System and method for critical parameter identification, process model calibration and variability analysis

Abstract

The present invention relates to a system and method for critical parameter identification, process model calibration and variability analysis. A virtual manufacturing environment for semiconductor device manufacturing is discussed, which includes an analysis module for performing critical parameter identification, process model calibration and variability analysis.

Description

[0001] Related patent applications

[0002] This application claims priority to and the benefit of U.S. Provisional Patent Application No. 62 / 521,506, filed on June 18, 2017, and entitled “System and Method for Analyzing Process Variations in a Virtual Manufacturing Environment for Improving Process Integration,” and U.S. Provisional Patent Application No. 62 / 631,022, filed on February 15, 2018, and entitled “System and Method for Process Model Calibration in a Virtual Manufacturing Environment,” the contents of both applications being incorporated herein by reference in their entirety. Technical Field

[0003] The present invention relates generally to semiconductor manufacturing and, more particularly, to systems and methods for critical parameter identification, process model calibration, and variability analysis in a virtual semiconductor device manufacturing environment. Background Art

[0004] Integrated circuits (ICs) implement a large number of functions in modern electronic devices. In order to make the development of ICs more efficient, semiconductor manufacturers will periodically develop common manufacturing processes or "techniques" to be used in the production of its integrated circuits (for ease of explanation, the term "technology" can be used herein to refer to the manufacturing process of the semiconductor device structure under development).

[0005] Semiconductor R&D organizations at integrated device manufacturers (IDMs) and independent foundries expend significant resources developing the sequence of integrated process operations used to manufacture chips ((ICs)) that are sold in wafer form (a "wafer" is a thin slice of semiconductor material, usually but not always composed of silicon crystals). Most of these resources are used to manufacture experimental wafers and associated measurement, metrology ("metrology" refers to specialized types of measurements performed in the semiconductor industry), and characterization structures, all to ensure that the integrated process produces the desired semiconductor device structure. These experimental wafers are used in a trial-and-error scheme to develop the individual processes used to manufacture the device structures, and also to develop the overall, integrated process flow. Due to the increased complexity of process flows at advanced technology nodes, the majority of experimental manufacturing runs result in negative or zero characterization results. These experimental runs are long in duration, ranging from weeks to months in a "fab" (manufacturing environment), and are expensive. Recent semiconductor technology advances, including FinFET, TriGate, High-K / Metal Gate, Embedded Memory, and Advanced Patterning, have greatly increased the complexity of integrated semiconductor manufacturing processes. The cost and duration of technology development using this trial-and-error experimental approach are increasing simultaneously.

[0006] Attempts have been made to model semiconductor device structures using both conventional mechanical computer-aided design (CAD) tools and specialized technology CAD (TCAD) tools, with the goal of reducing the effort expended in fabricating experimental wafers. General-purpose mechanical CAD tools have been found to be inadequate because they do not automatically simulate the material addition, removal, and modification processes that occur in an actual manufacturing environment. On the other hand, TCAD tools are physics-based modeling platforms that can simulate material composition changes that occur during diffusion and implantation processes, but cannot simulate all material addition and removal effects that occur during other processes including the integration process flow. Typically, 3D device structures are inputs to TCAD, not outputs. Furthermore, due to the large amount of data and computational effort required for the physics-based simulation process, TCAD simulations are practically limited to very small areas on the chip, typically containing only a single transistor. In state-of-the-art semiconductor manufacturing technology, most integration challenges involve the interaction between processes that may be widely separated in the integration process flow and multiple different devices and circuits (transistors, resistors, capacitors, memories, etc.) that comprise a complete technology suite. Structural failures caused by systematic and random effects are often the limiting factor in time to market for new process technology nodes. Therefore, a modeling platform and approach different from mechanical CAD or TCAD is needed to cover a larger scope of concern and model the entire integrated process flow in a structural predictive manner.

[0007] A virtual manufacturing environment for semiconductor device structures provides a platform that performs semiconductor process development at a lower cost and higher speed than what can be achieved with conventional trial-and-error physical experiments. Compared to conventional CAD and TCAD environments, virtual manufacturing environments are capable of virtual modeling of integrated process flows and predicting the complete 3D structure of all devices and circuits including the entire technology suite. Virtual manufacturing can be described in its simplest form as combining a description of an integrated process sequence with a subject design in the form of 2D design data (masks or layouts) and producing a three-dimensional structural model that predicts the expected results of a real / physical manufacturing run. The 3D structural model includes geometrically accurate 3D shapes of multiple layers of materials, implants, diffusions, etc., which include a chip or a portion of a chip. Virtual manufacturing is primarily done in geometric form, but the geometry involved is guided by the physics of the manufacturing process. By modeling at an abstract structural level (rather than based on physics simulation), the construction of structural models can be significantly accelerated, thereby enabling full technology modeling within the area range of the circuit level. Therefore, the use of a virtual manufacturing environment provides rapid verification of process assumptions and visualization of complex interrelationships between integrated process sequences and 2D design data. Summary of the invention

[0008] Embodiments of the present invention provide a virtual manufacturing environment for semiconductor device manufacturing, which includes an analysis module for identifying key parameters and for performing process model calibration and variability analysis. More specifically, for key parameter identification, the analysis module identifies the process steps and / or parameters that have the greatest impact on the results of the manufacturing process. In process model calibration, the analysis module adjusts the process parameters to match the 3D model generated in the virtual manufacturing environment with the measurement from the physical fab (such as transmission electron microscope (TEM) data or process targets). For variability analysis, the analysis module helps the user analyze and understand the variability of the metrology data obtained from a set of virtual 3D models generated in the virtual manufacturing environment.

[0009] In one embodiment, a non-transitory computer-readable medium contains computer-executable instructions for critical parameter identification in a virtual semiconductor manufacturing environment. The instructions, when executed, cause at least one computing device to receive 2D design data and a selection of a process sequence including multiple processes for a semiconductor device structure to be virtually manufactured in a virtual manufacturing environment generated by the computing device. The instructions, when executed, use the computing device to perform a virtual manufacturing run for the semiconductor device structure based on a design of experiments (DOE) using the 2D design data and the process sequence. Multiple virtual manufacturing runs build multiple 3D models. The instructions, when executed, also cause at least one computing device to receive a user identification of one or more targets for the semiconductor device structure, and execute an analysis module in the virtual manufacturing environment to identify one or more outliers in the measurement data of one or more targets in the 3D model generated by the virtual manufacturing run. The instructions, when executed, receive a user selection for one or more targets in the 3D model to add or remove one or more of the one or more identified outliers from the measurement data, and receive the selection via a user interface provided in the virtual manufacturing environment. The instructions, when executed, further perform regression analysis on the measurement data of the one or more targets using the analysis module after adding or removing the selected outliers from the measurement data, and based on the results of the regression analysis, identify one or more key parameters using the analysis module. The identification of the identified one or more key parameters is displayed or exported.

[0010] In another embodiment, a method for critical parameter identification in a virtual semiconductor manufacturing environment includes: for a semiconductor device structure to be virtually manufactured in a virtual manufacturing environment generated by a computing device, receiving 2D design data and a selection of a process sequence including a plurality of processes; the method further performs a virtual manufacturing run for the semiconductor device structure using the computing device based on a design of experiments (DOE) using the 2D design data and the process sequence. The virtual manufacturing run builds a plurality of 3D models. The method additionally receives a user identification of one or more targets of the semiconductor device structure, and executes an analysis module in the virtual manufacturing environment to identify one or more outliers in the measurement data of the one or more targets in the 3D model generated from the virtual manufacturing run. The method also receives a user selection to add or remove one or more of the one or more identified outliers from the measurement data of the one or more targets in the 3D model. The selection is received by a user interface provided in the virtual manufacturing environment. In addition, the method performs a regression analysis on the measurement data of the one or more targets using the analysis module after adding or removing the selected outliers from the measurement data, and identifies one or more critical parameters using the analysis module based on the results of the regression analysis. The identification of the identified one or more critical parameters is displayed or exported.

[0011] In one embodiment, a virtual manufacturing system includes a computing device equipped with a processor and configured to generate a virtual manufacturing environment including an analysis module. For a semiconductor device structure to be virtually manufactured, the virtual manufacturing environment receives a selection of 2D design data and a process sequence, the process sequence including a plurality of processes and performs a virtual manufacturing run for the semiconductor device structure based on a design of experiments (DOE) using the 2D design data and the process sequence. The virtual manufacturing run establishes a plurality of 3D models. The virtual manufacturing environment receives a user identification of one or more targets of the semiconductor device structure, executes an analysis module in the virtual manufacturing environment to identify one or more outliers in the measurement data of one or more targets in the 3D model generated by the virtual manufacturing run, and receives a user selection for one or more targets in the 3D model to add or remove one or more of the one or more identified outliers from the measurement data, and receives the selection via a user interface provided in the virtual manufacturing environment. After adding or removing the selected outliers from the measurement data, the virtual manufacturing environment performs a regression analysis on the measurement data of the one or more targets using the analysis module, and based on the results of the regression analysis, identifies one or more key parameters using the analysis module, and displays or derives the identification of the identified one or more key parameters. The virtual manufacturing system further includes a display surface in communication with the computing device. The display surface is configured to display the 3D structural model in a 3D view. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate one or more embodiments of the present invention and, together with the description, help explain the present invention. In the drawings:

[0013] Figure 1 An exemplary virtual manufacturing environment suitable for implementing embodiments of the present invention is depicted;

[0014] Figure 2 depicts an exemplary virtual manufacturing console in a virtual manufacturing environment;

[0015] Figure 3 depicts an exemplary layout editor in a virtual manufacturing environment;

[0016] Figure 4 depicts an exemplary process editor in a virtual manufacturing environment;

[0017] Figure 5 depicts an exemplary sequence of steps in a virtual manufacturing environment for generating virtual metrology measurement data;

[0018] Figure 6 An exemplary 3D viewer in a virtual manufacturing environment is depicted;

[0019] Figure 7 depicts an exemplary display of virtual metrology measurement data in a virtual manufacturing environment;

[0020] Figure 8 depicts an exemplary sequence of steps for calibrating a process sequence in a virtual manufacturing environment;

[0021] Fig. 9 An exemplary sequence of steps for setting up and executing a virtual experiment in a virtual manufacturing environment that generates virtual metrology measurement data for a plurality of semiconductor device structure models is depicted;

[0022] Fig.10 depicts an exemplary parameter browser view for providing process parameters for a virtual experiment in a virtual manufacturing environment;

[0023] Fig.11 depicts an exemplary tabular format display of virtual metrology data generated by a virtual experiment in a virtual manufacturing environment;

[0024] Fig.12 depicts an exemplary graphical display of virtual metrology data generated in a virtual experiment in a virtual manufacturing environment;

[0025] Fig.13 depicts an exemplary analysis flow in an exemplary embodiment;

[0026] Figures 14A-14Gdepicts an exemplary user interface provided by a virtual manufacturing environment when identifying key parameters in an exemplary embodiment;

[0027] Fig.15 depicts a series of steps performed in an exemplary embodiment to identify key parameters;

[0028] Fig.16 depicts a series of steps performed for process model calibration in an exemplary embodiment;

[0029] Fig.17 depicts target selection and desired value input options provided by a process model calibration UI in an exemplary embodiment;

[0030] Fig.18 depicts calibration options provided by a process model calibration UI in an exemplary embodiment;

[0031] Fig.19 depicts parameter range entry options provided by a process model calibration UI in an exemplary embodiment;

[0032] Fig. 20 depicts an exemplary display of results provided by a process model calibration UI in an exemplary embodiment;

[0033] Fig.21 depicts a series of steps for performing variability analysis in an exemplary embodiment;

[0034] Fig. 22 depicts an exemplary user interface displaying a variable analysis results window in an exemplary embodiment; and

[0035] Fig.23 An exemplary graphical user interface for displaying a comparison of variability analysis results for four separate targets in an exemplary embodiment is depicted. DETAILED DESCRIPTION

[0036] Embodiments of the present invention provide a virtual manufacturing environment for semiconductor device manufacturing, which includes an analysis module for identifying key parameters and for performing process model calibration and variability analysis. However, before discussing key parameter identification, process model calibration, optimization, variability analysis and other features provided by the embodiments, an exemplary 3D design environment / virtual manufacturing environment in which the analysis module of the present invention can be integrated is first described.

