Abstract: During a calculation technique, a modification to a reflective photo-mask is calculated. In particular, using information specifying a defect associated with a location on a top surface of the reflective photo-mask, the modification to the reflective photo-mask is calculated. For example, the calculation may involve an inverse optical calculation in which a difference between a pattern associated with the reflective photo-mask at an image plane in a photo-lithographic process and a reference pattern at the image plane in the photo-lithographic process is used to calculate the modification at an object plane in the photo-lithographic process. Note that the modification includes a material added to the top surface of the reflective photo-mask using an additive fabrication process. Moreover, the modification is proximate to the location.

Abstract: Disclosed is a system, method, and computer-readable medium for designing a circuit and/or IC chip to be provided using an optical shrink technology node. Initial design data may be provided in a first technology node and through the use of embedding scaling factors in one or more EDA tools of the design flow, a design (e.g., mask data) can be generated for the circuit in an optical shrink technology node. Examples of EDA tools in which embedded scaling factors may be provided are simulation models and extraction tools including LPE decks and RC extraction technology files.

Abstract: A charged particle beam writing apparatus and a charged particle beam writing method capable of shortening the time necessary to generate shot data and improving writing throughput. A graphic pattern defined in write data is divided into graphics represented in shot units. The divided graphics are temporarily stored in a memory and are distributed to their corresponding subfield areas while developing position information defined in a state of being compressed to write data. When each pattern is written by multi-pass writing, graphics divided at a first pass are used for distribution to subfield areas after a second pass.

Abstract: The present invention provides a method for compensating infidelities of a process that transfers a pattern to a layer of an integrated circuit, by minimizing, with respect to a photomask pattern, a cost function that quantifies the deviation between designed and simulated values of circuit parameters of the pattern formed on a semiconductor wafer.

Abstract: A method is disclosed for defining a multiple patterned cell layout for use in an integrated circuit design. A layout is defined for a level of a cell in accordance with a dynamic array architecture so as to include a number of layout features. The number of layout features are linear-shaped and commonly oriented. The layout is split into a number of sub-layouts for the level of the cell. Each of the number of layout features in the layout is allocated to any one of the number of sub-layouts. Also, the layout is split such that each sub-layout is independently fabricatable. The sub-layouts for the level of the cell are stored on a computer readable medium.

Abstract: Methods of semiconductor device fabrication techniques using double patterning are disclosed. According to various embodiments of the invention, methods of semiconductor device fabrication using self-aligned double patterning are provided. Particular embodiments of the invention allow creation of logic circuit patterns using two lithographic operations. One embodiment of the invention employs self-aligned double patterning to define two or more sets of parallel line features with a connection feature between two adjacent sets. In such embodiment, the sets of parallel line features along with the connection features are formed using two lithographic masks, without a need for an additional mask layer to form the connection features. In other embodiments, other features in addition to the connection features can be added in the same mask layer.

Abstract: A method of optical proximity correction (OPC) convergence control that includes providing a lithography system having a photomask and an illuminator. The method further includes performing an exposure by the illuminator on the photomask. Also, the method includes optimizing an optical illuminator setting for the lithography system with a defined gate pitch in a first direction in a first template. Additionally, the method includes determining OPC correctors to converge the OPC results with a target edge placement error (EPE) to produce a first OPC setting for the first template. The first OPC setting targets a relatively small EPE and mask error enhancement factor (MEEF)of the defined gate pitch in the first template. In addition, the method includes checking the first OPC setting for a relatively small EPE, MEEF and DOM consistency with the first template of the defined gate pitch in a second, adjacent template.

Abstract: The process for designed based assessment includes the following steps. First, the process defines multiple patterns of interest (POIs) utilizing design data of a device and then generates a design based classification database. Further, the process receives one or more inspection results. Then, the process compares the inspection results to each of the plurality of POIs in order to identify occurrences of the POIs in the inspection results. In turn, the process determines yield impact of each POI utilizing process yield data and monitors a frequency of occurrence of each of the POIs and the criticality of the POIs in order to identify process excursions of the device. Finally, the process determines a device risk level by calculating a normalized polygon frequency for the device utilizing a frequency of occurrence for each of the critical polygons and a criticality for each of the critical polygons.

