Abstract: A method and system for extracting the parasitic capacitance in an IC and generating a technology file for at least one or more IC design tools are provided. Parasitic extraction using the preferred method can significantly reduce field solver computational intensity and save technology file preparation cycle time. The network-based technology file generation system enables circuit designers to obtain a desired technology file in a timely manner. The common feature of the various embodiments includes identifying common conductive feature patterns for a given technology generation. Capacitance models created from the identified patterns are used to assemble the required technology files for IC design projects using different technology node and different process flows.

Abstract: Model-Based Sub-Resolution Assist Feature (SRAF) generation process and apparatus are disclosed, in which an SRAF guidance map (SGM) is iteratively optimized to finally output an optimized set of SRAFs as a result of enhanced signal strength obtained by iterations involving SRAF polygons and SGM image. SRAFs generated in a prior round of iteration are incorporated in a mask layout to generate a subsequent set of SRAFs. The iterative process is terminated when a set of SRAF accommodates a desired process window or when a predefined process window criterion is satisfied. Various cost functions, representing various lithographic responses, may be predefined for the optimization process.

Abstract: Some embodiments include a method for identifying high-temperature regions in a microchip. In some embodiments, the method includes selecting grids on the microchip, wherein each grid includes devices and interconnects connecting the devices. The method can also include determining, for each grid, a temperature factor value based on geometric area of the grid, geometric area occupied by the devices, switching factor of the of the interconnects, and length of the interconnects connecting the devices. The method can also include determining, for each grid, thermal sensitivity for the grid by generating a plot based on a Guassian equation.

Abstract: Mask design techniques for detection and removal of undesirable artifacts in SADP processes using multiple patterns are disclosed. Artifacts or spurs result from lithographic and chemical processing of semiconducting wafers. The spurs are undesirable because they can cause unwanted connections or act as electrical antennas. Spurs are detected using rule-based techniques and reduced by modifying lithographic masks. The severity of the detected spurs is determined, again using rule-based techniques. The effects of detected spurs can be reduced by modifying the decomposition of the drawn patterns into the two masks used for lithography. Mandrel masks are modified by add dummy mandrel material, and trim masks are modified by removing trim material. The resulting multi-pattern arrangement is used to fabricate the critical design elements that make up the semiconductor wafers.

Abstract: The invention discloses a computer implemented method of fracturing a surface into elementary features wherein the desired pattern has a rectilinear or curvilinear form. Depending upon the desired pattern, a first fracturing will be performed of a non-overlapping or an overlapping type. If the desired pattern is resolution critical, it will be advantageous to perform a second fracturing step using eRIFs. These eRIFs will be positioned either on the edges or on the medial axis or skeleton of the desired pattern. The invention further discloses method steps to define the position and shape of the elementary features used for the first and second fracturing steps.

Abstract: According to one embodiment of the present invention, a computer-implemented method for validating a design includes generating, using the computer, a first graph representative of the design, when the computer is invoked to validate the design, and decompose, using the computer, the first graph into at least three sets using a hybrid evolutionary algorithm to form a colored graph.

Abstract: Embodiments relate to polygon recovery from a +1/?1 description of a plurality of polygons of a very large scale integrated (VLSI) mask for production of a VLSI semiconductor device. An aspect includes receiving a set of data comprising the +1/?1 description of the plurality of polygons of the VLSI mask, the +1/?1 description comprising a plurality of corners. Another aspect includes determining a 4-directional data structure, a Mm value comprising a first limit value, and a Mp value comprising a second limit value for each of the plurality of corners. Another aspect includes recovering the plurality of polygons from the set of data by assigning each of the plurality of corners to a single polygon based on the 4-directional data structure, the Mm value, and the Mp value of each of the plurality of corners, and determining an order of the respective corners of each polygon.

Abstract: A photolithography mask design in simplified. In one example, a target mask design is optimized for a photolithography mask. Medial axes of the design and assist features on the optimized mask are identified. These are simplified to lines. Lines that are distant from a respective design feature are pruned. The remaining lines are simplified and then thickened to form assist features.

