithography (EUVL) requires the use of an electrostatic chuck to both support and flatten the mask during scanning exposure. The EUVL Mask Standard, SEMI P37, specifies the nonflatness of the mask frontside and backside, as well as the thickness variation, to be 30 to 100 nm peak-to-valley, dependent on the class of substrate. Thus, characterizing and predicting the capability of the electrostatic chuck to reduce mask nonflatness to meet these specifications are critical issues. In this research, the ability of such chucks to deal with the presence of particles trapped between the substrate and chuck is investigated. Analytical and finite element modeling are used to identify the forces needed to fully embed or deform a particle during electrostatic chucking. Simulation results (using an elastic analysis) show that the forces generated by both Coulomb and Johnsen-Rahbek chucks should be able to sufficiently deform, or flatten, particles that are nearly 1.0 µm in size.
Extreme Ultraviolet Lithography (EUVL) is one of the leading candidates for the next-generation lithography in the sub-30 nm regime. Stringent flatness requirements have been imposed for the front and back surfaces of EUVL masks to ensure successful pattern transfer that satisfies the image placement error budget. The EUVL Mask Standard (SEMI P-37) specifies the flatness of the two mask surfaces to be approximately 50 nm peak-to-valley. It is essential to measure the mask surface nonflatness accurately (without gravitational distortions) to the extent possible. The purpose of this research was to study the various mask mounting techniques and to compare these methods for repeatability and accuracy during the measurements.
The successful implementation of extreme ultraviolet lithography (EUVL) requires the use of an electrostatic chuck to
both support and flatten the mask during scanning exposure. The EUVL Mask Standard, SEMI P37, specifies the
nonflatness of the mask frontside and backside, as well as the thickness variation, to be 30 nm to 100 nm peak-to-valley,
dependent on the class of substrate. Thus, characterizing and predicting the capability of the electrostatic chuck to
reduce mask nonflatness to meet these specifications are critical issues. In this research, the ability of such chucks to
deal with the presence of particles trapped between the substrate and chuck is investigated. Analytical and finite
element modeling have been used to identify the forces needed to fully embed or deform a particle during electrostatic
chucking. Simulation results (using an elastic analysis) have shown that the forces generated by both Coulomb and
Johnsen-Rahbek chucks should be able to sufficiently deform, or flatten, particles which are nearly 1.0 μm in size.
KEYWORDS: Extreme ultraviolet lithography, Interferometry, Photomasks, Reticles, Data modeling, 3D modeling, Mathematical modeling, Photography, Image quality, Control systems
Extreme Ultraviolet Lithography (EUVL) is one of the leading candidates for Next-Generation Lithography in the sub-45-nm regime. Successful implementation of this technology will depend upon advancements in many areas,
including the quality of the mask system to control image placement errors. For EUVL, the nonflatness of both the
mask and chuck is critical, due to the nontelecentric illumination during exposure. The industry is proposing to use an
electrostatic chuck to support and flatten the mask in the exposure tool. The focus of this research is to investigate the
clamping ability of a pin-type chuck, both experimentally and with the use of numerical simulation tools, i.e., finite
element modeling. A status report on electrostatic chucking is presented, including the results obtained during
repeatability studies and long-term chucking experiments.
According to the International Technology Roadmap for Semiconductors, meeting the strict requirements on image
placement errors in the sub-45-nm regime may be one of the most difficult challenges for the industry. For Extreme
Ultraviolet Lithography (EUVL), the nonflatness of both the mask and chuck is critical as well, due to the
nontelecentric illumination during exposure. To address this issue, SEMI Standards P37 and P40 have established the
specifications on flatness for the EUVL mask substrate and electrostatic chuck. This study investigates the procedures
for implementing the Standards when measuring and characterizing the shapes of these surfaces. Finite element
simulations are used to demonstrate the difficulties in supporting the mask substrate, while ensuring that the measured
flatness is accurate. Additional modeling is performed to illustrate the most appropriate methods of characterizing the
nonflatness of the electrostatic chuck. The results presented will aid in identifying modifications and clarifications that
are needed in the Standards to facilitate the timely development of EUV lithography.
