Normalized Image Log Slope Research Articles

Influencing factors of self-aligned imaging in near-field lithography for the Fabry–Perot cavity effect

In near-field lithography, the Fabry–Perot (F-P) cavity enhancement effect can significantly improve image quality and resolution. This paper considers changes in the refractive index and air distance in self-aligned imaging. Simulation results demonstrate that the Fabry–Perot resonator effect achieves effective self-alignment in 3D imaging. The proposed structure builds on traditional near-field imaging structures and F-P resonator research, suggesting a Cu/SiO2 structure as the front layer. Rigorous coupled wave analysis (RCWA), finite element method (FEM), and finite-difference time-domain (FDTD) methods were employed to verify the self-alignment effect on single gratings and rectangular hole arrays. The results indicate that the self-alignment lithography method based on the F-P effect not only enhances lithography contrast and normalized image log-slope (NILS) but also shows robust performance against variations in air distance and complex refractive index. Notably, for the rectangular aperture array structure, with changes in air distance and complex refractive index within a certain range, the NILS remains stable above 2.8, and the contrast stays near 0.70. These simulation results confirm that the F-P resonator-based scheme is viable for plasma imaging lithography with small critical dimensions.

Exploring the optimal combination of Ru/Ta bilayer mask stacks and illumination source shapes to mitigate mask 3D effects at high-NA extreme ultraviolet lithography

The imaging performance of extreme ultraviolet (EUV) lithography is determined by the optical properties and thickness of the photomask absorber material and the illumination source shape. Optimizing the trade-offs between imaging metrics, such as normalized image log slope, telecentricity error, and best focus variation through pitch (collectively known as mask-3-dimensional (M3D) effects), is crucial to improve the throughput of the EUV lithography process. This study aims to optimize Ru/Ta bilayer photomask absorber stacks and illumination source shapes to mitigate M3D effects using mask diffraction analysis. It intends to raise questions about the conventional absorber reflectivity or induced phase shift-based approach.

Aperiodic multilayer masks for M3D mitigation in high- and hyper-NA extreme ultraviolet lithography

As extreme ultraviolet lithography tools with higher image numerical apertures (NAi) are introduced, the range of angles at the multilayer mask stack is also increased. Lithography systems are designed to fulfill the “abbe sine rule,” where NAm is related to NAi by the reduction factor. As a result, increases in NAi will increase NAm. High-NA and hyper-NA systems will be implemented with anamorphic optics, 4× in “X,” and 8× in “Y” to reduce the necessary angles. Even so, hyper-NA masks may see illumination angles as high as 13.4°, up from 10.8° for 0.33 NA. This represents a challenge for maintaining through-angle mask reflection using the current periodic mask multilayer structures. In addition to the reflectance amplitude, the phase of reflected light, which plays an important role in imaging, is also strongly influenced by increasing angles. The propagation of light through each bilayer in the stack imparts a phase shift based on the incidence angle. This is then accumulated over many layers, inducing phase effects, which are unique to each illumination point. This will become especially true for high-NA and hyper-NA mask applications. While adjustments to the multilayer period are sufficient to achieve acceptable reflectance, periodic multilayers may suffer in normalized image log slope (NILS) and image placement error (IPE) metrics as a result of strong oblique multilayer M3D phase effects. In this work, we present a first principles methodology for the systematic reduction of oblique multilayer M3D effects through the use of aperiodic multilayer design. We find that when used for low-k1, hyper-NA patterning NILS is improved by 40+%, while IPE through pitch is similarly improved. Under high-NA conditions, a 5%–25% NILS gain is found alongside the enhanced depth of focus.

High-fidelity source mask optimization for suppressing line-end shortening.

Source mask optimization (SMO) is a widely used computational lithography technique for compensating lithographic distortion. However, line-end shortening is still a key factor that cannot be easily corrected and affects the image fidelity of lithography at advanced nodes. This paper proposes a source mask optimization method that suppresses line-end shortening and improves lithography fidelity. An adaptive hybrid weight method is employed to increase the weights of the line end during the optimization, which adaptively updates the weights in each iteration according to the edge placement error (EPE). A cost function containing a penalty term based on the normalized image log slope (NILS) is established to ensure the fidelity of the overall feature when paying more attention to the line-end region. The scope of this penalty term is regulated by widening and extending the split contour to further reduce the line-end shortening. Simulation results show that the proposed method can effectively suppress the line-end shortening and improve the lithography fidelity compared with the traditional SMO method.