[0037] Exemplary Virtual Manufacturing Environment

[0038] Figure 1An exemplary virtual manufacturing environment 1 suitable for implementing an embodiment of the present invention is depicted. The virtual manufacturing environment 1 includes a computing device 10 accessed by a user 2. The computing device 10 communicates with a display 120. The display 120 may be a display screen that is part of the computing device 10, or may be a separate display device or display surface that communicates with the computing device 10. The computing device 10 may be a PC, a laptop, a tablet computing device, a server, or some other type of computing device equipped with one or more processors 11 and capable of supporting the operation of a virtual manufacturing application 70, a 3D modeling engine 75, and an analysis module 79 (described further below). The processor may have one or more cores. The computing device 10 may also include volatile and non-volatile memory, such as, but not limited to, a random access memory (RAM) 12, a read-only memory (ROM) 13, and a hard drive 14. The computing device 10 may also be equipped with a network interface 15 to enable communication with other computing devices. It should be understood that the computing device 10, rather than an isolated computing device, may also be implemented as a computing system with multiple computing devices or other combinations working in parallel.

[0039] The computing device 10 may store and execute a virtual manufacturing application 70 including a 3D modeling engine 75. The 3D modeling engine 75 may include one or more algorithms for virtually manufacturing semiconductor device structures, such as Algorithm 1 (76), Algorithm 2 (77), and Algorithm 3 (78). The 3D modeling engine 75 may accept input data 20 in order to perform a virtual manufacturing "run" that produces semiconductor device structure model data 90. The virtual manufacturing application 70 and the 3D modeling engine 75 may generate multiple user interfaces and views for creating and displaying the results of the virtual manufacturing run. For example, the virtual manufacturing application 70 and the 3D modeling engine 75 may display a layout editor 121, a process editor 122, and a virtual manufacturing console 123 for creating a virtual manufacturing run. The virtual manufacturing application 70 and the 3D modeling engine 75 may also display a tabular and graphical metrology result view 124 and a 3D view 125 for displaying the results of the virtual manufacturing run and the 3D structure model generated by the 3D modeling engine 75 during the virtual manufacturing of the semiconductor device structure, respectively. The virtual manufacturing application 70 may also include an analysis module 79 for performing analysis of the 3D model, as discussed further below.

[0040] The input data 20 includes 2D design data 30 and a process sequence 40. The process sequence 40 may consist of a plurality of process steps 43, 44, 47, 48, and 49. As further described herein, the process sequence 40 may also include one or more virtual metrology measurement process steps 45. The process sequence 40 may further include one or more sub-sequences including one or more process steps or virtual metrology measurement process steps. The 2D design data 30 includes one or more layers, such as layer 1 (32), layer 2 (34), and layer 3 (36), typically provided in an industry standard layout format such as GDS II (Graphic Design System Version 2) or OASIS (Open Artwork System Interchange Standard).

[0041] The input data 20 may also include a material database 60 that includes records of material types such as material type 1 (62) and material type 2 (64) and specific materials for each material type. Many process steps in a process sequence may refer to one or more materials in the material database. Each material has a name and some properties, such as a rendering color. The material database may be stored in a separate data structure. The material database may have a hierarchy in which materials may be grouped by type and subtype. Individual steps in a process sequence may involve individual materials or parent material types. The hierarchy in the material database allows for easier modification of process sequences that reference the material database. For example, in virtual manufacturing of semiconductor device structures, multiple types of oxide materials may be added to a structure model during a process sequence. After a particular oxide is added, subsequent steps may change that material. If there is no hierarchy in the material database and a step to add a new oxide material is inserted into an existing process sequence, all subsequent steps that may affect the oxide material must also be modified to include the new oxide material. For a material database that supports hierarchy, steps that operate on a particular class of materials (such as oxides) may only involve parent types, rather than a list of materials of the same type. Then, if a step is inserted into the process sequence that adds a new oxide material, subsequent steps involving only the oxide parent type do not need to be modified. Thus, graded materials make the process sequence more resilient to modifications. A further benefit of graded materials is that stock process steps and sequences involving only parent material types can be created and reused.

[0042] The 3D modeling engine 75 uses the input data 20 to perform the sequence of operations / steps specified by the process sequence 40. As further explained below, the process sequence 40 may include one or more virtual metrology steps 45, 49, which indicate points in the process sequence during the virtual manufacturing run at which material measurements should be made on the structural component. The measurements may be made using locator shapes of layers previously added to the 2D design data 30. Alternatively, the measurement locations may be specified by alternative means, such as (x, y) coordinates in the 2D design data, or some other means of specifying locations in the 2D design data 30, rather than by using locator shapes. Execution of the process sequence 40 during the virtual manufacturing run produces virtual metrology data 80 and 3D structural model data 90. The 3D structural model data 90 may be used to generate a 3D view of a structural model of a semiconductor device structure that may be displayed in a 3D viewer 125. The virtual metrology data 80 may be processed and presented to the user 2 in a tabular and graphical metrology results view 124.

[0043] Because a large number of structural dimensions are critical to the success of integrated technologies such as semiconductor devices, it is critical to find the relationship between the many interrelated process steps used to manufacture the device structure and the created structure. Because the structural modification produced by a step in the process sequence can be affected by the previous and subsequent steps in the sequence, a specific step may affect the structural dimensions in a non-obvious way. The virtual manufacturing environment enables the automatic extraction of structural measurements from the device being created. The automatic extraction of measurements is accomplished by specifying a virtual metrology measurement step in the process sequence at a point in the process when the measurement is critical. The locator shape of this virtual metrology measurement can be added to a layer in the design data and specified by the virtual metrology measurement step. The output data from this virtual metrology measurement can be used to provide quantitative comparisons with other modeling results or physical metrology measurements. This virtual metrology measurement capability is provided during the process sequence to extract critical physical dimensions at the correct point in the integration process flow.

[0044] The ability to provide virtual metrology measurement data at specified locations in a device structure provides a significant improvement over conventional physical manufacturing measurement techniques. Typically, physical in-fab measurements are completed on specific characterization structures that are manufactured at the cut line or cut kerf adjacent to the product wafer. In most cases, these characterization structures need to be designed to accommodate limitations on the measurement technology, such as spot size. Therefore, the characterization structure does not fully represent the actual structure on the product wafer. Due to these differences, users of in-fab measurements are often faced with the challenge of inferring the results of the product structure from measurements on the characterization structure. In a virtual manufacturing environment, measurement results can be added to any design layout at specified points in the process sequence, providing a deeper understanding of the impact of interrelated process steps on the virtual structure model being built. Therefore, the in-fab challenges of measuring characterization structures and inferring product structure results are eliminated.

[0045] Figure 2 An exemplary virtual manufacturing console 123 for establishing a virtual manufacturing run in a virtual manufacturing environment is depicted. The virtual manufacturing console 123 allows a user to specify a process sequence 202 and a layout (2D design data) 204 of a semiconductor device structure being virtually manufactured. However, it should be understood that the virtual manufacturing console can also be a text-based scripting console that provides a means for a user to enter script commands or establish a set of structural models corresponding to parameter value ranges for specific steps in the process sequence, which script commands specify the required inputs and initiate the construction of the structural models. The latter case is considered a virtual experiment (discussed further below).

[0046] Figure 3 An exemplary layout editor in a virtual manufacturing environment is depicted. The layout editor 121 displays a 2D design layout specified by a user in a virtual manufacturing console 123. In the layout editor, colors can be used to depict different layers in the design data. The areas surrounded by shapes or polygons on each layer represent areas where the photoresist coating on the wafer can be exposed to light or protected from exposure during the photolithography step in the integrated process flow. Shapes on one or more layers can be combined (perform Boolean operations) to form a mask used in the photolithography step. The layout editor 121 provides a means for inserting, deleting and modifying polygons on any layer and inserting, deleting or modifying layers within the 2D design data. Layers can be inserted only for containing shapes or polygons indicating the location of virtual metrology measurements. Rectangular shapes 302, 304, 306 have been added to the inserted layer (indicated by different colors) and mark the location of the virtual metrology measurement. As described above, other methods of specifying the location of virtual metrology measurements other than using locator shapes can also be used in the virtual manufacturing environment. The design data is used in conjunction with the process data and material database to build a 3D structure model.

[0047] The layer inserted in the design data displayed in the layout editor 121 may include an inserted locator shape. For example, the locator shape may be a rectangle whose long side indicates the measurement direction in the 3D structure model. Figure 3 , a first locator shape 302 may mark a double patterning mandrel for virtual metrology measurement, a second locator shape 304 may mark a gate stack for virtual metrology measurement, and a third locator shape 306 may mark a transistor source or drain contact for virtual metrology measurement.

[0048] Figure 4 An exemplary process editor 122 in a virtual manufacturing environment is depicted. A user defines a process sequence in the process editor. A process sequence is an ordered list of process steps to be performed in order to virtually manufacture a structure selected by the user. The process editor may be a text editor such that each line or group of lines corresponds to a process step, or may be a text editor such as Figure 4 A dedicated graphical user interface is shown. Process sequences can be hierarchical, meaning that process steps can be grouped into subsequences and subsequences of subsequences, and so on. Typically, each step in a process sequence corresponds to an actual step in manufacturing. For example, a subsequence for a reactive ion etching operation may include steps for spinning on photoresist, patterning photoresist, and performing an etching operation. The user specifies parameters for each step or substep that is appropriate for the type of operation. Some parameters reference materials in a material database and layers in 2D design data. For example, the parameters of a deposition operation primitive are the material to be deposited, the nominal thickness of the deposit, and the anisotropy or growth ratio in the lateral direction to the vertical direction. This deposition operation primitive can be used to model actual processes such as chemical vapor deposition (CVD). Similarly, the parameters of an etching operation primitive are the mask name (from the design data), a list of materials affected by the operation, and the anisotropy.

[0049] There may be hundreds of steps in a process sequence, and a process sequence can contain subsequences. Figure 4 As shown, the process sequence 410 may include a subsequence 412 consisting of multiple process steps such as a selected step 413. The process step may be selected from a library of available process steps 402. For the selected step 413, the process editor 122 enables the user to specify all required parameters 420. For example, the user may be able to select a material from a list of materials in the material database 404 and specify process parameters 406 used by the material in the process step 413.

[0050] One or more steps in the process sequence may be user inserted virtual metrology steps. For example, inserting step 4.17 "Measure CD" (414), where CD represents a critical dimension, in process sequence 412 will result in a virtual metrology measurement being made at that point in the virtual manufacturing run using one or more locator shapes that have previously been inserted onto one or more layers of the 2D design data. Inserting virtual metrology steps directly into the manufacturing sequence allows virtual metrology measurements to be made at critical points of interest during the manufacturing process. Because many steps in virtual manufacturing interact in the creation of the final structure, the ability to determine geometric properties of a structure, such as cross-sectional dimensions and surface area at different points in an integrated process flow, is of interest to both process developers and structural designers.

[0051] Figure 5 An exemplary sequence of steps in a virtual manufacturing environment for generating virtual metrology measurement data is depicted. The sequence begins with a user selecting a semiconductor device structure to be manufactured (step 502). The user can select from multiple sets of available design data files and then select a rectangular area in the design data. For example, the user can select a FinFET or a passive resistor or a memory cell. After determining / selecting the structure to be manufactured, the user enters a process sequence in the process editor 122 (step 504a) and selects the 2D design data expected to produce the desired structure (step 504b). Optionally, the user can create or modify the design data in the layout editor 121. In the process editor, the user can insert one or more virtual metrology steps in the process sequence, which specify the points at which the user wishes to perform virtual metrology measurements at specified locations in the evolving structure during virtual manufacturing (step 506a). The user can insert a locator shape in the 2D design data displayed in the layout editor 121, which will be used by the virtual measurement step to perform its measurement (step 506b). The importance of the locator shape depends on the type of measurement required. For example, the major axis of the rectangle may indicate the direction and extent of a length measurement to be made on a cross section of the structure, or the rectangle itself may specify the area of ​​a contact region between two materials to be measured. It should be appreciated that the above steps in the process editor may be performed before the steps in the layout editor, or vice versa in a virtual manufacturing environment.

