Wafer exposure method using a wafer model and a wafer manufacturing assembly

Abstract

The present invention discloses a wafer exposure method, which obtains critical dimension values from a wafer structure at a predetermined measurement site. Position-dependent process parameters of an exposure process for forming the wafer structure are obtained. Coefficients of a preset model and at least one further model are determined from the critical dimension values at the measurement site. Each further model differs from the preset model and other models in at least one item. The models estimate the critical dimension values, the process parameters, and / or corrected values of the process parameters that vary with at least two position coordinates. A residual between the estimated critical dimension values obtained from the models and the critical dimension values obtained at the measurement site is determined. An updated model is selected from the preset model and the at least one further model. The selection is based on a criterion that weights the residual, the number of terms of the model, and / or the order of the terms of the model.

Description

Technical Field

[0001] Embodiments of the present disclosure relate to the field of semiconductor lithography and patterning, and in particular, embodiments of the present disclosure relate to aspects of wafer models for process monitoring and process control. Background Art

[0002] In the manufacture of electronic devices such as integrated circuits, displays, and sensors, a lithography system transfers a pattern from a photomask to a semiconductor substrate. The photomask contains circuit design information. A photoresist layer is coated on the semiconductor substrate. An exposure process transfers the photomask pattern into the photoresist layer. Controllable parameters of the exposure process include focus and dose. The "focus" value can be given as "defocus", which describes the distance between the actual focal plane and a reference plane for optimal patterning conditions. The dose value gives a measure of the radiation power of the exposure beam. The optimal values of both focus and dose typically depend on the position coordinates of the exposure beam on the main surface. Since fluctuations in the process history of the substrate affect the exposure result, the optimal focus and dose values are also time-dependent. Feedback loops for focus and dose typically provide focus and dose correction values for the next exposure based on information obtained from previously exposed substrates. The correction values are typically derived from information obtained from relatively few measurement sites. A wafer model supports interpolation of field fine correction values or even intra-field correction values based on information obtained from the measurement sites.

[0003] There is a need for a steady improvement in process monitoring and process control of the patterning process. Summary of the Invention

[0004] Embodiments of the present application relate to a wafer exposure method. For the wafer exposure method, critical dimension values are obtained from a wafer structure at predetermined measurement sites. Position-dependent process parameters for an exposure process for forming the wafer structure are obtained. Coefficients of a preset model and at least one further model are determined from the critical dimension values at the measurement sites. Each further model differs from the preset model and other models in at least one item. Each model estimates the critical dimension values, the process parameters, and / or correction values of the process parameters that vary with at least two position coordinates. A residual between an estimated critical dimension value obtained from the model and the critical dimension value obtained at the measurement site is determined. An updated model is selected from the preset model and the at least one further model. The selection is based on a criterion that weights the residual, the number of terms, and / or the order of the terms of the wafer model.

[0005] Another embodiment of the present application relates to a wafer manufacturing assembly. The wafer manufacturing assembly includes an exposure tool assembly. The exposure tool assembly exposes a photoresist layer coated on a wafer substrate to an exposure beam, wherein the exposure tool assembly uses position-dependent process parameters to define a wafer structure from the exposed photoresist layer. A processor unit is data-connected to the exposure tool assembly. The processor unit receives and / or holds position-dependent process parameters for defining the wafer structure in the exposure tool assembly. The processor unit further receives a critical dimension value of the wafer structure obtained from the exposed photoresist layer at a predetermined measurement site. The processor unit determines coefficients of a preset model and at least one further model from the critical dimension value at the measurement site. Each further model differs from the preset model and other models in at least one item. The models estimate the critical dimension value, the process parameters, and / or a correction value of the process parameters that vary with at least two position coordinates. The processor unit determines a residual between the estimated critical dimension value obtained from the model and the critical dimension value obtained at the measurement site. The processor unit selects an updated model from the preset model and the at least one further model, wherein the selection is based on a criterion that weights the residual, the number of items of the model, and / or the order of the items of the model.

[0006] Those skilled in the art will recognize additional features and advantages upon reading the following detailed description and viewing the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The accompanying drawings are included to provide a further understanding of the embodiments and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the exposure method and the wafer manufacturing assembly and, together with the description, are used to explain the principles of the embodiments. Further embodiments are described in the following detailed description and the claims.

[0008] Figure 1 is a schematic block diagram of a section of a wafer manufacturing assembly including a processor unit for monitoring and / or controlling at least one exposure parameter according to an embodiment.

[0009] Figure 2 is a schematic diagram for illustrating the effect of a penalty term in a wafer model update process according to an embodiment.

[0010] Figure 3A and 3B schematically illustrate the selection of Zernike polynomials for updating a wafer model according to an example for illustrating the effect of an embodiment.

[0011] Figure 4 Shows a flowchart of a wafer exposure model update according to an embodiment. Detailed implementation manners

[0012] In the following detailed description, reference is made to the accompanying drawings, which form a part of the present disclosure and in which specific embodiments in which the embodiments can be practiced are shown by way of illustration. It should be understood that other embodiments can be utilized and structural or logical changes can be made without departing from the scope of the present disclosure. For example, the features illustrated or described for an embodiment can be used on or in combination with other embodiments to yield yet another embodiment. The present disclosure is intended to embrace such modifications and variations. The examples are described using specific language and should not be construed as limiting the scope of the appended claims. The figures are not drawn to scale and are for illustrative purposes only. If not otherwise stated, corresponding elements in different figures are denoted by the same reference numerals.

[0013] The terms "having", "containing", "including", "comprising" and the like are open-ended, and the terms indicate the presence of the described structure, element or feature, but do not exclude additional elements or features. Unless the context clearly indicates otherwise, the articles "a" and "the" are intended to include the plural and the singular.

[0014] Embodiments of the present disclosure relate to a wafer exposure method. The wafer exposure method includes obtaining a critical dimension value of a wafer structure at a predetermined measurement site.

[0015] The wafer structure can include a structure formed on or in a wafer substrate. The wafer substrate can be a thin disk including a substrate material. The substrate material can include a semiconductive material. For example, by way of example, the wafer substrate can be a semiconductor wafer, a glass substrate including one or more semiconductive layers, or a SOI (silicon-on-insulator) wafer.

[0016] The wafer substrate can include a trench extending from a main surface at the front side of the wafer substrate into the wafer substrate. The trench can be filled with a material different from the surrounding substrate material. Alternatively or additionally, the wafer structure can protrude from the main surface at the front side of the wafer substrate. The structure protruding from the main surface can include, for example, columns, bar-shaped ribs and / or line patterns. The structure protruding from the main surface can include a photoresist structure.

[0017] Each critical dimension value quantitatively describes a physical property of one of the wafer structures or a positional relationship between two wafer structures.

