The semiconductor design node shrinking requires tighter edge placement errors (EPE) budget. OPC error, as one major contributor of EPE budget, need to be reduced with better OPC model accuracy. In addition, the CD (Critical Dimension) shrinkage in advanced node heavily relies on the etch process. Therefore AEI (After Etch Inspection) metrology and modeling are important to provide accurate pattern correction and optimization. For nodes under 14nm, the etch bias (i.e. the bias between ADI (After Development Inspection) CD and AEI CD) could be -10 nm ~ -50 nm, with a strong loading and aspect-ratio dependency. Etch behavior in advanced node is very complicated and brings challenges to conventional rule based OPC correction. Therefore, accurate etch modeling becomes more and more important to make precise prediction of final complex shapes on wafer for OPC correction. In order to ensure the accuracy of etch modeling, high quality metrology is necessary to reduce random error and systematic measurement error. Moreover, CD gauges alone are not sufficient to capture all the effects of the etch process on different patterns. Edge placement (EP) gauges that accurately describe the contour shapes at various key positions are needed. In this work we used the AEI SEM images obtained from traditional CD-SEM flow, processed with ASML’s MXP (Metrology for eXtreme Performance) tool, and used the extracted CD gauges and massive EP gauges to train a deeplearning Newron Etch model. In the approach, MXP reduced the AEI metrology random errors and shape fitting measurement error and provides better pattern coverage with massive reliable CD and EP gauges, Newron Etch captures complex and unknown physical and chemical effects learned from wafer data. Results shows that MXP successfully extracted stable contour from AEI SEM for various pattern types. Three etch models are calibrated and compared: CD based EEB model (Effective Etch Bias), CD+EP based EEB model, and CD+EP based Newron etch model. CD based EEB model captures the major trend of the etch process. Including EP gauges helps EEB model with about 10% RMS reduction on prediction. Integration of MXP (CD+EP) and Newron Etch model gains about 45% prediction RMS reduction compared to baseline model. The good prediction of Newron Etch is also verified from wafer SEM overlay on complex-shape patterns. This result validates the effectiveness of ASML’s solution of deep learning etch model integration with MXP AEI’s massive wafer data extraction from etch process, and will help to provide accurate and reliable etch modeling for advanced node etch OPC correction in semiconductor manufacturing.
As the design node of memory device shrinks, OPC model accuracy is becoming ever more critical from development to manufacturing. To improve the model accuracy, more and more physical effects are analyzed and terms for those physical effects are added. But it is unachievable to capture the complete physical effects. In this study, deep neural network is employed and studied to improve model accuracy. Regularization is achieved using physical guidance model. To address overfitting issue, high volume of contour based edge placement (EP) gauges (>10K) are generated using fast eBeam tool (eP5) and metrology processing software (MXP) without increasing turnaround time. It is shown that the new approach improved model accuracy by >47% compared to traditional approach on >1.4K verification gauges.
In recent years, compact modeling of negative tone development (NTD) resists has been extensively investigated. Specific terms have been developed to address typical NTD effects, such as aerial image intensity dependent resist shrinkage and development loading. The use of photo decomposable quencher (PDQ) in NTD resists, however, brings extra challenges arising from more complicated and mixed resist effect. Due to pronounced effect of photoacid and base diffusion, the NTD resist with PDQ may exhibit opposite iso-dense bias trend compared with normal NTD resist. In this paper, we present detailed analysis of physical effects in NTD resist with PDQ, and describe respective terms to address each effect. To decouple different effects and evaluate the impact of individual terms, we identify a certain group of patterns that are most sensitive to specific resist effect, and investigate the corresponding term response. The results indicate that all the major resist effect, including PDQ-enhanced acid/base diffusion, NTD resist shrinkage and NTD development loading can be well captured by relevant terms. Based on these results, a holistic approach for the compact model calibration of NTD resist with PDQ can be established.
Focus shaping with highly focused cylindrical vector beam is an interesting and important topic in both applied optics and physical optics. In this paper, we describe optimization algorithms to design diffractive optical elements for various beam shaping applications. "Optical bubbles" with desired size and numbers for trapping particles and flat-top focusing with low side-lobe to improved micro printing are proposed. Ultra small focus spot with long depth of focus without energy split to extend the region around the image plane is also presented.