[0052] After one or more locator shapes have been added to one or more layers in the 2D design data (step 506b) and a virtual metrology step has been added to the process sequence (506a), the user uses the virtual manufacturing console 123 to establish a virtual manufacturing run (step (508)). During the virtual manufacturing run, the process steps in the process sequence 40 are executed in the order specified by the 3D modeling engine 75. When the virtual manufacturing reaches the virtual measurement step, a virtual "measurement" of the specified component in the structure being manufactured is performed. The calculations performed by the modeling engine depend on the nature of the measurement required and are generally consistent with similar physical measurement techniques in manufacturing. For example, critical dimension scanning electron microscope (CD-SEM) measurements in manufacturing locate sidewalls by detecting rapid changes in the orientation of the top surface of the structure. Similarly, in a virtual metrology operation, the 3D modeling engine extracts the top surface of the structure in the area specified by the locator rectangle, interrogating the surface along its intersection with the plane defined by the intersection of the horizontal and vertical axes of the rectangle to obtain slope changes that exceed a threshold value (e.g., 5 degrees). Large changes in slope define the faces of a feature, such as the bottom, top, and sides of a ridge in a structure. After establishing the positions of the bottom, top, and sides of the feature, the distance between the sides of the feature is calculated at the vertical position (bottom, middle, or top) specified by the metrology step. The 3D modeling engine generates one or more types of outputs as it builds the structural model. One type of output is the structural model itself, and may include its state at one or more points in the process sequence. The 3D model may be displayed to the user in the 3D viewer 125 (step 512a). The 3D modeling engine also outputs virtual metrology data (step 510). The virtual metrology data 80 may be exported to an automatic data analysis tool for further processing, or may be displayed to the user through a user interface such as a table and graphical metrology result view 124 or other view (step 512b). If the structure when viewed or analyzed is satisfactory (step 513), the virtual manufacturing run ends (step 514). If the structure created by the 3D modeling engine is not satisfactory, the user modifies the process sequence and / or 2D design data (step 516), and establishes a new virtual manufacturing run (step 508).

[0053] Figure 6 An exemplary 3D viewer 125 in a virtual manufacturing environment is depicted. The 3D viewer 75 may include a 3D view canvas 602 for displaying a 3D model generated by the 3D modeling engine 75. The 3D viewer 75 may display saved states 604 in a process sequence and allow a particular state 606 to be selected and appear in the 3D view canvas. The 3D viewer provides functions such as zoom in / out, rotate, pan, section, etc. Optionally, the user may activate a cross-sectional view in the 3D view canvas 602 and manipulate the position of the cross section using a mini top view 608.

[0054] Another type of output from the 3D modeling engine 75 is data generated by virtual metrology steps included in the process sequence. Figure 7 Depicted is an exemplary display of virtual metrology measurement data 80 resulting from a plurality of virtual metrology measurement steps in a virtual manufacturing environment. The virtual metrology measurement result data 80 may be displayed in tabular or graphical form including 2D XY plots and multi-dimensional graphs.

[0055] The techniques employed in the exemplary virtual manufacturing environment are geometry-based. Therefore, it is recommended to utilize actual experimental results from physical manufacturing to calibrate process step input parameters to make virtual experiments more predictive. Such calibration of process steps can improve the modeling accuracy of all structures including the complete technology suite. Calibration can be performed on individual process steps of measurement, metrology or other physical characterization methods that characterize structures or product structures. Calibration can be performed by comparing the modeling results including virtual metrology measurement data with the corresponding measurements or metrology (on the corresponding characterization or product structure) performed in physical manufacturing, and then adjusting the modeling parameters so that the resulting virtually manufactured structure better matches the physically manufactured structure. By properly calibrating the modeling process parameters, the virtual manufacturing environment becomes better at predicting the structures produced by physical manufacturing throughout the entire allowed design space.

[0056] Figure 8An exemplary sequence of steps for calibrating a process sequence in a virtual manufacturing environment is depicted. The sequence includes steps taken in a virtual manufacturing environment and a corresponding physical manufacturing environment. In the virtual manufacturing environment, a user selects a process sequence to be calibrated (for a structure to be virtually manufactured) and identifies relevant process parameters (step 802a). In physical manufacturing, a user identifies a group of representations or product structures for measurement during a manufacturing run (step 802b). Back in the virtual manufacturing environment, the user enters the process sequence in a process editor (step 804a), and 2D design data (layout) defining the representation structure is selected from available 2D design data or created for this purpose in the layout editor 121 (step 804b). The same design data is used for virtual manufacturing and actual representation. As described above, the user inserts one or more virtual metrology steps in the process sequence (step 806a) and adds measurement locator shapes to the 2D design data (step 806b). The user establishes a virtual manufacturing run in the virtual manufacturing console (step 808), and the 3D modeling engine establishes a 3D model and generates and outputs virtual metrology data (step 812a). In parallel or offset with the virtual manufacturing run, the physical manufacturing environment creates representations or product structures (step 810), and in-manufacturing images and measurements are taken on these structures (step 812b). The user can then compare the 3D view of the virtual model generated in the 3D viewer 75 with the in-manufacturing images of the physical device structure (step 814a). In addition, the set of representation structure measurements can be compared with the virtual metrology measurements as a result of the virtual metrology step inserted into the process sequence (step 814b). In most cases, this comparison will be made by the user, but it can be compared by automated data analysis tools based on predefined or interactively requested criteria. If there is a satisfactory agreement between the views and images and the virtual and actual measurements (step 815), the process sequence is considered to be calibrated (step 816). However, if there is no satisfactory agreement (step 815), the user modifies the values ​​of the process parameters in the process editor (step 818) and establishes a new virtual manufacturing run in the virtual manufacturing console (step 808). The sequence then iterates until a satisfactory agreement is reached and calibration is achieved.

[0057] It should be understood that there may be a number of different parameters that may be calibrated within the sequence. Although the above description notes the use of virtual metrology measurements performed using virtual measurement steps inserted into a process sequence in conjunction with the use of one or more 2D locator shapes, other techniques may be employed in a virtual manufacturing environment. For example, virtual measurements may be performed on a virtual device structure after fabrication is complete and then compared to physical measurements performed on a characterization structure during / after a physical manufacturing run.

[0058] While building a single structural model may be valuable, there is greater value in virtual manufacturing where a large number of models are built. A virtual manufacturing environment can enable users to create and run virtual experiments. In a virtual experiment, a range of process parameter values ​​can be explored. A virtual experiment can be set up by specifying a set of parameter values ​​to be applied to a single process throughout the process sequence (rather than a single value for each parameter). A single process sequence or multiple process sequences can be specified in this way. The 3D modeling engine 75 executed in virtual experiment mode then builds multiple models across the process parameter set, always using the above-mentioned virtual metrology measurement operations to extract metrology measurement data for each change. This capability may be used to mimic two basic types of experiments typically performed in a physical manufacturing environment. First, manufacturing processes naturally vary in a random (non-deterministic) manner. As explained herein, the basic deterministic method used for each virtual manufacturing run can still predict non-deterministic results by performing multiple runs. The virtual experiment mode allows the virtual manufacturing environment to model the entire statistical variation range of each process parameter and the variation combination of many / all process parameters. Second, experiments run in physical manufacturing can specify a set of parameters that are intentionally varied when manufacturing different wafers. The virtual experimentation mode enables the virtual manufacturing environment to simulate this type of experimentation as well by performing multiple virtual manufacturing runs for specific variations of parameter sets.

[0059] Each process in a manufacturing sequence has its own inherent variation. It is very difficult to understand the impact of all aggregated process variations in a complex process, especially when considering the statistical probability of the combination of variations. Once a virtual experiment is created, the process sequence is essentially described by a combination of digital process parameters contained in the process description. Each of these parameters can be characterized by its total variation (expressed as a standard deviation or σ value) and therefore by multiple points on a Gaussian distribution or other appropriate probability distribution. If a virtual experiment is designed and executed to examine all combinations of process variations (multiple points on each Gaussian curve, such as ±3σ, ±2σ, ±1σ and the nominal value of each parameter), then the graphical and numerical outputs generated from the virtual measurement steps in the sequence cover the total variation space of the technology. Although each case in this experimental study is deterministically modeled by the virtual manufacturing system, the aggregation of virtual metrology results contains statistical distributions. A total variation metric can be attributed to each experimental case using simple statistical analysis, such as the root sum square (RSS) calculation of statistically uncorrelated parameters. All (numerical and graphical) virtual metrology outputs can then be analyzed relative to the total variation metric.

[0060] In typical trial-and-error experiments in physical manufacturing, structural measurements produced by a nominal process are targeted, and process variations are accounted for by specifying excessive (conservative) margins for the total variation of structural measurements that must be predicted in subsequent processes (total structural margin). In contrast, virtual experiments in a virtual manufacturing environment can provide quantitative predictions of the total variation envelope of structural measurements at any point in the integrated process flow. The total variation envelope of structural measurements, rather than the nominal values, can then become the development target. This approach can ensure acceptable overall structural margins throughout the integrated process flow without sacrificing critical structural design goals. An approach targeting total variation may result in nominal intermediate or final structures that are inferior (or less aesthetically pleasing) than the nominal structure produced by targeting the nominal process. However, this suboptimal nominal process is not critical because the envelope of total process variation has already been accounted for and is more important in determining the robustness and yield of the integrated process flow. This approach is a paradigm shift in semiconductor technology development from emphasizing the nominal process to emphasizing the envelope of total process variation.

[0061] Fig. 9 An exemplary sequence of steps in a virtual manufacturing environment for setting up and executing a virtual experiment that generates virtual metrology measurement data for multiple semiconductor device structure models is depicted. The sequence begins with a user selecting a process sequence (which may have been calibrated in advance to make the results more structurally predictive (step 902a) and identifying / creating 2D design data (step 902b)). The user may select process parameter changes to analyze (step 904a) and / or design parameter changes to analyze (step 904b). The user inserts one or more virtual metrology steps in the process sequence as described above (step 906a) and adds measurement locator shapes to the 2D design data (step 906b). The user may set up the virtual experiment with the aid of a dedicated user interface, the automatic parameter browser 126 (step 908). The exemplary automatic parameter browser in Fig.10 , and can display and allow the user to change the list of process parameters 1002, 1004, 1006 to be changed and the 3D model to be constructed using their corresponding different parameter values ​​1008. The parameter range of the virtual experiment can be specified in a table format. The 3D modeling engine 75 builds the 3D model and outputs the virtual metrology measurement data for viewing (step 910). The virtual experiment mode provides output data processing from all virtual measurement / metrology operations. The output data from the virtual metrology measurement can be parsed and assembled into a useful form (step 912).

[0062] Through this parsing and assembly, subsequent quantitative and statistical analysis can be performed. A separate output data collector module 110 can be used to collect 3D model data and virtual metrology measurement results from a virtual manufacturing run sequence including virtual experiments, and present them in graphical and tabular form. Fig.11 An exemplary tabular format display of virtual metrology data generated by a virtual experiment in a virtual manufacturing environment is depicted. In the tabular format display, a list of virtual metrology data collected during a virtual experiment 1102 and a virtual manufacturing run 1104 may be displayed.

[0063] Fig.12 Depicted is an exemplary 2D XY graphical plot display of virtual metrology data generated by a virtual experiment in a virtual manufacturing environment. Fig.10 In the example shown, the total variation of shallow trench isolation (STI) step height due to changing three parameters in the previous steps of the process sequence is shown. Each diamond 1202 represents a virtual manufacturing run. The variation envelope 1204 is also shown as is the conclusion 1206 depicted that the downstream processing modules must support a total variation of about 10.5nm in STI step height to achieve robustness with 6σ of the incoming variation. The virtual experiment results can also be displayed in a multi-dimensional graphical format.