[0018] The wafer exposure method can further include obtaining position-dependent process parameters of an exposure process that has been used to form the wafer structure. The exposure process can use an exposure tool assembly. The exposure tool assembly can use an exposure beam to project a mask pattern into a photoresist layer coating the main surface of the wafer substrate. The process parameters include such parameters of the exposure process that affect the critical dimension value. The process parameters can include such parameters of the exposure process that can be controlled as a function of the position of the exposure beam on the main surface.

[0019] The coefficients of a preset model can be determined from critical dimension values obtainable at a predetermined measurement site. The preset model can be a model that has been used to determine exposure parameters for a previous exposure. Additionally, the coefficients of at least one further model can be determined, where each further model differs from the preset model in at least one respect and from other further models in at least one respect.

[0020] Each model can estimate the distribution of critical dimension values across the main surface in a closed mathematical form. The current model receives input information obtained from measurements at the measurement sites. The model derives output information that describes the distribution of critical dimension values across the entire main surface from the input information. The input information can include measured critical dimension values and / or process parameters derived from the measured critical dimension values. The output information can include estimated critical dimension values that vary with position, updated process parameters, and / or process parameter correction values. The output information can be displayed, transmitted to a higher-order process monitoring and / or management system, and / or used to control the exposure process across the entire main surface of the next wafer substrate or the reprocessing of the current wafer substrate.

[0021] The position can be described by position coordinates that uniquely define each point on the main surface of the substrate. For example, the position coordinates can be linear coordinates (such as orthogonal linear coordinates (x,y coordinate system)) or polar coordinates. The position coordinates can describe the position of the exposure field (for inter-field correction) and / or the position within each exposure field (for intra-field correction).

[0022] Each model is represented as a sum of terms. Each (model) term includes at least one position coordinate and a coefficient. For example, each term can be the product of a coefficient and an algebraic function of at least one position coordinate.

[0023] The coefficients of each model can be obtained by using a fitting algorithm. The fitting algorithm searches for coefficients that minimize the deviation between the critical dimension values output by the corresponding model ("model CD") and the actual critical dimension values ("actual CD"). The actual CD is the CD directly obtained from the wafer structure at a predetermined measurement site on the current wafer substrate. The model CD is the CD output by the corresponding model for the predetermined measurement site. The fitting algorithm can include the least squares method (LSM).

[0024] Next, for each relevant model individually, the residual between the output of the model and the actual CD value obtained from the wafer structure is determined. In other words, for each relevant model individually, the remaining difference between the model CD and the actual CD is determined.

[0025] Next, an updated model is selected from the preset model and at least one further model. The selection can be based on a criterion that weights the magnitude of the residuals with the number of terms of the corresponding model and / or the order of the terms of the model. The total residual generally decreases as the complexity of the model increases (e.g., as the number of model terms increases). However, only the terms that have a high impact on the overall model (e.g., relatively heavily weighted terms) generally represent the physical effects of the production line of the wafer substrate, while the low-weighted terms only or mainly reflect the noise effects. By treating the number of terms as a penalty term, the number of terms of the model can be limited to those that represent the significant physical effects of the production line and that can also have a systematic effect on the next exposure. On the other hand, the model terms that cannot be assigned to an entity background contribute little to improving the exposure process and can even have a direct effect on the efficiency of the model.

[0026] Controlling the exposure process using the updated model instead of the predefined model can be more effective because the updated model better matches the current dominant physical effects of the production line. New model terms and / or skipped model terms can indicate significant changes in the process in the production line of the wafer substrate.

[0027] According to an embodiment, information describing the terms of the updated model can be output. For example, any changes to the model terms can be displayed to a human operator or a higher-order process monitoring and / or management system. Any skipping of terms and any insertion of terms in the model can indicate some significant changes in the overall process characteristics. Therefore, information regarding the elimination of model terms and / or newly introduced model terms can be used for process control.

[0028] According to an embodiment, the position-dependent process parameters for the next exposure process can be updated based on the updated model. In this way, the information obtained from the predetermined measurement sites of the current wafer substrate can be used in real time to improve the next exposure process. The exposure process can immediately adapt to changes in the process characteristics.

[0029] By using online information to stabilize the updated model, the exposure process can follow process deviations that were not detected in the previously processed wafer substrates after their first occurrence and without intervention (e.g., without operator intervention).

[0030] According to an embodiment, the selection of the updated model can be based on a trade-off that weights the number of model terms with the total amount of residuals. For example, an auxiliary function that combines a first term and a second term can be defined. The first term represents the model quality that varies with the number of model terms. The first term can decrease steadily as the number of model terms increases. The second term can increase as the number of model terms increases. The second term can increase steadily, e.g., monotonically. The terms can be combined additively or multiplicatively.

[0031] According to an embodiment, the selection of the updated model can be based on at least one of BIC (Bayesian Information Criterion) or AIC (Akaike Information Criterion). BIC can be defined as Equation (1), and AIC can be defined as Equation (2).

[0032] Equation (1): BIC = k·ln(n) - 2·ln(^L)

[0033] Equation (2): AIC = 2k - 2·ln(^L)

[0034] In Equations (1) and (2), n gives the number of measurement sites, k gives the number of terms, and ^L indicates the maximum of the likelihood function, which can increase inversely with the total residual.

[0035] According to an embodiment, the model may include at least one of Zernike polynomials and / or Legendre polynomials. Zernike polynomials refer to a rotating coordinate system. Due to the shape and nature of the process of most wafer substrates, many process deviations result in errors that can be better described by Zernike polynomials.

[0036] For example, the model may include, for example, polynomial terms with polar coordinates for inter-field correction. Inter-field correction can reduce substrate-level deviations, such as based on deposition effects, wafer bending, and other effects. For example, the model may include Zernike polynomials. Additionally or alternatively, the model may include, for example, polynomial terms with Cartesian coordinates for intra-field correction. Intra-field correction can reduce mask effects and / or design-specific effects. For example, the model may include Legendre polynomials.

[0037] According to an embodiment, at least one of the further models may include all polynomials of a specific type up to the highest order. For example, at least one further model may include all Zernike polynomials up to the highest order. The highest order may be in the range from 3 to 10. The highest order may be the order at which the BIC or AIC has a minimum value.

[0038] According to an embodiment, a quality index may be determined for each coefficient of the updated model. The quality index may give information about the degree of dependence of the coefficient on the variation of the critical dimension values obtained at the sampling points.

[0039] The quality index may be derived from all predetermined measurement sites or only from some of the predetermined measurement sites. For example, the quality index may be derived only from the predetermined measurement sites that contribute significantly to the coefficient. The quality index may be higher when a slight variation in each of the critical dimension values has only a low impact on the value of the coefficient and / or when the value of the coefficient is robust to a single outlier compared to the critical dimension values.

[0040] The quality index may be transmitted to a higher-order process monitoring and / or management system or may be displayed to a human operator. Additionally or alternatively, the selection of the terms of the updated model may consider the quality index of the model terms. For example, the selection of the terms of the updated model may include skipping the terms whose coefficients have a quality index lower than a preset threshold value.