Abstract: There is provided a method comprising receiving data corresponding to a layout design for a plurality of input mask layers and generating a layout design for at least one generated mask layer. The relationship between a first geometric element in a first layout pattern comprising one or more of the generated mask layers and a second geometric element in a second layout pattern is then determined and verified to check if they comply with predetermined rules. If the relationship does not conform with the predetermined rules the design of at least one of the generated mask layers associated with the first or second layout pattern is modified.

Abstract: A method and system for quantifying manufacturing complexity of electrical designs randomly places simulated defects on image data representing electrical wiring design. The number of distinct features in the image data without the simulated defects and the number of distinct features in the image data with the simulated defects are determined and the differences between the two obtained. The difference number is used as an indication of shorting potential or probability that shorts in the wiring may occur in the electrical wiring design. The simulating of the defects in the image data may be repeated and the difference value from each simulation or run may be used to obtain a statistical average or representative shorting potential or probability for the design.

Abstract: There is provided a computer-implemented method of creating a recipe for a manufacturing tool and a system thereof. The method comprises: upon obtaining data characterizing periodical sub-arrays in one or more dies, generating candidate stitches; identifying one or more candidate stitches characterized by periodicity characteristics satisfying, at least, a periodicity criterion, thereby identifying periodical stitches among the candidate stitches; and aggregating the identified periodical stitches and the periodical sub-arrays into periodical arrays, said periodical arrays to be used for automated recipe creation.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: segmenting a plurality of the features into a plurality of polygons; determining the image log slope (ILS) value for each of the plurality of polygons; determining the polygon having the minimum ILS value, and defining a mask containing the polygon; convolving the defined mask with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and, assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.

Abstract: Obtaining a function by convoluting a function representing a light intensity distribution formed by an illumination apparatus on a pupil plane of a projection optical system and a pupil function of the projection optical system. Calculating a Fourier transformed function by Fourier transforming the product of the obtained function and a diffracted light distribution from a pattern on an object plane of the projection optical system. Producing data of the pattern of the mask based on the Fourier transformed function.

Abstract: Branching of the data-flow in a mask data preparation processes is described herein. In various implementations, the output stream from a first mask data processing operation is branched. Subsequently, the branched output stream may be connected to the input stream of a first independent mask data preparation operation and a second independent mask data preparation operation. This provides that the first and the second independent mask data preparation operations may operate in parallel. Furthermore, this provides that the first and the second independent mask data preparation operations may operate upon discrete “portions” of the data processed by the first mask data preparation operation.

Abstract: A background process installs a system hook for message interception of integrated circuit chip layout display software. A call message is intercepted through the system hook, and current layout coordinates are read from the integrated circuit chip layout display software. A representation of the current layout coordinates is entered into tool control software configured to control a physical tool for analyzing integrated circuits, and the physical tool is controlled with the tool control software. In an “inverse” approach, a background process is used to install at least one system hook for message interception of tool control software configured to control a physical tool for analyzing integrated circuits, and a call message is intercepted through the system hook. Current coordinates are read from the tool control software. A representation of the current coordinates is entered into integrated circuit chip layout display software, and at least a portion of an integrated circuit layout is displayed.

Abstract: In an example embodiment, an EDA application creates a physical PCell from a CAD database that relates the physical PCell to a collection of expected mask layers. The EDA application auto-places an identifying text label with the physical and converts the physical PCell and the text label to a format that represents the physical PCell and the text label as sequence of drawn layers. The EDA application generates an equation that performs transformational operations on the drawn layers to create a sequence of derived layers, where the sequence of derived layers defines a collection of logical mask layers. The EDA application executes the equation and compares a derived layer to the expected mask layers, if the derived layer interacts with the derived layer for the text label. If the compared derived layer varies from the expected mask layers, the EDA application reports a variance based on the text label.