Abstract: Manufacturing circuits with reference plane voids over vias with a strip segment interconnect permits routing critical signal paths over vias, while increasing via insertion capacitance only slightly. The transmission line reference plane defines voids above (or below) signal-bearing plated-through holes (PTHs) that pass through a rigid substrate core, so that the signals are not degraded by an impedance mismatch that would otherwise be caused by shunt capacitance from the top (or bottom) of the signal-bearing PTHs to the transmission line reference plane. In order to provide increased routing density, signal paths are routed over the voids, but disruption of the signal paths by the voids is prevented by including a conductive strip through the voids that reduces the coupling to the signal-bearing PTHs and maintains the impedance of the signal path conductor.

Abstract: Described herein is a method for obtaining a preferred layout for a lithographic process, the method comprising: identifying an initial layout including a plurality of features; and reconfiguring the features until a termination condition is satisfied, thereby obtaining the preferred layout; wherein the reconfiguring comprises evaluating a cost function that measures how a lithographic metric is affected by a set of changes to the features for a plurality of lithographic process conditions, and expanding the cost function into a series of terms at least some of which are functions of characteristics of the features.

Abstract: A method for designing a semiconductor ic chip includes dividing the chip into functional blocks such as a core portion and one or more other functional cells and applying design rules concerning the spatial arrangement of semiconductor fins to the core portion but not to the other functional cells. The design guidelines include the application of design rules to some but not all functional blocks of the chip, may be stored on a computer-readable medium and the design of the semiconductor ic chip and the generation of a photomask set for manufacturing the semiconductor ic chip may be carried out using a CAD or other automated design system. The semiconductor ic chip formed in accordance with this method includes semiconductor fins that are formed in both the core portion and the other functional cells but are only required to be tightly packed in the core portion.

Abstract: A method comprises: accessing data representing a layout of a layer of an integrated circuit (IC) comprising a plurality of polygons defining circuit patterns to be divided among a number (N) of photomasks for multi-patterning a single layer of a semiconductor substrate, where N is greater than one. For each set of N parallel polygons in the layout closer to each other than a minimum separation for patterning with a single photomask, at least N?1 stitches are inserted in each polygon within that set to divide each polygon into at least N parts, such that adjacent parts of different polygons are assigned to different photomasks from each other. Data representing assignment of each of the parts in each set to respective photomasks are stored in a non-transitory, computer readable storage medium that is accessible for use in a process to fabricate the N photomasks.

Abstract: Disclosed is a method, system, and computer program product for performing predictions for an electronic design. Embodiments of the invention allow the ability to efficiently update the model predictions at a later time once previously incomplete blocks are completed. Predictions can be efficiently updated after block designs are updated (e.g. after correcting problems detected from model predictions).

Abstract: An integrated circuit verification system provides an indication of conflicts between an OPC suggested correction and a manufacturing rule. The indication specifies which edge segments are in conflict so that a user may remove the conflict to achieve a better OPC result. In another embodiment of the invention, edge segments are assigned a priority such that the correction of a lower priority edge does not hinder a desired OPC correction of a higher priority edge.

Abstract: Systems and methods for process simulation are described. The methods may use a reference model identifying sensitivity of a reference scanner to a set of tunable parameters. Chip fabrication from a chip design may be simulated using the reference model, wherein the chip design is expressed as one or more masks. An iterative retuning and simulation process may be used to optimize critical dimension in the simulated chip and to obtain convergence of the simulated chip with an expected chip. Additionally, a designer may be provided with a set of results from which an updated chip design is created.

Abstract: The present disclosure provides one embodiment of an integrated circuit (IC) design method. The method includes providing an IC design layout of a circuit; applying an electrical patterning (ePatterning) modification to the IC design layout according to an electrical parameter of the circuit and an optical parameter of IC design layout; and thereafter fabricating a mask according to the IC design layout.

Abstract: Described herein is a method of processing a pattern layout for a lithographic process, the method comprising: identifying a feature from a plurality of features of the layout, the feature violating a pattern layout requirement; and reconfiguring the feature, wherein the reconfigured feature still violates the pattern layout requirement, the reconfiguring including evaluating a cost function that measures a lithographic metric affected by a change to the feature and a parameter characteristic of relaxation of the pattern layout requirement.

Abstract: A method of computational lithography includes collecting a critical dimension (CD) data set including CD data from printing a test structure including a set of gratings which provide a plurality of feature types including different ratios of line width to space width, where the printing includes a range of different focus values. The CD data is weighted to form a weighted CD data set using a weighting algorithm (WA) that assigns cost weights to the CD data based its feature type and its magnitude of CD variation with respect to a CD value for its feature type at a nominal focus (nominal CD). The WA algorithm reduces a value of the cost weight as the magnitude of variation increases. At least one imaging parameter is extracted from the weighted CD data set. A computational lithography model is automatically calibrated using the imaging parameter(s).

