Search

To overcome the limitations of long-term prediction of PM2.5 concentration, a multi-factor information flow causality analysis method is used to screen suitable meteorological and air pollutant-related factors and concatenate them with a PM2.5 sequence as the dataset. A modal decomposition algorithm is used as a module to be integrated into the autoformer (transformer improved with autocorrelation mechanism) model to improve it, and the modal autoformer (empirical modal decomposition combined with autoformer) is proposed. The constructed model decomposes the sequence into several components by using the modal decomposition module and uses the self-correlation mechanism and decomposition structure to decompose and extract features of different components at the time-feature level. Based on the matching method, the model is adjusted for different component features to improve the long-term prediction effect. The model is applied to three cities in Henan Province, Zhengzhou, Luoyang, and Zhumadian, as examples for experiments, and gated neural unit (GRU), informer, autoformer, and modal GRU (empirical modal decomposition combined with GRU model) are constructed for comparative verification. The results show that the modal autoformer can better cope with the complex characteristics of long-term prediction of the PM2.5 time series, has strong spatial adaptability and that its various indicators are optimal for the three cities, with R2 values being all above 0.96, where the highest is 0.987 in Zhengzhou; MAPE (Mean absolute percentage error) values all being less than 10, where the best is 7.602 in Zhumadian; and MAE (Mean absolute error) values all being less than 4. The prediction effect is stable enough, showing its feasibility and adaptability in long-term prediction. [ABSTRACT FROM AUTHOR]

In recent years, geographically weighted regression (GWR) models have been widely used to address the spatial heterogeneity and spatial autocorrelation of PM2.5, but these studies have not fully considered the effects of all potential variables on PM2.5 variation and have rarely optimized the models for residuals. Therefore, we first propose a modified GWR model based on principal component analysis (PCA-GWR), then introduce five different spatial interpolation methods of radial basis functions to correct the residuals of the PCA-GWR model, and finally construct five combinations of residual correction models to estimate regional PM2.5 concentrations. The results show that (1) the PCA-GWR model can fully consider the contributions of all potential explanatory variables to estimate PM2.5 concentrations and minimize the multicollinearity among explanatory variables, and the PM2.5 estimation accuracy and the fitting effect of the PCA-GWR model are better than the original GWR model. (2) All five residual correction combination models can better achieve the residual correction optimization of the PCA-GWR model, among which the PCA-GWR model corrected by Multiquadric Spline (MS) residual interpolation (PCA-GWRMS) has the most obvious accuracy improvement and more stable generalizability at different time scales. Therefore, the residual correction of PCA-GWR models using spatial interpolation methods is effective and feasible, and the results can provide references for regional PM2.5 spatial estimation and spatiotemporal mapping. (3) The PM2.5 concentrations in the study area are high in winter months (January, February, December) and low in summer months (June, July, August), and spatially, PM2.5 concentrations show a distribution of high north and low south. [ABSTRACT FROM AUTHOR]

A quantitative understanding of changes in water resources is crucial for local governments to enable timely decision-making to maintain water security. Here, we quantified natural-and human-induced influences on the terrestrial water storage change (TWSC) in Sichuan, Southwest China, with intensive water consumption and climate variability, based on the data from the Gravity Recovery and Climate Experiment (GRACE) and its Follow-on (GRACE-FO) during 2003–2020. We combined the TWSC estimates derived from six GRACE/GRACE-FO solutions based on the uncertainties of each solution estimated from the generalized three-cornered hat method. Metrics of correlation coefficient and contribution rate (CR) were used to evaluate the influence of precipitation, evapotranspiration, runoff, reservoir storage, and total water consumption on TWSC in the entire region and its five economic regions. The results showed that a significant improvement in the fused TWSC was found compared to those derived from a single model. The increase in regional water storage with a rate of 3.83 ± 0.54 mm/a was more influenced by natural factors (CR was 53.17%) compared to human influence (CR was 46.83%). Among the factors, the contribution of reservoir storage was the largest (CR was 42.32%) due to the rapid increase in hydropower stations, followed by precipitation (CR was 35.16%), evapotranspiration (CR was 15.86%), total water consumption (CR was 4.51%), and runoff (CR was 2.15%). Among the five economic regions, natural influence on Chengdu Plain was the highest (CR was 48.21%), while human influence in Northwest Sichuan was the largest (CR was 61.37%). The highest CR of reservoir storage to TWSC was in Northwest Sichuan (61.11%), while the highest CRs of precipitation (35.16%) and evapotranspiration (15.86%) were both in PanXi region. The results suggest that TWSC in Sichuan is affected by natural factors and intense human activities, in particular, the effect of reservoir storage on TWSC is very significant. Our study results can provide beneficial help for the management and assessment of regional water resources. [ABSTRACT FROM AUTHOR]