[0041] For example, a quality index may be calculated based on a statistical method such as bootstrapping. For example, the calculation of each coefficient may be repeated multiple times in different runs with different weights for the critical dimension values obtained from the sampling points. For example, in each repetition, at least another one of the sampling points may be completely ignored in the coefficient calculation and / or at least another sampling point may be weighted by a factor of 2. The smaller the difference between the results in different runs of the correlation coefficient, the higher the quality index assigned to the coefficient.

[0042] According to an embodiment, the selection may be based on a criterion that weights the distribution of the residuals. For example, the selection may be based on a normality test. The normality test includes determining the degree of consistency between the distribution of the residuals of the corresponding model and a normal distribution. For example, the updated model may be the model that results in the best fit between the residual distribution and the normal distribution. The degree of consistency may be derived from the minimum mean square error between the normal distribution and the distribution of the residuals of the corresponding model.

[0043] According to an embodiment for overlap error analysis and / or overlap correction, the critical dimension value may include an overlap difference value. Overlap errors occur between structures formed in different layers of a wafer substrate.

[0044] The overlap difference value describes the type and degree of the overlap error between a first wafer structure formed in a first horizontal layer and a second wafer structure formed in a second horizontal layer. The overlap error may be position-dependent and may include at least one of the following: a linear offset between the first wafer structure and the second wafer structure, an enlargement or size reduction of the second wafer structure relative to the first wafer structure, and a rotation of the second wafer structure relative to the first wafer structure. The second horizontal layer may be directly adjacent to the first horizontal layer. Alternatively, a third horizontal layer may be formed between the first horizontal layer and the second horizontal layer.

[0045] The measurement site from which the overlap difference value is obtained may be any area at the front side of the wafer substrate having a first usage structure in the first horizontal layer and a second usage structure in the second horizontal layer. Alternatively, the measurement site may be an area having a usage structure in the first of the first horizontal layer and the second horizontal layer and having an overlap mark in the second of the first horizontal layer and the second horizontal layer. According to another alternative, the overlap difference value may be obtained from an area including discrete overlap marks. The discrete overlap marks are specifically or at least mainly used to determine the overlap error.

[0046] The discrete overlap marks may include, for example, a group of parallel lines and / or frame-shaped marks. For example, the overlap mark may include a first frame in the first horizontal layer and a second frame in the second horizontal layer. The two frames may have different sizes. Each frame may include four linear strips arranged along the sides of a rectangle (e.g., a square).

[0047] For overlay analysis and / or overlay correction, the controllable process parameters may include position offsets. The position offsets may include linear offsets, such as an x-offset and a y-offset. The x-offset may include information about the lateral displacement of the wafer substrate from a reference position along a first horizontal axis (the x-axis). The y-offset may include information about the displacement of the wafer substrate from the reference position along a second horizontal axis (the y-axis). The second horizontal direction may extend orthogonally to the first horizontal direction.

[0048] Further for overlay analysis and / or overlay correction, each model may include a wafer overlay model. The wafer overlay model estimates the overlay difference value, the position offset, and / or the position offset correction value that vary with the position coordinates of the main surface of the substrate.

[0049] In terms reflecting the application of the wafer exposure method to overlay analysis and / or overlay correction, each wafer overlay model estimates the total overlay error across the main surface of the substrate in a closed mathematical form. Each overlay model is represented by the sum of terms. Each (model) term includes at least one position coordinate and a coefficient. For example, each term may be the product of a coefficient and a function of at least one position coordinate.

[0050] The current overlay model receives input information obtained from measurements at the overlay marks. The overlay model derives output information describing the position-dependent overlay error across the entire main surface of the substrate from the input information. The input information may include the measured overlay error at the overlay marks. The output information may include the estimated position-dependent overlay error that varies with the position coordinates, the updated position offset, and / or the position offset correction value.

[0051] According to an embodiment, the overlay model may include the terms represented in equations (3) and (4).

[0052] Equation (3): Δx = Γ1·x + R1·x·y + WM1·y

[0053] Equation (4): Δy = Γ2·y + R2·x·y + WM2·x

[0054] The coefficients Γ1, Γ2, R1, R2, WM1, WM2 of each overlay model may be obtained from a fitting algorithm. The fitting algorithm searches for the coefficient values that minimize the deviation between the modeled overlay error and the actual overlay error at the overlay marks. The actual overlay error is the overlay error directly obtained from the (several) overlay marks of the current wafer substrate. The modeled overlay error is the overlay error output by the overlay model for the positions of the overlay marks. The fitting algorithm may include the least squares method.

[0055] Next, for each relevant overlay model individually, the residual between the output of the overlay model and the overlay error obtained at the overlay marks is determined. In other words, for each relevant overlay model individually, the remaining difference between the modeled overlay error and the actual overlay error is determined.

[0056] Next, an updated overlay model is selected from a preset overlay model and at least one further overlay model. The selection can be based on criteria that minimize the magnitude and / or distribution of the residuals and / or the highest order weighting of the number of terms and / or the terms of the wafer overlay model.

[0057] Output information can be displayed, transmitted to a higher order process monitoring and / or management system and / or used for rework. For example, the second wafer structure can be a photoresist structure. The photoresist structure can be removed and a further photosensitive layer can be patterned and deposited in a further exposure process where the output information of the updated overlay model can be used. According to an embodiment, the position-dependent position offset for exposure of the wafer substrate can be updated based on the updated overlay model.

[0058] According to an embodiment for exposure analysis and / or exposure correction, the critical dimension value can include a critical dimension (CD hereinafter) that quantitatively describes at least one physical property of an actual wafer structure. For example, the CD can include the diameter of a circular photoresist feature, the length of the short axis of a non-circular photoresist feature, the length of the long axis of a non-circular photoresist feature, the line width of a bar-shaped photoresist feature, the width of a space between two photoresist features or between two substrate features in the same plane, the sidewall angle of a photoresist feature, the surface area of a photoresist feature, or the line edge roughness of a photoresist feature.

[0059] The measurement site from which the critical dimension is obtained can be a sampling point. The sampling point can be within the exposure field, outside the exposure field (e.g., in the wafer edge region), within the die area, and / or outside the die area (e.g., in the saw street area of the wafer substrate). The number and position of the sampling points can be defined in a sampling plan. The sampling plan can be static or can be dynamic. In a dynamic sampling plan, the position of one or more sampling points can change and / or the number of sampling points can change over time.

[0060] Also for exposure analysis and / or exposure correction, the controllable process parameters can include position-dependent exposure parameters of the exposure process in the process for forming the wafer structure. The exposure parameters affect the critical dimension. The exposure parameters can include an absolute focus value, a defocus value, a focus correction value, a dose value, a dose correction value, and / or any other parameter or parameter group from which input parameters of the exposure method can be explicitly derived (e.g., input parameters of the exposure tool assembly). The exposure parameters can include a single parameter (e.g., exposure dose or focus value) or can include a combination of an exposure dose and a focus value.