In this paper, design of diffractive optical element (DOE) for optical bubble creating and controlling with radially polarized incident beam focused by a high numerical aperture (NA) aplanatic lens is proposed and its application in optical trapping is discussed. We use a DOE to modify the phase of the incident radial polarization beam to form different kinds of optical bubbles. Optimization algorithms are used to design the DOE to adjust the bubble size and depth to meet the requirements. The results show that the size of the bubble is inversely proportional to its depth. Owing to the overlapping of the field strengths around the focus, the bubble tends to merge into flattop distribution as it is getting smaller and smaller. With a fixed DOE design, bubbles with smaller size and larger depth can be generally obtained with higher NA, owing to a more confined field strength distribution from the strong longitudinal field component.
KEYWORDS: Diffractive optical elements, Data storage, Interfaces, Wave propagation, Solids, Optical storage, Beam propagation method, 3D optical data storage, Dielectric polarization, Near field optics
In solid immersion lens (SIL) system, both propagating waves and evanescent waves contribute to the total field strength with different properties. By using diffractive optical element to modify the cylindrical vector incident beam, we study how the field strength changes when propagating (evanescent) waves are balanced against each other and the evanescent (propagating) waves dominate the field strength. The simulation results show that for radially polarized incident beam, the rate of slope of axial field strength v.s transverse field strength by evanescent waves contribution is greater than that by propagating waves contribution. With general cylindrical vector incident beams, increasing (the rotation angle of polarization from the radial direction) will also make the axial field strength decrease while the variation of the transverse field strength is small. These methods can be used to control the aspect ratio of three dimensions storage dot, which may find applications in near field optical data storage system.
This paper describes a fast simulation annealing algorithm for the optimum design and applies to beam shaping by diffractive optical elements. The algorithm introduced the corresponding utilities function, and used Tsallis statistic for optimum design. The simulated results show that to converge the incident energy into the desired region with the same mean square error, our method only cost 1% percent of time that needed by the traditional SA. This algorithm brings forward a new and fast method for the design of Diffractive Optical Elements, and potentially for other optimization problems.
Beam shaping theory is naturally one of the inverse problems and it is unable to get a unique minimum resolution. In the case of high demands to target beam quality such as uniform illumination, or the complex style of incident beams, one still needs to improve the classical design algorithm to satisfy fabrications and applications.
In this paper, new iteration algorithm based on phase mixture algorithm (PMA) and input-output (IO) algorithm is presented. By using random phase mixture factor instead of fixed phase mixture factor in PMA and random feedback factor in IO algorithm, and introducing a selection rule in each loop of the iteration, the degree of freedom of the iteration is increased and better target beam quality is obtained. A continuous diffractive optical element (DOE) for uniform illumination of annular Gaussian incident beam with diameter 240 mm is shown as a design example. Comparison of iteration results between the new algorithm and classical PMA or IO shows that the new algorithm provided better target beam quality and thinner DOE phase thickness. The design result of new algorithm only has 2.25% top profiled error (TPE) with a phase thickness of about 8 π while the best simulated result of PMA and IO algorithm has 3.42% TPE with a phase thickness of 12.4 π.
We present a vector angular spectrum approach by using self-iterative algorithms for beam shaping. It is rigorous and still valid to sub-wavelength feature size. The approach bases on scalar angular spectrum theory and modifies by keeping the variation of the beam's polarization. The comparison of this approach with Fraunhofer diffraction integrals by using different self-iterative algorithms to design the diffractive optical elements for beam shaping shows the former one is more efficient. Design example in the near field for beam shaping with sub-wavelength minimum feature is also presented.
An integrated DOE is designed for beam combination and shaping. The DOE is double-faced carved. One is transmission blazed grating to convert four declined incident incoherent beams to parallel beams, the other is continuous profile relief for shaping. The simulated intensity focal-plane profile has little modulation in the main lobe and high diffraction efficiency.
Proc. SPIE. 4914, High-Power Lasers and Applications II
KEYWORDS: Staring arrays, Diffraction, Digital filtering, High power lasers, Fourier transforms, Beam shaping, Algorithm development, Optimization (mathematics), Personal protective equipment, Fusion energy
The phase distribution design process of the pure phase element (PPE) used for quasi-annular beam shaping is introduced in this paper. A new optimization algorithm named Quasi-Gradient Descent (Quasi-GD) algorithm has been developed and used here to meet such design requirement. With a more restrictive sampling mode named precise sampling in the optimization, the simulated result shows that the uniformity of energy distribution on the focal plane is invariant with different sampling intervals and the true beam shaping effect is achieved.