Methods for fine-tuning process models

Abstract

The present invention discloses a method for constructing a process model for simulating the characteristics of a product of photolithography based on patterns produced under different processing conditions. The method uses the deviation between the variation of the simulated characteristics and the variation of the measured characteristics to adjust the parameters of the process model.

Description

[0001] This application is a divisional application of the international application PCT / EP2018 / 051669, which entered the Chinese national phase on January 24, 2018 and has application number 201880008283.0.

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This application is based on and claims the benefit of U.S. Provisional Application No. 62 / 451,048, filed on January 26, 2017, entitled “Method for Fine-tuning a Process Model,” the entirety of which is incorporated herein by reference. Technical Field

[0004] The description in this invention relates to methods and systems for process modeling. Background Art

[0005] Lithographic projection apparatus may be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (e.g., a mask) may contain or provide a circuit pattern corresponding to a single layer of the IC (a "design layout"), and the circuit pattern may be transferred to a target portion (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material (a "resist"), such as by irradiating the target portion through the circuit pattern on the patterning device. Typically, a single substrate includes a plurality of adjacent target portions, to which the circuit pattern is transferred successively, one target portion at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the circuit pattern on the entire patterning device is transferred to one target portion at a time; such apparatus is generally referred to as a stepper. In an alternative apparatus, generally referred to as a stepper-scan apparatus, a projection beam is scanned over the patterning device in a given reference direction (the "scanning" direction) while synchronously moving the substrate parallel or antiparallel to the reference direction. Different parts of the circuit pattern on the patterning device are transferred stepwise onto a target portion. Typically, since the lithographic projection apparatus will have a reduction ratio M (e.g., 4), the speed F at which the substrate is moved will be 1 / M times the speed at which the projection beam scans the patterning device. More information about lithographic apparatus as described herein can be gleaned, for example, from US 6,046,792, which is incorporated herein by reference.

[0006] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various processes, such as primer coating, resist coating and soft baking. After exposure, the substrate may undergo other processes, such as post-exposure baking (PEB), development, hard baking, and measurement / detection of the transferred circuit pattern. This series of processes is used as the basis for manufacturing a single layer of a device (e.g., IC). Afterwards, the substrate may undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to complete a single layer of the device. If the device requires multiple layers, the entire process or its variation will be repeated for each layer. Ultimately, the device will be present in each target portion on the substrate. Afterwards, these devices are separated from each other by techniques such as slicing or sawing, so that each device can be mounted on a carrier, connected to a pin, etc.

[0007] As noted, photolithography is a central step in the fabrication of ICs, where patterns formed on a substrate define the functional elements of the IC, such as microprocessors, memory chips, etc. Similar photolithographic techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0008] As semiconductor manufacturing processes continue to develop, the size of functional elements is continuously reduced, while the number of functional elements (such as transistors) per device has been steadily increasing for decades following a trend generally referred to as "Moore's Law." In the case of the prior art, the layers of the device are manufactured by using a lithography projection device that projects a design layout onto a substrate using illumination from an illumination source (e.g., deep ultraviolet (DUV) or extreme ultraviolet (EUV)), thereby producing individual functional elements with a size well below 100 nm, i.e., the size of the functional element is less than half the wavelength of the radiation of the illumination source (e.g., a 193 nm illumination source).

[0009] The process of printing features with dimensions smaller than the classical resolution limit of a lithographic projection apparatus is often referred to as low-k1 lithography, according to the resolution formula, CD = k1 × λ / NA, where λ is the wavelength of radiation employed (currently 248 nm or 193 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (usually the smallest feature size printed), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it becomes to replicate a pattern on a substrate (similar to the shape and dimensions designed by a circuit designer to obtain specific electrical functions and performance). To overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus, the design layout, or the patterning device. These include, for example, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifted patterning devices, multiple patterning, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement technology (RET)", etc. The term "projection optics" as used herein should be broadly interpreted to include various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and refractive-reflective optics. The term "projection optics" may also collectively or individually include components that operate according to any of these design types for guiding, shaping, or controlling a radiation projection beam. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located on the optical path of the lithographic projection apparatus. The projection optics may include optical components for shaping, adjusting, and / or projecting radiation from a source before the radiation passes through a patterning device, and / or optical components for shaping, adjusting, and / or projecting radiation after the radiation passes through a patterning device. Projection optics typically do not include a source and a patterning device. Summary of the invention

[0010] A method is disclosed herein, comprising: obtaining a simulated characteristic by simulating a characteristic of a product of lithography under multiple processing conditions using a process model including parameters; determining a variation of the simulated characteristic; obtaining a measured characteristic by measuring the characteristic of the product according to a pattern generated under the multiple processing conditions; determining a variation of the measured characteristic; determining a first deviation between the variation of the simulated characteristic and the variation of the measured characteristic; and adjusting the parameter based on the first deviation.

[0011] According to one embodiment, the method further comprises adjusting processing conditions based on simulations performed by the process model.

[0012] According to one embodiment, the method further comprises selecting a set of locations on a substrate produced by the lithography for inspection based on simulations performed by the process model.

[0013] According to one embodiment, the plurality of processing conditions are selected randomly.

[0014] According to one embodiment, the plurality of process conditions comprises nominal process conditions.

[0015] According to an embodiment, the variation of the measured characteristic is selected from the group consisting of: a standard deviation of the measured characteristic, a variance of the measured characteristic, and a range of the measured characteristic.