[0061] The exposure parameters in the exposure process for defining an entity wafer structure can be previously determined exposure parameters or can be received from an instance that manages the exposure parameters. The instance that manages the exposure parameters can be a processor unit integrated in the exposure tool assembly in which the exposure occurs or assigned to the exposure tool assembly. Alternatively or additionally, the processor unit can be integrated in a server device that is data-connected to the exposure tool assembly or assigned to the server device.

[0062] Further for exposure analysis and / or exposure correction, each model can include a wafer exposure model. The wafer exposure model estimates CD, exposure parameters, and / or exposure parameter correction values that vary with the position coordinates of the main surface of the substrate. Each wafer exposure model is represented as a sum of terms, as described above.

[0063] The wafer exposure model can include, for example, polynomial terms with polar coordinates for inter-field correction. Inter-field correction can reduce substrate-level deviations, such as those based on deposition effects, wafer bending, and other effects. Intra-field correction can reduce design-specific effects. For example, the wafer model can include Zernike polynomials. Additionally or alternatively, the wafer exposure model can include, for example, polynomial terms with rectangular coordinates for intra-field correction. For example, the wafer exposure model can include Legendre polynomials.

[0064] The current wafer exposure model receives input information obtained from measurements at sampling points. The wafer exposure model derives output information from the input information that describes the distribution of critical dimensions across the entire main surface. The input information can include measured CD and / or exposure parameters derived from the measured CD. The output information can include estimated CD, updated exposure parameters, and / or exposure parameter correction values that vary with the position coordinates. The output information can be displayed, transmitted to a higher-order process monitoring and / or management system, and / or can be used to control the exposure process across the entire main surface of the next wafer substrate.

[0065] The total value of the residuals is a measure of the remaining deviation between the modeled CD and the actual CD. Specifically, the total value of the residuals can give an impression of the quality of the corresponding physical model. As the number of terms in the physical model increases, the total residuals become lower. But as the number of terms increases to a point of stable increase, additional terms tend to make the wafer exposure model accompany negligible noise in the process. Selecting the wafer exposure model based on a criterion that considers not only the residuals but also the number of terms in the wafer exposure model can result in an updated wafer exposure model that only highly accompanies systematic errors, and thus errors that can be actually attributed to process effects of the process history.

[0066] The wafer structure can include a photoresist structure that can be formed on the main surface of a wafer substrate. The wafer substrate can be a thin disk that includes a substrate material. The substrate material can include a semiconductive material. For example, for instance, the wafer substrate can be a semiconductor substrate, a glass substrate that includes one or more semiconductive layers, or an SOI (silicon-on-insulator) wafer.

[0067] The photoresist structure may include an activated or deactivated photoactive component. The photoresist structure is obtained by developing an exposed photoresist layer. The photoresist structure may include a plurality of laterally separated photoresist features. In other words, the photoresist structure may cover one or more first portions of the main surface of the substrate and may expose one or more second portions of the main surface of the substrate.

[0068] According to an embodiment, forming the photoresist structure may include exposing a first photoresist layer formed on the main surface of the substrate. The exposure uses position-dependent exposure parameters.

[0069] The exposed first photosensitive layer may be developed, wherein the photoresist structure is obtained from the exposed first photosensitive layer. To this end, the exposed section of the first photosensitive layer may be selectively removed relative to the unexposed section or the exposed section of the first photosensitive layer may be selectively removed relative to the exposed section.

[0070] Applying a technique for updating a wafer exposure model based on a criterion considering both the number of terms of the residual and the wafer exposure model facilitates the manufacture of semiconductor devices (such as memory devices, microprocessors, logic circuits, analog circuits, power semiconductor devices) with high reproduction fidelity and can improve the yield of the manufacturing process of semiconductor devices (specifically, semiconductor devices having a small lateral feature size of less than 100 nm).

[0071] According to an embodiment, a second photoresist layer may be exposed on a second wafer substrate, wherein the exposure uses a pair of position-dependent exposure parameters obtained from updating the wafer exposure model.

[0072] According to another embodiment, the present disclosure relates to a wafer manufacturing assembly. Unless otherwise specified, the description of the wafer manufacturing assembly uses the terms and concepts introduced with reference to the above wafer exposure method.

[0073] An exposure tool assembly may expose a photoresist layer coating a substrate to an exposure beam according to position-dependent process parameters. Then, the exposure tool assembly forms a photoresist structure from the exposed photoresist layer. For example, the exposure tool assembly may include a lithography exposure unit and a developer unit. In the exposure unit, a photomask laterally modulates the exposure beam. The laterally modulated exposure beam activates the photoactive compound at the exposure positions of the photoresist layer. The developer unit may selectively remove the exposed portion or the unexposed portion of the photoresist layer. The residue of the photoresist layer forms the photoresist structure.

[0074] The photoresist structure and / or the substrate structure derived from the photoresist structure form a wafer structure. For example, the substrate structure may be obtained by etching a wafer substrate using the photoresist structure as an etching mask.

[0075] The processor unit can be data-connected to the exposure tool assembly. For example, the processor unit can receive position-dependent process parameters in the exposure tool assembly for forming a photoresist structure. The processor unit and the exposure tool assembly can be directly data-connected, where the processor unit can directly receive position-dependent process parameters from the exposure tool assembly. Alternatively or additionally, the processor unit and the exposure tool assembly can be data-connected via another data management unit (such as a server), where the processor unit can directly receive position-dependent process parameters from the data management unit. Alternatively or additionally, the processor unit can store previously used process parameters and can use previously determined process parameters.

[0076] The processor unit can also receive critical dimension values of the photoresist structure and / or the substrate structure obtained from the photoresist structure at the measurement site.

[0077] The processor unit can determine coefficients of a preset model and at least one further model from the critical dimension values at the measurement site, where each further model differs from the preset wafer model and other wafer models in at least one item, and where the wafer model estimates the critical dimension values and / or correction values of process parameters varying with at least two position coordinates. The processor unit can further determine the residual between the output of the model and the critical dimension values obtained from the wafer structure for each relevant model individually. The processor unit can select an updated model from the preset model and at least one further model, where the selection is based on a criterion that weights the residual with the number of items and / or the order of the items of the model.

[0078] The critical dimension values can include overlay difference values and / or CDs, as described above. The process parameters can include exposure parameters and / or position offsets, as described above. The models can include wafer exposure models and / or wafer overlay models, as described above.

[0079] According to an embodiment, the processor unit can be configured to output information describing the items of the updated model.

[0080] According to an embodiment, the processor unit can be configured to update the position-dependent process parameters based on the updated model and output the updated position-dependent process parameters to the exposure tool assembly.