Abstract: A mask blank is provided by forming a plurality of films, including at least a thin film to be a transfer pattern, on a board. At the time of patterning a resist film of the mask blank according to pattern data, film information to check with a pattern is obtained for each of a plurality of the films.

Abstract: In various embodiments, a method of designing an integrated circuit (IC) layout for a multiple patterning layout fill process includes: providing a pre-characterized mask tile library including a plurality of distinct mask tiles each having a distinct mask density on a plurality of distinct exposures each associated with a patterning process in the multiple patterning process; determining a density of a mask group in a first layout window in the IC layout, the first layout window including an open space unfilled by the mask group; and selecting a set of mask tiles from the plurality of distinct mask tiles to fill a portion of the open space, the selecting based upon the determined density of the mask group in the first layout window and the distinct mask density of the selected set of mask tiles on the plurality of distinct exposures.

Abstract: The present disclosure provides one embodiment of an integrated circuit (IC) method. The method includes receiving an IC design layout having a plurality of IC regions each including an IC pattern; performing a dissection process to the IC design layout; and performing a correction process to the IC design layout using a correction model that includes proximity effect and location effect. The correction process includes performing a first correction step to a first IC region of the IC regions, resulting in a first corrected IC pattern in the first IC region; and performing a second correction step to a second IC region of the IC regions, starting with the first corrected IC pattern, resulting in a second corrected IC pattern.

Abstract: Optical proximity correction techniques performed on one or more graphics processors improve the masks used for the printing of microelectronic circuit designs. Execution of OPC techniques on hardware or software platforms utilizing graphics processing units. GPUs may share the computation load with the system CPUs to efficiently and effectively execute the OPC method steps.

Abstract: A computer is programmed to use at least one rule to identify from within a layout of an IC design, a set of regions likely to fail if fabricated unchanged. An example of such a rule of detection is to check for presence of two neighbors neither of which fully overlaps a short wire or an end of a long wire. The computer uses at least another rule to change at least one region in the set of regions, to obtain a second layout which is less likely to fail in the identified regions. An example of such a rule of correction is to elongate at least one of the two neighbors. The computer may perform optical rule checking (ORC) in any order relative to application of the rules, e.g. ORC can be performed between detection rules and correction rules i.e. performed individually on each identified region prior to correction.

Abstract: A method includes receiving a device layout file in a computing apparatus defining a plurality of device structures in a semiconductor device. A foundry truth table designating valid device structures for a fabrication process is received in the computing apparatus. Device structures in the device layout file are designated as supported device structures by comparing the device structures in the device layout file to the valid device structures in the foundry truth table using the computing apparatus. Device structures in the device layout file that do not correspond to valid device structures for the fabrication process are designated as unsupported devices using the computing apparatus. A list of the unsupported device structures is generated using the computing apparatus.

Abstract: Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. The use of the calculated cross-correlation of the mask and the optical system, and the translation property of the Fourier transform for perturbing the design reduces the computation time needed for determining required changes in the design rules.

Abstract: The disclosed aspects relate to controlling density of photomasks. One or more unprintable auxiliary patterns can be placed near a mask feature as well as onto a location of a feature of the main pattern. If a density is measured and is not within an acceptable density range, one or more printable auxiliary patterns can be replaced with unprintable auxiliary patterns and/or one or more unprintable auxiliary patterns can be replaced with printable auxiliary patterns. The disclosed aspects can be utilized to create a photomask and/or a semiconductor device, such as a large scale integrated circuit device, that comprises the photomask.

Abstract: Systems and techniques for modeling the EUV lithography shadowing effect are described. Some embodiments described herein provide a process model that includes an EUV lithography shadowing effect component. Polygon edges in a layout can be dissected into a set of segments. Next, the EUV lithography shadowing effect component can be used to bias each segment. The modified layout having the biased segments can then be used as input for other components in the process model.

