Lithography equipment adjustment method

Abstract

A method comprises determining an aberration caused by each lithographic apparatus in a set of lithographic apparatuses; calculating an adjustment for the lithographic apparatus that minimizes a difference between the aberrations caused by each lithographic apparatus; and applying the adjustment to the lithographic apparatus to provide a better match between the aberrations of a pattern projected by the lithographic apparatus.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of European Patent Application No. 17189220.1 filed on September 4, 2017, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to methods that can be used to adjust a lithographic apparatus. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a target portion of a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a pattern forming device, also known as a mask or reticle, can be used to generate a circuit pattern corresponding to a separate layer of the IC, and the pattern can be imaged onto a target portion (e.g., a portion including one or more dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Typically, a single substrate will contain a network of adjacent target portions that are successively exposed.

[0005] A semiconductor fabrication plant for making integrated circuits will include many (usually between 10 and 50) photolithography equipment. A semiconductor substrate (which may be referred to as a wafer) is exposed to different patterns in series to form multiple patterned layers on the substrate. The number of patterned layers may typically be 30 or more. Each projected pattern is aligned with the pattern projected onto the previous layer. This ensures that the structures formed by the layers are correctly connected to each other. If the layers are not aligned, the integrated circuit formed on the substrate will not function properly.

[0006] The problem that arises is that the projection system of each lithographic apparatus includes some aberrations, and this causes some deformation of the pattern projected by the lithographic apparatus. Aberrations and associated pattern deformations may also be caused by the support structure holding the mask and the substrate table holding the substrate. The aberrations caused by each lithographic apparatus are different and can be referred to as aberration fingerprints. In some instances, the deformations caused by the aberration fingerprints may reduce the accuracy with which successive pattern layers can be projected onto the substrate. This in turn may cause the semiconductor device formed on the substrate to not function.

[0007] It would be desirable to provide methods that, for example, obviate or mitigate one or more of the problems in the prior art whether identified herein or elsewhere. Summary of the invention

[0008] According to a first aspect of the invention, a method is provided, the method comprising: determining an aberration caused by each lithographic device in a set of lithographic devices; calculating an adjustment for the lithographic device that minimizes a difference between the aberrations caused by each lithographic device in the lithographic device; and applying the adjustment to the lithographic device.

[0009] The present invention provides a better match between the aberrations of the patterns projected by the lithographic apparatus. As a result, when the patterns are projected onto the substrate, the patterns are more accurately aligned with each other. In other words, the overlay of the patterns is improved.

[0010] Computational adjustments to lithography equipment may use merit functions.

[0011] Computational lithography equipment tuning can use optimization algorithms.

[0012] The optimization algorithm may be an artificial intelligence algorithm.

[0013] The optimization algorithm can be an evolutionary algorithm, a genetic algorithm, or a simulated annealing algorithm.

[0014] The optimization algorithm may modify the merit function during the calculation of the adjustments.

[0015] Calculating an adjustment for a lithographic apparatus may include calculating an average of aberrations caused by all lithographic aberrations; determining the worst performing lithographic apparatus; and then calculating an adjustment for the worst performing lithographic apparatus that brings the aberrations caused by the worst performing lithographic apparatus closer to the average.

[0016] This calculation can be iterated multiple times.

[0017] The calculated adjustment may increase an average aberration caused by the at least one lithographic apparatus relative to an average aberration caused by the at least one lithographic apparatus before using the method.

[0018] The method may be applied during setup of a lithographic apparatus.Aberrations may be determined via measurements performed during setup of a lithographic apparatus.

[0019] This method can be applied periodically.

[0020] The method may use a moving average of the aberrations introduced by the lithographic apparatus.

[0021] The method can be applied between production exposures of a substrate. The aberrations can be measured periodically.

[0022] The aberration can be measured by exposing a reference substrate to a pattern using a lithography apparatus and then measuring the exposed pattern.

[0023] Aberrations can be measured using sensors located within the lithographic apparatus.

[0024] The method may be applied between exposures of target areas of the substrate.

[0025] The method may include minimizing differences between lithographic apparatuses for the selected Zernike.

[0026] The selected Zernike can be Zernike Z2 and Zernike Z3.

[0027] The selected Zernike may be a Zernike from Z2 up to a predetermined Zernike value.

[0028] The predetermined Zernike value may be greater than 30.

[0029] Weights can be applied to Zernike.

[0030] The weights may correspond to the sensitivity to the Zernike overlap.

[0031] According to a second aspect of the present invention, there is provided a computer program comprising computer readable instructions configured to cause a computer to perform a method according to the first aspect of the present invention.

[0032] According to a third aspect of the present invention, there is provided a computer readable medium carrying a computer program according to the third aspect of the present invention.

[0033] According to a fourth aspect of the present invention, a computer device is provided, the computer device comprising: a memory storing processor-readable instructions; and a processor arranged to read and execute the instructions stored in the memory, wherein the processor-readable instructions include instructions arranged to control a computer to perform a method according to the first aspect of the present invention.

[0034] According to a fifth aspect of the present invention, there is provided one or more integrated circuits configured to perform the method according to the first aspect of the present invention.

[0035] The one or more integrated circuits may include one or more field programmable gate arrays (FPGAs).

[0036] According to a sixth aspect of the present invention, a collection of lithographic devices is provided, each of which comprises: an irradiation system for providing a radiation beam; a support structure for supporting a pattern forming device, the pattern forming device being used to impart a pattern to the radiation beam in a cross section of the radiation beam; a substrate table for holding a substrate; and a projection system for projecting the patterned radiation beam onto a target portion of the substrate; wherein each lithographic device is adjustable to adjust the aberration caused by the lithographic device when projecting the pattern, and wherein the device further comprises a processor configured to: determine the aberration caused by each lithographic device in the collection of lithographic devices, calculate an adjustment of the lithographic device that minimizes the difference between the aberrations caused by each lithographic device, and apply the adjustment to the lithographic device.