[0016] According to an embodiment, the variation of the modeled characteristic is selected from the group consisting of: a standard deviation of the measured characteristic, a variance of the measured characteristic, and a range of the measured characteristic.

[0017] According to one embodiment, adjusting the parameter comprises determining a value of the parameter such that the function of the first deviation is at a local or global extremum.

[0018] According to one embodiment, adjusting the parameter is based on a combination of the first deviation and a second deviation, the second deviation being between the simulated characteristic and the measured characteristic under the same process conditions.

[0019] According to an embodiment, the plurality of processing conditions comprises characteristics of a source of the lithographic apparatus, characteristics of projection optics of the lithographic apparatus, and characteristics of a patterning device having thereon an arrangement of features representing the design layout.

[0020] According to one embodiment, said characteristics of said product comprise characteristics of an image.

[0021] According to one embodiment, the image is an aerial image, a resist image or an etched image.

[0022] According to one embodiment, the characteristic of the product comprises a process window of a feature of a design layout.

[0023] According to one embodiment, the characteristics of the product include statistical parameters of features at a plurality of locations.

[0024] A method is disclosed herein, comprising: obtaining a plurality of first deviations, each of the plurality of first deviations being between a variation of a simulated characteristic of a product of lithography and a variation of a measured characteristic of the product of lithography, wherein the simulated characteristic is obtained by simulating the characteristic of the product using a process model including parameters; constructing a plurality of cost functions, the cost functions being combinations of the plurality of first deviations; and adjusting the parameters of the process model by using the cost functions.

[0025] According to one embodiment, the method further comprises adjusting processing conditions based on simulations performed by the process model.

[0026] According to one embodiment, the method further comprises selecting a set of locations on a substrate produced by the lithography for inspection based on simulations performed by the process model.

[0027] According to one embodiment, the variations are across the same set of processing conditions.

[0028] According to one embodiment, the method further comprises obtaining a second deviation between the simulated characteristic and the measured characteristic under the same process conditions, wherein the cost function is a combination of the plurality of first deviations and the second deviation.

[0029] According to an embodiment, at least one of said cost functions is not affected by all of said parameters.

[0030] According to one embodiment, adjusting the parameter comprises determining a value of the parameter that causes the cost function to be at a local minimum or a global minimum.

[0031] According to one embodiment, said characteristics of said product comprise characteristics of an image.

[0032] According to one embodiment, the image is an aerial image, a resist image or an etched image.

[0033] According to one embodiment, the characteristic of the product comprises a process window of a feature of a design layout.

[0034] According to one embodiment, the characteristics of the product include statistical parameters of features at a plurality of locations.

[0035] Disclosed herein is a computer program product, including a non-transitory computer-readable medium having instructions recorded thereon, wherein the instructions implement any one of the above methods when executed by a computer. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A block diagram of the various subsystems of a lithography system is shown.

[0037] Figure 2 A flow chart for simulating lithography in a lithographic projection apparatus is shown.

[0038] Figure 3 It is schematically shown that for each of a set of process conditions, a deviation between a simulated characteristic and a measured characteristic under said process condition is determined and the deviation is used to determine a value of a parameter of a process model.

[0039] Figure 4 It is schematically shown that for each of a set of process conditions, a deviation between the change of a simulated characteristic and the change of a measured characteristic is determined in the vicinity of the process condition and the value of a parameter of the process model is determined using the deviation.

[0040] Figure 5A The measured characteristic in the vicinity of the process conditions (curve marked with “O”) and the simulated characteristic by the process model M1 (curve marked with “M1”) are schematically shown.

[0041] Figure 5B The measured behavior in the vicinity of the process conditions (curve labeled “O”) and the simulated behavior by the process model M2 (curve labeled “ M2 ”) are schematically shown.

[0042] Fig. 6A A flowchart for constructing a process model according to an embodiment is schematically shown.

[0043] Figure 6B A flowchart for constructing a process model according to an embodiment is schematically shown.

[0044] Figure 7 is a block diagram of an example computer system.

[0045] Figure 8 Schematic diagram of a lithography projection device.

[0046] Fig. 9 A schematic diagram of another lithography projection apparatus.

[0047] Fig.10 for Fig. 9 A more detailed view of the devices in the

[0048] Fig.11 for Fig. 9 and Fig.10 A more detailed view of the source collector module SO of the device. DETAILED DESCRIPTION

[0049] Although detailed reference is made herein to manufacturing ICs, it should be clearly understood that the descriptions described herein may have many other possible applications. For example, they may be used to manufacture integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art should recognize that in the case of such alternative applications, any use of the terms "reticle", "chip" or "die" herein is considered to be interchangeable with the more general terms "mask", "substrate" or "target portion", respectively.

[0050] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including: UV radiation (e.g. having a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultraviolet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[0051] The pattern forming device may include or may form one or more design layouts. The design layout may be generated using a CAD (computer-aided design) program, which is commonly referred to as EDA (electronic design automation). Most CAD programs follow a set of predetermined design rules for generating functional design layouts / pattern forming devices. These rules are set by processing and design constraints. For example, the design rules define the spacing tolerance between circuit devices (such as gates, capacitors, etc.) or interconnects to ensure that the circuit devices or lines do not interact with each other in an undesirable manner. One or more of the design rule constraints may be referred to as a "critical dimension" (CD). The critical dimension may be defined as the minimum width of a line or hole or the minimum spacing between two lines or two holes. Therefore, CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit manufacturing is to faithfully reproduce the original circuit design on a substrate (via a pattern forming device).