[0081] According to an embodiment, the wafer manufacturing assembly can include a metrology unit that obtains (such as measures) critical dimension values of the wafer structure at a predetermined measurement site. The metrology unit can output the measured critical dimension values to the processor unit.

[0082] Figure 1Shows a part of a wafer manufacturing assembly 900 having an exposure tool assembly 300. The exposure tool assembly includes a coater unit 310, a lithographic exposure unit 320, and a developer unit 330. A plurality of pre-treated wafer substrates 100 are continuously supplied to the exposure tool assembly 300. For example, the wafer substrate 100 can be a semiconductor wafer, a glass substrate on which a semiconductor layer or semiconductor element is formed, or a SOI (semiconductor-on-insulator) wafer. Each of the coater unit 310 and the developer unit 330 can include two or more sub-units that apply the same type of process.

[0083] The wafer substrates 100 of a substrate lot (e.g., a wafer lot) can be subjected to the same processes for forming the same electronic circuit. For example, the wafer substrates 100 of a substrate lot can be continuously supplied to different process units of the same type, where the process units of the same type apply the same type of process. Alternatively, the wafer substrates 100 can be continuously supplied to the same process unit, where each process unit can include one or more sub-units in which some wafer substrates 110 can be processed in parallel.

[0084] For example, the wafer substrate 100 can be supplied to the coater unit 310. The coater unit 310 deposits a photoresist layer on the main surface of each substrate 100. In addition to the photoresist layer, the coater unit 310 can also deposit one or more auxiliary layers, such as an anti-reflection coating. For example, the coater unit 310 can include a spin coater unit that dispenses a photoresist material onto the main surface of the substrate and evenly distributes the photoresist material by rotating the wafer substrate 100. The photoresist material can contain a photoactive component (PCA), a solvent, and a resin. The coater unit 310 can include heating facilities for evaporating at least a portion of the solvent after coating. The photoresist-coated wafer substrate 100 is transferred to the exposure unit 320.

[0085] In the lithographic exposure unit 320, an exposure beam transfers a target pattern into the photoresist layer, where the exposure beam can selectively activate or deactivate the photoactive component of the photoresist layer in the exposure portion. The exposure beam can be an electromagnetic radiation beam or a particle beam. According to an embodiment, the exposure beam includes light or electromagnetic radiation having a wavelength shorter than 365 nm (e.g., 193 nm or less), where the electromagnetic radiation passes through or reflects at a photomask and images the photomask pattern into the photoresist layer.

[0086] In the portion of the photoresist layer exposed by the exposure beam, the photoactive component can activate or deactivate a photoactive compound. For example, the exposure beam can affect the polymerization of a previously unpolymerized compound or the depolymerization of a previously polymerized compound. After exposure, the photoresist layer contains a latent image of the photomask pattern.

[0087] The exposure of a wafer substrate 100 may include a single exposure of the entire substrate main surface or may include multiple exposures in adjacent exposure fields on the main surface. In the latter case, the same pattern may be imaged into each exposure field. Each exposure is defined by exposure parameters such as focus and dose, as defined above. At least one of the focus and dose may vary for different exposure fields on the same wafer substrate 100, between wafer substrates 100 of the same substrate lot, and / or between different substrate lots. The wafer substrate 100 having the exposed photoresist layer is transferred to the developer unit 330.

[0088] The lithography exposure unit 320 may further include a substrate stage. During exposure, the wafer substrate may be fixed on the substrate stage having an exposure field in the exposure position. The substrate stage may move relative to the exposure beam such that the exposure beam may scan the exposure field along a linear scan direction (y direction) and / or anti-parallel to the scan direction. The exposure beam may scan each exposure field once or several times at a uniform scan speed. After completion of the exposure of the exposure field, the substrate stage may move in at least one lateral direction, where another exposure field is placed in the exposure position.

[0089] The developer unit 330 selectively dissolves the exposed portion relative to the unexposed portion using the different dissolution rates of the exposed and unexposed portions of the photoresist layer, or vice versa. The developer unit 330 may include a heating chamber for post-exposure baking for evaporating solvent residues and / or chemically modifying the developed photoresist layer. For example, the heat treatment may harden the developed photoresist layer or may enhance the adhesion of the developed photoresist layer on the substrate main surface. The developed photoresist layer forms a photoresist structure. The photoresist structure may include a plurality of laterally separated photoresist features or may include one or more photoresist features having openings.

[0090] The metrology unit 400 may determine the critical dimension of a critical photoresist feature at a sampling point, as described above. The metrology unit 400 may be an integrated part of the exposure tool assembly 300, or the wafer substrate 100 may be transferred to a remote metrology unit 400. The metrology unit 400 may also determine the critical dimension of a wafer structure defined by the photoresist structure. For example, the metrology unit 400 may determine the critical dimension of a substrate feature obtained by using the photoresist structure as an etch mask. The sampling point is a position on the wafer substrate 100 defined in a sampling plan. The metrology unit 400 may obtain information on the critical dimension value by, for example, OCD (Optical Critical Dimension) scatterometry, inspecting an image obtained by SEM (Scanning Electron Microscope), and inspecting an image obtained by an optical microscope.

[0091] The critical dimension value can include any of the above physical dimensions. Hereinafter, the abbreviation "CD" shall be understood to include all kinds of critical dimension values and is not limited to the width of the lines and spaces of the critical photoresist features or the area of the critical photoresist features.

[0092] Before being transferred to the metrology unit 400, the post-exposure process can use the photoresist pattern (for example) as an etch mask for forming grooves and / or trenches in the wafer substrate 100, as an implantation mask, or as a mask for other modification processes. In this case, the metrology unit 400 can measure the CD of the features of the post-processed substrate rather than the photoresist structure.

[0093] The processor unit 200 can receive the measured CD obtained from the developed photoresist structure and / or the post-processed wafer substrate 100 at the sampling points. The processor unit 200 can include advanced process control (APC) functions. In other words, based on the CD obtained from one or more wafer substrates 100 previously processed at the same exposure tool assembly 300 or another exposure tool assembly, the processor unit 200 can continuously update at least one exposure parameter in response to the current CD measurement.

[0094] To this end, the processor unit 200 can use a preset wafer exposure model that interpolates the field fine and / or in-field fine correction values of at least one exposure parameter based on relatively few sampling points. Additionally, the processor unit 200 can update the coefficients of the preset wafer exposure model based on the current CD obtained at the sampling points of the current substrate.

[0095] The processor unit 200 further includes the above wafer exposure model update function. Each wafer exposure model update can include at least one of two steps. The first step can determine the highest order of the polynomial used to update the wafer model. The second step can remove the polynomials that do not improve or only insignificantly improve the updated wafer exposure model from all polynomials up to the highest order in view of the deviation from the actual critical dimension value.