[0064] Once the results of the virtual experiment are assembled, the user can view the 3D model that has been generated in the 3D viewer (step 914a) and view the virtual metrology measurement data and metrology presented for each virtual manufacturing run (step 914b). Depending on the purpose of the virtual experiment, the user can analyze the output from the 3D modeling engine to develop a process sequence that achieves a desired nominal structural model, for further calibration of process step input parameters, or for optimizing the process sequence to achieve a desired process window.

[0065] The task of building multiple structural models for a range of parameter values ​​(including virtual experiments) by the 3D modeling engine 75 is very computationally intensive, so if performed on a single computing device, it may take a long time (days or weeks). In order to provide the expected value of virtual manufacturing, model building for virtual experiments must be many times faster than physical experiments. Achieving this goal with modern computers requires taking advantage of any and all parallel opportunities. The 3D modeling engine 75 uses multiple cores and / or processors to perform the various modeling steps. In addition, structural models for different parameter values ​​in a group are completely independent, so they can be built in parallel using multiple cores, multiple processors, or multiple systems.

[0066] The 3D modeling engine 75 in the virtual manufacturing environment can represent the potential structural model in the form of voxels. Voxels are essentially 3D pixels. Each voxel is a cube of the same size and can contain one or more materials, or no materials. Those skilled in the art will recognize that the 3D modeling engine 75 can also represent the structural model in other formats. For example, the 3D modeling engine can use a conventional NURBS-based solid modeling kernel, such as used in 3D mechanical CAD tools, although the modeling operations based on digital voxel representation are more robust than the corresponding operations in the conventional analog solid modeling kernel. This solid modeling kernel usually relies on a large number of heuristic rules to handle various geometric situations, and when the heuristic rules cannot correctly predict the situation, the modeling operation will fail. Aspects of semiconductor structure modeling that cause problems for NURBS-based solid modeling kernels include very thin layers produced by deposition processes and the propagation of etching fronts that cause merged surfaces and / or geometric fragmentation.

[0067] The virtual manufacturing environment can achieve the performance of multiple etching processes including process sequences, which allows the 3D modeling engine 75 to model a wide range of process and material specific etching behaviors. Patterning operations in the process flow of highly scaled semiconductor devices are often performed using plasma etching. Plasma etching is known by many different names: dry etching, reactive ion etching (RIE), inductively coupled plasma (ICP) etching, etc. A wide variety of operating conditions and chemical properties allow process engineers to fine-tune plasma etching behavior to selectively achieve a variety of etching physical phenomena in a variety of different types of materials. This behavioral flexibility is critical to obtaining ideal 3D structures when patterning through multiple layers of materials. Several different types of physical phenomena are typically involved, including but not limited to: chemical etching, sputtering, deposition or re-deposition of polymer materials, electrostatic charging, electrostatic focusing, and shadowing. This diverse physical spectrum produces a considerable range of etching behaviors and, therefore, structural shapes.

[0068] Directly simulating the physics involved in plasma etching with sufficient accuracy is very difficult and slow. Multi-etch process steps avoid the difficulties of physics-based simulations by simulating plasma etching using a reduced set of behavioral parameters specific to the etch type and the material being etched. This allows a wide range of physical etching behaviors to be captured without directly simulating the physics of the etching process. For example, three main types of etching behavior can be simulated: isotropic, tapered, and sputtering. A fourth etch behavior can also be optionally simulated: shadowing.

[0069] The basic (isotropic) behavior is caused by chemical etching (physically) and causes material to be removed at a similar rate from all directions of a point on the etchable surface, regardless of the local orientation of the etchable surface. The basic behavior can be modeled with a single input parameter, "lateral ratio", which controls the ratio between the lateral and longitudinal etch rates. For example, a lateral ratio value of 1 (1.0) indicates that the etch rate is uniform in all directions. A lateral ratio value less than 1 indicates that the etch rate in the lateral direction (on a vertical surface) is slower than the etch rate in the vertical direction (on a horizontal surface).

[0070] The tapered behavior is caused (physically) by a combination of directional etching behavior and polymer deposition. Polymer deposition occurs as a side effect of the directional etching process. During directional etching processes where horizontal surfaces are etched much faster than vertical surfaces, polymer may accumulate on near-vertical surfaces. This competition between etching and deposition results in a tapered sidewall profile. The tapered behavior can be modeled with a single input parameter, the taper angle. The taper angle describes the critical angle at which the deposition and etching rates are balanced. The optional second parameter, the lateral ratio, has the same meaning as defined above in the basic behavior.

[0071] Sputtering behavior refers to the direct physical removal of material by energetic ion bombardment and results in preferential removal of protruding edges (convex edges) and, in some cases, corners. Sputtering can be modeled using two parameters: the maximum sputtering yield angle and the sputtering rate versus the vertical etch rate.

[0072] Shadowing is the reduction in directional ion flux caused by local elevation changes, effectively reducing the etch rate of certain structures. This effect can be significant in some cases, resulting in different etch rates throughout the cell. Shadowing can be modeled using a single parameter to describe the angle of incidence of the energetic ions relative to the vertical axis.

[0073] In order to model multi-material, multi-physics etching, the above input parameters must form a suitable numerical modeling algorithm in a virtual manufacturing environment. The numerical simulation algorithm includes single-material and multi-material velocity functions and surface evolution techniques. The single-material velocity function defines the etching rate as a function of the local surface orientation (i.e., the surface normal direction) and is determined empirically to produce the desired etching behavior. Note also that the single-material velocity function can combine multiple types of etching behavior; for example, both tapered and sputter etching include parameters related to basic (isotropic) etching. The multi-material velocity function is a combination of single-material velocity functions and calculates the local etching rate based on the local surface orientation and the local material type. The etching ratio parameter defines the relative etching rate of the etchable materials and is a multiplication factor of the single-material velocity.

[0074] With a velocity function defined, the position of a three-dimensional etchable surface can be located and evolved using a suitable surface evolution technique. The etchable surface is advected or moved in the direction of its local normal according to the local scalar velocity determined by evaluating the velocity function. The scalar velocity must be calculated at points of interest on the etchable surface and must be recalculated periodically as the geometry of the etchable surface evolves.

[0075] Many different types of surface evolution techniques can be used by numerical algorithms to simulate multiple etching processes in a virtual manufacturing environment. Any suitable numerical spatial discretization can be used to represent the moving surface. Explicit interface tracking methods can be used: examples include string methods, point-line methods (2D), and polygonal surfaces (3D). Alternative implicit surface representations can also be used, such as distance fields, fluids, or volumes of voxels. Any suitable time-dependent numerical technique can be used to advance the moving surface in time.

[0076] A selective epitaxy process can be included in a process sequence used to virtually manufacture a semiconductor device structure. The selective epitaxy process actually models the epitaxial growth of a crystalline material layer on top of a crystalline substrate surface of a semiconductor device structure. Selective epitaxy is widely used in contemporary semiconductor process flows, typically to apply mechanical stress on the transistor channel to improve performance. A key feature of epitaxial growth is its dependence on crystal orientation. Semiconductor devices are typically manufactured on single-crystal silicon wafers; that is, the atoms of the silicon material are arranged in a repeating lattice structure that is continuous across most of the wafer. The silicon crystal structure is anisotropic (that is, not symmetric in all directions), and the silicon surface is more stable in a few specific crystal orientations. These orientations are defined by a family of principal crystal planes, determined using their Miller indices as <100> , <110> and <111> , and has the strongest influence on the growth characteristics. By varying the pressure, temperature, and chemical precursors in the epitaxial process, engineers can control the relative growth rates of the three major crystal planes. Secondary crystal planes (e.g. <211> , <311> , <411> ) also varies, but often has no effect on determining the final shape of the epitaxially grown structure.

[0077] A virtual manufacturing environment can use a surface evolution algorithm to simulate epitaxial growth. The surface on which epitaxial growth occurs (the growth surface) is advected or moved according to a scalar advection velocity. The growth rate is calculated at selected points based on the local surface normal direction and fixed input parameters, the growth rate is local in both distance and time, and the surface is moved along the normal direction. Any suitable numerical spatial discretization can be used to represent the growth surface. Explicit interface tracking methods can be used: examples include string methods, point-line methods (2D), and polygonal surfaces (3D). Alternative implicit surface representations can also be used, such as distance functions, fluids, or volumes of voxels. Any suitable time-dependent numerical technique can be used to advance the growth surface in time.

[0078] The selective epitaxial process in a virtual manufacturing environment utilizes three major crystal plane families ( <100> , <110> and <111> ) as fixed input parameters. These input parameters define the growth rate of the surface aligned with any of their associated crystal planes. Further input parameters may include the growth rate of adjacent amorphous materials. When calculating the epitaxial growth rate, the relationship between the 3D modeling coordinate system and the lattice of the wafer may also be considered. The 3D modeling coordinate system typically uses the same X and Y axes as the 2D design data, while the Z axis is typically perpendicular to the wafer surface. Alternative coordinate systems may also be used. On an actual wafer, the orientation of the lattice is represented by a "flat" or "notch" on the edge of an otherwise circular wafer. The notch can be used as a reference to orient the 2D design data in the desired direction relative to the lattice. The input parameters specifying the notch (or plane) type and direction may define the lattice orientation and the associated crystal plane of the wafer relative to the 2D design data. It should be noted that this relationship can be described as a coordinate transformation between the 3D model coordinate system and the lattice coordinate system.

[0079] By using the growth rate of the family of principal crystal planes and knowing the orientation of the lattice, the epitaxial growth rate can be calculated anywhere on the growth surface. The region of the growth surface with a normal direction aligned with the principal crystal plane direction is assigned the speed of the principal crystal plane. For the growth surface region that is not aligned with the principal crystal plane direction, the appropriate speed must be found by interpolating between the adjacent principal crystal plane directions. In addition, the behavior of epitaxial growth at the boundary of the crystalline material will also be important. Epitaxial growth is usually carried out after several previous process steps in which amorphous materials have been deposited and patterned. These amorphous materials can be adjacent to crystalline materials and therefore closely adjacent to epitaxial growth. Examples of amorphous adjacent materials are silicon dioxide, silicon nitride, or any other material commonly seen in semiconductor processing. In some cases, epitaxial growth slowly spreads (overgrowth) along adjacent amorphous materials, but not in other cases. Overgrowth behavior can be modeled using fixed input parameters, which define the adjacent material group (overgrowth material) where overgrowth occurs and the speed at which the growth surface spreads along the overgrowth material. The overgrowth speed changes the epitaxial growth rate at the surface of the overgrowth material so that the growth surface moves at a specified speed along the overgrowth material. Furthermore, the speed at which the growth surface moves along the overgrowth material may depend on the angle between the overgrowth material surface and the growth surface. If the angle between the two surfaces is greater than a threshold angle, the overgrowth speed may be negligible.

[0080] Design rule checking (DRC) or optical rule checking (ORC) can be performed in a virtual manufacturing environment. Dedicated software typically performs DRC and ORC on 2D design data as part of the process of preparing 2D design data for conversion into lithography masks. These checks are performed to identify errors in the layout that may cause the chip to be non-functional or poorly functional. These checks are also performed after adding compensation for optical effects such as optical proximity correction (OPC). Typical design rules (as published in design manuals and encoded in DRC platforms) are simple 2D standards designed to prevent problems that are fundamentally 3D in nature. However, with the increasing complexity of semiconductor process technologies, design manuals have evolved into thousand-page documents with thousands of two-dimensional design rules to codify and interpret. In many cases, a single 3D failure mechanism / concern can drive hundreds of 2D design rules. The development of these 2D design rules requires making important assumptions about the 3D nature of the integrated process flow and the resulting structure.

[0081] 2D DRCs are developed from relatively simple calculations and can lead to overly conservative designs. For example, consider the 2D design rules required to ensure a minimum contact area between a line on a metal interconnect layer and an underlying via. A via is a vertical conductive connector between two interconnect layers (also called metal layers), or between an interconnect layer and a device such as a transistor, resistor, or capacitor.