[0052] The terms "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that may be used to impart to an incident radiation beam a patterned cross-section corresponding to the pattern to be produced in a target portion of the substrate; the term "light valve" may also be used in this context. In addition to classical masks (transmissive or reflective; binary, phase-shift, hybrid, etc.), examples of other such patterning devices include:

[0053] -Programmable mirror arrays. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle on which such an apparatus is based is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as non-diffracted radiation. Using suitable filters, the non-diffracted radiation can be filtered out of the reflected beam, so that only the diffracted radiation remains; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed by using suitable electronic devices. More information about such mirror arrays can be found, for example, in U.S. Patents No. 5,296,891 and No. 5,523,193, which are incorporated herein by reference.

[0054] - Programmable LCD array. An example of such a configuration is given in US Patent No. 5,229,872, which is incorporated herein by reference.

[0055] As a brief introduction, Figure 1 An exemplary lithographic projection apparatus 10A is shown. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or other type of source including an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself need not have such a radiation source); an illumination optics device, which defines a partial coherence (labeled sigma) and may include optics 14A, 16Aa and 16Ab, which shape the radiation from source 12A; a patterning device 14A; and a transmission optics device 16Ac, which projects an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics may limit the range of beam angles impinging on the substrate plane 22A, with the largest possible angle defining the numerical aperture NA of the projection optics = sin(θ max ), n is the refractive index of the medium between the last element of the projection optics and the substrate, and Θ max is the maximum angle of the beam emerging from the projection optics that can still impinge on the substrate plane 22A.

[0056] In a lithographic projection apparatus, a source provides illumination (i.e., radiation) to a pattern forming device, and a projection optical device guides and shapes the illumination onto a substrate via the pattern forming device. The projection optical device may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. An aerial image (AI) is a distribution of radiation intensity at substrate level (e.g., on the surface of a resist or inside a resist; i.e., a 2D or 3D intensity distribution). A resist layer on the substrate is exposed, and an aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. A resist image (RI) may be defined as a spatial (2D or 3D) distribution of the solubility of the resist in the resist layer. A resist model may be used to calculate a resist image from an aerial image, an example of which may be found in U.S. Patent Application Publication No. 2009-0157360, the disclosure of which is incorporated herein by reference in its entirety. The resist model is only related to the properties of the resist layer (e.g. the effects of the chemical processes occurring during exposure, PEB and development). The optical properties of the lithographic projection apparatus (e.g. the properties of the source, patterning device and projection optics) dictate the aerial image. Because the patterning device used in the lithographic projection apparatus can be varied, it may be desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and projection optics.

[0057] exist Figure 2 An exemplary flow chart for simulating lithography in a lithographic projection apparatus is shown in FIG. The characteristics 31 of the source (e.g., radiation intensity distribution and / or phase distribution), the characteristics 32 of the projection optical device (e.g., changes in the radiation intensity distribution and phase distribution caused by the projection optical device), and the characteristics 33 of the patterning device (e.g., changes in the radiation intensity distribution and phase distribution caused by the arrangement of features representing a given design layout formed on or by the patterning device) are provided to a process model 34 as inputs to the process model 34. The process model 34 may have other inputs, such as characteristics of the exposure process, including dose and focus, or characteristics of post-exposure processes, including development, PEB, and etching. The process model 34 uses these inputs to simulate characteristics 35 (e.g., profile and CD, etc.) of the product of the lithography (e.g., aerial image, resist image, or etching image). Examples of the characteristics 35 may include process windows of features of the design layout, statistical parameters, such as standard deviations of features at multiple locations.

[0058] More specifically, it is noted that characteristic 31 may include optical characteristics of the source, including but not limited to numerical aperture settings, illumination sigma (σ) settings, and any specific illumination shapes (e.g., off-axis radiation sources such as annular, quadrupole, and dipole, etc.). Characteristic 32 may include optical characteristics of the projection optical device, including aberrations, distortions, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc. Characteristic 33 may include one or more physical characteristics of the physical pattern forming device, as described, for example, in U.S. Patent No. 7,587,704, the entire contents of which are incorporated herein by reference. Simulations can predict, for example, edge placement, spatial image intensity slope, and / or CD, which can then be compared to an expected design. The expected design is typically defined as a pre-OPC design layout, which can be provided in a standard digital file format (such as GDSII or OASIS) or other file format.

[0059] The process model 34 may have one of many possible forms. In each form, the process model 34 may have one or more parameters. The value of the parameter may be determined based on the deviation between the characteristic 35 simulated by the process model 34 (the "simulated characteristic") and the characteristic 35 measured from the physical substrate under the same processing conditions (e.g., the processing conditions represented by multiple sets of values ​​of the inputs to the process model 34) (the "measured characteristic"). For example, the deviation may be the difference between the CD simulated by the process model 34 and the CD actually measured on the physical substrate produced under the same processing conditions as used in the simulation. In an example, determining the value of the parameter may be simplified to finding a cost function CF1({p})=∑ C∈{c} F(M({p}, C), O(C)) is the value of the parameter {p} of the process model 34 that is at a local or global extreme. C is a process condition, which can be represented by a set of values ​​of the input to the process model 34; {c} is a set of process conditions; M({p}, C) is the simulated characteristic under process condition C; O(C) is the measured characteristic measured from a substrate produced under process condition C; F is the deviation between the simulated characteristic and the measured characteristic under process condition C. An example of F may be (M({p}, C) - O(C)) 2 . Figure 3 It is schematically shown that for each of the process conditions 315A, 315B, 315C, ... that is a member of the set {c}, a deviation F is determined and used to determine a value for a parameter {p} of the process model 34 .