Design and large-scale nanofabrication of plasmonic solar light absorbers

Surface plasmon resonances have been exploited for many applications due to their tunability, which is directly related to the geometry of nanostructures. Based on their dimension and material stack, the resonances can be tailored to achieve high absorbing or reflecting nanopatterned surfaces designed for specific wavelengths. While the preferred lithographic printing techniques in the field allow high precision and control of the structures, they are limited in throughput, thus restricting possible large-scale applications. In this work, we present a full process flow, which can produce hundreds of square meters of nanopillar arrays by combining resolution enhancement techniques (RETs) on a deep-UV stepper for fabricating a silicon master and roll-to-roll extrusion coating (R2R-EC) for its replication. We demonstrate optimized exposures with the combination of dipole off-axis illumination, triple cross-exposure, and the addition of assisted features on the mask design. By simulating the RETs compared to a conventional setup, we show how lithographic parameters such as the normalized image log-slope (NILS) improve from 0.90 to 2.05 or the resist image contrast (RIC) increases from 0.429 to 0.813. We confirm these results by printing wafer-size hexagonal and rectangular arrays of nanopillars with 340, 350, and 360 nm pitches and diameters ranging from 100 to 200 nm. We show the successful replication of both designs by R2R-EC, an industrial process, which produces hundred-meter rolls of patterned polymer. We demonstrate that after metallization, the samples are suitable for solar absorption by measuring their absorptance (absorbed to incident intensity) and comparing it with the solar irradiance peak. We achieve a 70% efficiency for both hexagonal and rectangular arrays at resonant peaks of 550 and 600 nm, respectively, where the hexagonal array better matches the solar irradiance peak. Additionally, the plasmonic samples block 78% of the heat radiation when compared to a plain black polymer foil for reference, making them more efficient for solar harvesting applications.

Evaluation of Ta-Co alloys as novel high-k extreme ultraviolet mask absorber

BackgroundA plausible approach for mitigating the mask 3-D (M3D) effects observed in extreme ultraviolet (EUV) lithography is to replace the existing mask absorber with alternative materials. Absorbers with a high EUV extinction coefficient k allow for lower best focus variation (BFV) through pitch and reduced telecentricity errors (TCEs).AimWe aim to evaluate Ta-Co alloys as potential high-k mask absorbers from material suitability and imaging standpoints.ApproachWe study the film morphology, surface composition, and stability of Ta-Co alloys in mask cleaning solutions and a hydrogen environment as present in the EUV scanner to assess the material suitability from an experimental aspect. Optical constants for three selected compositions, viz., TaCo, Ta2Co, and TaCo3, were determined from EUV angle-dependent reflectivity measurements. Next, utilizing rigorous simulation software, the imaging performance of Ta-Co alloys is evaluated and compared with the reference absorber. The recommended absorber thickness for Ta-Co alloy absorbers is based upon normalized image log slope (NILS) enhancement, threshold to size, and balancing of diffraction order amplitudes. A 10 nm line and space pattern with a pitch of 20 nm and 14 nm square contact holes with a pitch of 28 nm are used for the simulation study using high numerical aperture 0.55 EUV lithography process settings. The primary imaging metrics for through pitch evaluation include NILS, TCE, and BFV.ResultsThe Ta-Co alloys exhibit a higher EUV extinction coefficient k compared with the currently used Ta-based absorber. TaCo and Ta2Co demonstrate smooth surfaces and are stable in a hydrogen environment and in mask-cleaning solutions.ConclusionTa-Co alloys allow for a reduction in M3D effects at a lower absorber thickness compared with a 60 nm Ta-based reference absorber.

Initiative global NILS control in source and mask optimization for process window enhancement.

