Optical micro-phase-shift dropvolume in a diffractive deep neural network.

To provide a desirable number of parallel subnetworks as required to reach a robust inference in an active modulation diffractive deep neural network, a random micro-phase-shift dropvolume that involves five-layer statistically independent dropconnect arrays is monolithically embedded into the unitary backpropagation, which does not require any mathematical derivations with respect to the multilayer arbitrary phase-only modulation masks, even maintaining the nonlinear nested characteristic of neural networks, and generating an opportunity to realize a structured-phase encoding within the dropvolume. Further, a drop-block strategy is introduced into the structured-phase patterns designed to flexibly configure a credible macro-micro phase dropvolume allowing for convergence. Concretely, macro-phase dropconnects concerning fringe griddles that encapsulate sparse micro-phase are implemented. We numerically validate that macro-micro phase encoding is a good plan to the types of encoding within a dropvolume.

Rigorous simulation model of double-Ronchi shearing interferometry on lithographic tools.

Double-Ronchi shearing interferometry is widely used in wavefront aberration measurements for advanced lithography projection lens systems. A rigorous simulation model of double-Ronchi shearing interferometry on lithographic tools is the precondition for phase-shifting retrieval algorithm design and error analysis. This paper presents a rigorous simulation model of double-Ronchi shearing interferometry considering the vector nature of light. The model is accurate and can be used in the study of double-Ronchi shearing interferometry.

Effects and elimination of image grating defocusing on a double-Ronchi shearing interference field.

Double-Ronchi shearing interferometry is a promising wavefront aberration measurement system for advanced lithography projection lens systems. The image grating defocusing is a key systematic error of the interferometer. However, the effects and elimination of this error have not been systematically researched. In this work, the interference field effects caused by the image grating defocusing are analyzed based on the theories of scalar diffraction, and a method to eliminate the effects is proposed. The theoretical analysis has been verified by a simulation and experiments. The results show that the error of image grating defocusing is mainly expressed as the Zernike Z4 term and Z9 term in the reconstructed wavefront, and the coefficients of Z4, and Z9, respectively, are related to NA2, NA4, and the defocus distance z. When the numerical aperture (NA) of the under-test projection lens is 0.6, 99.8384% of the errors caused by the image grating defocusing can be removed. When the NA is reduced to 0.3, 99.9854% of the errors can be removed. Additionally, when the NA is less than 0.1, almost all the errors can be eliminated.

Phase defect characterization using generative adversarial networks for extreme ultraviolet lithography.

The multilayer defects of mask blanks in extreme ultraviolet (EUV) lithography may cause severe reflectivity deformation and phase shift. The profile information of a multilayer defect is the key factor for mask defect compensation or repair. This paper introduces an artificial neural network framework to reconstruct the profile parameters of multilayer defects in the EUV mask blanks. With the aerial images of the defective mask blanks obtained at different illumination angles and a series of generative adversarial networks, the method enables a way of multilayer defect characterization with high accuracy.

Optical random micro-phase-shift DropConnect in a diffractive deep neural network.

The formulation and training of unitary neural networks is the basis of an active modulation diffractive deep neural network. In this Letter, an optical random phase DropConnect is implemented on an optical weight to manipulate a jillion of optical connections in the form of massively parallel sub-networks, in which a micro-phase assumed as an essential ingredient is drilled into Bernoulli holes to enable training convergence, and malposed deflections of the geometrical phase ray are reformulated constantly in epochs, allowing for enhancement of statistical inference. Optically, the random micro-phase-shift acts like a random phase sparse griddle with respect to values and positions, and is operated in the optical path of a projective imaging system. We investigate the performance of the full-drilling and part-drilling phenomena. In general, random micro-phase-shift part-drilling outperforms its full-drilling counterpart both in the training and inference since there are more possible recombinations of geometrical ray deflections induced by random phase DropConnect.

Through-focus EUV multilayer defect compensation considering optical proximity correction.

Extreme ultraviolet (EUV) multilayer defects result in the degradation of through-focus imaging quality. The optical proximity effect is another crucial factor that degrades the imaging quality. Both the impacts of the defects and the optical proximity effects could be mitigated by modifying the original mask patterns. A heuristic-based defect compensation method considering optical proximity correction and through-focus optimization is proposed in this paper. The edge of the mask pattern and the insertion of sub-resolution assist features (SRAFs) are optimized by covariance matrix adaptation evolution strategy (CMA-ES) to compensate for the degradation of the imaging quality with a certain defocus range. New encoding strategies for the edge pixels of the mask pattern and the SRAFs are proposed and utilized in this paper to ensure the manufacturability of the mask and the efficiency of the optimization at the same time. The rigorous database approach based on the scattering matrix is adopted to simulate the mask diffraction spectrum efficiently. Simulations verify that the through-focus imaging quality of both the defective masks with bump defects and pit defects could be obviously improved by the proposed defect compensation method.