[0060] Any change in the value of the input (i.e., any change in the process condition represented by the input) can affect the simulated characteristics and the measured characteristics. Examples of these changes can include changes in pattern size in the design layout, changes in the source, changes in the projection optics, and changes in post-exposure processes (e.g., development and PEB). If the set of process conditions {c} is not representative (e.g., the set of process conditions {c} has very few members), the process model 34 constructed using the set of process conditions {c} can have large errors, especially when the process model 34 is used with inputs that are not fully represented in {c}.

[0061] Increasing the size of the set of processing conditions {c} will undoubtedly improve its representativeness, but will also increase the amount of computation required to construct the process model 34.

[0062] In an embodiment, the deviation between the variation of the simulated characteristic and the variation of the measured characteristic among the process conditions (e.g., in the neighborhood of, e.g., ±10% of the process conditions), alone or together with the deviation between the simulated characteristic and the measured characteristic under the same process conditions, can be used to determine the value of the parameter of the process condition 34. This is because a good process model 34 should accurately model not only the characteristic 35 under several process conditions, but also the variation of the characteristic 35 around these process conditions. For example, the deviation can be the difference between the standard deviation of the CD simulated by the process model 34 for a set of process conditions and the standard deviation of the CD actually measured on a physical substrate produced under the same set of process conditions. In an example, determining the value of the parameter can be simplified to finding a cost function CF2({p})=∑ C∈{c} G(V(M( {p} , C)), V(O(C))) is the value of the parameter {p} of the process model 34M({p}, C) at a local extreme or a global extreme. C is a process condition (e.g., a nominal process condition), which can be represented by a set of values ​​of the input of the process model 34; {c} is a set of process conditions; M({p}, C) is a simulated characteristic under process condition C; O(C) is a measured characteristic measured from a substrate produced under process condition C; V(M({p}, C)) and V(O(C)) are the changes in the simulated characteristic and the changes in the measured characteristic between process conditions near process condition c, respectively. G is the deviation between the changes V(M({p}, C)) and V(O(C)). An example of G may be (V(M({p}, C))-V(O(C))) 2 In another example, the variation V may be the curvature of two Poisson curves, and the deviation G may be the difference between these curvatures. Figure 4It is schematically shown that for each of the process conditions (315A, 315B and 315C...) that are members of the set {c}, a deviation G is determined in the vicinity (316A, 316B or 316C...) of the process condition, and the deviation G is used to determine the value of the parameter of the process model 34.

[0063] In the example, determining the value of the parameter can be simplified to finding the value of the parameter {p} of the process model 34 M({p}, C) that causes the combination of CF1 and CF2 to be at a local or global extreme.

[0064] The values ​​of the parameters {p} of the process model 34 may be determined using algorithms such as a Gauss-Newton algorithm, a Levenberg-Marquardt algorithm, a Broyden-Fletcher-Goldfarb-Shannon algorithm, a gradient descent algorithm, a simulated annealing algorithm, an interior point algorithm, and a genetic algorithm.

[0065] Figure 5A Schematically, the measured characteristic (curve labeled "O") and the simulated characteristic (curve labeled "M1") by the process model M1 near the process condition C are shown. In this example, the deviation between the simulated characteristic and the measured characteristic under the same process condition is large; the deviation between the change of the simulated characteristic and the change of the measured characteristic under the same change of the process condition is small. That is, the cost function CF1 will be large, but the cost function CF2 will be small. Figure 5B Schematically shown are: a characteristic measured near process condition C (curve labeled "0") and a characteristic simulated by process model M2 (curve labeled "M2"). In this example, the deviation between the simulated characteristic and the measured characteristic under the same process condition is small; the deviation between the change in the simulated characteristic and the change in the measured characteristic under the same change in process condition is large. That is, the cost function CF1 will be small, but the cost function CF2 will be large. Neither process model M1 nor process model M2 is extremely accurate. When a combination of cost functions CF1 and CF2 is used to determine the parameters of the process model, both types of deviations can be reduced.

[0066] The process model 34 may have many parameters {p}. Using a cost function (e.g., CF1, CF2, or a combination of CF1 and CF2) to determine these many parameters {p} may cause the parameters to fall into local extremes. In an embodiment, many cost functions may be used to determine the parameters {p} of the process model 34. For example, these cost functions may be a combination of a plurality of deviations F between the simulated characteristics and the measured characteristics under a plurality of process conditions C and a plurality of deviations G between the changes in the simulated characteristics and the changes in the measured characteristics (e.g., among process conditions near process condition C). These deviations F and deviations G may be at a plurality of different process conditions. Some of the deviations F and deviations G may be selected to be sensitive only to a subset of the parameters {p}.

[0067] Fig. 6A A flow chart for constructing a process model according to an embodiment is schematically shown. In process 6010, a simulated characteristic is obtained by simulating a characteristic 35 under multiple processing conditions using a process model 34 having multiple parameters. The multiple processing conditions may be randomly selected. The multiple processing conditions may be within a range including a nominal processing condition. In process 6020, a variation of the simulated characteristic is determined. In process 6030, a measured characteristic is obtained by measuring the characteristic 35 from a pattern generated under multiple processing conditions, for example, using a metrology tool. In process 6040, a variation of the measured characteristic is determined. In process 6050, a deviation between the variations is determined. Examples of variations may include standard deviation, variance, range, or any other quantity that describes the difference between simulated or measured characteristics. In process 6060, parameters of the process model 34 are adjusted based at least in part on the deviations. Adjusting the parameters based on the deviations may include determining the value of the parameter that causes a function of the deviation to be at a local extreme or a global extreme. The parameters of the process model 34 may be adjusted based on a combination of the deviations determined in process step 6050 and the deviations between the simulated and measured characteristics under the same process conditions. In optional process step 6070, the process conditions (e.g., characteristics of the source, projection optics, patterning device, or a combination thereof) may be adjusted based on the simulations performed by the process model 34 under the adjusted parameters. In optional process step 6080, a set of locations on the substrate may be selected for inspection based on the simulations performed by the process model 34 under the adjusted parameters.