[0082] Many additional 2D DRCs are required to meet a criterion that is very simple to state in 3D: the contact area between the metal line and the via must exceed a specified threshold. The 2D DRC situation becomes more complicated when considering the multiple manufacturing variations that affect the contact area, including over- or under-exposure during the photolithography step, misregistration of the mask, planarization of the via layer (by chemical mechanical polishing (CMP)), and sidewall tapering produced by plasma etching. It is not feasible to include all of these statistical variables in the simple formula that drives the 2D DRCs, so the DRCs are more stringent than necessary to prevent manufacturing variations. These overly stringent 2D DRCs can lead to suboptimal designs with wasted area on the chip.

[0083] Compared to a 2D DRC environment, a virtual manufacturing environment can perform checks such as minimum line width, minimum spacing between features, and minimum contact area directly in 3D without assuming a conversion from 2D to 3D. Checks performed directly in 3D are referred to herein as "3D DRC." ​​One benefit of 3D DRC is that the number of checks required is much smaller than that required in a 2D environment. Therefore, these checks are more robust and easier to carry out than 2D checks. In addition, with a smaller set of 3D rules, the virtual manufacturing environment can perform checks on a range of statistical variations in process parameters.

[0084] It should be appreciated that 3D-DRC is different from virtual measurement / metrology operations that can also be performed in a virtual manufacturing environment. Virtual measurement metrology operations mimic actual measurement and metrology operations in manufacturing, whereby measurement locations are specified and metrics such as distance values ​​or areas are output. On the other hand, for 3D DRC, geometric standards are specified and the locations and values ​​of the standards are required. That is, the location is the output rather than the input of the 3D DRC operation. For example, a virtual metrology operation may specify an oxide film thickness measurement at a specific location indicated by a locator in the 2D design data, while a 3D DRC for minimum layer thickness may request any location in the 3D model where the oxide film thickness is less than a specified threshold. The 3D structural model may then be searched for locations that meet a specific minimum size standard. Similarly, a 3D DRC may also cause the structural model to be searched to see if a maximum size standard is met. Such a 3D DRC therefore provides some advantages in identifying the causes of unexpected failures that cannot be achieved with virtual measurement / metrology operations.

[0085] Examples of 3D-DRC include:

[0086] Grid Isolation: Find the shortest distance between selected conductors. Conductors are masses that can be composed of one or more conductive materials (a "mass" is a discrete volumetric region within a 3D structural model (technically a 3-manifold). A mass can be composed of a single material or multiple materials);

[0087] Minimum separation: find the shortest distance between any pair in a set of selected clusters;

[0088] Minimum line width: find the shortest distance through any blob in a set of selected blobs;

[0089] Minimum layer thickness: find the shortest distance through any blob in the set of blobs containing the material layer;

[0090] Minimum Contact Area: Find the minimum contact area between all selected clumps.

[0091] The clumps may be selected based on constituent material, conductivity, or other properties. Each 3D DRC check may be extended by specifying a threshold. For example, specifying a threshold for a minimum line width check generates a list of locations where the minimum line width is less than the threshold. Those skilled in the art will recognize that other checks of this nature may be defined.

[0092] Analysis Module

[0093] In one embodiment, the virtual manufacturing environment includes an analysis module. The analysis module is designed to simulate workflows in use cases encountered by semiconductor process integrators. Exemplary use cases encountered by semiconductor process integrators and addressed by the analysis module may include, but are not limited to, key parameter identification, process model calibration, and variability analysis. In key parameter identification, the analysis module can find the process steps / parameters that most strongly affect the results (calibration, defect mode, etc.). In process model calibration, process parameters can be adjusted to match the 3D model to measurements from physical manufacturing, such as but not limited to transmission electron microscopy (TEM) data or process targets. In variability analysis, the analysis module can help users analyze and understand the variability of metrology data obtained for a set of virtual 3D models, such as but not limited to by estimating the variability of structural or electrical parameters used for specification limit setting.

[0094] The analysis module described herein can generate process variations through experimental design or Monte Carlo simulations applied to parameters and settings in a virtual semiconductor manufacturing environment, and then perform automatic statistical analysis, optimization, and visualization for the user. The data analyzed may include the settings of the input process parameters and (but not limited to) metrology, structural search, DTC inspection, and electrical analysis to evaluate the 3D virtual semiconductor structure generated in the virtual manufacturing environment. The embodiments utilize selected and customized to solve problems and solve problems unique to virtual semiconductor manufacturing, and correct errors that may occur when the result data is exported to conventional third-party statistical tools.

[0095] Embodiments also provide more efficient techniques for experimental design because the specific way in which the virtual semiconductor manufacturing environment of the present invention constructs 3D models results in some common problems that other experimental design methods must solve. For example, if the platform and parameter settings do not change, the same 3D model will be generated every time in the virtual semiconductor manufacturing environment. Therefore, there is no random component to the 3D model output, and there is no need to perform three common tasks in experimental design, namely randomization, replication, and blocking.

[0096] In one embodiment, the analysis module is integrated into the virtual manufacturing environment, resulting in improved and new functionality that is not available through third-party statistical solutions. In one embodiment, the UI and algorithms can be organized by use case, and follow the step-by-step flow UI on the left for each use case. This design may strongly guide users (who may lack statistical training) to perform the correct analysis steps to avoid errors in the analysis. The analysis module may also include a statistical analysis engine that uses a set of analysis algorithms to correctly analyze each specific use case. The analysis module can solve problems that are not properly solved by third-party statistical software, such as multicollinearity and outliers (discussed below), and as previously mentioned, avoid the use of unnecessary methods, such as randomization during experimental design. The analysis results can be provided to the user or third-party software in a variety of formats.

[0097] Fig.13 Depicted is an exemplary analysis flow in an exemplary embodiment. The input of the analysis module may include, but is not limited to, selecting an analysis type that can be organized by use case. (e.g., identifying key parameters, optimization, calibration, variability analysis). Additional exemplary inputs include process parameters of interest (e.g., specified as nominal values ​​and / or ranges) and targets of interest (e.g., metrology values, structural searches, DTC checks, electrical analysis values). In one embodiment, the input values ​​may be references to 3D model files. The analysis module may perform run list generation to establish an experimental design (DOE) for the experiment (e.g., screening DOE, full factorial DOE, Monte Carlo simulation), then run list execution and cluster computing may be utilized to improve efficiency during execution. Execution outputs may include outlier detection and statistical analysis results, such as determining parameter importance / ranking. Outputs may also include exploratory plots (e.g., bivariate plots, response surfaces) and indirect optimization. In one embodiment, the results may also be output to third-party tools for further analysis.

[0098] Identification of key parameters

[0099] An exemplary use case using an embodiment of the analysis module as described herein is key parameter identification. In key parameter identification, the analysis module receives a user selection of a platform, including a 2D layout and a process step. The purpose of the key parameter identification use case is to determine which parameters are related to and affect the target. These parameters are then ranked to show their relative importance. In one embodiment, the use case has seven steps:

[0100] 1) Select the experimental design;

[0101] 2) Select the parameter to change and input the user-selected level into the design;

[0102] 3) Generate the design and run (export if necessary);

[0103] 4) Select the measurement target;

[0104] 5) Set regression options;

[0105] 6) Select identified outliers from the DOE results data for addition or removal; and

[0106] 7) Run the regression and review the results. Identify important / critical parameters.

[0107] In this example, the first step is to select the Design of Experiments (DOE) step, also known as experimental design. DOE is a method for calculating the number of experiments for a particular combination of parameter settings to obtain more information with less experimental work. The analysis module provides three methods for creating experimental designs to sample the parameter space: full factorial design, definitive screening design (DSD), and Monte Carlo simulation. Fig.14A An exemplary UI 1400 for selecting a design of experiments 1402 type provided in a virtual manufacturing environment is depicted.

[0108] The full factorial design is the most classic experimental design. All possible combinations are created. Full factorial designs are best used when the number of parameters is small, from about 2 to 7. For each parameter setting selected, the user enters the number of levels and the values ​​of those levels through the UI. In one embodiment, up to 10 levels can be entered for each parameter setting.

[0109] The final screening design (DSD) is a screening design used when the number of parameters is large or the running cost (time) is high. For the same number of parameters, it produces far fewer runs than a full factorial design. An embodiment can implement the DSD enhancement method only for continuous variables. In one embodiment, for DSD, only three levels are specified for each parameter.

[0110] Monte Carlo simulation is a DOE option that allows for random generation of parameter settings using a normal distribution or a uniform distribution. In an embodiment, the UI allows the user to enter the mean and standard deviation of a normal distribution parameter, or the minimum and maximum values ​​of a uniform distribution parameter, and generate random values ​​accordingly. In an embodiment, the user can also enter the desired number of runs.

[0111] Fig. 14B An exemplary UI 1410 is depicted in an embodiment through which a user may specify the level of each parameter that varies in a design. Fig. 14BScreen shot showing parameters for selecting a full factorial DOE. The left pane contains a list of parameters in the platform. Each can be selected and added to the right pane. There, the user enters the desired number of levels 1414 and values ​​1416 for each level. For example, if three parameters are selected and they have 3, 2, and 4 levels respectively, they will generate 3*2*4=24 runs.

[0112] In an embodiment, the DOE created in the previous step is run by the virtual semiconductor manufacturing environment in batch mode, thereby generating a 3D model for each run in the DOE. The DOE can also be exported to a csv or other type of file.

[0113] In the fourth step of the critical parameter identification workflow, users can select metrology targets to obtain measurement results of the 3D model produced by the DOE. Fig. 14C An exemplary UI 1420 for making selection of a metering target 1422 is depicted in FIG.

[0114] To perform key parameter identification, a regression model is built in the fifth step of the workflow. Fig.14D In an exemplary embodiment, UI 1430 enables the user to select 1432 whether to establish only a regression model with main effects (original parameters) or to build a complete quadratic model. In another embodiment, the type of regression model is automatically selected. In one embodiment, a default option can be provided for any type of regression model and can be changed by the user. In another embodiment, additional options can be provided for more knowledgeable users. These additional options 1434 can include a cutoff value for collinearity test and two entry / exit p-value cutoff values ​​for stepwise linear regression. Collinearity test can correctly handle multiple linear variables and correctly identify and exclude outliers in statistical analysis performed in a virtual semiconductor manufacturing environment. When two or more predictor variables / independent variables in a multiple regression model are highly correlated, multiple collinearity occurs, so that other variables can be predicted with high accuracy. The fitting of a quadratic model usually produces multiple linear variables, and an embodiment solves this problem, as further described below.

[0115] In a set of 3D models created from an experimental design, one or more 3D models may have a target (metrology, CD, etc.) that contains data values ​​that are unusual in some way (outliers) that can adversely affect or hinder (correct) statistical analysis. The analysis module identifies outliers for the user. Fig.14EIn the exemplary embodiment, UI1440 enables the user to select from the identified outliers 1442 to determine which ones should be omitted from the target data when performing the statistical analysis. Four types of outliers are tested for the targets in this step. Empty cells - If the run fails, an empty data cell for the target is returned (the 3D model cannot be built). This type of run is automatically marked as an outlier that is removed during the statistical analysis and cannot be put back by the user. NOVAL - If the run is completed, but the target measurement value cannot be calculated, the text value "NOVAL" is returned. This type of run is automatically marked as an outlier that is removed during the statistical analysis and cannot be put back by the user. Constant values ​​- Multiple values ​​of the target can be the same. If many results for the target are the same, this will hinder or distort statistical modeling. The target data is tested to check whether a certain amount of data (e.g., 50% or more of the data) is the same / constant by comparing it to the median. These runs are deleted. If all target data is the same, an error is reported. Statistical outliers - These data points are sufficiently far from the center of the data and may need to be excluded from the analysis. The median absolute deviation (MAD) method can be used to statistically test whether each data point is an outlier. Assuming MAD = median (|x-median(x)|), the robustness equivalent to the standard deviation can be calculated as SM = 1.4826*MAD. Data values ​​that exceed MAD ± K*SM (K = 3 by default, equivalent to 3 standard deviations) can be considered outliers and marked for user inspection. In one embodiment, the user can put any of these outliers back into the analysis. It should be understood that there may be outliers in the measured data that are not a problem when using the design types discussed here (i.e., DSD, full factorial, or Monte Carlo simulation) because, by definition, these data points are within the range unless the user makes a typographical or other error when setting the level / range.