With the stringent requirements on image placement (IP) errors in the sub-65-nm regime, all sources of mask
distortion during fabrication and usage must be minimized or corrected. For extreme ultraviolet lithography, the
nonflatness of the mask is critical as well, due to the nontelecentric illumination during exposure. This paper outlines
a procedure to predict the IP errors induced on the mask during the fabrication processing, e-beam tool chucking, and
exposure tool chucking. Finite element (FE) models are used to simulate the out-of-plane and in-plane distortions at
each load step. The FE results are compiled to produce a set of Correction Tables that can be implemented during e-beam
writing to compensate for these distortions and significantly increase IP accuracy. A previous version of this paper appeared in the Proceedings of the European Mask and Lithography Conference (EMLC), SPIE, 6533, 653314 (2007). The paper has been updated, retitled, and published here as a result of winning the Best Paper Award at the EMLC.
With the stringent requirements on image placement (IP) errors in the sub-65 nm regime, all sources of mask
distortion during fabrication and usage must be minimized or corrected. For extreme ultraviolet lithography, the
nonflatness of the mask is critical as well, due to the nontelecentric illumination during exposure. This paper outlines
a procedure to predict the IP errors induced on the mask during the fabrication processing, e-beam tool chucking, and
exposure tool chucking. Finite element (FE) models are used to simulate the out-of-plane and in-plane distortions at
each loading step. The FE results are compiled to produce a set of Correction Tables that can be implemented during
e-beam writing to compensate for these distortions and significantly increase IP accuracy.
Characterizing the effect of electrostatic chucking on the flatness of Extreme Ultraviolet Lithography (EUVL) reticles is
necessary for the implementation of EUVL for the sub-32 nm node. In this research, finite element (FE) models have
been developed to predict the flatness of reticles when clamped by a bipolar Coulombic pin chuck. Nonflatness
measurements of the reticle and chuck surfaces were used to create the model geometry. Chucking was then simulated
by applying forces consistent with the pin chuck under consideration. The effect of the nonuniformity of electrostatic
forces due to the presence of gaps between the chuck and reticle backside surfaces was also included. The model
predictions of the final pattern surface shape of the chucked reticle have been verified with chucking experiments and
the results have established the validity of the models. Parametric studies with varying reticle shape, chuck shape, chuck
geometry, and chucking pressure performed using FE modeling techniques are extremely useful in the development of
SEMI standards for EUVL.
Stringent flatness requirements have been imposed for the front and back surfaces of extreme ultraviolet
lithography masks to ensure successful pattern transfer within the image placement error budget. During exposure, an
electrostatic chuck will be used to support and flatten the mask. It is therefore critical that the electrostatic chucking
process and its effect on mask flatness be well-understood. The current research is focused on the characterization of
various aspects of electrostatic chucking through advanced finite element (FE) models and experiments. FE models that
use flatness measurements of the mask and the chuck to predict the final flatness of the pattern surface have been
developed. Pressure was applied between the reticle and chuck to simulate electrostatic clamping. The modeling results
are compared to experimental data obtained using a bipolar Coulombic pin chuck. Electrostatic chucking experiments
were performed in a cleanroom, within a vacuum chamber mounted on a vibration isolation cradle, to minimize the
effects of particles, humidity, and static charges. During these experiments, the chuck was supported on a 3-point
mount; the reticle was placed on the chuck with the backside in contact with the chucking surface and the voltage was
applied. A Zygo interferometer was used to measure the flatness of the reticle before and after chucking. The FE
models and experiments provide insight into the electrostatic chucking process which will expedite the design of
electrostatic chucks and the development of the SEMI standards.
Extreme Ultraviolet Lithography (EUVL) is one of the leading candidates for Next-Generation Lithography in the sub-45-nm regime. One of the key components in the development of EUVL is understanding and characterizing the response of the mask when it is electrostatically chucked in the exposure tool. In this study, finite element (FE) models have been developed to simulate the reticle / chuck system under typical exposure conditions. FE simulations are used to illustrate (a) the effects of the nonflatness of the reticle and chuck, (b) the image placement errors induced by back-side particulates, (c) the influence of the coefficient of friction between the reticle and chuck during exposure scanning, and (d) the effects of contact conductance on the thermomechanical response of the reticle. The focus of this paper is to illustrate that mechanical modeling and simulation has now become a fundamental tool in the design of electrostatic pin chucks for the EUVL technology.