[0068] Figure 6BA flowchart for constructing a process model according to an embodiment is schematically shown. In process 7010, multiple deviations are obtained, each of which is between the change of the simulated characteristic and the change of the measured characteristic across the same set of process conditions, using processes 6010 to 6050 in the flowchart of Figure 6. In optional process 7020, one or more deviations between the simulated characteristic and the measured characteristic under the same process conditions are obtained. In process 7030, multiple cost functions are constructed. The cost function is a combination of multiple deviations between the change of the simulated characteristic and the change of the measured characteristic, and optionally one or more deviations between the simulated characteristic and the measured characteristic under the same process conditions. In an embodiment, at least one of the cost functions is not affected by all parameters of the process model 34. In process 7040, the parameters of the process model 34 are adjusted by using the cost function. For example, adjusting the parameters may include determining the values ​​of the parameters that make the multiple cost functions at local extremes or global extremes. In optional process step 7050, processing conditions (e.g., characteristics of the source, projection optics, patterning device, or a combination thereof) may be adjusted based on simulations performed by process model 34 under the adjusted parameters. In optional process step 7060, a set of locations on the substrate may be selected for inspection based on simulations performed by process model 34 under the adjusted parameters.

[0069] Figure 7 1 is a block diagram illustrating a computer system 100 that can assist in implementing the methods, processes, devices, or systems disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 further includes a read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and is coupled to the bus 102 for storing information and instructions.

[0070] The computer system 100 may be coupled via the bus 102 to a display 112, such as a cathode ray tube (CRT) or a flat panel display or a touch screen display, for displaying information to a computer user. An input device 114, including alphanumeric keys and other keys, is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor controller 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. The input device typically has two degrees of freedom in two axes, a first axis (e.g., an x-axis) and a second axis (e.g., a y-axis), which allows the device to specify a position in a plane. A touch screen (screen) display may also be used as an input device.

[0071] According to one embodiment, parts of the optimization process may be performed by the computer system 100 in response to the processor 104 executing one or more sequences of one or more instructions contained in the main memory 106. Such instructions may be read into the main memory 106 from another computer-readable medium, such as a storage device 110. The execution of the sequence of instructions contained in the main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors may also be used to execute the sequence of instructions contained in the main memory 106 in a multi-processing arrangement. In an alternative embodiment, hard-wired circuits may be used instead of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0072] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. The medium can take many forms, including but not limited to non-volatile media, volatile media and transfer media. Non-volatile media include, for example, optical disks or magnetic disks, such as storage devices 110. Volatile media include dynamic memory, such as main memory 106. Transfer media include coaxial cables, copper wires and optical fibers, including wires containing bus 102. Transfer media can also take the form of sound waves or light waves, such as light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tapes, any other physical media with hole patterns, RAMs, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or boxes, carriers as described below, or any other media that a computer can read.

[0073] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A local modem of computer system 100 may receive data on the telephone line and use an infrared transmitter to convert the data into an infrared signal. An infrared detector coupled to bus 102 may receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after being executed by processor 104.

[0074] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides a bidirectional data communication coupling to a network link 120, which is connected to a local area network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem connected to a telephone line of a corresponding type in order to provide data communication. As another example, the communication interface 118 may be a local area network (LAN) card connected to a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such implementation, the communication interface 118 sends and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0075] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide a connection to a host computer 124 or a data device operated by an Internet Service Provider (ISP) 126 through a local area network 122. ISP 126, in turn, provides data communication services through a global packet data communication network, now commonly referred to as the "Internet" 128. Both the local area network 122 and the Internet 128 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which carry the digital data to and from the computer system 100, are exemplary forms of carrier waves that transport the information.

[0076] The computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, a server 130 might transmit code requested for an application program through Internet 128, ISP 126, local area network 122, and communication interface 118. One such downloaded application may provide, for example, irradiation optimization of an embodiment. The received code may be executed by processor 104 as it is received, and / or stored in storage device 110 or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[0077] Figure 8 An exemplary lithographic projection apparatus, the illumination of which may be optimized using the method described herein, is schematically depicted, the apparatus comprising:

[0078] - an illumination system IL for conditioning the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO;

[0079] a first object table (e.g. patterning device table) MT provided with a patterning device holder for holding a patterning device MA (e.g. a reticle) and connected to a first positioner for accurately positioning the patterning device relative to the object PS;

[0080] a second object table (e.g. substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a silicon wafer coated with resist) and connected to a second positioner for accurately positioning said substrate relative to the object PS;

[0081] - a projection system ("lens") PS (eg a refractive, reflective or catadioptric optical system) for imaging the irradiated portion of the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0082] As described herein, the apparatus is transmissive (i.e., has a transmissive patterning device). However, for example, it may also be reflective (have a reflective patterning device) in general. The apparatus may employ a patterning device of a different type than a classical mask; examples include a programmable mirror array or an LCD matrix.