Semiconductor processing is becoming more challenging as integrated circuit dimensions shrink. An increasing number of technologies are being developed for the purpose of ensuring pattern fidelity, and source and mask optimization (SMO) method has outstanding performances. In recent times, owing to the development of the process, more attention has been paid to the process window (PW). As a crucial parameter in lithography, the normalized image log slope (NILS) is strongly correlated with the PW. However, previous methods ignored the NILS in the inverse lithography model of the SMO. They regarded the NILS as the measurement index for forward lithography. This implies that the optimization of the NILS is the result of passive rather than active control, and the final optimization effect is unpredictable. In this study, the NILS is introduced in inverse lithography. The initial NILS is controlled by adding a penalty function to ensure that it continuously increases, thus increasing the exposure latitude and enhancing the PW. For the simulation, two masks typical of a 45-nm-node are selected. The results indicate that this method can effectively enhance the PW. With guaranteed pattern fidelity, the NILS of the two mask layouts increase by 16% and 9%, and the exposure latitudes increase by 21.5% and 21.7%.

Generation of inverse assist features using generative adversarial networks

Adding the assist feature in the optical proximity correction (OPC) procedure is crucial for improving the process window. The rule-based assist feature placement is very fast; however, the resultant process window still requires improvement. The model-based assist feature placement presents a better process window, but its iterative nature makes it extremely time-consuming. The assist features (AFs) that are optimized by using the inverse lithography technique perform best in terms of lithographic metrics such as the Depth of Focus, Mask Error Enhancement Factor, and Normalized Image Log Slope; these features can be added to the objective function. However, the inverse lithography technique is a pixel-level correction method, which is even more time-consuming. Consequently, it is typically used to provide guidance for rule-based AF placement. In this study, we design novel generative adversarial networks (GANs) that can generate AFs to increase the speed of assist feature placement while maintaining relatively high lithographic performance using inverse lithography techniques. The results demonstrate that the proposed generative adversarial network methods are three orders of magnitude faster than the inverse lithography techniques. Additionally, they exhibit lower edge placement errors and process variation bands when compared to the inverse lithography techniques.

Mitigating the forbidden pitch of extreme ultraviolet lithography using mask optimization based on genetic algorithm

BackgroundIn advanced technology nodes, forbidden pitches (FPs) can reduce the depth of focus and limit the overlapped process window of lithography. In extreme ultraviolet (EUV) lithography, one pattern in a different orientation or different position of arc slit field will have a different shadowing effect, due to the chief ray angle and azimuthal angle of the incident light. Therefore, it is necessary to mitigate the FP effect of EUV lithography.AimWith the purpose of mitigating the phenomenon of FPs in the arc slit exposure field, we propose an optimization method based on a genetic algorithm (GA).ApproachThe optimization method is derived from the basic flow of the GA. Three mask parameters are selected as the variables, including the mask bias and the width and position of the assist feature. The cost function is designed to evaluate the process window, normalized image log slope, and contrast of different fields in the arc slit. After multiple iterations, an optimal combination of three variables is obtained.ResultsThe simulation results show that the optimized mask structure given by the proposed method in the arc slit exposure field can improve the process window in the horizontal and vertical orientations, respectively.ConclusionsThe limitation of FPs to the process window is removed using mask optimization based on the GA. The proposed optimization method has the potential to be an effect candidate for FPs mitigation.

Extend 0.33 NA extreme ultraviolet single patterning to pitch 28-nm metal design by low-n mask

Extending 0.33 NA extreme ultraviolet single patterning to 28-nm pitch becomes challenging in stochastic defectivity, which demands high-contrast lithographic images. The low-n attenuated phase-shift mask (attPSM) can provide superior solutions for individual pitches by mitigating mask three-dimensional effects. The simulation and experiment results have shown substantial imaging improvements: higher depth of focus at similar normalized image log slope and smaller telecentricity error values than the best binary mask configuration. In this work, the exploration of low-n attPSM patterning opportunity for pitch 28-nm metal design is investigated. Using generic building block features, the lithographic performance of the low-n attPSM is compared with the standard binary Ta-based absorber mask. In addition, the impact of mask tone (bright field (BF) versus dark field) on the pattern fidelity and process window is evaluated both by simulations and experiments. The results indicate that BF low-n attPSM provides the best patterning performance. Consequently, the BF low-n attPSM patterning performance is assessed with an actual imec N3 pitch 28-nm random logic metal design. The wafer data indicate BF low-n attPSM enables good patterning fidelity, as well as good overall process window with high exposure latitude (∼20 % ).