Abstract: Porting a first integrated circuit design targeted for implementation in a first semiconductor manufacturing process, and implementing a second circuit design in a second semiconductor manufacturing process wherein the electrical performance of the second integrated circuit meets or exceeds the requirements of the first integrated circuit design even if the threshold voltage targets of the second integrated circuit design are different from those of the first integrated circuit design; and wherein physical layouts, and in particular the gate-widths and gate-lengths of the transistors, of the first and second integrated circuit designs are the same or substantially the same. The second integrated circuit design, when fabricated in the second semiconductor manufacturing process and then operated, experiences less off-state transistor leakage current than does the first integrated circuit design, when fabricated in the first semiconductor manufacturing process, and then operated.

Abstract: Among other things, one or more techniques and systems for performing design layout are provided. An initial design layout is associated with an electrical component, such as a standard cell. The initial design layout comprises a first pattern, such as a mandrel pattern, and a second pattern, such as a passive fill pattern. An initial cut pattern is generated for the initial design layout. Responsive to identifying a design rule violation associated with the initial cut pattern, the initial design layout is modified to generate a modified initial design layout. An updated cut pattern, not resulting in the design rule violation, is generated based upon the modified initial design layout. The updated cut pattern is applied to the modified initial design layout to generate a final design layout. The final design layout can be verified as self-aligned multiple patterning (SAMP) compliant.

Abstract: A method for generating a layout for a device having FinFETs from a first layout for a device having planar transistors is disclosed. The planar layout is analyzed and corresponding FinFET structures are generated in a matching fashion. The resulting FinFET structures are then optimized. Dummy patterns and a new metal layer may be generated before the FinFET layout is verified and outputted.

Abstract: A system for analyzing IC layouts and designs by calculating variations of a number of objects to be created on a semiconductor wafer as a result of different process conditions. The variations are analyzed to determine individual feature failures or to rank layout designs by their susceptibility to process variations. In one embodiment, the variations are represented by PV-bands having an inner edge that defines the smallest area in which an object will always print and an outer edge that defines the largest area in which an object will print under some process conditions.

Abstract: A process and apparatus are provided for automated pattern-based semiconductor design layout correction. Embodiments include scanning a drawn semiconductor design layout to determine a difficult-to-manufacture pattern within the drawn semiconductor design layout based on a match with a pre-characterized difficult-to-manufacture pattern, determining a corrected pattern based on a pre-determined correlation between the corrected pattern and the pre-characterized difficult-to-manufacture pattern, and replacing the difficult-to-manufacture pattern with the corrected pattern within the drawn semiconductor design layout.

Abstract: The invention is directed to a method for checking a die seal ring on a layout. The method comprises steps of receiving a digital database of a layout corresponding to at least a device with a text information corresponding to the layout. Tape-out information corresponding to the layout is received. A checking process is performed according to the digital database of the layout and the tape-out information and, meanwhile, a mask design procedure for designing a mask pattern corresponding to the layout is performed by using the digital database of the layout, the text information and the tape-out information. A result of the checking process is recorded in an inspection table corresponding to the layout.

Abstract: Universal target based inspection drive metrology includes designing a plurality of universal metrology targets measurable with an inspection tool and measurable with a metrology tool, identifying a plurality of inspectable features within at least one die of a wafer using design data, disposing the plurality of universal targets within the at least one die of the wafer, each universal target being disposed at least proximate to one of the identified inspectable features, inspecting a region containing one or more of the universal targets with an inspection tool, identifying one or more anomalistic universal targets in the inspected region with an inspection tool and, responsive to the identification of one or more anomalistic universal targets in the inspected region, performing one or more metrology processes on the one or more anomalistic universal metrology targets with the metrology tool.