[0083] A source SO (e.g. a mercury lamp or an excimer laser, an LPP (laser produced plasma) EUV source) generates a radiation beam. This radiation beam is fed, for example, directly into an illumination system (illuminator) IL or after passing through a conditioning device (such as a beam expander Ex). The illuminator IL may comprise an adjustment device AD ​​for setting the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. In addition, it will typically comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the pattern forming device MA has a desired uniformity and intensity distribution in its cross section.

[0084] about Figure 8 It should be noted that the source SO can be located inside the housing of the lithographic projection device (which is often the case when the source SO is, for example, a mercury lamp), but it can also be remote from the lithographic projection device, the radiation beam it generates being guided into the device (for example, with the aid of suitable directional reflectors); the latter case is typically the case when the source SO is an excimer laser (for example an excimer laser based on KrF, ArF or F2 lasers).

[0085] The radiation beam PB is subsequently intercepted by the patterning device MA held on the patterning device table MT. After having passed through the patterning device MA, the radiation beam B passes through a lens PL which focuses the radiation beam B onto a target portion C of the substrate W. With the aid of the second positioning device (and the interferometer measurement device IF), the substrate table WT can be precisely moved, for example in order to position different target portions C in the path of the beam PB. Similarly, the first positioning device can be used to precisely position the patterning device MA relative to the path of the radiation beam B, for example after mechanical retrieval of the patterning device MA from a patterning device library or during a scan. Typically, the long-stroke module (coarse positioning) and the short-stroke module (fine positioning) (not shown) are used to precisely position the patterning device MA relative to the path of the radiation beam B. Figure 8 ), movement of the object table MT, WT will be achieved. However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to a short-stroke actuator only or may be fixed.

[0086] The tools shown can be used in two different modes:

[0087] In step mode, the patterning device table MT may be kept substantially stationary and an image of the entire patterning device may be projected at once (i.e. in a single “flash”) onto a target portion C. The substrate table WT is then moved in the x and / or y direction so that a different target portion C may be irradiated by the beam PB.

[0088] - In scan mode, essentially the same situation applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT can be moved in a given direction (the so-called "scanning direction", e.g. the y-direction) at a speed v, so as to cause the projection beam B to scan over the image of the patterning device; while the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed, without compromising on resolution.

[0089] Fig. 9 Another exemplary lithographic projection apparatus 1000 is schematically shown, the illumination of which may be optimized using the methods described herein.

[0090] The lithography projection device 1000 comprises:

[0091] - Source collector module SO;

[0092] - an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. EUV radiation);

[0093] a support structure (e.g., patterning device table) MT configured to support a patterning device (e.g., mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0094] a substrate table (eg wafer table) WT configured to hold a substrate (eg resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0095] - a projection system (eg a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0096] As shown here, the apparatus 1000 is reflective (e.g., employing a reflective patterning device). It should be noted that since most materials are absorptive in the EUV wavelength range, the patterning device can have a multilayer reflector, including, for example, multiple stacks of molybdenum and silicon. In one example, the multilayer reflector has 40 layers of paired molybdenum and silicon, each layer being a quarter wavelength thick. Even smaller wavelengths can be produced using X-ray lithography. Since most materials are absorptive in EUV and X-ray wavelengths, a thin sheet of absorbing material patterned on the topology of the patterning device (e.g., a TaN absorber on top of a multilayer reflector) defines areas where features will be printed (positive resist) or not (negative resist).

[0097] Reference Fig. 9 , the illuminator IL receives a beam of extreme ultraviolet radiation from the source collector module SO. Methods for generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element having one or more emission lines in the EUV range, such as xenon, lithium, or tin. In one such method, generally referred to as laser produced plasma ("LPP"), the plasma may be generated by irradiating a fuel, such as a droplet, a stream, or a cluster of a material having an element with line emission, with a laser beam. The source collector module SO may be a laser (in Fig. 9 The laser and source collector module may be separate entities, for example when a CO2 laser is used to provide the laser beam for fuel excitation.

[0098] In this case, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is delivered from the laser to the source collector module by means of a beam delivery system comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, commonly referred to as a DPP source.

[0099] The illuminator IL may comprise an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. Furthermore, the illuminator IL may comprise various other components, such as faceted field mirror means and pupil mirror means. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0100] The radiation beam B is incident on the patterning device (e.g. mask) MA held on a support structure (e.g. patterning device table) MT and is patterned by the patterning device. After having been reflected from the patterning device (e.g. mask) MA, the radiation beam B passes through a projection system PS which focuses the radiation beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g. interferometer equipment, a linear encoder or a capacitive sensor), the substrate table WT can be precisely moved, for example in order to position a different target portion C in the path of the radiation beam B. Similarly, the first positioner PM and a further position sensor PS1 may be used to precisely position the patterning device (e.g. mask) MA relative to the path of the radiation beam B. The patterning device (e.g. mask) MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0101] The illustrated device 1000 may be used in at least one of the following modes:

[0102] 1. In step mode, the support structure (e.g. patterning device table) MT and the substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam is projected onto a target portion C at one time (i.e. a single static exposure). The substrate table WT is then moved in the X and / or Y direction so that a different target portion C can be exposed.

[0103] 2. In scan mode, the support structure (e.g. patterning device table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure (e.g. patterning device table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0104] 3. In another mode, the support structure (e.g. patterning device table) MT holding the programmable patterning device is held substantially stationary and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation may be readily applicable to maskless lithography using a programmable patterning device such as a programmable mirror array of the type described above.