Extreme ultraviolet (EUV) masks and mask chucks require extreme flatness in order to meet the performance and timing specified by the International Technology Roadmap for Semiconductors (ITRS). The EUVL Mask and Chucking Standards, SEMI P37 and SEMI P40, specify the nonflatness of the mask frontside and backside, as well as the chucking surface, to be no more than 50 nm peak-to-valley (p-v). Understanding and characterizing the clamping ability of the electrostatic chuck and its effect on the mask flatness is a critical issue. In the present study, chucking experiments were performed using an electrostatic pin chuck and finite element (FE) models were developed to simulate the chucking.
The frontside and backside surface flatness of several EUV substrates were measured using a Zygo large-area interferometer. Flatness data for the electrostatic chuck was also obtained and this data along with the substrate flatness data was used as the input for the FE modeling. Data from one substrate was selected for modeling and testing and is included in this paper. Electrostatic chucking experiments were conducted in a clean-room facility to minimize contamination due to particles. The substrate was chucked using an electrostatic pin chuck and the measured flatness was compared to the predictions obtained from the FE simulation.
The mechanical distortion of an EUVL mask from mounting in an exposure tool can be a significant source of wafer-level image placement error. In particular, the presence of debris lodged between the reticle and chuck can cause the mask to experience out-of-plane distortion and in-plane distortion. A thorough understanding of the response of the reticle/particle/chuck system during electrostatic chucking is necessary to predict the resulting effects of such particle contamination on image placement accuracy. In this research, finite element modeling is employed to simulate this response for typical clamping conditions.
Successful implementation of Extreme Ultraviolet Lithography (EUVL) depends on advancements in many areas, including the quality of the mask and chuck system to control image placement (IP) errors. One source of IP error is the height variations of the patterned mask surface (i.e., its nonflatness). The SEMI EUVL mask and chucking standards (SEMI P37 and SEMI P40) describe stringent requirements for the nonflatness of the mask frontside and backside, and the chucking surfaces. Understanding and characterizing the clamping ability of the electrostatic chuck and the effect on the mask flatness is therefore critical in order to meet these requirements. Legendre polynomials have been identified as an effective and efficient means of representing EUVL mask surface shapes. Finite element (FE) models have been developed to utilize the Legendre coefficients (obtained from measured mask and chuck data) as input data to define the surfaces of the mask and the chuck. The FE models are then used to determine the clamping response of the mask and the resulting flatness of the pattern surface. The sum of the mask thickness nonuniformity and the chuck surface shape has a dominant effect on the flatness of the patterned surface after chucking. The focus of the present research is a comprehensive analysis of the flatness and interaction between the nonflat chuck and the mask. Experiments will be conducted using several sample masks chucked by a slab type electrostatic chuck. Results from the study will support and facilitate the timely development of EUVL mask/chuck systems which meet required specifications.
The development of a low-distortion mask is of prime importance to Extreme Ultraviolet (EUV) Lithography. The mask consists of a standard ultra low expansion (ULE®) substrate measuring 152.4 mm x 152.4 mm x 6.35 mm, with a 280 nm thick reflective multilayer deposited on the top surface. Nonflatness of the mask patterned surface will manifest itself as image placement errors on the device wafer. Bottom surface nonflatness can interfere with securely holding the mask in the patterning and exposure tools as well as exacerbating patterned surface nonflatness. Of great concern is the effect of the mounting technique employed in the patterning and exposure tools on mask flatness. One such design, the electrostatic pin chuck, consists of a 'bed of pins' on the top surface of the chuck that will support the EUV mask during patterning and exposure. The pin design has been proposed to minimize the likelihood of particulates becoming lodged between the mask and chuck that would adversely distort the mask. To ensure that a chuck of this design will minimize image placement errors while still securely holding the mask, three-dimensional finite element (FE) models have been created to predict the influence of the electrostatic pin chuck on mask flatness. Legendre polynomials were used as input to the models to represent experimentally-measured substrate bottom surface shapes. The FE results illustrate that mechanical modeling provides an invaluable tool for quantifying the influence of mounting techniques on mask flatness, and, ultimately optimizing system parameters to successfully meet the stringent requirements at the 45-nm node (and below).