Elucidating the role of imaging metrics for variability and after etch defectivity

Background: In extreme ultraviolet lithography, maximum printable feature density is limited by stochastic defectivity. One of the methods to reduce it is the optimization of the aerial image via source mask optimization. To guide this optimization, we need to know which aerial image metric predicts defectivity. Feature variability is linked to defectivity. Aim: Find which aerial image metric best predicts variability and defectivity. Approach: We construct seven pupils that vary aerial image metrics [normalized image log slope (NILS), depth-of-focus (DoF), maximum intensity] in a controlled way. We measure variability and defectivity after development and after two different etch processes and correlate them to aerial image metrics. Results: Stochastic critical dimension uniformity (CDU) is best predicted by NILS. Systematic CDU is determined by mask roughness through spatial frequency, with low frequencies differentiating outer and inner sigma pupils. Defectivity is best predicted by maximum intensity for missing holes and minimum intensity for merging holes. NILS and maximum intensity are strongly correlated. DoF has minimal impact. Conclusions: Optimization toward maximum intensity reduces defectivity. Outer sigma pupils reduce variability. Increasing numerical aperture in next-generation EUV lithography is expected to reduce missing hole defects.

Compensation of EUV lithography mask blank defect based on an advanced genetic algorithm.

Mask blank defect is one of the most important factors that degrades the image quality of extreme ultraviolet (EUV) lithography system, and further leads to a yield lose. In order to compensate the amplitude and phase distortions caused by the EUV mask blank defects, this paper proposes an advanced algorithm to optimize the mask absorber pattern based on genetic algorithm. First, a successive approximation correction method is used to roughly compensate the effect of mask blank defect. Then, an advanced genetic algorithm is proposed to obtain higher efficiency and compensation accuracy, which uses an adaptive coding strategy and a fitness function considering normalized image log slope of lithography image. For illustration, the proposed method is verified based on rectangular contact patterns and complex pattern with different defects. The aerial images of optimized masks are evaluated by a commercial lithography simulator. It will show that the proposed method can mitigate the impact of mask defects, and improve the fidelity of lithography print image. The simulation results also demonstrate the higher convergence efficiency and mask manufacturability can be guaranteed by the proposed method.

Study of novel EUVL mask absorber candidates

Novel mask absorber designs are catching the attention of the EUVL community due to their ability to mitigate mask 3D effects. Material selection is part of such an optimization. We propose several candidates as novel EUV lithography mask absorbers, namely TaTeN, Ru–Ta, and Pt–Mo alloys. The choice of these materials is based on their theoretical performance evaluated by EUV imaging simulation based on their complex refractive index N ( λ ) = n ( λ ) + ik ( λ ) , where the optical constants n and k relate to the phase velocity and the absorption of electromagnetic radiation with a wavelength λ, respectively. The materials are deposited as thin films on Si substrate with an additional Ru layer to mimic the cap of the multilayer mirror on the real mask. The experimental n and k values are determined by analyzing EUV reflectivity data obtained using a 13.5-nm synchrotron EUV radiation. The imaging simulation presented consists of calculating several imaging metrics including non-telecentricity, normalized image log-slope, and threshold-to-size for specific use cases using the novel absorber. It also compares the proposed materials with the reference TaBN absorber. TaTeN shows higher absorption than TaBN and refraction closer to 1, which improves phase matching for a high k absorber. The refractive index of Ru–Ta and Pt–Mo alloys exhibits a large difference from that of air and provides the required phase shift of attenuated phase shift masks. The characterizations of these materials target the requirements of an EUVL mask: durability for mask cleaning, mask lifetime, and etchability for mask patterning. The stability is first tested against several standard mask cleaning solutions by a beaker test for up to 24 h. The samples are also exposed to hydrogen plasma to imitate the working environment in an EUV scanner. Concerning material patterning, chemical reactive ion etch is applied for preliminary tests. A proper etch recipe is found for TaTeN with a good etch rate (about 60 nm / min) and good selectivity to the Ru underlayer (Ru etch is negligible).