[0105] Fig.10The apparatus 1000 is shown in more detail, including a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment is maintained within an enclosure 220 of the source collector module SO. A plasma 210 emitting EUV radiation may be formed by a discharge-generated plasma source. EUV radiation may be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein an extremely high temperature plasma 210 is generated to emit radiation in the EUV range of the electromagnetic radiation spectrum. The extremely high temperature plasma 210 is generated by, for example, a discharge that causes at least partially ionized plasma. For example, a partial pressure of 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required to effectively generate radiation. In an embodiment, an excited plasma of tin (Sn) is provided to generate EUV radiation.

[0106] The radiation emitted by the high temperature plasma 210 is transferred from the source chamber 211 to the collector chamber 212 via a gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or fin trap in some cases) optionally positioned within or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further shown here includes at least a channel structure, as known in the prior art.

[0107] The collector cavity 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation passing through the collector CO may be reflected off the grating spectral filter 240 to be focused at a virtual source point IF along the optical axis shown by the dashed line 'O'. The virtual source point IF is often referred to as an intermediate focus, and the source collector module is arranged so that the intermediate focus IF is located at or near the opening 211 in the enclosing structure 220. The virtual source point IF is an image of the plasma 210 for emitting radiation.

[0108] The radiation then passes through an illumination system IL which may comprise a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and a desired uniformity of radiation intensity at the patterning device MA. When the radiation beam 21 is reflected at the patterning device MA held by the support structure MT, a patterned beam 26 is formed and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0109] There may typically be more elements present in the illumination optics unit IL and the projection system PS than are shown. Grating spectral filter 240 may optionally be present, depending on the type of lithographic apparatus. Furthermore, there may be more mirrors than are shown, for example, there may be more than one mirror in the projection system PS. Fig.10 1-6 additional reflective elements beyond the elements shown.

[0110] Collector optics CO (eg Fig.10 As just one example of a collector (or collector mirror), a nested collector is shown with grazing incidence reflectors 253, 254 and 255. The grazing incidence reflectors 253, 254 and 255 are arranged axially symmetrically around the optical axis O, and this type of collector optics CO can be used in conjunction with a discharge produced plasma source, often referred to as a DPP source.

[0111] Alternatively, the source collector module SO may be as follows Fig.11 A portion of the LPP radiation system shown. The laser LA is arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of several tens of eV. The high-energy radiation generated during the deexcitation and recombination of these ions is emitted by the plasma, collected by the near normal incidence collector optics CO and focused onto an opening 221 of the enclosing structure 220.

[0112] U.S. Patent Application Publication No. US 2013-0179847 is hereby incorporated by reference in its entirety.

[0113] The embodiments may be further described using the following aspects:

[0114] 1. A method comprising:

[0115] obtaining the simulated characteristic by simulating the characteristic of a product of lithography under a plurality of processing conditions using a process model including the parameters;

[0116] determining a change in the simulated characteristic;

[0117] obtaining a measured characteristic by measuring the characteristic of the product according to a pattern produced under the plurality of processing conditions;

[0118] determining a change in the characteristic being measured;

[0119] determining a first deviation between the change in the modeled characteristic and the change in the measured characteristic; and

[0120] The parameter is adjusted based on the first deviation.

[0121] 2. The method of aspect 1 further comprises adjusting processing conditions based on simulations performed by the process model.

[0122] 3. The method of clause 1, further comprising selecting a set of locations on a substrate produced by the lithography process for inspection based on simulations performed by the process model.

[0123] 4. The method of any one of aspects 1 to 3, wherein the plurality of processing conditions are selected randomly.

[0124] 5. The method of any one of aspects 1 to 3, wherein the plurality of processing conditions comprises nominal processing conditions.

[0125] 6. The method of any one of aspects 1 to 5, wherein the variation of the measured characteristic is selected from the group consisting of: a standard deviation of the measured characteristic, a variance of the measured characteristic, and a range of the measured characteristic.

[0126] 7. A method as described in any one of aspects 1 to 6, wherein the variation of the simulated characteristic is selected from the group consisting of: a standard deviation of the measured characteristic, a variance of the measured characteristic, and a range of the measured characteristic.

[0127] 8. A method as described in any one of aspects 1 to 7, wherein adjusting the parameter includes determining a value of the parameter that causes the function of the first deviation to be at a local extreme value or a global extreme value.

[0128] 9. The method of any one of aspects 1 to 8, wherein adjusting the parameter is based on a combination of the first deviation and a second deviation, the second deviation being between the simulated characteristic and the measured characteristic under the same process conditions.

[0129] 10. A method as described in any one of aspects 1 to 9, wherein the multiple processing conditions include characteristics of a source of the lithography device, characteristics of a projection optical device of the lithography device, and characteristics of a pattern forming device, wherein the pattern forming device has an arrangement of features representing a design layout.

[0130] 11. The method of any one of aspects 1 to 10, wherein the characteristic of the product comprises a characteristic of an image.

[0131] 12. The method of clause 11, wherein the image is an aerial image, a resist image, or an etched image.

[0132] 13. The method of any one of clauses 1 to 12, wherein the characteristic of the product comprises a process window of a feature of a design layout.

[0133] 14. The method of any one of aspects 1 to 13, wherein the characteristic of the product comprises statistical parameters of features at a plurality of locations.