Abstract: Various embodiments identify some constraints for multiple mask designs of multi-patterning lithography processes for manufacturing an electronic design and colors multiple routing tracks in a layer of the electronic design with certain colors. These embodiments color fixed object(s) in the design with one or more of these certain colors based on coloring of the multiple routing tracks. Some embodiments further color movable object(s) based on results of coloring the fixed object(s) or coloring routing track(s). Some embodiments route the physical design with coloring of fixed object(s), coloring of movable object(s), or routing connectivity. Multiple-patterning conflicts may be detected based on the coloring of fixed object(s), coloring of movable object(s), or routing connectivity. Some embodiments route with search-and-repair strategy(ies) to improve or resolve conflict(s). Some embodiments color objects upon their creation, and the layout is thus multiple-patterning design rule clean as constructed.

Abstract: A computer-implemented method for retargeting an Integrated Circuit (IC) layout is disclosed. In one embodiment, the method includes generating a diffraction pattern for the IC layout including a set of diffraction-orders, the IC layout including a set of features defined by a set of target edges, analyzing the diffraction pattern with a merit function to estimate printability of the IC layout, monitoring a change in value of the merit function as a position of at least one of the set of target edges is adjusted across a range, and retargeting the set of target edges based on the monitoring of the merit function.

Abstract: An inspection method for a photo-mask in a semiconductor process is provided. First, a first photo-mask with a first wafer anchor point (1st wafer FAM) is provided. Then, Dmax and Dmin are calculated according to the 1st wafer FAM. A second photo-mask and a second mask anchor point (2nd mask FAM) of the second photo-mask are provided. A CD average, and a CD range of the second photo-mask are measured. Finally, the second photo-mask is inspected by using equation A and/or equation B: CD average?2nd mask FAM<Dmax?CD range/2??(equation A) 2nd mask FAM?CD average<Dmin?CD range/2??(equation B).

Abstract: Systems and methods for determining a position of output of an inspection system in design data space are provided. One method includes merging more than one feature in design data for a wafer into a single feature that has a periphery that encompasses all of the features that are merged. The method also includes storing information for the single feature without the design data for the features that are merged. The information includes a position of the single feature in design data space. The method further includes aligning output of an inspection system for the wafer to the information for the single feature such that positions of the output in the design data space can be determined based on the design data space position of the single feature.

Abstract: A three-dimensional mask model of the invention provides a more realistic approximation of the three-dimensional effects of a photolithography mask with sub-wavelength features than a thin-mask model. In one embodiment, the three-dimensional mask model includes a set of filtering kernels in the spatial domain that are configured to be convolved with thin-mask transmission functions to produce a near-field image. In another embodiment, the three-dimensional mask model includes a set of correction factors in the frequency domain that are configured to be multiplied by the Fourier transform of thin-mask transmission functions to produce a near-field image.

Abstract: A design system for designing an integrated circuit that includes a processor, a memory coupled to the processor, and instructions to generate and edit a schematic of the integrated circuit, generate at least one recommended layout parameter of an integrated circuit device within the integrated circuit, extract the at least one recommended layout parameter during a layout stage of the integrated circuit, and calculate a circuit performance parameter of the integrated circuit using the at least one recommended layout parameter, and a user interface configured to display at least one of the circuit performance parameter and layout constraints of the integrated circuit device of the integrated circuit.

Abstract: The use of design rule checks for failure analysis of semiconductor chips is described. The smaller geometries of recent semiconductor devices lead to a much higher level of sensitivity of devices to photolithography related systematic problems. Failure analysis to date has focused on physical, randomly distributed defects of devices rather than systematic problems caused by the mask manufacturing or mask application process. Methods and systems are described which allow for online searches of a layout database for geometric features defined by a set of rules. The rules may be defined as two-dimensional Boolean operations including shape or distance based as well as any kind of combination. The result is graphically and interactively presented.

Abstract: Provided is a system and method for assessing a design layout for a semiconductor device level and for determining and designating different features of the design layout to be formed by different photomasks by decomposing the design layout. The features are designated by markings that associate the various device features with the multiple photomasks upon which they will be formed and then produced on a semiconductor device level using double patterning lithography, DPL, techniques. The markings are done at the device level and are included on the electronic file provided by the design house to the photomask foundry. In addition to overlay and critical dimension considerations for the design layout being decomposed, various other device criteria, design criteria processing criteria and their interrelation are taken into account, as well as device environment and the other device layers, when determining and marking the various device features.