Pattern roughness analysis using power spectral density: application and impact in photoresist formulation

Linewidth roughness (LWR) remains a difficult challenge for improvement in resist materials. We intend to review work that focused on the impact of key components of LWR by analyzing the unbiased power spectral density (PSD) curves. We studied systematic changes to ArF resist formulations and correlated these changes to the overall PSD curves. In this manner, we could extract LWR 3σ values and resist correlation length and the low/high-frequency roughness components. We also investigated the relationship between PSD and LWR through lithographic/etch processing and demonstrated which PSD components correspond to the largest impact on LWR. This work was extended further to investigate how frequency components are influenced by basic resist properties such as diffusion and aerial image properties such as normalized image log-slope (NILS). Particular attention was given to how changes in correlation length affected LWR as feature size decreases. We also looked at the impact of diffusion or resist blur on PSD(0) as a function of NILS. Finally, we will review how LWR improvement can be achieved by several strategies that focus on both PSD(0) and correlation length (ξ) and not a single LWR number. The trends presented highlight the true nature of LWR with respect to its high and low-frequency components. It also shows the benefits of measuring and developing resists as a function of roughness power spectral density and not as a function of a single LWR measurement.

Gradient-based source mask and polarization optimization with the hybrid Hopkins–Abbe model

Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.

Challenges of anamorphic high-NA lithography and mask making

Abstract Chip makers are actively working on the adoption of 0.33 numerical aperture (NA) EUV scanners for the 7-nm and 5-nm nodes (B. Turko, S. L. Carson, A. Lio, T. Liang, M. Phillips, et al., in ‘Proc. SPIE9776, Extreme Ultraviolet (EUV) Lithography VII’, vol. 977602 (2016) doi: 10.1117/12.2225014; A. Lio, in ‘Proc. SPIE9776, Extreme Ultraviolet (EUV) Lithography VII’, vol. 97760V (2016) doi: 10.1117/12.2225017). In the meantime, leading foundries and integrated device manufacturers are starting to investigate patterning options beyond the 5-nm node (O. Wood, S. Raghunathan, P. Mangat, V. Philipsen, V. Luong, et al., in ‘Proc. SPIE. 9422, Extreme Ultraviolet (EUV) Lithography VI’, vol. 94220I (2015) doi: 10.1117/12.2085022). To minimize the cost and process complexity of multiple patterning beyond the 5-nm node, EUV high-NA single-exposure patterning is a preferred method over EUV double patterning (O. Wood, S. Raghunathan, P. Mangat, V. Philipsen, V. Luong, et al., in ‘Proc. SPIE. 9422, Extreme Ultraviolet (EUV) Lithography VI’, vol. 94220I (2015) doi: 10.1117/12.2085022; J. van Schoot, K. van Ingen Schenau, G. Bottiglieri, K. Troost, J. Zimmerman, et al., ‘Proc. SPIE. 9776, Extreme Ultraviolet (EUV) Lithography VII’, vol. 97761I (2016) doi: 10.1117/12.2220150). The EUV high-NA scanner equipped with a projection lens of 0.55 NA is designed to support resolutions below 10 nm. The high-NA system is beneficial for enhancing resolution, minimizing mask proximity correction bias, improving normalized image log slope (NILS), and controlling CD uniformity (CDU). However, increasing NA from 0.33 to 0.55 reduces the depth of focus (DOF) significantly. Therefore, the source mask optimization (SMO) with sub-resolution assist features (SRAFs) are needed to increase DOF to meet the demanding full chip process control requirements (S. Hsu, R. Howell, J. Jia, H.-Y. Liu, K. Gronlund, et al., EUV ‘Proc. SPIE9048, Extreme Ultraviolet (EUV) Lithography VI’, (2015) doi: 10.1117/12.2086074). To ensure no assist feature printing, the assist feature sizes need to be scaled with λ/NA. The extremely small SRAF width (below 25 nm on the reticle) is difficult to fabricate across the full reticle. In this paper, we introduce an innovative ‘attenuated SRAF’ to improve SRAF manufacturability and still maintain the process window benefit. A new mask fabrication process is proposed to use existing mask-making capability to manufacture the attenuated SRAFs. The high-NA EUV system utilizes anamorphic reduction; 4× in the horizontal (slit) direction and 8× in the vertical (scanning) direction (J. van Schoot, K. van Ingen Schenau, G. Bottiglieri, K. Troost, J. Zimmerman, et al., ‘Proc. SPIE. 9776, Extreme Ultraviolet (EUV) Lithography VII’, vol. 97761I (2016) doi: 10.1117/12.2220150; B. Kneer, S. Migura, W. Kaiser, J. T. Neumann, J. van Schoot, in ‘Proc. SPIE9422, Extreme Ultraviolet (EUV) Lithography VI’, vol. 94221G (2015) doi: 10.1117/12.2175488). For an anamorphic system, the magnification has an angular dependency, and thus, familiar mask specifications such as mask error factor (MEF) need to be redefined. Similarly, mask-manufacturing rule check (MRC) needs to consider feature orientation.

