Optical Proximity Correction Methods Research Articles

Method for optical proximity correction based ona vector imaging model.

Optical proximity correction (OPC) has become an indispensable step in integrated circuit manufacturing. It requires a huge amount of calculation to obtain a sufficiently accurate OPC model and implement pattern correction. In this paper, the authors proposed an edge-based OPC method built on a vector imaging model, where the analytical correlation between the cost function and movement of each edge segment is established by the chain rule. First, the mask pattern is segmented and downsampled to get the mask image in order to reduce the total data. Second, the aerial image, various parameters on each evaluating point, and the final cost value are obtained in proper sequence. In each part of the OPC process, the procedures of solution and derivation are both recorded. After obtaining the cost value, the chain rule is applied, by which the differential relation between the cost value and movement of each segment is built. According to this differential relation, the next movement of each segment is decided under a quasi-Newton method. All results obtained by the proposed method are compared with results from commercial software. The comparison shows that the proposed OPC method has good OPC accuracy in few iterations.

Implicit function characterization of the curvilinear mask to realize parametric optical proximity correction with a neighborhood parallel tabu search.

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.

3D OPC method for controlling the morphology of micro structures in laser direct writing.

A 3D optical proximity correction (OPC) method for controlling the morphology of micro-structures in laser direct writing is proposed, considering both the optical proximity effect and nonlinear response of a thick-film photoresist. This method can improve the manufacturability and optical performance of devices, and can be used for most 3D micro\nano structures. Its application in the fabrication of a quadratic curvature microlens array shows that the shape of the lens is well controlled; that is, when the height of the lens is 5.25 µm, the average height error of the lens shape is less than 5.22%.

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.

Optical Proximity Correction Using Bidirectional Recurrent Neural Network With Attention Mechanism

Recurrent neural network (RNN) is employed as a machine learning model for fast optical proximity correction (OPC). RNN consists of a number of neural network instances which are serially connected, with each instance in charge of one segment. RNN thus allows some localized segments to be corrected together in one execution, which offers higher accuracy. A basic RNN is extended by introducing gated recurrent unit (GRU) cells in recurrent hidden layers, which are then connected in both forward and backward directions; attention layer is adopted to help output layer predict mask bias more accurately. The proposed RNN structure is used for OPC implementation. A choice of input features, sampling of training data, an algorithm of mapping segments to neural network instances, and final mask bias calculation are addressed toward efficient implementation. Experiments demonstrate that the proposed OPC method corrects a mask layout with 36% lower EPE compared to state-of-the-art OPC method using artificial neural network structure.

PV-Aware Analog Sizing for Robust Analog Layout Retargeting with Optical Proximity Correction

For analog integrated circuits (ICs) in nanometer technology nodes, process variation (PV) induced by lithography may not only cause serious wafer pattern distortion, but also result in device mismatch, which can readily ruin circuit performance. Although the conventional optical proximity correction (OPC) operations can effectively improve the wafer image fidelity, an analog circuit without robust device sizes is still highly vulnerable to such a mismatch effect. In this article, a PV-aware sizing-inclusive analog layout retargeting framework, which encloses an efficient hybrid OPC scheme for yield enhancement, is proposed. The device sizes are tuned during the layout retargeting process by using a deterministic circuit-sizing algorithm considering PV conditions. Our hybrid OPC method combines global rule-based OPC with local model-based OPC functions to boost the wafer image quality improvement but without degrading the computational efficiency. The experimental results show that our proposed framework can achieve the best wafer image quality and circuit performance preservation compared to any other alternative approaches.

Fast optical proximity correction method based on nonlinear compressive sensing.

Optical proximity correction (OPC) is an extensively used resolution enhancement technique (RET) in optical lithography. To date, the computational efficiency has become a big issue for pixelated OPC techniques due to the increasing complexity of lithographic masks in modern integrated circuits. This paper is the first to apply nonlinear compressive sensing (CS) theory to break through the computational efficiency of gradient-based pixelated OPC methods. The proposed method reduces the dimensionality of the OPC problem by downsampling the layout pattern. Then, a nonlinear cost function is established to guarantee the lithography imaging performance on the downsampled layout. Under the sparsity assumption of the mask, the OPC problem is formulated as an inverse nonlinear CS reconstruction problem. The iterative hard thresholding (IHT) algorithm is then used to solve for the OPC problem. The proposed method proves to improve the computational efficiency of traditional gradient-based OPC methods, while improving the process windows of the lithography systems. Benefiting from the sparse property of the mask patterns, the mask manufacturability can also be improved compared to traditional methods.