[0116] After removing the outliers, a variety of statistical analyses can be performed on the data of the target. For example, in one embodiment, the analysis module can make input parameters for the regression model (if square / cross terms are selected). This allows the basic curve relationship between the fitting x parameter and the target y. A set of variables X can be fitted into the linear regression model, and the equation can be represented by linear algebra symbols as: X*b=y, where X is a matrix with n rows (runs) and k columns (variables). In an embodiment, the analysis module can also perform multicollinearity checks for all possible input variable pairs, calculate the correlation coefficient r, and remove one parameter of each pair with |r|>0.9 (this cutoff value can be adjusted by the user). This solves the multicollinearity problem in most cases.

[0117] In an embodiment, the analysis module may also perform an underdetermined matrix check to check if X is underdetermined (K>n). If there are more variables than data points (runs), there is not enough data to find a unique regression solution using the standard equation (the algorithm cannot return an answer). There are two solutions: 1) remove variables (using only main effects instead of a full second-order model), or 2) use a method such as principal component regression. In one embodiment, the analysis module applies a first type of solution to remove variables. If k>p, then the squared terms and cross terms will be removed and checked again. If X is still underdetermined, the regression cannot be performed and an error is returned to the user.

[0118] The analysis module may further run a numerical check on the data. After outlier removal, depending on the design selected by the user and its size, there may not be enough run time to solve the regression problem. In one embodiment, the check will determine if the number of runs n is < 10, in which case there is not enough data and an error is returned to the user.

[0119] In an embodiment, the analysis module can perform a stepwise linear regression. A forward approach can be used: the initial model includes only the intercept (β0 weight), and all variables are tested for statistical significance to determine which (if any) should be entered into the model. Once a variable is selected, say variable x3, all remaining variables are tested for inclusion in the new model. This process continues until no variables meet the inclusion criteria (p-value < 0.05, user adjustable). Variables in the model are also tested (p-value > 0.10, user adjustable).

[0120] In an embodiment, the analysis module can perform a relative importance calculation to identify key parameters. If two or more statistically significant parameters are used to generate the model, only these variables are used to calculate the new linear regression, but after they have been automatically scaled. In order to automatically scale the variables, the mean of the variable is subtracted from all data points, and then the resulting value is divided by the original standard deviation of the variable. This makes the mean of all variables 0 and the standard deviation 1. The reason for this is the scaling of the variables. One variable can range from 0 to 1, while another variable can range from 50 to 80. The importance of the regression (the size of the weight, the beta value) is affected by the scaling of the variables. If you want to know which variables are more important by checking the beta value, you must convert the variables in the regression model to have the same variance that is done with automatic scaling.

[0121] The results may be presented to the user via user interface 1450 in a variety of different formats, such as, but not limited to, a graph with annotations 1452, such as Fig.14FThe table 1454 shown in . The plot is a plot of predicted target versus actual target. In one embodiment, it can be annotated with: r2 (the regression squared correlation coefficient, ranging from 0 to 1, indicating the fraction of the target variation explained by the model), root mean square error (RMSE, a measure of prediction accuracy), and n (the actual data points / number of runs used in the regression model). In one embodiment, the output table 1454 of the regression results can have five columns, such as Figure 14G Shown in larger form. Column 1: Parameter Name. These are the names of the original variables, and if included, the squared and cross terms. Column 2: p-values ​​for the significant variables. Column 3: Regression Weights (β). Column 4: Relative Weights. The regression weights (β) used for the regression are calculated with the automatically scaled variables. These can be used to rank the important parameters. For example, the parameter Etch4 Lateral Ratio may be determined to be more important than Etch1 Etch Ratio when calculating relative importance. Column 5: Status. In one embodiment, there are four possible results: Not Significant, Significant, Remove Highly Collinear, and Remove Underdetermined. In one embodiment, the significant parameters have non-zero weights and scaled importance, which indicates how important a given process parameter is to the selected metrology.

[0122] This method of key parameter identification is Fig.15 , which depicts a series of steps performed in an exemplary embodiment to identify key parameters. The sequence begins with a user identification of a platform (layout data and process steps) being received by a virtual manufacturing environment (step 1500). A plurality of virtual manufacturing runs are then performed for a DOE of a semiconductor device of interest (step 1502). In one embodiment, a user selection of a type of DOE and additional DOE-related input selections is received through a user interface provided in the virtual manufacturing environment. Alternatively, in another embodiment, the type of DOE and DOE parameters are automatically selected by the virtual manufacturing environment. A user selection of a target (e.g., metrology measurement, structural search, DTC check, and / or electrical analysis) is received (step 1504), and an analysis module identifies outliers in the target data generated by the virtual manufacturing run as described above (step 1506). The identified outliers are displayed to the user, and a user selection is then received through a provided user interface to add one or more outliers back to the target data or remove outliers from the target data (step 1508). The analysis module then performs a regression analysis using the adjusted target data after outlier determination to identify one or more key parameters of the DOE (step 1510). An indication (eg, list, line graph, chart) of the identified key parameters is then displayed to the user, or the identified key parameters may be exported to a third party application for additional processing (step 1512).

[0123] Process model calibration

[0124] The analysis module may also perform process model calibration. In process model calibration, process step parameters and settings are adjusted in the virtual manufacturing environment so that the virtual 3D model generated from the virtual manufacturing process matches the physical semiconductor produced in the physical manufacturing environment. Once calibrated, the parameters and their settings in the virtual semiconductor manufacturing environment can be changed to introduce changes in the 3D model and provide information about which process changes will improve various semiconductor performance. In one embodiment, a wizard program user interface is provided to guide the user through the process of optimizing the virtual 3D model to match the physical semiconductor. If there are multiple targets, the user selects the measurement targets and their expected values ​​(one or more), weights the importance of the targets, sets parameter limits, runs one or more experiments, and receives optimized parameter values ​​and corresponding measurement target results.

[0125] Conventional virtual manufacturing environments that adjust process parameters in calibration work lack system-level components that can perform appropriate process model calibration. In addition, many semiconductor process integration engineers have little or no statistical knowledge. Therefore, these engineers usually perform process model calibration by adjusting parameters in a primitive trial-and-error manner through a one-factor-at-a-time (OFAT) method. When it eventually finds any solution, this method is very time-consuming and obtains a solution of poor quality. The OFAT method guarantees that the optimal parameter set cannot be found because it does not consider the influence of any interaction between the parameters.

[0126] To address these issues, an embodiment provides automatic statistical analysis, optimization, and visualization to users (e.g., semiconductor process integrators who may have limited or no statistical knowledge) using an analysis module integrated into a virtual manufacturing environment. More specifically, an embodiment provides a programmatic approach to solving calibration problems without confusing engineers who are not trained in statistics. The statistical analysis engine in the analysis module uses a set of analysis algorithms to analyze each specific use case with very little user input. In one embodiment, the user interface (UI) is a wizard whose purpose is to strongly guide the user to perform the correct analysis steps. The wizard can be organized by use case and operated according to the step-by-step process UI on the left side of each use case.

[0127] exist Fig.16An exemplary workflow for process model calibration performed in an exemplary embodiment is depicted in . The sequence begins with a virtual manufacturing environment (layout data and process steps) receiving a platform identification, from which a virtual 3D model of a semiconductor device of interest is generated. In most cases, the platform will be retrieved after user selection / specification provided through a UI provided in the virtual manufacturing environment. The UI also receives a user identification of one or more measurement targets on the 3D model that the user desires to match the measurement targets on the corresponding physical semiconductor (step 1602). The targets can be, but are not limited to, values ​​related to metrology values, structural searches, DTC checks, electrical analysis, etc. evaluated on the virtual semiconductor structure. In another embodiment, the platform can be selected programmatically without user input.

[0128] The parameters (key parameters) that are important and should be adjusted to match the 3D model target values ​​with the experimental data are then determined (step 2904). In one embodiment, this determination is done by a key parameter identification process performed by the analysis module as described above. Alternatively, in another embodiment, the key parameters can be manually selected by the user through the UI.

[0129] The sequence continues by receiving a user specification of a desired value (DV) for each target through the UI (step 1606). The DV may be, but is not limited to, the distance obtained from the TEM, or the quality of match or spectrum between a slice of a 3D model and the entire TEM. Relative weights are applied to each target by default or by user instruction, e.g., for two targets A and B, target A may be weighted to be twice as important as target B if the user desires.

[0130] The sequence continues by receiving user specifications for each parameter to be adjusted in the calibration with user set lower and upper bounds (step 1608). The optimization algorithm provided in the analysis module keeps the parameters within these bounds as it iterates towards a solution.

[0131] The analysis module next executes the optimization algorithm (step 1610). The optimization algorithm can perform indirect or direct optimization, both of which are further described below. In one embodiment, the user may have options to select or specify, such as the number of iterations, convergence tolerance, scoring function type (L-2 or L-1), number of trials, etc. In some embodiments, for multiple trials, random starting values ​​of parameters within previously specified lower and upper limits may be created.

[0132] The results of the optimization algorithm are displayed to the user (step 1612). In one embodiment, the user can select a test from the displayed results through the UI to trigger the creation of a 3D model in the virtual manufacturing environment (step 1614).

[0133] The Analysis Module can use two different types of optimization algorithms. Indirect optimization applies an optimization algorithm to the regression equation created during the key parameter identification process. Indirect optimization has the advantage of being very fast because it does not call upon the virtual manufacturing environment to build additional 3D models, and it generally avoids local minima because the regression equation provides a set of planes on which to make a response surface (the response surface indicates the relationship of the parameter to the error between the 3D model target and the desired value). Trials that start from random starting points in parameter space tend to converge to similar results, so the user may be able to perform their optimization task using only a small number of trials. It should also be noted that a disadvantage of indirect optimization is that if the regression equation does not predict the target well, for example if the response surface is highly nonlinear, the quality of the results is poor.

[0134] Direct optimization is much slower than indirect optimization and can be used in embodiments in which the key parameter identification process discussed above is not followed. In this method, the optimization algorithm calls the virtual manufacturing environment at each iteration, generates a new 3D model and related measurement values, and updates the optimization algorithm, and then adjusts the parameter values. This is a sequential optimization process. Direct optimization has the advantage of being the most realistic method, and will be better used for nonlinear response surfaces, and does not necessarily require the key parameter identification process described above to be run first (no regression equation is required, the user only needs to select parameters for optimization). It has the disadvantage of being slow because direct optimization calls the virtual manufacturing environment to build a 3D model at each iteration of each trial and may fall into a local minimum. These disadvantages can be alleviated by using multiple licenses (speed) and more trials to provide a wider sampling of the parameter space to avoid the algorithm from falling into a local minimum.

[0135] Various optimization algorithms can be used to perform direct and indirect optimization. As a non-limiting example, in one embodiment, an interior point algorithm with parameter bounds can be used for indirect optimization, but other algorithms can also be used. For direct optimization, as a non-limiting example, genetic algorithms can be used because they can handle complex response surfaces with discontinuities and binary objectives (presence / absence).

[0136] As a non-limiting illustration of performing process model calibration using indirect optimization, in one embodiment, the user first completes the key parameter identification process through the analysis module as described herein. More specifically, the user performs experimental design and regression on a set of parameters and targets (measurement, structural search, DTC inspection, electrical analysis, etc. evaluated on virtual semiconductor structures). This identifies the statistically significant parameters of each target and creates a regression equation that predicts each target using these statistically significant parameters. As described above, the user selects one or more targets, enters the expected value (DV) of each target, and weights its importance. A default weighting of 1 for each target can be provided. For calibration options, the user can choose to use (default) or not use (default) squared error, and can set advanced options such as but not limited to the number of optimization trials, the number of iterations, and the convergence tolerance. A default value can be provided for each option. For example, the number of optimization trials can be set to a default value of 10, the number of iterations per trial can be set to a default value of 100, and the convergence tolerance can be set to a default value of 1e-6. After setting the advanced options, the user can set the lower and upper limits allowed for each parameter to be optimized through the provided UI. During the optimization by the analysis module, the parameter values ​​will be maintained within these bounds. The user initiates a calibration run and begins the optimization through the UI. In one embodiment, the underlying computational engine may use an interior point algorithm. Once the optimization runs are complete, the optimized parameters and target values ​​are displayed for each run, along with completion / error messages, and the user may select a run to build in the virtual manufacturing environment to evaluate the resulting 3D model.