The non-ideal mask absorber can cause an increase in critical dimension error (CDE) and decrease in process window (PW). However, the random mask absorber errors induced during mask fabricating and measuring are not considered in computational lithography. The problem cannot be neglected as the continuous scaling of lithography technology node. In this work, for the first time to our knowledge, a source, numerical aperture (NA), and process parameters co-optimization (SNPCO) method is developed to reduce the CDE induced by absorber errors and improve the PW. First, the source is represented by Zernike polynomials to balance computational burden and flexibility of source. Then a weighted cost function containing CDE and PW that incorporates the influences of absorber errors is created. Finally, a statistical optimization method is used to optimize the lithographic system parameters. Simulations of 1D mask pattern show that for the system with extreme absorber errors, the pattern errors of the proposed method are reduced by 62.1% and 58.9%, and the PWs are increased by 40.3% and 36.4%, respectively. The results illustrate that this method is effective in mitigating the CDE caused absorber errors and improving process robustness. [ABSTRACT FROM AUTHOR]

The curvilinear mask structures provide significant benefits in improving lithographic resolution. Curvilinear masks, as opposed to rectilinear masks, have a wider range of structure types that can be used precisely to correct the contour of diffraction at sharp technological nodes. However, the curvilinear structure also makes the inverse design of mask in optical proximity correction (OPC) flow difficult. The current OPC of curvilinear masks uses pixel-based inverse optimization, which is extremely computationally intensive and takes up a lot of design data storage space. This paper proposes an implicit function to represent a large number of curve types with a small number of parameters to reduce computational complexity and the R&D cycle. Therefore, the ultra-high dimensional pixel-based OPC problem is transformed into a low-dimensional parameter search problem in the critical diffraction area of the mask pattern. The tabu search algorithm and neighborhood parallel computing strategy are then used to quickly search for optimal characterized parameters. The results of the simulation show that the parametric curvilinear OPC method achieves a higher image fidelity than that of rectilinear OPC. At the same time, it addresses the shortcomings of the traditional pixelated curvilinear mask OPC method, including high computational complexity, low manufacturability, and storage space occupancy.

Inverse lithography technology (ILT), such as source mask optimization (SMO), is used to improve lithography performance. Usually, a single objective cost function is selected in ILT, and an optimal structure for one field point is achieved. The optimal structure is not the case for other images at full field points where the aberrations of the lithography system are different, even in high-quality lithography tools. The optimal structure that must match the high-performance images at the full field is urgently required for extreme ultraviolet lithography (EUVL). In contrast, multi-objective optimization algorithms (MOAs) limit the application of multi-objective ILT. Assigning target priority is incomplete in current MOAs, which results in the over-optimization of some targets and under-optimization of others. In this study, multi-objective ILT and a hybrid dynamic priority (HDP) algorithm were investigated and developed. High-performance images with high fidelity and high uniformity were obtained at multi-field and multi-clip areas across the die. A hybrid criterion was developed for the completion and reasonable prioritization of each target to ensure sufficient improvement. Compared to the current MOAs, the uniformity of images at full-field points was improved by up to 31.1% by the HDP algorithm in the case of multi-field wavefront error-aware SMO. The multi-clip source optimization (SO) problem showed the universality of the HDP algorithm to deal with different ILT problems. It acquired higher imaging uniformity than existing MOAs, which indicated that the HDP is more qualified for multi-objective ILT optimization than existing MOAs.

Current source and mask optimization (SMO) research tends to focus on advanced inverse optimization algorithms to accelerate SMO procedures. However, innovations of forward imaging models currently attract little attention, which impacts computational efficiency more significantly. A sampling-based imaging model is established with the innovation of an inverse point spread function to reduce computational dimensions, which can provide an advanced framework for fast inverse lithography. Simulations show that the proposed SMO method with the help of the proposed model can further speed up the algorithm-accelerated SMO procedure by a factor of 3.