Abstract: A method and system arrangement for controlling and determining mask operation activities. Upon obtaining chip physical layout design data and running resolution enhancement technology on the chip physical layout design to generate mask features which may include any sub-resolution assist features, a placement sensitivity metric is determined for each of the generated mask features or edge fragments. In one alternative embodiment an edge placement sensitivity metric is determined for each edge of the generated mask features or edge fragments. The determined sensitivity metrics for each feature are classified and applied to subsequent mask operational activities such as post processing, write exposure and mask repair.

Abstract: Disclosed is an improved method, system, and computer program product for preparing multiple levels of semiconductor substrates for three-dimensional IC integration. Some embodiments utilize the process and design models to check and fabricate the insulating dielectric layer (IDL) separating the first and the second film stacks on separate substrates and then prepare the surface of the IDL to receive an additional layer of semiconductor substrate for further fabrication of the chips. Yet some other embodiments further employ the design and process models to ensure the IDL and the semiconductor substrate are sufficiently flat, or are otherwise satisfactory, so the three-dimensional integrated circuits meet the reliability, manufacturability, yield, or performance requirements. Yet some other embodiments further employ design and process models to place the vias connecting the multiple film stacks.

Abstract: Embodiments of the disclosure include identifying circuit elements for selective inclusion in speed-push processing and related circuit systems, apparatus, and computer-readable media. A method for altering a speed-push mask is provided, including analyzing a circuit design comprising a plurality of cells to which a speed-push mask is applied to identify at least one of the plurality of cells as having performance margin. The speed-push mask is altered such that the at least one of the plurality of cells having performance margin may be fabricated as a non-speed-pushed cell. Additionally, a method for creating a speed-push mask is provided, including analyzing a circuit design comprising a plurality of cells to identify at least one of the plurality of cells below a performance threshold. A speed-push mask is created such that the at least one of the plurality of cells below the performance threshold may be fabricated as a speed-pushed cell.

Abstract: A circuit design system includes a schematic design tool configured to generate schematic information and pre-coloring information for a circuit. The circuit design system also includes a netlist file configured to store the schematic information and the pre-coloring information on a non-transitory computer readable medium and an extraction tool configured to extract the pre-coloring information from the netlist file. A layout design tool, included in the circuit design system, is configured to design at least one mask based on the schematic information and the pre-coloring information. The circuit design system further includes a layout versus schematic comparison tool configured to compare the at least one mask to the schematic information and the pre-coloring information.

Abstract: A method of via patterning mask assignment for a via layer using double patterning technology, the method includes determining, using a processor, if a via of the via layer intercepts an underlying or overlaying metal structure assigned to a first metal mask. If the via intercepts the metal structure assigned to the first metal mask, assigning the via to a first via mask, wherein the first via mask aligns with the first metal mask. Otherwise, assigning the via to a second via mask, wherein the second via mask aligns with a second metal mask different from the first metal mask.

Abstract: An approach is provided in which an enhanced routing module creates connection objects on a double patterning layout that are correct-by-construction and do not require a semiconductor fabrication stitching process. The enhanced routing module efficiently tracks accumulated mask selection constraints, during maze expansion, when the enhanced routing module traverses possible connection routes from a source grid point to a target grid point. In turn, the enhanced routing module avoids grid points that impose mask selection constraints that are incompatible with existing mask selection constraints of the possible connection routes. As a result, a connection object created by any one of the possible connection routes can be assigned to a specific mask, thus avoiding stitching process requirements from a semiconductor fabrication facility.

Abstract: A method for forming an integrated circuit (IC) is presented. The method includes providing a wafer having a substrate prepared with a photoresist layer. The photoresist layer is processed by passing a radiation from an exposure source of a lithography tool through a mask having a pattern. The process parameters of the lithography tool are determined by performing a pattern matching process. The photoresist layer is developed to transfer the pattern on the mask to the photoresist layer.

Abstract: An integrated circuit with standard cells with top and bottom metal-1 and metal-2 power rails and with lateral standard cell borders that lie between an outermost vertical dummy poly lead from one standard cell and an adjacent standard cell. A DPT compatible standard cell design rule set. A method of forming an integrated circuit with standard cells constructed using a DPT compatible standard cell design rule set. A method of forming DPT compatible standard cells.

Abstract: A method and system for fracturing or mask data preparation is disclosed in which a plurality of charged particle beam shots is determined which will produce a pattern on a reticle, where the reticle is to be used to form an aerial image on a resist-coated substrate using an optical lithographic process. A simulated reticle pattern is then calculated from the plurality of charged particle beam shots. A calculated aerial substrate image is then calculated using the simulated reticle pattern, and a shot in the plurality of shots is modified to improve the calculated aerial substrate image. Similar methods for forming a pattern on a reticle and for manufacturing an integrated circuit are also disclosed.