[0134] 15. A method comprising:

[0135] obtaining a plurality of first deviations, each of the plurality of first deviations being between variations of a simulated characteristic of a product of lithography and variations of a measured characteristic of the product of lithography, wherein the simulated characteristic is obtained by simulating the characteristic of the product using a process model including a parameter;

[0136] constructing a plurality of cost functions, wherein the cost functions are combinations of the plurality of first deviations; and

[0137] The parameters of the process model are adjusted by using the cost function.

[0138] 16. The method of clause 15, further comprising adjusting processing conditions based on simulations performed by the process model.

[0139] 17. The method of clause 15, further comprising selecting a set of locations on a substrate produced by the lithography for inspection based on simulations performed by the process model.

[0140] 18. The method of any one of aspects 15 to 17, wherein the variation is across the same set of treatment conditions.

[0141] 19. The method of any one of aspects 15 to 18, further comprising obtaining a second deviation between the simulated characteristic and the measured characteristic under the same processing conditions, wherein the cost function is a combination of the plurality of first deviations and the second deviation.

[0142] 20. A method as claimed in any one of clauses 15 to 19, wherein at least one of the cost functions is unaffected by all of the parameters.

[0143] 21. The method of any one of aspects 15 to 20, wherein adjusting the parameter comprises determining a value of the parameter that causes the cost function to be at a local minimum or a global minimum.

[0144] 22. A method as claimed in any one of clauses 15 to 21, wherein the characteristics of the product comprise characteristics of an image.

[0145] 23. The method of clause 22, wherein the image is an aerial image, a resist image, or an etched image.

[0146] 24. The method of any one of clauses 15 to 23, wherein the characteristic of the product comprises a process window for a feature of a design layout.

[0147] 25. The method of any one of aspects 15 to 24, wherein the characteristic of the product comprises statistical parameters of features at a plurality of locations.

[0148] 26. A computer program product, comprising a non-transitory computer-readable medium having instructions recorded thereon, the instructions implementing the method according to any one of aspects 1 to 25 when executed by a computer.

[0149] The concepts disclosed in this invention can simulate or mathematically model any general imaging system for imaging sub-wavelength features, and can be particularly useful for emerging imaging technologies that can produce shorter and shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography that can produce 193nm wavelengths by using ArF lasers and even 157nm wavelengths by using fluorine lasers. In addition, EUV lithography can produce wavelengths in the range of 5 to 20nm by using synchrotrons or by applying high energy electrons to a material (solid or plasma) to produce photons in this range.

[0150] Although the concepts disclosed in the present invention may be used for imaging on substrates such as silicon wafers, it will be understood that the disclosed concepts may be used in any type of lithography imaging system, such as a lithography imaging system for imaging on substrates other than silicon wafers.

[0151] The above description is intended to be illustrative rather than limiting. It will therefore be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth hereinafter.

Claims

1. A method for fine-tuning a process model, comprising: The simulated characteristics are obtained by simulating the characteristics of a product of lithography under a plurality of processing conditions by a computer system using a process model including the parameters, determining a statistical variation of the simulated characteristic; obtaining a measured characteristic by measuring the characteristic of the product according to a pattern produced under the plurality of processing conditions; determining a statistical variation of a characteristic of said measurement; determining a first deviation between the simulated change in the characteristic and the measured change in the characteristic; and The parameter is adjusted based on the first deviation.

2. The method of claim 1, further comprising adjusting processing conditions of manufacturing based on simulations performed by the process model.

3. The method of claim 1, further comprising selecting a set of locations for inspection on a substrate processed using the lithography technique based on simulations performed by the process model.

4. The method of claim 1, wherein: The plurality of treatment conditions are selected randomly. The method of claim 1 , wherein the plurality of processing conditions comprises nominal processing conditions.

6. The method of claim 1, wherein the variation of the measured characteristic is selected from the group consisting of: a standard deviation of the measured characteristic, a variance of the measured characteristic, and a range of the measured characteristic.

7. The method of claim 1, wherein the variation of the simulated characteristic is selected from the group consisting of: a standard deviation of the simulated characteristic, a variance of the simulated characteristic, and a range of the simulated characteristic.

8. The method of claim 1 , wherein adjusting the parameter comprises: A value of the parameter is determined that causes the function of the first deviation to be at a local or global extremum.

9. The method of claim 1, wherein adjusting the parameter is based on a combination of the first deviation and a second deviation, the second deviation being between the simulated characteristic and the measured characteristic under the same processing conditions.

10. The method of claim 1, wherein the plurality of processing conditions comprises characteristics of a patterning device illuminated by a lithographic apparatus, characteristics of a projection optical device of the lithographic apparatus, and characteristics of a patterning device having an arrangement of features representing a design layout thereon.

11. The method according to claim 1, wherein: Wherein the characteristics of the product include characteristics of an image.

12. The method according to claim 1, wherein: The characteristics of the product include a process window for characteristics of a design layout.

13. The method of claim 1, wherein the characteristics of the product include statistical parameters of features at a plurality of locations.

14. A method for fine-tuning a process model, comprising: obtaining a plurality of first deviations, each of the plurality of first deviations being between a statistical variation of a simulated characteristic of a product of lithography and a statistical variation of a measured characteristic of the product of lithography, wherein the simulated characteristic is obtained by simulating the characteristic of the product by a computer system using a process model including a parameter; constructing a plurality of cost functions, the cost functions being combinations of the plurality of first deviations; and adjusting the parameters of the process model by using the cost functions.

15. The method of claim 14, further comprising adjusting processing conditions of manufacturing based on simulations performed by the process model.

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