Recently, a single vectorial pupil optimization (VPO) was proposed to compensate for the polarization effect induced by thick mask and image optics at one field point in a lithography system, which does not work at full field points. In this paper, we propose a multi-objective VPO (MOVPO) method to obtain a universal vectorial pupil that can compensate for the polarization aberration at full field points. A novel multi-objective cost function, to the best of our knowledge, is built and includes uneven image pattern errors causing by polarization aberration (PA) at full field points in the MOVPO method. Comprehensive simulations demonstrate that the proposed MOVPO method can effectively improve the consistency of imaging and enlarge the overlapped process window at full field points.

Extreme ultraviolet (EUV) lithography is a new generation of integrated circuit manufacturing technology with great development prospects. EUV lithography has more significant demand for high exposure latitude (EL) due to greater requirements for the stability of the light source. Source and mask optimization (SMO) technology is widely used to compensate for imaging distortion. In this paper, we propose an EL-aware SMO (ELASMO) method that uses a low-resist threshold sensitivity (LRS) penalty function to improve the EL in EUV lithography. Compared to conventional SMO, the proposed ELASMO method can significantly enhance the aerial image contrast, improve the EL, and enlarge the process window while ensuring high imaging fidelity.

Imaging-based measurement methods of polarization aberration (PA) are indispensable in hyper-numerical aperture projection optics for advanced lithography. However, the current methods are derived from the Kirchhoff model and ignore the 3D mask effect of the test mask, which will impact the measurement accuracy. In this paper, a novel imaging-based measurement method of PA is proposed based on a rigorous imaging model to improve the measurement accuracy. Through the quantitative description of the 3D mask effect, a rigorous imaging-based measurement model of PA is established. A synchronous orientation measurement method is designed to effectively reduce the cost of establishing the overdetermined equations. A deep neural network is used to retrieve the PA accurately. Simulations show that the proposed method effectively eliminates the impact of the 3D mask effect of test mask on PA measurement, and the measurement error is reduced by 72% compared with the measurement method based on the Kirchhoff model.

Polarization distortion innately exists in hyper numerical aperture immersion lithography system. Polarization distortion, mainly including polarization aberration (PA) of lithography projection optics and thick mask induced polarization distortion, would seriously impact on lithography imaging quality. Some computational lithography technologies, such as robust optical proximity correction and robust source and mask optimization, have been introduced and developed to reduce the impact of polarization distortion on lithography imaging. In this paper, we innovate a vectorial pupil optimization (VPO) method to further extend degrees of freedom for pupil optimization and compensate polarization distortion for immersion lithography system. An analytical relationship between lithography imaging and active vectorial pupil, and the gradient-based algorithm is adopted to effectively solve VPO. Extensive simulations demonstrate the VPO method simultaneously compensate the PA of projection optics and the thick mask induced polarization distortion sufficiently. Based on PA-aware source mask optimization, the VPO method can further reduce the impact of polarization distortion on lithography imaging. Compared to current pupil wavefront optimization, the proposed VPO effectively reduces the pattern error by 37.2%, which demonstrates the VPO method can improve lithography pattern fidelity.

Fast source optimization (SO) is in demand urgently for holistic lithography on-line at 14-5 nm nodes. Our earlier works of fast compressive sensing (CS) SO methods adopted randomly sampling monitoring pixels on layout patterns, consequently resulting in failure of SO sometimes and poor image fidelity compared to gradient-based SO with complete sampling (SD-SO). This paper proposes a novel certain contour sampling-Bayesian compressive sensing SO (CCS-BCS-SO) method to achieve the goals of fast SO and high fidelity patterns simultaneously. The CCS assures the optimized source uniquely and reduces the computational complexity significantly. The BCS theory, to our best knowledge, is for the first time applied to resolution enhancement techniques (RETs) in lithography systems to ensure high fidelity patterns. The results demonstrate that CCS-BCS-SO simultaneously achieves fast SO like CS-SO and high fidelity patterns like SD-SO.