Predictive Formulae for OPC With Applications to Lithography-Friendly Routing

Due to the subwavelength lithography, manufacturing sub-90-nm feature sizes require intensive use of resolution-enhancement techniques, among which optical proximity correction (OPC) is the most popular technique in industry. Considering the OPC effects during routing can significantly alleviate the cost of postlayout OPC operations. In this paper, we present an efficient, accurate, and economical analytical formula for intensity computation and develop the first modeling of postlayout OPC based on a quasi-inverse lithography technique. The technique provides key insights into a new direction for postlayout OPC modeling during routing. Extensive simulations with SPLAT, the golden lithography simulator in academia and industry, show that our intensity formula has high fidelity. Incorporating the OPC costs computed by the quasi-inverse lithography technique for our postlayout OPC modeling into a router, the router can be guided to maximize the effects of the correction. Compared with a rule-based OPC method, the experimental results show that our approach can achieve 15% and 16% reductions in the maximum and average layout distortions, respectively.

Binary mask optimization for forward lithography based on the boundary layer model in coherent systems

Recently, a set of generalized gradient-based optical proximity correction (OPC) optimization methods have been developed to solve for the forward and inverse lithography problems under the thin-mask assumption, where the mask is considered a thin 2D object. However, as the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent, and thus these effects must be taken into account in OPC optimization methods. OPC methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength regime. This paper focuses on developing model-based forward binary mask optimization methods that account for the thick-mask effects of coherent imaging systems. The boundary layer (BL) model is exploited to simplify and characterize the thick-mask effects, leading to a model-based OPC method. The BL model is simpler than other thick-mask models, treating the near field of the mask as the superposition of the interior transmission areas and the boundary layers. The advantages and limitations of the proposed algorithm are discussed, and several illustrative simulations are presented.

Intelligent optical proximity correction using genetic algorithm with model- and rule-based approaches

Optical lithography is one of the key technologies in semiconductor material and device fabrications. It is a process to transfer the layouts of desired pattern onto the wafers. However, the exposure on wafer has distortions due to the proximity effects. As the minimum feature sizes of explored samples continue to shrink, the mismatch between the pattern and the experimental result on wafer is significant. Corrections of mask patterns between the sample and post exposure result are thus necessary. Optical proximity correction (OPC) is the process of modifying the geometries of the layouts to compensate for the non-ideal properties of the lithography process. Given the shapes desired on the wafer, the mask is modified to improve the reproduction of the critical geometry. In this work, we propose an intelligent OPC technique for process distortion compensation of layout mask. To perform the mask correction in sub-wavelength era, two different strategies including the genetic algorithm (GA) with model-based OPC and the GA with rule-based OPC methods are examined. The proposed intelligent system consists of three parts: the preprocess, the OPC engine, and the post-process. During the pre-process, the pattern analyzer will analysis all patterns and then divided them into many segments for model-based OPC or generates assistant patterns for rule-based OPC. Secondly, the OPC module is applied to correct the mask. The intelligent module searches the whole problem domain to find out the best combination of the mask shape by the GA. The corrected mask is verified by performing lithographic simulation to get the error norm between exposed result and desired layout. Finally, the mask verification is conducted in the post-process. By testing on several fundamental patterns, this approach shows good correction accuracy and efficiency, compared with experimentally fabricated samples. It can be applied to perform the mask correction in sub-wavelength era.

Application of optical proximity correction technology

As process technology scales down to very deep sub-micron (VDSM) in semiconductor manufacturing technology, intrinsic size becomes close to or even shorter than the wavelength used for optical lithography. Thus, some distortions and deformations are introduced by optical proximity effects (OPE) mainly caused by the diffraction and interference of exposure light when layout patterns on a mask are transcribed to a wafer, which influence on the yield and performance of IC circuit. In order to compensate for the deformations, optical proximity correction (OPC) is the most commonly used methodology. Presently, the OPC method is to use a unitary toleration on the whole chip layer, which makes the run time of OPC algorithm longer, causes the size of GDSII files to follow exponential growth, and results in the cost of making mask grow immensely. Firstly, this paper proposes a self-adaptation OPC method with preprocessing function of patterns classification. According to the need of the correction precision, the OPC system divides patterns corrected into two groups with different toleration: critical patterns and general patterns, which enhance the efficiency of the OPC approach. Secondly, a model-based OPC method is presented based on pattern subsection and classification, which keeps the precision of the correction as well as enhances the efficiency. We also propose a rule-based OPC method with general, concise and complete correction rules, and achieve automatic-built rules-based and its looking-up. Thirdly, we also implement an OPC system, called MR-OPC; the MR-OPC system integrates both rule-based OPC and model-based OPC into a whole, so it can solve the confliction between the efficiency and precision. Experimental results show that the MR-OPC system we suggested has advantages of the efficiency and expansibility.