Effects of illumination non-uniformity on the double-Ronchi lateral shearing interference field.

Double-Ronchi shearing interferometry is a promising technique for insitu wavefront aberration measurement of the projection lens in photolithography systems. In practice, the non-uniformity of illumination is an important issue affecting the interference field, which has not been systematically researched. In this work, the interference field errors caused by non-uniform illumination distributions are analyzed utilizing the theories of scalar diffraction. The theoretical analysis has been verified by simulation and fundamental experiments. Results show that the uniformity requirements for the abrupt annular, Gaussian, and uniform random illumination distribution (RD) are 0.9434, 0.8439, and 0.2751, respectively, with a shear ratio of 5% and a relative wavefront reconstruction error of 1%. The uniformity of the three distributions is reduced to 0.6513, 0.5864, and 0.1234, respectively, with the shear ratio shrunk to 3%. When the shear ratio is less than 1%, there is no specific requirement for illumination uniformity.

Fast heuristic-based source mask optimization for EUV lithography using dual edge evolution and partial sampling.

Extreme ultraviolet (EUV) lithography is essential in the advanced technology nodes. Source mask optimization (SMO) for EUV lithography, especially the heuristic-based SMO, is one of the vital resolution enhancement techniques (RET). In this paper, a fast SMO method for EUV based on dual edge evolution and partial sampling strategies is proposed to improve the optimization efficiency and speed of the heuristic algorithm. In the source optimization (SO) stage, the position and intensity of the source points are optimized in turn. Using the sparsity of the optimized source, a partial sampling encoding method is applied to decrease the variables' dimension in optimization. In the mask optimization (MO) stage, the main features (MF) and the sub-resolution assistant features (SRAF) are optimized in turn. A dual edge evolution strategy is used in the MF optimization and the partial sampling encoding method is used in SRAF optimization. Besides, the imaging qualities at different focal planes are improved by SRAF optimization. The optimization efficiency is greatly improved by the dimensionality reduction strategies. Simulations are carried out with various target patterns. Results show the superiority of the proposed method over the previous method, especially for large complex patterns.

Efficient optical proximity correction based on virtual edge and mask pixelation with two-phase sampling.

Optical proximity correction (OPC) is a widely used resolution enhancement technique (RET) in optical lithography to improve the image fidelity and process robustness. The efficiency of OPC is very important, especially for full-chip modification with complicated circuit layout in advanced technology nodes. An efficient OPC method based on virtual edge and mask pixelation with two-phase sampling is proposed in this paper. All kinds of imaging distortions are classified into two categories of imaging anomalies, the inward shrinkage anomaly and the outward extension anomaly. The imaging anomalies are detected around the corners and along the boundaries of the mask features with several anomaly detection templates. Virtual edges are adaptively generated according to the local imaging anomalies. The virtual edges are shifted to adjust the distribution of transparent regions on the mask and modify the local imaging anomalies. Several constraints and strategies are applied for efficient modifications and global control of the contour fidelity. In addition, the diffraction-limited property of the imaging system is fully utilized to separate the imaging evaluations at a coarse sampling level and the mask modifications at a fine sampling level, through the mask pixelation with two-phase sampling. It accelerates the imaging evaluations and guarantees the modification resolution as well. Simulations and comparisons demonstrate the superior modification efficiency of the proposed method.

Source mask optimization for extreme-ultraviolet lithography based on thick mask model and social learning particle swarm optimization algorithm.

Extreme ultraviolet (EUV) lithography plays a vital role in the advanced technology nodes of integrated circuits manufacturing. Source mask optimization (SMO) is a critical resolution enhancement technique (RET) or EUV lithography. In this paper, an SMO method for EUV lithography based on the thick mask model and social learning particle swarm optimization (SL-PSO) algorithm is proposed to improve the imaging quality. The thick mask model's parameters are pre-calculated and stored, then SL-PSO is utilized to optimize the source and mask. Rigorous electromagnetic simulation is then carried out to validate the optimization results. Besides, an initialization parameter of the mask optimization (MO) stage is tuned to increase the optimization efficiency and the optimized mask's manufacturability. Optimization is carried out with three target patterns. Results show that the pattern errors (PE) between the print image and target pattern are reduced by 94.7%, 76.9%, 80.6%, respectively.

Optical random phase dropout in a diffractive deep neural network.