Some pupil wavefront optimization (PWO) approaches were studied to compensate the thick mask effects considering only a field point, and these PWO methods neglect the inherent wave aberration in a realistic lithography system. Particularly, the wave aberration of lithography projection optics is exposure field dependent, and the wave aberrations at different fields of view (FOVs) would seriously and unevenly impact the results and effects of PWO. The current PWO method for single FOV cannot match full FOV. In this paper, we propose a multiple-field-point PWO (MPWO) method to improve lithography imaging quality for full FOV. A multiple-field-point cost function is built including the uneven impact of multiple aberrations on lithography imaging at full FOV. The comprehensive simulations demonstrate that the proposed MPWO method can effectively improve consistency of lithography imaging and enlarge the overlapped process window for full FOV. The most important point is that the optimized wavefront attained by MPWO can be realized via pupil wavefront manipulator FlexWave in lithography equipment, which is significant in holistic lithography for the next technology node.

Source and mask optimization (SMO) technology based on vectorial image model is indispensable in immersion lithography process at advanced technology node. Many kinds of algorithms have achieved successes in aspect of fast and robust SMO without accounting polarization aberration (PA). However, because the PA arising from immersion projection optics unevenly impacts on imaging performance, the conventional SMO would not be applicable in real lithography system. In this paper, we first investigate the serious impact of PA on SMO in details. The SMO accounting the assigned PA of one field point is not applicable to other field points, where the pattern fidelity is fiercely worse and the pattern error (PAE) is nearly doubled. Then, we innovate a MOSMO method to reduce the uneven impact of PA on lithography imaging at full exposure field. Compared to the assigned PA aware SMO, the proposed MOSMO reduces the standard deviation of PAE distribution by 53.3% and enlarges the maximum exposure latitude from 4% to 6.7%, which demonstrates the MOSMO is very significant to balance imaging quality and improve process robustness at full exposure field.

Extreme ultraviolet lithography is regarded as the most attractive technology to achieve 7 nm node and below. A new high-numerical-aperture anamorphic objective lens is designed to extend the single exposure resolution limit. However, the polarization aberrations (PAs) induced by the multilayer coatings on mirrors cause pattern distortions that cannot be neglected. In this paper, a source, mask, and process parameter co-optimization method is developed to compensate for the pattern distortions caused by PAs and increase the process window (PW). We first present an asymmetric source represented by the superposition of Zernike polynomials to reduce the pattern placement error (PPE). Then, a weighted cost function that incorporates the influences of PAs is innovated. Finally, a gradient-based statistical optimization method is adopted to minimize the cost function by optimizing the lithography system parameters alternately. Simulations at the 7 nm node of the 1D mask pattern indicate that for the system with a PA of marginal field, compared with our earlier work, the critical dimension error and PPE of the proposed method are reduced by 75.0% and 82.4%, respectively, and the PW is increased by 97.4%.

Source and mask optimization (SMO) is an important method to improve lithography imaging fidelity. However, constrained by the computational inefficiency, the current SMO method can be used only in clip level applications. In this paper, to our best knowledge, the fast nonlinear compressive sensing (CS) theory is for the first time applied to solve the nonlinear inverse reconstruction problem in SMO. The proposed method simultaneously downsamples the layout pattern in the SMO procedure, which can effectively reduce the computation complexity. The space basis and two-dimensional (2D) discrete cosine transform (DCT) basis are selected to sparsely represent the source pattern and mask pattern, respectively. Based on the sparsity assumption of source and mask pattern, the SMO can be formulated as a nonlinear CS reconstruction problem. A Newton-iteration hard thresholding (Newton-IHTs) algorithm, by taking into account the second derivative of the cost function to accelerate convergence, is innovated to realize nonlinear CS-SMO with high imaging fidelity. Simulation results show the proposed method can significantly accelerate the SMO procedure over a traditional gradient-based method and IHTs-based method by a factor of 9.31 and 7.39, respectively.

Polarization aberrations (PA) can be presented by Jones pupil and can also impact the imaging performance of immersion projection optics significantly. Precise PA measurement is most important for resolution enhancement technology and holistic lithography at 7nm node and below, in order to improve the pattern fidelity and processing stability. However, the current imaging-based measurement method of PA by linear approximation has not taken the coupling effect of the PA coefficients into account. This paper proposes a nonlinear measurement method of PA based on a rigorous nonlinear model to improve the measurement accuracy significantly. In this invention, the new spectrum modulation theory is developed to establish a rigorous quadratic form of PA and aerial image spectrum. A hybrid genetic algorithm is developed to solve the quadratic form inversely to obtain the PA accurately. An overall simulation validates that this method provides a superior quality of PA measurement with very high precision of 10 -4 λ.