Potential of phase-shifted optical proximity correction for 65nm T-shaped pattern in high numerical aperture lithography

Optical proximity correction (OPC) has been employed as a key enabling resolution enhancement technique required to meet image size control requirements imposed by state-of-the-art integrated circuit product programs. However, at the sub-65-nm node, the line end shortening effect for T-shaped pattern becomes pronounced and it is hard to correct using OPC due to the small gap size. Phase shift masks (PSMs) can improve lithography resolution and will be used at 65nm node. However, phase conflicts occur when imaging a T-shaped pattern with PSM. Hence, it is becoming increasingly more challenging to print T-shaped patterns for sub-65-nm nodes. A new OPC method, phase-shifted optical proximity correction (PSOPC), has been proposed to improve the imaging fidelity for T-shaped pattern and avoid the phase conflict caused by the use of PSM. A PSOPC mask has phase-shifted segments that can simultaneously modify the intensity and phase of the incident light. PROLITH 9.0 and in-house-software microcruiser were applied to demonstrate the new approach of PSOPC. The authors’ results show that the line end shortening can be reduced to 4.6nm and the depth of focus can be improved to over 200nm. These results showed that PSOPC has significant potential as a new resolution enhancement technology for 65nm T-shaped pattern lithography.

Orthogonal Functional Method for Optical Proximity Correction of Thermal Processes in Optical Lithography

The patterning of very small features is a difficult challenge for current lithography technology. The thermal process is an easy and simple solution involving no any additional processes. This process is one of extension techniques for 248 nm KrF and 193 nm ArF lithography equipment and chemically amplified resists (CARs). However, thermal effects are severe, thus, more critical approaches are needed for small pattern formation. In this paper, thermal processes are described and modelled for evaluating property changes in 248 and 193 nm CARs. The simulated results agree well with experimental results. Those processes can be used to shrink not only contact hole patterns but also space patterns. For the optical proximity correction (OPC) of thermal effects, an orthogonal functional method is introduced. These orthogonal functions depend on pattern types such as contact holes and spaces. By using this method, underbaked postexposure bake and thermal reflow are performed for the below-45-nm contact hole pattern for a 248 nm KrF CAR and the 32 nm contact hole pattern for a 193 nm ArF CAR. Thus, an orthogonal functional method is useful for carrying out the OPC for thermal effects.

Process Extension Techniques for Optical Lithography: Thermal Treatment, Polarization and Double Patterning

Current 193-nm optical lithography and commercially available 193-nm resists have been pushed far beyond the previously expected critical dimension by using process extension technology for resolution enhancement technology. This paper deals with three kinds of process extension technologies, thermal treatment, polarization, and double patterning. These technologies are modeled and analyzed. If a 50 % pattern shrinkage due to thermal treatment, a 25 % resolution enhancement due to polarization, and a 50 % pattern shrinkage due to double patterning are supposed, an effective combination can generate a sub-50-nm pattern. When the pattern size is smaller, optical proximity effects are more severe. After describing optical proximity effects for each of these technologies, we discuss optical proximity correction methods.

Novel algorithms for placement of rectangular covers for mask inspection in advanced lithography and other VLSI design applications

The continuous drive of very large scale integrated (VLSI) chip manufacturers to meet Moore's law has spurred the development of novel resolution enhancement techniques (RETs) and optical proximity correction (OPC) methodologies in optical microlithography. These RET and OPC methods have increased the complexity of mask-manufacturing manifold and have, at the same time, put added emphasis on the mask inspection procedure. A technique to simplify mask inspection is to identify rectangular regions on the mask that do not require inspection. Such a region is referred to as a do not inspect region (DNIR). A novel and practical algorithm to place DNIR rectangles on the mask is presented. It is shown that the most general DNIR placement problem is at least NP-Hard (Garey and Johnson, 1979). However, under certain relaxed criteria, there exists a polynomial-time algorithm for DNIR placement using dynamic programming. However, the optimal algorithm has very-high-degree polynomial bounds on its runtime and space complexities. On the other hand, a very simple greedy algorithm extended by lookahead and randomization, or by simulated annealing, can greatly improve the performance of the DNIR placement and produce near-optimal results. Although the algorithm developed in this work is targeted primarily toward DNIR placement, it has many other VLSI design applications.