The International Technology Roadmap for Semiconductors for Extreme Ultraviolet Lithography (EUVL) places strict requirements on the quality and flatness of the substrate and patterned mask. The SEMI EUVL Mask Substrate Standard (SEMI P37) specifies that the substrate frontside and backside nonflatness be no more than 50 nm peak-to-valley (p-v). Recent technological advances in polishing and finishing techniques have placed the 50 nm p-v specification within reach. A key ingredient in the development of EUVL is understanding and characterizing the clamping ability of the electrostatic chuck and the resulting effect on the flatness of the chucked mask. By implementing the shape of a representative EUVL mask surface into a numerical model, the effect of electrostatic chucking on the shape of the mask was determined. Legendre polynomials have been identified as an effective and efficient means of representing EUVL mask surface shapes. Finite element (FE) models have been developed to utilize the Legendre coefficients as input data to define the surfaces of an EUVL mask. The FE models were then used to determine the clamping response of the mask. In particular, the maximum mask-to-chuck gap within the Flatness Quality Area and over the entire mask has been tracked as a function of clamping pressure for representative EUVL surfaces. One of the important parameters in this study was the chuck's mechanical stiffness (comprised of the thickness and modulus). The flatness of the EUVL mask also depends on the intrinsic stress and thickness of the multilayer and backside layers. The results in this paper show that the recent advances in EUVL substrate polishing have resulted in masks that can be chucked relatively flat.
The challenges in fabricating next-generation lithography (NGL) masks are distinct from those encountered in optical technology. The masks for electron proximity lithography, as well as those for ion and electron projection, use freestanding membranes incorporating layers that are different from the traditional chrome-on-glass photomask blanks. As a promising NGL technology, low-energy electron-beam proximity-projection lithography (LEEPL) will be subject to strict error budgets, requiring high pattern placement accuracy. Meeting these stringent conditions will necessitate an optimization of the design parameters involved in the mask fabrication process. Consequently, comprehensive simulations can be used to characterize the sources of the mechanical distortions induced in LEEPL masks during fabrication, pattern transfer, and mounting. For this purpose, finite element (FE) structural models have been developed to identify the response of the LEEPL mask during fabrication and chucking. Membrane prestress, which is used as input in the FE models, was measured on a 200-mm test mask and found to low in magnitude with excellent cross-mask uniformity. The numerical models were also validated both analytically and experimentally considering intrinsic and extrinsic loading of the mask. Finally, simulations were performed to predict the response of the LEEPL mask during electrostatic chucking. FE results indicate that the mask structure is sufficiently stiff to remain relatively flat under gravitational loadings. The results illustrate that mechanical modeling and simulation can facilitate the timely and cost-effective implementation of the LEEPL technology.
Extreme ultraviolet lithography (EUVL) is one of the leading candidates for next-generation lithography in the sub-65 nm regime. The International Technology Roadmap for Semiconductors proposes overlay error budgets of 18 nm and 13 nm for the 45 nm and 32 nm nodes, respectively. Full three-dimensional finite element (FE) models were developed to identify the optimal mask thickness to minimize image placement (IP) errors. Five thicknesses of the EUVL reticle have been investigated ranging from 2.3 mm to 9.0 mm. The mask fabrication process was simulated, as well as the e-beam mounting, pattern transfer, and exposure mounting, utilizing FE structural models. Out-of-plane distortions and in-plane distortions were tracked for each process step. Both electrostatic and 3-point mounts were considered for the e-beam tool and exposure tool. In this case, increasing the thickness of the reticle will reduce the magnitude of the distortions. The effect of varying the reticle thickness on chucking was also studied. FE models were utilized to predict how changing the reticle thickness would affect the overall clamping response. By decreasing the reticle thickness (and therefore the effective bending stiffness), the deformed reticle is easier to flatten during chucking. In addition, the thermomechanical response of the reticle during exposure was investigated for different reticle thicknesses. Since conduction to the chuck is the main heat dissipation mechanism, decreasing the reticle thickness results in more energy being conducted away from the reticle, which reduces the maximum temperature rise and the corresponding thermal distortion.
The FE simulations illustrate the optimal thickness to keep IP errors within the allotted error budget as well as provide the necessary flatness during typical chucking procedures.
The focus of this paper is on the development and implementation of a correction strategy that enables mask manufacturers to maintain the yields at current levels while simultaneously reducing registration errors by several nanometers. An alternate consequence is that yields at current registration specifications are improved. Previous work has shown that one source of image placement error is the chrome stress relief caused by etching. This can cause over 25 nm of distortion from the resist pattern to the final etched chrome pattern. Theoretical and experimental data have shown that the distortion has a radial signature, which can be significantly reduced by traditional magnification correction. If the magnitude of this correction term can be predicted before patterning, the magnification can be implemented as a correction term in the writing process, minimizing registration errors. Studies have shown that the percent clear area of the mask, x-field size, y-field size, and chrome stress are the key parameters that will affect the correction term. Data based on finite element simulations were first fit to these parameters to obtain a predictive curve based upon theory. Experimental reticles were then written to test the theoretical prediction. The predictions were found to coincide well with the experimental data; registration improvements of over 20 nm were observed. The correlation was then applied to a set of production reticles. There was an observable improvement in registration after the correlation was implemented, although less than that seen in the experimental reticles.