[0096] The terms "first step" and "second step" should not be understood to imply an implicit timing. The second step can be after the first step, can be interleaved with the first step, or can be implemented simultaneously with the first step, such that the result of the second step can be used simultaneously with the first step or even before the first step ends.

[0097] Alternatively or additionally, the processor unit 200 may receive an overlay difference obtained from overlay marks formed at least in part in the developed photoresist structure and / or the post-processed wafer substrate 100. The processor unit 200 may include a stage control function. Based on the overlay information obtained from one or more wafer substrates 100 previously processed at the same exposure tool assembly 300 or another exposure tool assembly, the processor unit 200 may add a position offset to the exposure position.

[0098] To this end, the processor unit 200 may use a preset wafer overlay model that interpolates field fine and / or in-field fine correction values of the position offset based on the detected overlay error at the overlay marks. Additionally, the processor unit 200 may update the coefficients of the preset wafer overlay model based on the currently obtained overlay difference value at the overlay marks.

[0099] The processor unit 200 further includes the above-described wafer overlay model update function. Each wafer overlay model update may include at least one of the above two steps for the wafer exposure update function.

[0100] Figure 2 The first step involving wafer model update. Line 501 illustrates the RMSE (root mean square error), and line 502 illustrates the BIC of the wafer model using up to different highest orders of Zernike polynomials. Illustration 503 schematically visualizes an exemplary CD distribution on the main surface of the substrate, where different grayscales indicate different critical dimension values. The exemplary CD distribution is clearly symmetric with respect to the center point of the main surface of the substrate.

[0101] For the exemplary CD distribution of Illustration 503, the Zernike polynomial of the first order that describes the unidirectional CD variation does not contribute to any improvement of the wafer model.

[0102] One of the second-order Zernike polynomials describes a point-symmetric variation. By adding a polynomial of the second order, both the RMSE and the BIC can be significantly decreased. Illustration 504 schematically visualizes the CD distribution described by the wafer model that can use all Zernike polynomials up to the second order.

[0103] A further significant decrease in both the RMSE and the BIC can be observed when transitioning from the wafer model using the third-order Zernike polynomial to the wafer model using the fourth-order Zernike polynomial. Illustration 505 schematically visualizes the CD distribution described by the wafer model using all Zernike polynomials up to the fourth order. Illustration 505 shows a much greater consistency with the exemplary CD distribution of Illustration 503 than Illustration 504.

[0104] Using terms beyond the fourth order can further reduce the RMSE. However, the increasing BIC value instead indicates that further orders only contribute to imaging noise. For this example, the wafer model using up to the fourth order Zernike polynomials has the minimum BIC value. The minimum BIC value indicates with high probability the highest Zernike order that best fits the wafer model. In other words, the minimum BIC indicates up to which order the Zernike polynomials contribute to the imaging system effects and from which order the Zernike polynomials instead accompany noise.

[0105] The second step can include validating the relevance of each polynomial up to a determined highest order. In Figure 2 's example, the polynomials of the first order and the third order do not significantly affect the RMSE, and the wafer model can continue without the polynomials of the first order and the third order. If it is proven for the substrate exposed at a later time point that the wafer model using one of the first order or the third order polynomials results in a reduced RMSE, then this can indicate a significant change in the process characteristics. The wafer model can adapt to the new process characteristics in a timely manner when the newly detected process characteristics first appear.

[0106] Referring again to Figure 1 , the processor unit 200 can output information about the composition of the updated wafer model through the interface unit 290. The interface unit 290 can include a display where the information can be presented to a human operator. Alternatively or additionally, the interface unit 290 can include a data link to a higher order process monitoring and / or management system. Alternatively or additionally, the processor unit 200 can use the updated wafer model to determine updated exposure parameters for the next exposure.

[0107] Figure 3A and 3B Visualize possible wafer model updates. The result of the first wafer model update step can be that terms beyond the fourth order do not improve the wafer model. Then, the quality of the wafer models of all 32768 possible combinations including up to 15 Zernike polynomials of the fourth order can be verified.

[0108] The quality of each wafer model can be determined based on a first term (such as RMSE) indicating the total amount of residuals and a second term (such as BIC) indicating the number of polynomials.

[0109] For the first substrate, the result of the second wafer model update step can be that the wafer model including all Zernike polynomials of up to the second order and the point-symmetric Zernike polynomials of the fourth order achieves the best fit wafer model.

[0110] In Figure 3A , the Zernike polynomials of the optimal wafer model determined for the first substrate are marked by the dashed circles.

[0111] For a second substrate that is processed later at the same exposure tool, the result of the second wafer model update step can be that a wafer model that includes one of the third-order Zernike polynomials rather than one of the second-order Zernike polynomials can achieve a better wafer model than the optimal wafer model of the first substrate.

[0112] In Figure 3B the Zernike polynomials of the best-fit wafer model of the second substrate are marked by the dashed circles.

[0113] A change in the wafer model at the polynomial level can indicate a change in the characteristics of a process feature. This change can be signaled to a higher-order process monitoring and / or management system or a human operator. Additionally, the updated wafer model can be used for the exposure tool to respond in a timely manner to the changed process feature.

[0114] Alternatively, the "updated" wafer model is only used to communicate the change in the process feature, while the wafer model that uses all Zernike polynomials up to a determined highest order can be used to update the exposure parameters.

[0115] Alternatively or in addition to the second wafer model update step, the wafer model update can further include a third wafer model update step. The third wafer model update step can use a quality index as a stability criterion for selecting the polynomials of the updated wafer model. The quality index can be based on geometric considerations and / or can be based on statistical considerations.

[0116] Figure 4 A flowchart showing an embodiment of using wafer exposure model update 700 is presented. In step 702, a default wafer model can be selected as the current wafer model. The selection can be based on empirical knowledge.

[0117] Step 710 determines the model coefficients 795 of the current wafer exposure model based on the fiducial metrology data 705 obtained from a metrology tool at a predetermined measurement site (e.g., sampling points defined in a sampling plan). The model coefficients 795 can be transmitted to the APC system.

[0118] If wafer exposure model update is enabled, then wafer exposure model update 700 can replace the default wafer exposure model with an updated wafer exposure model in step 710, provided that the updated wafer exposure model meets specific requirements.

[0119] To this end, wafer exposure model update can initialize the updated wafer exposure model with a preset default wafer exposure model in step 720.

[0120] Step 730 generates a further wafer exposure model that is different from the updated wafer exposure model and all previously examined wafer exposure models in at least one aspect.

[0121] Step 740 checks which of a further wafer exposure model and an updated wafer exposure model provides a better coefficient selection, such as a better BIC value. For example, if the BIC value of the further wafer exposure model is not lower than the BIC value of the updated wafer exposure model, then it is expected that the further wafer exposure model will perform worse than a preset wafer exposure model, and the wafer exposure model update proceeds to step 780. Otherwise, the wafer exposure model update proceeds to step 750.