Abstract: In one embodiment, a spacing is determined for each edge of a number of features in a photolithographic design. The edges have at least a partially predictable layout. Based on the spacing and the predictable layout, a bridge structure is generated. Each bridge of the bridge structure connects one of the edges to an edge of a neighboring feature. Then, the features and the bridge structure are provided for a phase assignment. The phase assignment assigns features at opposite ends of each bridge in the bridge structure to opposite phases. In another embodiment, a sub-resolution assist feature (SRAF) is introduced for an edge of a feature and a bridge is generated from the feature to the SRAF. Then, the feature and the SRAF are assigned to opposite phases based on the relationship defined by the bridge.

Abstract: Some embodiments relate to a method for pre-coloring data within an integrated chip layout to avoid overlay errors that result from mask misalignment during multiple patterning lithography. The method may be performed by generating a graphical IC layout file containing an integrated chip layout having a plurality of IC shapes. The IC shapes within the graphical IC layout file are assigned a color during decomposition. The IC shapes are further pre-colored in a manner that deliberately assigns the pre-colored data to a same mask. During mask building data associated with IC shapes that have been pre-colored is automatically sent to a same mask, regardless of the colors that are assigned to the shapes. Therefore, the pre-colored shapes are not assigned to a masked based upon a decomposition, but rather based upon the pre-coloring. By assigning IC shapes to a same mask through pre-coloring, overlay errors can be reduced.

Abstract: Provided is a method of performing a maskless lithography process. The method includes providing a proximity correction pattern. The method includes generating a deformed pattern based on the proximity correction pattern. The method includes performing a first convolution process to the proximity correction pattern to generate a first proximity correction pattern contour. The method includes processing the first proximity correction pattern contour to generate a second proximity correction pattern contour. The method includes performing a second convolution process to the deformed pattern to generate a first deformed pattern contour. The method includes processing the first deformed pattern contour to generate a second deformed pattern contour. The method includes identifying mismatches between the second proximity correction pattern contour and the second deformed pattern contour. The method includes determining whether the deformed pattern is lithography-ready in response to the identifying.

Abstract: Methods and systems for lithographic simulation and verification comprising a process in the frequency domain or in the spatial domain of calculating intensity at a location (x, y) for a number of defocus values. In addition, evaluating the intensity calculation result to determine if the intensity level will result in the mask pattern being written onto a wafer. The verification process may be calculated in the spatial domain or in the frequency domain. The calculations may be done such that full focus window calculations may be obtained by isolating the defocus parameter “z” in the calculations.

Abstract: Semiconductor device identification using quantum dot technology. A semiconductor nanocrystal based target is fabricated. A guard ring superjacent the fluorescing surface of the nanocrystal surface is provided to ensure repeatability of spectral mapping and analysis data. A transparent cap on the target may enhance performance. A system for coding a semiconductor device is described. A method is described for fabricating quantum dot targets in a methodology compatible with subsequent semiconductor fabrication process steps.

Abstract: A method for patterning a workpiece in a direct write machine in the manufacturing of a multilayer stack, wherein a first circuit pattern comprising patterns for connection points is transformed according to determined fitting tolerances to fit to connection points of a second circuit pattern and to circuit pattern(s) of specific features such as random placed dies, or group of dies, on or in the workpiece. The second layer may be a previously formed layer or a layer to be formed on the same workpiece or on a different workpiece for the stack. Pattern data associated with selected die is transformed into adjusted circuit pattern data using the transformation defined by the transformed positions such that the circuit pattern is fitted to the selected die(s).

Abstract: A mask build system includes a program for configuring mask layers and a fabrication site for compiling configured mask layers. The system includes at least one database configured by a system processor, the database comprising drawn layers for fabricating reticles of a semiconductor device; and a marker layer configured to define layer dependent features, the marker layer handed off with that part of the at least one database which will support subsequent layers of the database without altering flow of mask build at the fabrication site.

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: Some embodiments include methods in which a mathematical representation of a photomask construction is defined, with such representation comprising a plurality of pillars that individually contain a plurality of distinct layers. Each of the layers has two or more characteristic parameters which are optimized through an optimization loop. Subsequently, specifications obtained from the optimization loop are utilized to form actual layers over an actual reticle base. Some embodiments include photomask constructions in which a radiation-patterning topography is across a reticle base, with such topography including multiple pillars that individually contain at least seven distinct layers.