Abstract: A plurality of diagnosis methods are provided for enabling hardware debugging. A first diagnosis method enables hardware debugging by means of time abstraction. A second diagnosis method enables hardware debugging by means of abstraction and refinement. A third diagnosis method enables hardware debugging by means of QBF-formulation for replicated functions. A fourth diagnosis method enables hardware debugging by means of a max-sat debugging formulation. A system and computer program for implementing the diagnosis methods is also provide.

Abstract: A method includes determining model parameters for forming an integrated circuit, and generating a techfile using the model parameters. The techfile includes at least two of a C_worst table, a C_best table, and a C_nominal table. The C_worst table stores greatest parasitic capacitances between layout patterns of the integrated circuit when lithography masks comprising the layout patterns shift relative to each other. The C_best table stores smallest parasitic capacitances between the layout patterns when the lithography masks shift relative to each other. The C_nominal table stores nominal parasitic capacitances between the layout patterns when the lithography masks do not shift relative to each other. The techfile is embodied on a tangible non-transitory storage medium.

Abstract: The present disclosure provides one embodiment of an integrated circuit (IC) method. The method includes building a pattern bank including a pattern having an area of interest. The method further includes recognizing that the pattern of the pattern bank corresponds to a pattern of an IC design layout. The method further includes identifying an area of interest of the pattern of the IC design layout that corresponds to the area of interest of the pattern of the pattern bank. The method further includes performing pattern recognition dissection on the area of interest of the pattern of the IC design layout to dissect the area of interest of the pattern of the IC design layout into a plurality of segments. The method further includes after performing pattern recognition dissection, producing a modified IC design layout.

Abstract: A method of designing an IC design layout having similar patterns filled with a plurality of indistinguishable dummy features, in a way to distinguish all the patterns, and an IC design layout so designed. To distinguish each pattern in the layout, deviations in size and/or position from some predetermined equilibrium values are encoded into a set of selected dummy features in each pattern at the time of creating dummy features during the design stage. By identifying such encoded dummy features and measuring the deviations from image information provided by, for example, a SEM picture of a wafer or photomask, the corresponding pattern can be located in the IC layout. For quicker and easier identification of the encoded dummy features from a given pattern, a set of predetermined anchor dummy features may be used.

Abstract: A mask overlay method, and a mask and a semiconductor device using the same are disclosed. According to the disclosed mask overlay technique, test marks and front layer overlay marks corresponding to a plurality of overlay mark designs are generated in a first layer of a semiconductor device. The test patterns generating the test marks each include a first sub pattern and a second sub pattern. Note that the first sub pattern has the same design as a front layer overlay pattern (which generates the front layer overlay mark corresponding thereto). Based on the test marks, performances of the plurality of overlay mark designs are graded. The front layer overlay mark corresponding to the overlay mark design having the best performance is regarded as an overlay reference for a mask of a second layer of the semiconductor device.

Abstract: Systems and methods are disclosed for a stochastic model of mask process variability of a photolithography process, such as for semiconductor manufacturing. In one embodiment, a stochastic error model may be based on a probability distribution of mask process error. The stochastic error model may generate a plurality of mask layouts having stochastic errors, such as random and non-uniform variations of contacts. In other embodiments, the stochastic model may be applied to critical dimension uniformity (CDU) optimization or design rule (DR) sophistication.

Abstract: A method for fracturing or mask data preparation or proximity effect correction or optical proximity correction or mask process correction is disclosed in which a set of charged particle beam shots is determined that is capable of forming a pattern on a surface, wherein critical dimension (CD) split is reduced through the use of overlapping shots.

Abstract: A method identifies, as an independent node, any node representing a circuit pattern in any odd loop of a layout of a region of a layer of an IC that is not included in any other odd loop of the layout. The layer is to have a plurality of circuit patterns to be patterned using at least three photomasks. The method identifies, as a safe independent node, any independent node not closer than a threshold distance from any other independent nodes in another odd loop of the layout. The layout is modified, if the circuit patterns in the layout include any odd loop without any safe independent node, so that that after the modifying, each odd loop has at least one safe independent node.