Unitary learning is a backpropagation (BP) method that serves to update unitary weights in fully connected deep complex-valued neural networks, meeting a prior unitary in an active modulation diffractive deep neural network. However, the square matrix characteristic of unitary weights in each layer results in its learning belonging to a small-sample training, which produces an almost useless network that has a fairly poor generalization capability. To alleviate such a serious over-fitting problem, in this Letter, optical random phase dropout is formulated and designed. The equivalence between unitary forward and diffractive networks deduces a synthetic mask that is seamlessly compounded with a computational modulation and a random sampling comb called dropout. The dropout is filled with random phases in its zero positions that satisfy the Bernoulli distribution, which could slightly deflect parts of transmitted optical rays in each output end to generate statistical inference networks. The enhancement of generalization benefits from the fact that massively parallel full connection with different optical links is involved in the training. The random phase comb introduced into unitary BP is in the form of conjugation, which indicates the significance of optical BP.

Fast mask model for extreme ultraviolet lithography with a slanted absorber sidewall.

A fast mask model for extreme ultraviolet (EUV) lithography is vital to process simulation and resolution enhancement techniques. As the target pattern sizes have decreased, the impact of the absorber sidewall angle (SWA) has become a serious problem. In order to model the EUV mask with a slanted absorber sidewall quickly and accurately, a fast mask model based on the absorber sublayer decomposition is proposed. Since the absorber sidewall is slanted but not perpendicular to the multilayer surface, the absorber is decomposed into several thin pattern layers. For each thin layer, the diffraction is calculated by the edge point pulses model. The light propagation between two layers is calculated by spectrum superposition in the frequency domain with Hopkins frequency shift. The fast EUV mask model with slanted absorber sidewall is established by combining the accurate absorber model and the equivalent layer multilayer model. Simulations and comparisons validate the effectiveness of the proposed model. For the 22 nm vertical line-space pattern, the calculation errors of critical dimension via the proposed model are lower than 0.05 nm for different SWA values.

Extreme ultraviolet phase defect characterization based on complex amplitudes of the aerial images.

The profile deformation of a phase defect in an extreme ultraviolet (EUV) mask blank is the key factor to simulate its optical effects accurately and to compensate for it precisely. This paper provides a new, to the best of our knowledge, profile characterization method based on complex amplitudes of the aerial images for phase defects in EUV mask blanks. Fourier ptychography is adopted to retrieve the complex amplitudes of the aerial images and improve the lateral resolution. Both amplitude and phase impacted by the defect are taken into consideration to reconstruct the defect profile parameters (the height and the full width at half maxima of the defect's top and bottom profiles). A conformal convolutional neural network model is constructed to map the amplitudes and phases of aerial images to the defect profile parameters. The Gaussian-shaped defect models with the mapped profile parameters can be used to simulate the amplitude and phase properties of the defects when compensating for them. The proposed method is verified to reconstruct the defect profile parameters of both bump defects and pit defects accurately. The involvement of both the amplitude and phase information makes the reconstructed defect profile parameters more appropriate to simulate the optical effects of the defects.

Source mask optimization using the covariance matrix adaptation evolution strategy.

Source mask optimization (SMO) is one of the indispensable resolution enhancement techniques to guarantee the image fidelity and process robustness for the 2Xnm technology node and beyond. The optimization capacity and convergence efficiency of SMO are important, especially for full-chip SMO. An SMO method using the covariance matrix adaptation evolution strategy (CMA-ES), together with a new source representation method, is proposed in this paper. Based on the forward vector imaging formulation, the encoding and decoding methods of the source and the mask, and the constructed merit function, the source and the mask are optimized using the CMA-ES algorithm. The solution search space and the search step size are adaptively updated during the optimization procedure. Considering the sparsity of the optimal source, the source is represented by a set of ideal point sources with unit intensity and adjustable positions. The advantageous spatial frequency components of the source for imaging performance improvement are identified through the aggregation of the point sources. Simulations and comparisons verify the superior optimization capacity and convergence efficiency of the proposed method.

Critical pattern selection method for full-chip source and mask optimization.

Source and mask optimization (SMO) is one of the most important resolution enhancement techniques for integrated circuit manufacturing in 2X nm technology node and beyond. Nowadays full-chip SMO is alternatively realized by applying SMO to limited number of selected critical patterns instead of to full-chip area, since it is too computational expensive to be apply SMO in full-chip area directly. The critical patterns are selected by a pattern selection method which enables SMO in full-chip application by balancing the performance and computation consumption. A novel diffraction-based pattern selection method has been proposed in this paper. In this method, diffraction-signatures are sufficiently described with widths in eight selected directions. Coverage rules between the diffraction-signatures are specifically designed. Diffraction-signature grouping method and pattern selection strategy are proposed based on the diffraction-signatures and coverage rules. A series of simulations and comparisons performed using ASML's Tachyon software, which is one of the state of the art commercial SMO platforms, verify the validity of the proposed method.