Abstract: Some aspects of the present disclosure provide for a method of accurately simulating variations in an operating parameter, due to processing variations caused by a multi-patterning exposure, by reducing the impact of layout sections having a large width and spacing. The method assigns a skew sensitive index to one or more sections of a multi-patterning layer formed with a first mask. Runlengths of the one or more sections are respectively multiplied by an assigned skew sensitive index to determine a skew variation for each of the one or more sections. The overall skew variation sum is then determined by summing the skew variation for each of the one or more sections. By separately determining the effects of processing variations (e.g., mask misalignment) for different sections of a multi-patterning layer, an accurate measurement of operating parameter variations is achieved.

Abstract: This invention discloses a photomask manufacturing method. A pattern dimensional map is generated by preparing a photomask in which a mask pattern is formed on a transparent substrate, and measuring a mask in-plane distribution of the pattern dimensions. A transmittance correction coefficient map is generated by dividing a pattern formation region into a plurality of subregions, and determining a transmittance correction coefficient for each of the plurality of subregions. The transmittance correction value of each subregion is calculated on the basis of the pattern dimensional map and the transmittance correction coefficient map. The transmittance of the transparent substrate corresponding to each subregion is changed on the basis of the transmittance correction value.

Abstract: A system and method for providing a cell layout for multiple patterning technology is provided. An area to be patterned is divided into alternating sites corresponding to the various masks. During a layout process, sites located along a boundary of a cell are limited to having patterns in the mask associated with the boundary site. When placed, the individual cells are arranged such that the adjoining cells alternate the sites allocated to the various masks. In this manner, the designer knows when designing each individual cell that the mask pattern for one cell will be too close to the mask pattern for an adjoining cell.

Abstract: A method for decomposing design shapes in a design level into a plurality of target design levels is provided. Design shapes including first-type edges and second-type edges having different directions is provided for a design level. Inner vertices are identified and paired up. Vertices are classified into first-type vertices and second-type vertices. First mask level shapes are generated so as to touch the first-type vertices, and second mask level shapes are generated so as to tough the second-type vertices. Cut mask level shapes are generated to touch each first-type edges that are not over a second-type edge and to touch each second-type edges that are not over a first-type edge. Suitable edges are sized outward to ensure overlap among the various shapes. The design shapes are thus decomposed into first mask level shapes, the second mask level shapes, and the cut mask level shapes.

Abstract: A method for designing a mask set including at least one mask includes the implementation of at least one design rule from a set of design rules. The design rules include rules relating to allowable spacing between adjacent features, overlap of features defined by different masks in the mask set, and other characteristics of the mask set.

Abstract: A method and system for measuring layer overlay and for inspecting a mask for defects unrelated to overlay utilizing a singe comprehensive tool is disclosed. An exemplary method includes receiving a mask design database that corresponds to a mask and has a die area with a mask database feature. A mask image of the mask is received, and a comprehensive inspection system compares the mask image to the mask design database in order to detect mask defects that are not related to layer alignment. The system produces mask defect information corresponding to the mask defects. The comprehensive inspection system also compares the mask image to the mask design database to determine a database-to-mask offset. From the database-to-mask offset, a mask overlay characteristic is determined.

Abstract: A pattern inspection apparatus can be provided, for example, in a scanning electron microscope system. When patterns of a plurality of layers are included in a SEM image, the apparatus separates the patterns according to each layer by using design data of the plurality of layers corresponding to the patterns. Consequently, the apparatus can realize inspection with use of only the pattern of a target layer to be inspected, pattern inspection differently for different layers, or detection of a positional offset between the layers.

Abstract: A method for compensating an effect of a patterning process is illustrated. The main concept of the method for compensating the effect of the patterning process is to add or subtract the correction amounts for all segments according to the set of the comparison values at the set of the evaluation points. Compared with the delta-chrome optical proximity correction method, the run time of the method for compensating the effect of the patterning process is reduced, the memory usage of the method for compensating the effect of the patterning process not increased, and the correction accuracy of the method for compensating the effect of the patterning process is not reduced.