Theoretical study of relationships among resolution, line width roughness, and sensitivity of chemically amplified extreme ultraviolet resists with photodecomposable quenchers

The resolution of chemically amplified extreme ultraviolet (EUV) resists has reached 13–15 nm. However, the line width roughness (LWR) and sensitivity are still inadequate for their application to the high-volume production of semiconductor devices. In this study, the performance of chemically amplified resists with photodecomposable quenchers were investigated by simulation based on the sensitization and reaction mechanisms of chemically amplified EUV resists. The relationships among resolution, LWR, and sensitivity were evaluated in the half-pitch ranges of 12–16 nm. The requirements for 20 mJ cm−2 and 10% critical dimension (CD) LWR are considered to be within the physical limits in the half-pitch range of 12–16 nm when an optical image with a contrast of 1 (normalized image log slope of π) is given. Depending on the given image quality and the required sensitivity, the optimization of sensitizer concentration and the increase in resist absorption coefficient and/or effective reaction radius for deprotection are required to achieve 10% CD LWR.

Multistack structure for an extreme-ultraviolet pellicle with out-of-band radiation reduction

We report on out-of-band (OoB) radiation that can cause degradation to the image quality in extreme-ultraviolet (EUV) lithography systems. We investigated the effect of OoB radiation with an EUV pellicle and found the maximum allowable reflectivity of OoB radiation from the EUV pellicle that can satisfy certain criteria (i.e., the image critical dimension error, contrast, and normalized image log slope). We suggested a multistack EUV pellicle that can obtain a high EUV transmission, minimal reflectivity of OoB radiation, and sufficient deep ultraviolet transmission for defect inspection and alignment without removing the EUV pellicle in an EUV lithography system.

Actinic critical dimension measurement of contaminated extreme ultraviolet mask using coherent scattering microscopy

The authors evaluated the feasibility of using coherent scattering microscopy (CSM) as an actinic metrology tool by employing it to determine the critical dimension (CD) and normalized image log-slope (NILS) values of contaminated extreme ultraviolet (EUV) masks. CSM was as effective as CD scanning electron microscopy (CD-SEM) in measuring the CD values of clean EUV masks in the case of vertical patterns (nonshadowing effect); however, only the CSM could detect shadowing effect for horizontal patterns resulting in smaller clear mask CD values. Owing to weak interaction between the low-density contaminant layer and EUV radiation, the CSM-based CD measurements were not as affected by contamination as were those made using CD-SEM. Furthermore, CSM could be used to determine the NILS values under illumination conditions corresponding to a high-volume manufacturing tool.

Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step

Inverse mask synthesis is achieved by minimizing a cost function on the difference between the output and desired patterns. Such a minimization problem can be solved by a level-set method where the boundary of the pattern is iteratively evolved. However, this evolution is time-consuming in practice and usually converges to a local minimum. The velocity of the boundary evolution and the size of the evolution step, also known as the descent direction and the step size in optimization theory, have a dramatic influence on the convergence properties. This paper focuses on developing a more efficient algorithm with faster convergence and improved performance such as smaller pattern error, lower mean edge placement error, wider defocus band, and higher normalized image log slope. These improvements are accomplished by employing the conjugate gradient of the cost function as the evolution velocity, and by introducing an optimal time step for each iteration of the boundary evolution. The latter is obtained from an extended Euler time range by using a line search method. The authors present simulations demonstrating the efficacy of these two improvements.