Fast rigorous mask model for extreme ultraviolet lithography.

The calculation of extreme ultraviolet (EUV) mask diffraction spectrum is the key of EUV lithography simulation. In this paper, a fast rigorous EUV mask model is proposed to calculate the diffraction spectrum fast and accurately. Based on the mask structure decomposition method, the relationship among the region diffraction, the boundary diffraction of the absorber, and the direction of incident light is analyzed at first. Then the frequency-domain functions related to angle of incidence and diffraction angle are established to model the geometrical and boundary diffraction of the absorber. The fast rigorous EUV mask model is established by combining the equivalent layer multilayer model based on the Fresnel formula and the accurate absorber model. Simulations and comparisons show the effectiveness of the proposed model. For the 14 nm vertical line-space pattern, the calculation errors of critical dimension (CD) via the proposed model are reduced by 80.6% and 93.9% compared with the structure decomposition method for dense and isolate features.

Micromirror array allocation algorithm based on deconvolution.

Freeform illumination is one of the necessary techniques in 28 nm technology nodes and beyond. The micromirror array (MMA) has been widely used in lithography freeform illumination systems due to its programmability and high free degree. The MMA allocation algorithm is the key to generate the target freeform illumination source. Its computational speed and precision affect the generation speed and precision of the target illumination source as well as the process window size of the generated illumination pupil directly. In this paper, an MMA allocation method based on deconvolution is proposed. The target freeform illumination source can be obtained directly with the deconvolution and quantization processes. Without the iterative optimization process, the computational speed of the proposed method is much faster than that of the traditional method. The numerical simulation results show that the difference between the target source and the MMA source generated using the proposed method is less than 0.2%. Compared with the process window loss of the target source, the process window loss of the MMA source generated by the proposed deconvolution method is less than 0.5%. Compared with the traditional allocation method, the runtime of the proposed method is less than 0.05 s and has improved by 1463 times.

Fast thermal aberration model for lithographic projection lenses.

A novel fast thermal aberration model for lithographic projection lenses is proposed. In the model, optical intensity calculation is simplified by using pupil intensity mapping, and simplified formulas for temperature calculation are derived to realize fast simulation of thermal aberration. The simulation results using the proposed model are compared with that of experiments carried out on a commercial lithography tool. The R-square of the simulation is better than 0.99 and the simulation time is about 10 minutes. Experiments and simulations show that the model is capable of predicting the thermal aberration or the variation trend of the thermal aberration of lithographic projection lenses fast and accurately. The model is applicable in projection lens design, evaluating degree of production risk posed by thermal aberration, etc.

Jones pupil metrology of lithographic projection lens and its optimal configuration in the presence of error sources.

Mueller matrix imaging polarimeter (MMIP) can be used to measure the polarization aberration (PA) of a lithographic projector in the form of the Mueller pupil, while the Jones pupil is required for lithographic imaging simulations, projection lens design and PA evaluation. In this paper, a Jones pupil measurement method of lithographic projection lens is proposed. The measurement device of the method is the same as an MMIP, but a new polarimetric measurement equation is derived to solve the Jones pupil directly from the Kronecker product of the Jones matrix and the measured intensities. Two new polarimeter configurations with the minimum condition number are designed to further improve the accuracy in the presence of error sources. The performance of the method is evaluated by measurement errors of a typical Jones pupil in the presence of error sources. Comparisons between the proposed method and the conventional method, in which the Jones pupil is converted from the Mueller pupil measured by MMIP, are given. The results validate that the measurement accuracy of the Jones pupil is significantly improved without increasing the complexity of existing measurement systems.

Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry.

Owing to gamma-effect robustness and high-speed imaging capabilities, projector defocusing of binary-coded fringe patterns is by far the most widely used and effective technique in generating sinusoidal fringe patterns for three-dimensional optical topography measurement with digital fringe projection techniques. However, this technique is not trouble-free. It is borne with uncertainty and challenges mainly because it remains somewhat difficult to quantify and ascertain the level of defocus required for desired fidelity in sinuousness of the projected fringe pattern. Too much or too little defocusing will affect the sinuosity accuracy of fringe patterns and consequently jeopardize the quality of the measurement results. In this paper, by combining intrinsic phase spectral sensitivities and normed Fourier transform, a method to quantify the amount of defocus and subsequently select the optimal degree of sinuosity for generating digital sinusoidal fringe patterns with projector defocusing for fringe pattern optical three-dimensional profilometry is proposed. Numerical simulations plus experiments give evidence of the feasibility and validity of the proposed method in enabling an improved digital binary defocusing technique for optical phase-shift profilometry using the digital fringe projection technique.