Abstract: Integrated circuit (IC) methods for optical proximity correction (OPC) modeling and mask repair are described. The methods include use of an optical model that generates a simulated aerial image from an actual aerial image obtained in an optical microscope system. In the OPC modeling methods, OPC according to stage modeling is simulated, and OPC features may be added to a design layout according to the simulating OPC. In the mask repair methods, inverse image rendering is performed on the actual aerial image and diffraction image by applying an optical model that divides an incoherent exposure source into a plurality of coherent sources.

Abstract: A method for predicting pattern critical dimensions in a lithographic exposure process includes defining relationships between critical dimension, defocus, and dose. The method also includes performing at least one exposure run in creating a pattern on a wafer. The method also includes creating a dose map. The method also includes creating a defocus map. The method also includes predicting pattern critical dimensions based on the relationships, the dose map, and the defocus map.

Abstract: The present invention provides a method for compensating infidelities of a process that transfers a pattern to a layer of an integrated circuit, by minimizing, with respect to a photomask pattern, a cost function that quantifies the deviation between designed and simulated values of circuit parameters of the pattern formed on a semiconductor wafer.

Abstract: A method of performing a resolution enhancement technique such as OPC on an initial layout description involves fragmenting a polygon that represents a feature to be created into a number of edge fragments. One or more of the edge fragments is assigned an initial simulation site at which the image intensity is calculated. Upon calculation of the image intensity, the position and/or number of initial simulation sites is varied. New calculations are made of the image intensity with the revised placement or number of simulation sites in order to calculate an OPC correction for the edge fragment. In other embodiments, fragmentation of a polygon is adjusted based on the image intensities calculated at the simulation sites. In one embodiment, the image intensity gradient vector calculated at the initial simulation sites is used to adjust the simulation sites and/or fragmentation of the polygon.

Abstract: In a first process, a process A, an actually measured transfer position measured by a measurement/inspection instrument is indicated by a black circle. A targeted transfer position indicated by x in a process B is located at the same position as the black circle. Assuming that the weights in the subsequent processes are the same, a targeted transfer position Xtarget indicated by x in processes C, D and E is located at a moderate position with which the total deviation from an actual transfer position (black circle) measured by the measurement/inspection instrument in a process preceding the current process is minimized, that is, at a proper position with respect to a plurality of other processes. Accordingly, the productivity of devices can be improved.

Abstract: A method for defining a full phase layout for defining a layer of material in an integrated circuit is described. The method can be used to define, arrange, and refine phase shifters to substantially define the layer using phase shifting. Through the process, computer readable definitions of an alternating aperture, dark field phase shift mask and of a complimentary mask are generated. Masks can be made from the definitions and then used to fabricate a layer of material in an integrated circuit. The separations between phase shifters, or cuts, are designed for easy mask manufacturability while also maximizing the amount of each feature defined by the phase shifting mask. Cost functions are used to describe the relative quality of phase assignments and to select higher quality phase assignments and reduce phase conflicts.

Abstract: A multivariable solver for proximity correction uses a Jacobian matrix to approximate effects of perturbations of segment locations in successive iterations of a design loop. The problem is formulated as a constrained minimization problem with box, linear equality, and linear inequality constraints. To improve computational efficiency, non-local interactions are ignored, which results in a sparse Jacobian matrix.

Abstract: Methods for fabricating semiconductor devices are provided. In an embodiment, a method of fabricating a semiconductor device includes scanning a circuit design layout and proposing patterns for decomposed layouts. The proposed patterns are then compared with a library of prior patterns including a category of forbidden patterns and a category of preferred patterns. If a selected proposed pattern matches a forbidden pattern, the selected proposed pattern is eliminated. If the selected proposed pattern matches a preferred pattern, then the selected proposed pattern is identified for use in the decomposed layouts. Decomposed layouts are generated from the identified patterns. A plurality of masks is fabricated based on the decomposed layouts. Then a multiple patterning lithographic technique is performed with the plurality of masks on a semiconductor substrate.