Image fidelity is one of the fundamental requirements in lithography and it is becoming more important as feature sizes shrink below 90 nm. Image distortion depends on the mask deformation caused by the intrinsic stress in the film-substrate system. To develop an understanding of stress generation and to control film quality, measuring film stress is essential. In recent years, research laboratories and industry have increasingly adopted indirect methods for determining film stress. All of these methods are based on the measurement of substrate deformation, and the film stress is calculated from the substrate curvature by the local application of Stoney’s equation. When the two principal stresses at each point in the film plane are not equal to each other and their distribution is not uniform, the local application of Stoney’s equation is invalid. Even though the accuracy of the measurement may be high, the stress determined may not be. An alternative technique based on numerical analysis has been developed. The limitations of using Stoney’s equation and the new stress measurement technique are discussed in this paper.
The reflective reticles used for extreme ultraviolet (EUV) lithography are subject to the stringent image placement and flatness requirements for 70 nm and smaller feature sizes. Stresses in the reflective multilayer coatings can produce substantial bowing of the reticle, and variations in the flatness and thickness of the reticle substrate, as well as entrapped debris particles, can contribute to flatness errors on the patterned surface after reticle chucking. Reticles will also be subjected to high stage accelerations and thermal loadings during exposure. The chuck in the exposure tool will be required to clamp the reticle flat, crush entrapped debris, remove absorbed EUV energy, and prevent slippage during stage accelerations. Additionally, the thermal and structural behavior of the chuck will influence the reticle response, and thus the reticle and chuck must be considered as a system. In order to determine reticle and chucking requirements, finite element models have been developed to analyze many of the key issues in the mechanical design of the reticle and chuck. The analyses are being used to support the development of reticle and chuck standards for EUV lithography.
Extending 157-nm lithography to the 70 nm node will be a difficult challenge due to the stringent requirements on image placement accuracy. At the University of Wisconsin Computational Mechanics Center, numerical and experimental studies are being conducted to investigate materials, fabrication processing, and system parameters necessary to achieve the required overlay error budget. This paper provides our latest results for 157-nm reticles, including the photomask / pellicle system. Mask blank fabrication and pattern transfer effects were simulated utilizing three-dimensional finite element (FE) structural models. The pattern-specific in-plane distortions (IPD) induced by each fabrication process step have been determined using the IBM Nighteagle / Falcon layout. To complete the static structural analysis, the effects of bonding a pellicle were also identified. The thermomechanical response of reticles during e-beam patterning and exposure were evaluated utilizing FE heat transfer models. Results from e-beam writing simulations indicate that transient thermal distortions from patterning the Nighteagle / Falcon design are not critical. However, under high throughput conditions, the IPD induced during scanning exposure can become relatively large. The simulation results provide an indication of the total overlay error budget to be expected, and demonstrate the importance of using predictive models to optimize mask system performance in a cost-effective manner.
Potential transmission problems for polymeric pellicle membranes at 157 nm have led to alternative designs incorporating ultra-thin modified fused silica, i.e., so-called 'hard pellicles.' The mechanical characteristics of hard pellicles are unique. Forces can be generated between the pellicle frame and the patterned reticle during bonding because of misalignment and warpage. These forces create out-of-plane distortions of the reticle, which can subsequently induce in-plane distortions. Also, since the hard pellicle is an optical element, its deflection can be a source of error. In addition, because the reticle is rapidly repositioned during exposure, vibration of the pellicle could be excited by stage motion. It is important, therefore to understand the structural and modal response of the composite pellicle / reticle system. Experimental analyses were conducted to determine changes in the reticle and hard pellicle profiles (out-of-plane) due to bonding. Finite element modeling was used to support the experimental study, as well as identify the gravitational distortions of the pellicle. A modal analysis was also performed on the hard pellicle after bonding. The experimental measurements and finite element results were in excellent agreement, both for mode shapes and vibration frequencies.