Mutual optimization of resolution enhancement techniques

As subhalf wavelength optical lithography is pursued, the variety of imaging requirements increases. This can result in complex combinations of various resolution enhancement techniques. Optimization based on simple standards or rules is not possible. Problems often arise as analysis is carried out in a spatial domain, where mask and image properties are evaluated using sizing or dimensional evaluations. A more appropriate perspective for image optimization is that of the lens pupil, in a spatial frequency domain. In this paper, we describe the common characteristics of resolution enhancement, beyond the historical comparisons of alternating phase shifting masking (PSM) and strong OAI. Enhancement techniques including assist feature optical proximity correction (OPC), custom illumination, attenuated PSM, and pupil filtering are described from a spatial frequency standpoint where each can be utilized to take advantage of strengths and avoid weaknesses. As a result of this type of analysis, we will also describe an alternative OPC method in which assist features of varying tone, referred to as gray bars, provide significant image improvement.

Development of An Accurate Optical Proximity Correction System for 1 Gbit Dynamic Random Access Memory Fabrication

In this paper, we demonstrate the feasibility of a refined one-dimensional (1D) optical proximity correction (OPC) method incorporated into a hierarchical mask data processing system. The correction accuracy was examined using experimental and lithography simulation by application to test patterns of a 1 Gbit dynamic random access memory (DRAM) metal layer. In the case of the 0.16 µm rule, the standard deviation of the refined 1D OPC was reduced to 9 nm, which is 70% of the standard deviation of 13 nm of the conventional 1D OPC method. The proposed OPC system, using an engineering workstation, succeeded in correcting the metal layer in a miniature model of a 1 Gbit DRAM within 2-4 days. Well-designed hierarchical management in the mask data processing system suppressed mask data volume expansion to within 4% compared to the data volume without OPC. These results suggest that the refined 1D OPC method is useful for the correction of 1 Gbit and future DRAM devices.

Large-Area Optical Proximity Correction with a Combination of Rule-Based and Simulation-Based Methods

We have developed a practical one-dimensional (1D) optical proximity correction (OPC) system based on a combination method. Our OPC system integrates a rule-based and a simulation-based method so that correction time can be reduced to a minimum, while maintaining sufficient accuracy for the correction. The correction accuracy depends on a simulator implemented in the system. By incorporating the 1D context within the range of the proximity effect into the rule table, higher accuracy in the OPC is obtained as compared with conventional methods which involve looking up tables based on duty ratio, or distance to the nearest neighbor. We applied this system to the linewidth correction of 0.3-µm rule logic gates, and obtained width specifications within ±10% and DOF ±0.4 µm. Since correction is basically carried out at the speed of a rule-based correction, our OPC method is applicable to large area layouts. The correction time for a layout of 116 mm2 was only 64.2 min. The results of OPC for real devices such as SRAMs and DRAMs are also given, demonstrating the feasibility of large-area 1D OPC.

Neural networks application for OPC (optical proximity correction) in mask making

In this paper a neural network method for optical proximity correction is presented. A non linear two-dimensional spatial inverse filter is proposed as deconvolutional factor over pattern plane. Test sets for the different correction strategies were prepared. Boltzmann machine neural network for training set preparation is proposed. For actual correction optimal autoassociative neural network configuration have been chosen. This strategy also opens the way to use a sub-resolution, non-printable correction structures. Additionally, such a system is available for interfacing with next step of correction - for electron proximity effects. Possibility of merging them in one unit were investigated. Some initial results concerning one step OPC and EPC (electron proximity correction) neurocorrector are presented. Different aggressiveness of the correction can be chosen straightforwardly by simple change of the correction kernels in neurocorrector. There is no structural difference of neurocorrector for attenuated, sized rim, Levenson's, outrigger or chromeless methods, thought different attitudes towards training tests generation have to be applied. Both, feature biasing and feature assisted techniques were investigated. Some attempts to quasi-analytical representation of the correction kernel to minimise or even avoid learning process is also presented. For the full power of artificial neural networks to be exploited from hardware implementation rather, initial considerations on VLSI architecture of the neurocorrector are also included.