[0137] As described above, in one embodiment, the process model calibration sequence may be guided via a UI wizard. Fig.17 Depicted is the selection of a metrology target for the process model calibration sequence described above, wherein the user is directed to select a target from targets for which regression data has been previously generated during the key parameter identification process. As further explained below, the regression data is then used when performing indirect optimization. In one embodiment, UI 1700 presents a selectable list of targets 1702, but restricts the user to selecting from metrology targets for which regression models already exist. In an embodiment, no other parameters are provided and no other metrology targets are provided. Fig.17 Also depicted is a table in the UI that enables the user to specify the DV for the selected target 1704. In the table in the right pane, the user enters the DV (these cells may be empty initially) and the weight, which may be 1 by default and may be changed by the user.

[0138] Fig.18An exemplary user interface 1800 is depicted that enables selection of calibration options 1802 that may be provided by a process model calibration wizard. As depicted, in one embodiment, an optimization method (indirect vs. direct) may be selected 1804 and the virtual manufacturing environment may provide a pre-selection check box 1806 to enable the user to specify options such as the number of optimization trials, the number of iterations per trial, and the tolerance desired by the user. Default values ​​may be initially provided, which, in one embodiment, may be changed by the user.

[0139] The process model calibration wizard may also provide a user interface 1900 that enables the user to select parameter limits, such as Fig.19 A list of all statistically significant parameters in the user-selected regression may be created by the analysis module and displayed in a table format 1902. For each parameter, the associated target 1904 is listed. For example, Fig.19 In the table shown, parameter 2.1.15: Thickness is important for the three regression targets FinCD_Top, FinCD_Bot, GapCD_Top. The user enters the desired lower and upper limits on each parameter.

[0140] Then, the process model calibration wizard program may provide a run button to start the calibration, and may display the results to the user through the user interface 2000, such as Fig. 20 For example, the results 2002 may be displayed in a tabular format from an internal or external simulation environment and may display the trial number, optimization results, predicted target results, and values ​​of parameters 2004. In one embodiment, the displayed view may enable a user to select a column in the table to use the parameters from a particular successful trial to export or automatically build a model in a 3D view of the virtual manufacturing environment.

[0141] Variability Analysis

[0142] Variability analysis helps users analyze and understand the variability of metrology data obtained for a set of virtual 3D models. In one embodiment, an analysis module in a virtual manufacturing environment can perform variability analysis to generate a user interface that displays a table of calculated information about target distributions, a histogram of target data, and a plot of normal quantiles, and provides the ability to switch to a second plot window, select up to four targets, and plot / compare their empirical cumulative distribution functions. In addition, variability analysis as described herein provides an estimate of the precision of the standard deviation (σ) and its correlation with sample size, a method for assessing whether target data is normally distributed, and a consistent method for visual comparison.

[0143] Variability analysis is the task of evaluating the distribution of target values ​​(metrology, structure search, DTC check, electrical analysis, etc.) obtained from multiple virtual semiconductor structures created in a virtual manufacturing environment. The goal is to determine the nominal value, range, specification limit, etc. of that target. Conventional virtual manufacturing environments for semiconductor device structures lack system-level components to implement proper variability analysis. Many semiconductor process integration engineers have little or no statistical knowledge, so these engineers perform variability analysis in an incomplete and / or incorrect manner. The target data may be assumed to be normally distributed, but this may not be the case, and if the target data is not normally distributed, the mean and σ values ​​are misleading. Even if the target data is normally distributed, the appropriate sample size required to obtain useful σ accuracy is not usually addressed in Monte Carlo simulations / experimental design. Users often overestimate or underestimate sample size, which wastes time and / or results in poor quality answers. In addition, visualization and comparison of distributions is done in different ways in different software packages, or not done at all, which leads to confusion among users.

[0144] To address these issues, in one embodiment, an analysis module is designed to perform variability analysis to provide automatic statistical analysis, optimization, and visualization for users (eg, semiconductor process integrators with limited or no statistical knowledge) in a virtual manufacturing environment.

[0145] Fig.21A series of steps for performing variability analysis in an exemplary embodiment are depicted. The sequence begins with receiving a user identification of a platform used by a virtual manufacturing environment (layout data and process steps) to generate a virtual 3D model of a semiconductor device structure of interest (step 2100). The user creates a Monte Carlo DOE and identifies the targets of the 3D model (step 2102). The Monte Carlo DOE is then subjected to multiple virtual manufacturing runs (step 2104). As discussed further below, in one embodiment, a reduced set of approximately 200 runs is performed. The analysis module identifies outliers in the target data generated by the virtual manufacturing run in the manner described above (step 2106). The identified outliers are displayed to the user, and a user selection is received through a provided user interface to add one or more outliers back to the target data or remove outliers from the target data for each target (step 2108). The user selects a variability analysis option through the user interface and selects one or more targets for analysis (step 2110). The variability analysis results are then displayed to the user in different forms, such as but not limited to tabular distribution data, target data histograms, and plots of normal quantiles, or the results can be exported to a third-party application for additional processing (step 2112). If desired, the user can switch to a second plotting window, the Empirical Cumulative Distribution Function (ECDF) window, and select up to four targets, and the analysis module will plot / compare their empirical distribution functions.

[0146] Fig. 22 An exemplary user interface showing a variability analysis results window 2200 in an exemplary embodiment is depicted. For a selected target, the variability analysis main window displays a table 2202 and two plots, a histogram 2204 and normal quantiles 2206. The table 2202 contains a number of calculated information for the selected target: For example:

[0147] n is the number of data points used in the calculation (the user can add / remove outliers, so the actual number of data points used is shown here);

[0148] Mean values ​​and 95% CI (confidence interval) of the means;

[0149] Standard Deviation and 95% Confidence Interval for the Standard Deviation. The 95% confidence interval is very important to the user because it is an estimate of the precision of the standard deviation (σ). If n=200, the 95% confidence interval is approximately ±10%, which is found to be useful for estimating specification limits. The sample size of 200 is much smaller than the sample size typically recommended for Monte Carlo simulations (10,000 is typically recommended), but can provide a precision of ±10%, which is acceptable in some use cases. The user can adjust the sample size (n) as needed to improve the precision of σ (CI) and the mean. In another embodiment, the sample size used for the Monte Carlo simulation is less than five hundred.

[0150] Normality Test - The results of the Lilliefors normality test are applied to the selected target and reported as a p-value and whether it is statistically significant (yes / no). This is the first of many methods used by the analysis module to assess whether the target data is normally distributed;

[0151] Percentile values ​​- Minimum, 0.5%, 2.5%, 5%, 25%, 50% (median), 75%, 95%, 97.5%, 99.5%, Maximum of the selected target.

[0152] The Variability Analysis main window can also display a histogram, a histogram of the data for the selected target with a normal pdf overlaid for visual comparison of normality. If the histogram bars follow the normal pdf, the target data are said to be normally distributed. This is the second method provided by the Analysis module for testing the normality of the target data.

[0153] The variability analysis main window can further display a normal quantile graph of the selected target data. If the points are close to or on a line, the target data can be said to be normally distributed. This is a third method provided by the analysis module for testing the normality of the target data. It should be understood that other methods for testing the normality of the target data that are not explicitly discussed herein can also be performed by the analysis module and should be considered to be within the scope of the present invention.

[0154] The analysis module may also generate a display of a second window for displaying the variability analysis results. Fig.23 An exemplary graphical user interface 2300 is depicted for displaying a comparison of the empirical cumulative distribution functions of two separate targets 2302, 2304 in an exemplary embodiment. For example, a user can click on the tab 2306 of the ECDF window and select up to four targets to plot and compare their empirical cumulative distribution functions. The x-axis is the target data scaled to a range of 0 to 1, while the y-axis is the cumulative probability from 0 to 1. This enables the user to compare the target distributions in an equivalent manner and examine tail effects that are important in setting specification limits.

[0155] The multiple methods implemented by the analysis module for assessing normality allow the user to determine whether they should consider the target data to be normally distributed. If the target data is normally distributed, the user can use the mean and standard deviation to estimate the commonly used three or four σ points to set the specification limits. If the data is not normally distributed, the user can estimate useful specification limit points from the percentiles and minimum / maximum values ​​displayed in the table and the tail of the ECDF plot. In another embodiment, the target data can be automatically fit to a Gaussian mixture model and thereby used to estimate useful points for specification limit setting. In an embodiment, a variation of this method allows the user to fit features of the data with various other known distributions (e.g., F or t distributions) and thereby estimate useful points for specification limit setting.

[0156] Some or all embodiments of the present invention may be provided as one or more computer readable programs or codes implemented on or in one or more non-transitory media. The medium may be, but is not limited to, a hard disk, a compact disk, a digital versatile disk, a flash memory, a PROM, a RAM, a ROM, or a magnetic tape. In general, the computer readable program or code may be implemented in any computing language.

[0157] Since certain changes may be made without departing from the scope of the present invention, all content contained in the above description or shown in the accompanying drawings is to be interpreted as illustrative rather than literal. Those skilled in the art will recognize that the order of the steps and architectures depicted in the accompanying drawings may be changed without departing from the scope of the present invention, and the illustrations contained herein are single examples of multiple possible descriptions of the present invention.

[0158] The foregoing description of exemplary embodiments of the present invention provides illustration and description, but is not intended to be exhaustive or to limit the present invention to the precise form disclosed. In view of the above teachings, modifications and variations are feasible or can be obtained from the practice of the present invention. For example, although a series of actions have been described, the order of the actions can be modified in other embodiments consistent with the principles of the present invention. In addition, non-dependent actions can be performed in parallel.

[0159] Partial text translation of some drawings

[0160] Figure 2

[0161] Process file:

[0162] Layout Options: Layout Options

[0163] Top Cell: Top cell

[0164] Cell6×6: Cell 6×6

[0165] Scan: Scan

[0166] GDS Layer Names: GDS layer names

[0167] Ocadence Virtuoso Bridge (Not connected): Ocadence Virtuoso Bridge (Not connected)

[0168] Build Options: Build options

[0169] Model Resolution 1.0: Model resolution 1.0

[0170] Save Model After Every Step: Save the model after each step

[0171] Start 3D Viewer After Building Model: Start the 3D viewer after building model

[0172] Figure 4

[0173] File: Document

[0174] Edit:

[0175] View:

[0176] Tools:

[0177] Widows:

[0178] Number:

[0179] Step Name: Step name

[0180] Material Name: Material name

[0181] Thickness:

[0182] Mask Name: Mask name

[0183] SOI Wafer Setup: SOI Wafer Setup

[0184] Fin Module: Fin module

[0185] Fincut Module: Fincut module

[0186] Gate Module: Gate Module

[0187] High-K Gate Dielectric Deposition:

[0188] Measure Film Thickness:

[0189] PWF TIN Deposition:

[0190] Measure Film Thickness:

[0191] Barrier TaN Deposition:

[0192] WF Resist Deposition:

[0193] Resist:

[0194] WF Lithography:

[0195] WF TiN Removal Etch:

[0196] WF Resist strip: WF resist stripping

[0197] NWF TiN Depositon:NWF TiN Deposition

[0198] Gate Amorphous Silicon Deposition:

[0199] Gate Amorphous Silicon CMP: Gate Amorphous Silicon CMP

[0200] Gate Hard Mask Deposition: Gate Hard Mask Deposition

[0201] Gate Patterning:

[0202] Gatecut Patterning: Gate cut patterning

[0203] Gate Etch-Composite: Gate Etch-Composite

[0204] Measure CD:

[0205] Save Model Components: Save model components

[0206] SiGe Module:

[0207] Action:

[0208] Deposit:

[0209] Wafer: chip

[0210] to operate on: to operate on

[0211] Mask Field: Mask field

[0212] Dark: dark

[0213] Light:

[0214] Top side:

[0215] Bottom side:

[0216] Material:

[0217] Thinkness: Thickness

[0218] Distribution:

[0219] Nominal Value: Nominal value

[0220] Scalar: Zoom

[0221] Anisotropy:

[0222] Corner Type: Corner type

[0223] Rounded: Round

[0224] Process Library:

[0225] Modeling Steps: Modeling steps

[0226] Comments: Comments

[0227] Cross Section: Cross Section

[0228] Custom Python: Custom Python

[0229] Deposit: Deposition

[0230] Electroplate: Electroplating

[0231] Etch: Etching

[0232] Export Geometry: Export geometry

[0233] Expose Material: Expose Material

[0234] Fragment Operations: Fragment Operations

[0235] Generate Mesh: Generate a mesh

[0236] Grow Oxide: Grow Oxide

[0237] Implant: implant

[0238] Interface Growth: Interface Growth

[0239] Mask Operations: Mask Operations

[0240] Measurement: Measurement

[0241] Modeling Parameters: Modeling parameters

[0242] Planar Deposit: Flat Deposit

[0243] Planarize: Flatten

[0244] Remove Material: Remove material

[0245] Replace Material: Replace material

[0246] Save Model: Save the model

[0247] Wafer Operations: Wafer Operations

[0248] Wafer Setup: Wafer Setup

[0249] CMOS steps: CMOS steps

[0250] Implant: implant

[0251] Oxidize: Oxidize

[0252] Grow oxide-LOCO: Grow oxide-LOCO

[0253] Diffusion:

[0254] Salicide: Silicide

[0255] Polysilicon Deposit: Polysilicon Deposition

[0256] Oxide Fill&Via Etch: Oxide filling and via etching

[0257] Interconnect

[0258] Fig.14A

[0259] Use Case

[0260] Design Method: Design method

[0261] Analytics

[0262] DOE Options:

[0263] Select Input Factors: Select input factors

[0264] Run DOE: run DOE

[0265] Select Analysis Targets: Select analysis targets

[0266] Import Regression Data for Calibration: Import regression data for calibration

[0267] Fig. 14B

[0268] Available Inputs: Available Inputs

[0269] Variables

[0270] Number of Runs: Number of runs

[0271] Fig. 14C

[0272] Available Analysis: Available Analysis

[0273] Fig.14D

[0274] Include in Regression: Included in regression

[0275] Fig.14E

[0276] Outlier Table: Outlier Table

[0277] Statistical Outlier: Statistical Outliers

[0278] Fig.14F

[0279] Metrology Target: Metrology Target

[0280] Actual vs Predicted: Actual vs Predicted

[0281] ShowConfidenceInterval: Display confidence interval

[0282] Figure 14G

[0283] p-Value: p-value

[0284] Highly Collinear: Highly Collinear

[0285] Fig.17

[0286] Parameter Bounds:

[0287] Run Calibration: Run Calibration

[0288] Remove:

[0289] Fig.18

[0290] Optimization

[0291] Scoring Function: Scoring Function

[0292] Fig.19

[0293] Relevant Targets:

[0294] Lower Bound: Lower limit

[0295] Upper Bound: upper limit

[0296] Fig. 20

[0297] Predicted Target Valve: Predicted target value

[0298] Converged: Converged

[0299] Fig. 22

[0300] Quantile Plot: Quantile Plot

[0301] Histogram with Gaussian Overlay: Histogram with Gaussian Overlay

[0302] Fig.23

[0303] Empirical CDFs: Empirical CDFs

[0304] Probability

Claims

1. A non-transitory computer-readable medium containing computer-executable instructions for critical parameter identification in a virtual semiconductor manufacturing environment, the instructions, when executed, causing at least one computing device to: receiving 2D design data and a selection of a process sequence including a plurality of processes for a semiconductor device structure to be virtually manufactured in a virtual manufacturing environment generated by a computing device; executing, using the computing device, a plurality of virtual manufacturing runs for the semiconductor device structure based on a design of experiments DOE using the 2D design data and the process sequence, the plurality of virtual manufacturing runs constructing a plurality of 3D models; receiving a user identification of one or more targets for the semiconductor device structure; executing an analysis module in the virtual manufacturing environment to identify one or more outliers in measurement data for the one or more objects in the plurality of 3D models generated from the virtual manufacturing run; receiving a user selection to add or remove one or more of the one or more identified outliers from the measurement data for the one or more objects in the plurality of 3D models, the selection being received via a user interface provided in the virtual manufacturing environment; performing a regression analysis on the measurement data of the one or more targets using the analysis module after adding or removing the selected outliers from the measurement data; Based on the results of the regression analysis, identifying one or more key parameters using the analysis module; and An identification of the one or more key parameters identified is displayed or exported.

2. The medium of claim 1 , wherein the instructions, when executed, further cause the at least one computing device to: The identified one or more key parameters are programmatically ranked.

3. The medium of claim 1 , wherein the instructions, when executed, further cause the at least one computing device to: A user interface is provided in the virtual manufacturing environment for receiving a user selection of at least one of a DOE type, a parameter to be varied in the DOE, a number of levels, and values ​​of the levels of the DOE. 4 . The medium of claim 1 , wherein the selected target is at least one of metrology measurement, structural search, DTC check, and electrical analysis.

5. The medium of claim 1 , wherein the instructions, when executed, further cause the at least one computing device to: A multicollinearity check is performed on the target data of the plurality of 3D models.

6. The medium of claim 1, wherein the instructions, when executed, further cause the at least one computing device to: receiving, through the user interface in the virtual manufacturing environment, a user's selection of a desired value of a selected target, the selected target consisting of a group of targets associated with key parameters; receiving, via a user interface in the virtual manufacturing environment, a user selection of an upper limit and a lower limit for each identified key parameter; executing an optimization algorithm for the plurality of 3D models using the identified key parameters, desired values, and upper and lower bounds; and Display or export the results of the optimization algorithm.

7. The medium of claim 6, wherein a selected objective from the set of objectives is associated with a key parameter previously identified by the analysis module and for which regression data exists, and wherein the optimization algorithm performs an indirect optimization using the regression data.

8. The medium of claim 6, wherein the key parameters are manually identified by a user, and wherein the optimization algorithm performs a direct optimization.

9. The medium of claim 6, wherein the instructions, when executed, further cause the at least one computing device to: Calibration options for the optimization algorithm are received from a user via the user interface, and the calibration options include one or more of a number of iterations, a convergence tolerance, a number of trials, and a scoring function type.

10. The medium of claim 1, wherein the DOE is a Monte Carlo simulation, and wherein the instructions, when executed, further cause the at least one computing device to: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Provides results that allow an assessment of the accuracy of σ.

11. The medium of claim 1 , wherein the DOE is a Monte Carlo simulation, and wherein the instructions, when executed, further cause the at least one computing device to: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Provides results that allow an assessment of the normality of the target data.

12. The medium of claim 1, wherein the DOE is a Monte Carlo simulation and a sample size for the Monte Carlo simulation is less than 500.

13. The medium of claim 1, wherein the DOE is a Monte Carlo simulation and the user can adjust the number of virtual manufacturing runs to achieve a desired sigma accuracy.

14. The medium of claim 1, wherein the DOE is a Monte Carlo simulation, and wherein the instructions, when executed, further cause the at least one computing device to: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Displays results for multiple selected targets simultaneously.

15. A method for identifying key parameters in a virtual semiconductor manufacturing environment, comprising: receiving 2D design data and a selection of a process sequence including a plurality of processes for a semiconductor device structure to be virtually manufactured in a virtual manufacturing environment generated by a computing device; executing, using the computing device, a plurality of virtual manufacturing runs for the semiconductor device structure based on a design of experiments DOE using the 2D design data and the process sequence, the plurality of virtual manufacturing runs constructing a plurality of 3D models; receiving a user identification of one or more targets for the semiconductor device structure; executing an analysis module in the virtual manufacturing environment to identify one or more outliers in measurement data for the one or more objects in the plurality of 3D models generated from the virtual manufacturing run; receiving a user selection to add or remove one or more of the one or more identified outliers from the measurement data for the one or more objects in the plurality of 3D models, the selection being received via a user interface provided in the virtual manufacturing environment; performing, using the analysis module, a regression analysis on the measurement data of the one or more targets after adding or removing the selected outliers from the measurement data; Based on the results of the regression analysis, identifying one or more key parameters using the analysis module; and An identification of the identified one or more key parameters is displayed or exported.

16. The method according to claim 15, further comprising: The identified one or more key parameters are programmatically ranked.

17. The method according to claim 15, further comprising: A user interface is provided in the virtual manufacturing environment for receiving a user selection of at least one of a DOE type, a parameter to be varied in the DOE, a number of levels, and values ​​of the levels of the DOE.

18. The method according to claim 15, further comprising: A multicollinearity check is performed on the target data of the plurality of 3D models.

19. The method of claim 15, further comprising: receiving, through the user interface in the virtual manufacturing environment, a user's selection of a desired value of a selected target, the selected target consisting of a group of targets associated with key parameters; receiving, via the user interface in the virtual manufacturing environment, a user selection of an upper limit and a lower limit for each identified critical parameter; executing an optimization algorithm for the plurality of 3D models using the identified key parameters, desired values, and upper and lower bounds; and Display or export the results of the optimization algorithm.

20. The method of claim 19, further comprising: Calibration options for the optimization algorithm are received from a user via the user interface, and the calibration options include one or more of a number of iterations, a convergence tolerance, a number of trials, and a scoring function type.

21. The method of claim 15, wherein the DOE is a Monte Carlo simulation, and further comprising: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Provides results that allow an assessment of the accuracy of σ.

22. The method of claim 15, wherein the DOE is a Monte Carlo simulation, and further comprising: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Provides results that allow an assessment of the normality of the target data.

23. The method of claim 15, wherein the DOE is a Monte Carlo simulation, and further comprising: receiving a user selection to perform a variability analysis on the plurality of virtual manufacturing runs; executing the plurality of virtual manufacturing runs; and Displays results for multiple selected targets simultaneously.

24. A virtual manufacturing system, comprising: A computing device equipped with a processor and configured to generate a virtual manufacturing environment including an analysis module, the virtual manufacturing environment: For a semiconductor device structure to be virtually manufactured, receiving 2D design data and a selection of a process sequence including a plurality of processes; performing a plurality of virtual manufacturing runs for the semiconductor device structure based on a design of experiments (DOE) using the 2D design data and the process sequence, the plurality of virtual manufacturing runs constructing a plurality of 3D models; receiving a user identification of one or more targets for the semiconductor device structure; executing the analysis module in the virtual manufacturing environment to identify one or more outliers in measurement data for the one or more objects in the plurality of 3D models generated from the virtual manufacturing run; receiving a user selection to add or remove one or more of the one or more identified outliers from the measurement data for the one or more objects in the plurality of 3D models, the selection being received via a user interface provided in the virtual manufacturing environment; performing, using the analysis module, a regression analysis on the measurement data of the one or more targets after adding or removing the selected outliers from the measurement data; Based on the results of the regression analysis, identifying one or more key parameters using the analysis module; and displaying or exporting an identification of the identified one or more key parameters; as well as A display surface is in communication with the computing device, the display surface being configured to display the 3D structural model in a 3D view.

25. The virtual manufacturing system according to claim 24, wherein the virtual manufacturing environment: The identified one or more key parameters are programmatically sorted.

26. The virtual manufacturing system according to claim 24, wherein the virtual manufacturing environment: receiving, through the user interface, a user's selection of a desired value of a selected target, the selected target consisting of a group of targets associated with key parameters; receiving, via the user interface, a user selection of an upper limit and a lower limit for each identified critical parameter; executing an optimization algorithm for the plurality of 3D models using the identified key parameters, desired values, and upper and lower bounds; and Display or export the results of the optimization algorithm.

27. The virtual manufacturing system according to claim 24, wherein the virtual manufacturing environment: receiving, through the user interface, a user's selection of a desired value of a selected target, the selected target consisting of a group of targets associated with key parameters; receiving, via the user interface, a user selection of an upper limit and a lower limit for each identified critical parameter; executing an optimization algorithm for the plurality of 3D models using the identified key parameters, desired values, and upper and lower bounds; and Display or export the results of the optimization algorithm.

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