The vibratory response of Electron-beam Projection Lithography (EPL) masks has been characterized for two applications: to support the processes for mask cleaning (e.g., PLASMAX) and to preclude resonance conditions during metrology and inspection. The analysis of a 200-mm SCALPEL mask has been completed using experimental and numerical procedures to determine the dynamic response; the procedures characterized transverse vibrations by identifying the natural frequencies with their respective mode shapes. For mask cleaning applications, dominant modes were superimposed to form a more uniform acceleration field within the grillage area for effective removal of contaminants. In order to assess potential resonance issues, a finite element model was used to simulate the four-pad support, which is currently proposed for the EPL mask standard chuck. The fundamental frequency of the mask in the four-pad support was over 300Hz.
The development of pellicles for 157 nm lithography includes not only the determination of appropriate materials, but also the minimization of pellicle-induced distortions contributing to overlay error. In particular, the attachment of the pellicle to the reticle surface can cause both out-of-plane and in-plane distortions (OPD and IPD) which contribute to pattern placement errors. This research focused on identifying the mechanical characteristics of thin-film pellicles, and the effect of bonding the pellicle frame to the reticle. Several different pellicle designs and films were analyzed and compared, using experimental, analytical, and finite element (FE) methods. The pellicle film stress was determined via two experimental procedures. The first, a resonant frequency test, identified the natural frequencies and mode shapes. The film stress values were subsequently determined from their relation to the frequencies. In the second procedure, static measurements of the displaced shape due to applied loads were taken using an MTI Fotonic Sensor. The film stresses from these independent measurements were between 200 and 300 kPa. The effect of the pellicle bonding was determined interferometrically by measuring the change in OPD of the reticle. The OPD values corresponded to IPD magnitudes of approximately 10 to 20 nm. These distortions were also simulated with FE models to replicate the mounting process. Using these methods, alternative mounting schemes, procedures, and materials can be developed, tested, and analyzed to reduce distortions in future designs.
As optical lithography error budgets on pattern placement become more and more stringent for sub-130 nm technology, all mask-related distortions must be quantified, controlled, and minimized. To optimize the mask fabrication process, it is essential to identify the stress magnitudes of the thin films and determine the resulting effect on pattern placement errors. Experiments utilizing surface mapping technique have been used to quantify the stress magnitudes of current thin film deposition parameters used in photomask blank fabrication. The effect of pattern transfer on image placement errors was determined experimentally for an anisotropic metrology pattern. The stress magnitudes obtained in the thin film stress measurements were incorporated into a finite element model that simulated the mechanical effect of pattern transfer utilizing equivalent modeling techniques. Analytical, experimental, and finite element procedures have been integrated to accurately quantify thin film stress magnitudes and the corresponding pattern transfer distortions.
Finite element models have been developed and refined to simulate the mechanical distortions associated with mask blank fabrication, pattern transfer, and exposure clamping. By modeling the substrate with layers associated with the mask fabrication process and then by prestressing specified layers, the resulting out-of-plane and in-plane distortions of the mask blank have been determined. Etching procedures were subsequently simulated to assess the pattern transfer distortions associated with both dark and bright field masks. Investigations included substrate materials which have acceptable optical transmission for wavelengths below 180 nm. Additional mechanical distortions associated with clamping the reticle into the exposure mount have also been considered.
Finite element (FE) models have been developed to determine mechanical distortions produced by photomask blank fabrication. The fabrication process involves the deposition of stressed thin films and the removal of parts of those films, the latter of which is referred to as pattern transfer. By creating a model of the substrate with thin layers associated with the mask fabrication process, then by prestressing these layers and simulating pattern transfer, the resulting out-of-plane displacements (OPD) and in-plane distortions (IPD) can be identified. Pattern-specific, global distortions induced during pattern transfer have been calculated for both dark and light field masks.
Finite element (FE) models have been created to investigate mechanical distortions associated with mask blank fabrication and mounting in a horizontal orientation. A modal analysis was completed to quantify the natural frequencies for the mask blank as a predictive tool for possible vibration prevention or control. By modeling the substrate with layers associated with the mask fabrication process and then by prestressing these layers, the resulting out-of-plane distortions (OPD) and in-plane distortions (IPD) can be determined. Utilizing these models, the magnitude of the maximum IPD and OPD due to gravity have been determined as a function of the mounting location to optimize the mounting position.
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