[0122] Step 750 checks whether the further wafer exposure model will perform stably enough and meet the stability criterion. For example, if the further wafer exposure model fails the above-mentioned bootstrap test, then it is expected that the further wafer exposure model will not perform stably enough, and the wafer exposure model update proceeds to step 780. Otherwise, the wafer exposure model update proceeds to step 760.

[0123] Step 760 checks whether the further wafer exposure model passes a normality test. For example, if the further wafer exposure model fails the above-mentioned normality test, then it is expected that the further wafer exposure model does not cover all significant process features, and the wafer exposure model update proceeds to step 780. Otherwise, the wafer exposure model update proceeds to step 770.

[0124] In step 770, the current further wafer exposure model that is considered to perform stably enough and better than the previously updated wafer exposure model is defined as the newly updated wafer exposure model. Then, the wafer exposure model update proceeds to step 780.

[0125] Step 780 checks whether there is another possible wafer exposure model that has not been checked previously. If there is, then the wafer exposure model update returns to step 730. Otherwise, the wafer exposure model update proceeds to step 790.

[0126] Step 790 replaces the default wafer exposure model used in step 710 with the most recently updated wafer exposure model.

[0127] For illustration, various scenarios have been described with respect to methods of monitoring process features and methods of adapting an exposure method to changes in process features. Similar techniques can be implemented in combination with methods of monitoring alignment of a substrate in an exposure tool assembly and methods of monitoring overlap of successive exposures on the same substrate. Hereinafter, previously defined terms are used in the same sense as above.

[0128] According to an embodiment, an alignment method may include:

[0129] measuring geometric values of alignment marks formed on and / or in a substrate;

[0130] Determine coefficients of a preset alignment model and at least one further alignment model from the geometric values, where each further alignment model differs from the preset alignment model and other models in at least one term, and where the alignment models estimate the geometric values and / or corrected values of the geometric values that are dependent on at least two position coordinates;

[0131] Determine the residual between the output of the alignment model and the geometric values; and

[0132] Select an updated alignment model from the preset alignment model and the at least one further alignment model, where the selection is based on a criterion that takes into account the residual and the number of terms of the alignment model.

[0133] Alignment marks may comprise one or more spatially separated substrate features, such as grooves or structures of a material different from the surrounding material. Alignment marks on a substrate are typically used to align the substrate with a mask of an exposure unit.

[0134] After positioning the substrate on the stage of the exposure tool and (if applicable) after automatic pre-alignment and before exposure, geometric values of one or more alignment marks may be obtained, for example, by a metrology unit integrated in the exposure tool. The geometric values may describe misalignment of the substrate in the exposure tool, such as the misalignment between the protrusions of (some) alignment marks of a mask on the substrate and (some) alignment marks on the substrate.

[0135] Coefficients of a preset alignment model may be determined from the obtained geometric values. The preset alignment model may comprise an alignment model that has been used to determine stage parameters for a previous exposure. The stage parameters may comprise an x-offset value and a y-offset value. The x-offset value and the y-offset value may describe the displacement of the stage from its normal position. Additionally, coefficients of at least one further alignment model may be determined, where each further alignment model may differ from the preset alignment model in at least one term and may differ from other further alignment models in at least one term.

[0136] Each alignment model estimates geometric values ("misalignment") across the main surface of the substrate in a closed mathematical form. The alignment model receives input information obtained from measurements at the alignment marks. The alignment model derives output information from the input information that describes the misalignment across the entire main surface of the substrate. The input information may comprise measured misalignment at the alignment marks. The output information may comprise estimated position-dependent misalignment that varies with position, updated position-dependent x / y-offset values, and / or position-dependent x / y-offset correction values. The output information may be displayed, transmitted to a higher-order process monitoring and / or management system, and / or may be used to improve the alignment of the current substrate, where the position of the stage may be fine-tuned in response to the position-dependent x / y-offset values.

[0137] The position coordinates that can clearly define each point on the main surface of the substrate describe the position. The position coordinates can be orthogonal linear coordinates (x, y coordinate system) or polar coordinates

[0138] Each alignment model is represented by the sum of terms. Each (model) term contains at least one position coordinate and a coefficient. For example, each term can be the product of a coefficient and a function of at least one position coordinate.

[0139] According to an embodiment, the alignment model can include the terms represented in equations (5) and (6).

[0140] Equation (5): Δx = Γ3·x + R3·x·y + WM3·y

[0141] Equation (6): Δy = Γ4·y + R4·x·y + WM4·x

[0142] The coefficients of each alignment model can be obtained from a fitting algorithm. The fitting algorithm searches for the coefficients that minimize the deviation between the modeled misalignment and the actual misalignment at the alignment marks. The actual misalignment is directly obtained from the (several) alignment marks of the current substrate. The modeled misalignment is the misalignment output by the alignment model for the positions of the alignment marks. The fitting algorithm can include the least squares method.

[0143] Next, for each relevant alignment model individually, the residual between the output of the alignment model and the misalignment obtained at the alignment marks is determined. In other words, for each relevant alignment model individually, the remaining difference between the modeled misalignment and the actual misalignment is determined.

[0144] Next, an updated alignment model is selected from a preset alignment model and at least one further alignment model. The selection is based on a criterion that weights the magnitude and / or distribution of the residuals and the number of terms of the alignment model, as described above for the wafer model.

[0145] According to an embodiment, information describing the terms of the updated alignment model can be output. For example, any changes to the terms of the alignment model can be displayed to a human operator or a higher-order process monitoring and / or management system. Any skipping of terms and any insertion of terms in the alignment model can indicate some significant changes in the substrate history or the performance of the exposure tool. Therefore, information regarding the elimination of alignment model terms and / or newly introduced alignment model terms can be used for process control.

[0146] According to an embodiment, the position-dependent x / y offset values used in the exposure of the substrate can be updated based on the updated alignment model.

[0147] According to an embodiment, an exposure method can include:

[0148] Obtain critical dimensions of a wafer structure at a sampling point and position-dependent exposure parameters in an exposure process for defining the wafer structure;

[0149] Determine coefficients of a preset wafer exposure model and at least one further wafer exposure model from the critical dimensions at the sampling point, wherein each further wafer exposure model differs from the preset wafer exposure model and other wafer exposure models in at least one term, and wherein the wafer exposure model estimates the critical dimensions, exposure parameters, and / or exposure parameter correction values varying with at least two position coordinates;

[0150] Determine a residual between an estimated critical dimension obtained from the wafer exposure model and the critical dimension obtained at the sampling point; and

[0151] Select an updated wafer exposure model from the preset wafer exposure model and the at least one further wafer exposure model, wherein the selection is based on a criterion that weights the residual, the number of terms of the wafer exposure model, and / or the order of terms of the wafer exposure model.

[0152] According to another embodiment, an overlay metrology method may include:

[0153] According to an embodiment, an overlay analysis and correction method may include:

[0154] Obtain an overlay difference value from a wafer substrate at a measurement site;

[0155] Obtain a position-dependent position offset in an exposure process for affecting the overlay difference value;

[0156] Determine coefficients of a preset wafer overlay model and at least one further wafer overlay model from the overlay difference value at the measurement site, wherein each further wafer overlay model differs from the preset wafer overlay model and other wafer overlay models in at least one term, and wherein the wafer overlay model estimates the overlay difference value, position offset, and / or position offset correction values varying with at least two position coordinates;

[0157] Determine a residual between an estimated overlay difference value obtained from the wafer overlay model and the overlay difference value obtained at the measurement site; and

[0158] Select an updated wafer overlay model from the preset wafer overlay model and the at least one further wafer overlay model, wherein the selection is based on a criterion that weights the residual, the number of terms of the wafer overlay model, and / or the order of terms of the wafer overlay model.

[0159] The measurement site may include overlay marks. The overlay difference value may be obtained from an overlay. The wafer overlay model may include the terms given in equations (3) and (4).

Claims

1. A wafer exposure method, comprising: Obtaining a critical dimension value from a wafer structure at a predetermined measurement site; Obtaining position-dependent process parameters for an exposure process for forming the wafer structure, the process parameters including exposure parameters; Determining a preset model from a model for determining the exposure parameters of a previous exposure; Determining coefficients of the preset model and coefficients of at least one further model from the critical dimension value at the measurement site, wherein the preset model and the at least one further model are represented by a sum of terms, the terms comprising at least one position coordinate and coefficients, wherein each of the further models differs from the preset model and other further models in at least one term, and wherein each of the preset model and the at least one further model estimates the critical dimension value, the process parameters, and / or a corrected value of the process parameters varying with two position coordinates; Determining a residual between an estimated critical dimension value obtained from each of the preset model and the at least one further model and the critical dimension value obtained at the measurement site; And Selecting an updated model from the preset model and the at least one further model, wherein the selection is based on a criterion that weights the residual, the number of terms of the preset model and the at least one further model, and / or the order of the terms of the preset model and the at least one further model.

2. The wafer exposure method according to claim 1, further comprising: Outputting information describing the terms of the updated model.

3. The wafer exposure method according to claim 1, further comprising: Updating the position-dependent process parameters based on the updated model.

4. The wafer exposure method according to claim 1, wherein The selection of the updated model is based on a trade-off that weights the number of terms of the preset model and the at least one further model and the total amount of the residual.

5. The wafer exposure method according to claim 1, wherein The selection of the updated model is based on at least one of Bayesian Information Criterion and Akaike Information Criterion.

6. The wafer exposure method according to claim 1, wherein The preset model and the at least one further model comprise at least one of Zernike polynomials and Legendre polynomials.

7. The wafer exposure method according to claim 1, wherein The at least one further model comprises all Zernike polynomials up to the highest order.

8. The wafer exposure method according to claim 1, further comprising: Determining a quality index for each coefficient of the updated model, wherein the quality index gives information about the degree of dependence of the coefficient on the variation of the critical dimension value.

9. The wafer exposure method according to claim 1, wherein The selection is based on a criterion that weights the distribution of the residual.

10. The wafer exposure method according to claim 1, wherein The critical dimension value includes an overlay difference value, The process parameters for the exposure process include a position offset, and Each of the preset model and the at least one further model includes a wafer overlay model that estimates the overlay difference value, the position offset, and / or the correction value of the position offset that vary with the position coordinates.

11. The wafer exposure method according to claim 1, wherein the critical dimension value includes the critical dimension of the wafer structure, the process parameters for the exposure process include the exposure parameters, and each of the preset model and the at least one further model includes a wafer exposure model that estimates the critical dimension, the exposure parameters, and / or the correction value of the exposure parameters that vary with the position coordinates.

12. The wafer exposure method according to claim 1, wherein the wafer structure includes a photoresist structure.

13. The wafer exposure method according to claim 12, further comprising: exposing a first photoresist layer formed on a first wafer substrate (100), wherein the exposure uses the position-dependent exposure parameters; and developing the exposed first photoresist layer, wherein a patterned photoresist structure is obtained from the exposed photoresist layer.

14. The wafer exposure method according to claim 13, further comprising: exposing a second photoresist layer formed on a second wafer substrate (100), wherein the exposure uses the position-dependent exposure parameters obtained from an updated wafer exposure model.

15. A wafer manufacturing assembly, comprising: an exposure tool assembly (300) configured to expose a photoresist layer coated on a wafer substrate (100) to an exposure beam using position-dependent process parameters and to define a wafer structure based on the exposed photoresist layer; a processor unit (200) data-connected to the exposure tool assembly (300), wherein the processor unit (200) is configured to: receive and / or hold the position-dependent process parameters in the exposure tool assembly (300) for defining the wafer structure, the process parameters including exposure parameters; determine a preset model from a model for determining the exposure parameters of a previous exposure; receive the critical dimension value of the wafer structure at a predetermined measurement site; determine the coefficients of the preset model and at least one further model from the critical dimension value at the predetermined measurement site, wherein both the preset model and the at least one further model are represented by a sum of terms, the terms including at least one position coordinate and a coefficient, wherein each of the further models differs from the preset model and other further models in at least one term, and wherein the preset model and the at least one further model estimate the critical dimension value, the process parameters, and / or the correction value of the process parameters that vary with at least two position coordinates; determine the residuals between the estimated critical dimension values obtained from each of the preset model and the at least one further model and the critical dimension value obtained at the measurement site (111); and Select an updated model from the preset model and the at least one further model, wherein the selection is based on a criterion that weights the number of terms of the residual, the preset model, and the at least one further model and / or the order of the terms of the preset model and the at least one further model.

16. The wafer manufacturing assembly according to claim 15, wherein the processor unit (200) is further configured to output information describing the terms of the updated model.

17. The wafer manufacturing assembly according to claim 15, wherein the processor unit (200) is further configured to update the position-dependent process parameter based on the updated model and output the updated position-dependent process parameter to the exposure tool assembly (300).

18. The wafer manufacturing assembly according to claim 17, further comprising a metrology unit (400) configured to obtain the critical dimension value of the wafer structure at the measurement site and output the measured critical dimension value to the processor unit (200).

19. The wafer manufacturing assembly according to claim 15, wherein the critical dimension value includes an overlap difference value, the corrected process parameter for the exposure process includes a position offset, and each model includes a wafer overlap model that estimates the overlap difference value, the position offset, and / or the correction value of the position offset that vary with the position coordinates.

20. The wafer manufacturing assembly according to claim 15, wherein the critical dimension value includes the critical dimension value of the wafer structure, the corrected process parameter for the exposure process includes the exposure parameter, and each model includes a wafer exposure model that estimates the critical dimension value, the exposure parameter, and / or the correction value of the exposure parameter that vary with the position coordinates.

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