[0037] The present invention provides a better match between the aberrations of the patterns projected by the lithographic apparatus. As a result, when the patterns are projected onto the substrate, the patterns are more accurately aligned with each other. In other words, the overlay of the patterns is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which corresponding reference numerals indicate corresponding parts, and in which:

[0039] Figure 1 depicts a lithographic apparatus according to an embodiment of the present invention;

[0040] Figure 2 is a diagram schematically depicting aberrations caused by a collection of five lithographic apparatuses;

[0041] Figure 3 is a diagram schematically depicting the use of known methods to reduce aberrations;

[0042] Figure 4 is a diagram schematically illustrating the use of one embodiment of the present invention to reduce aberrations;

[0043] Figure 5 is a flow chart of an optimization algorithm that may form part of an embodiment of the present invention;

[0044] Figure 6 and Figure 7 is a diagram schematically illustrating the use of another embodiment of the present invention to reduce aberrations; and

[0045] Figure 8 and Fig. 9 is a diagram schematically illustrating how aberrations are reduced using yet another embodiment of the present invention. DETAILED DESCRIPTION

[0046] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications (e.g., the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal displays (LCDs), thin film magnetic heads, etc.). Those skilled in the art will understand that in the context of such alternative applications, any use of the terms "wafer" or "die" herein may be considered synonymous with the more general terms "substrate" or "target portion", respectively. The substrate referred to herein may be processed before or after exposure, for example in a track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), or a metrology tool or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, a substrate is processed more than once, for example to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0047] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm-20 nm), as well as particle beams (e.g., ion beams or electron beams).

[0048] The term "patterning device" as used herein should be broadly interpreted as referring to any apparatus that can be used to impart a radiation beam with a pattern in its cross-section so as to create a pattern in a target portion of a substrate. It should be noted that the pattern imparted to the radiation beam may not correspond exactly to the desired pattern in the target portion of the substrate. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device that is created in the target portion (such as an integrated circuit).

[0049] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. One example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions; in this way, the reflected beam is patterned.

[0050] The support structure holds the patterning device. The support structure holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (e.g., such as whether the patterning device is held in a vacuum environment). The support may use mechanical clamping, vacuum, or other clamping techniques (e.g., electrostatic clamping under vacuum conditions). The support structure may be, for example, a frame or a stage that may be fixed or movable as desired and may ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device."

[0051] The term "projection system" as used herein should be broadly interpreted as covering various types of projection systems, including refractive optical systems, reflective optical systems and catadioptric optical systems, which are suitable, for example, for the exposure radiation used or other factors (e.g., use of immersion liquid or use of vacuum). Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0052] The illumination system may also encompass various types of optical components, including refractive, reflective and catadioptric optical components for directing, shaping or controlling the radiation beam, and such components may also be collectively or individually referred to as "lenses" hereinafter.

[0053] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and / or two or more support structures). In such a "multi-stage" lithographic apparatus, the additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure.

[0054] The lithographic apparatus may also be of a type in which the substrate is immersed in a liquid having a relatively high refractive index (e.g., water) to fill the space between the final element of the projection system and the substrate. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems.

[0055] Figure 1 A lithographic apparatus according to a particular embodiment of the invention is schematically depicted. The apparatus comprises:

[0056] - an illumination system (illuminator) IL configured to condition a radiation beam PB (e.g. DUV radiation or EUV radiation);

[0057] a support structure (eg support structure) MT for supporting a patterning device (eg mask) MA and connected to a first positioning device PM for accurately positioning the patterning device relative to the item PL;

[0058] a substrate table (e.g. wafer stage) WT for holding a substrate (e.g. resist coated wafer) W and connected to a second positioning device PW for accurately positioning the substrate relative to the item PL; and

[0059] - a projection system (eg, a refractive projection lens) PS configured to project the pattern imparted to the radiation beam PB by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0060] As depicted here, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a reflective mask or a programmable mirror array as noted above).

[0061] The illuminator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithographic apparatus may be separate entities. In such a case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL with the aid of a beam delivery system BD, which comprises, for example, suitable directional mirrors and / or a beam expander. In other cases, for example, when the source is a mercury lamp, the source may be an integral part of the apparatus. The source SO and the illuminator IL, together with the beam delivery system BD (where necessary), may be referred to as a radiation system.

[0062] The illuminator IL may include an adjustment component AM for adjusting the angular intensity distribution of the radiation beam. Typically, the intensity distribution of at least the outer radial extent and / or the inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) in a pupil plane of the illuminator can be adjusted. Additionally, the illuminator IL typically includes various other components such as an integrator IN and a condenser CO. The illuminator provides an adjusted radiation beam PB having a desired uniformity and intensity distribution in its cross-section.

[0063] The radiation beam PB is incident on a patterning device (e.g. a mask) MA held on a support structure MT. After passing through the patterning device MA, the radiation beam PB passes through a projection system PL which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioning device PW and a position sensor IF (e.g. an interferometry device), the substrate table WT can be precisely moved, for example, to position a different target portion C in the path of the radiation beam PB. Similarly, the first positioning device PM and a further position sensor (in the example of FIG. 1 ) can be used to accurately position the substrate table WT, for example, after mechanical retrieval from a mask library or during scanning. Figure 1The support structure MT may be connected to a short-stroke actuator only, or may be fixed. The patterning device MA and substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0064] The depicted device can be used in the following preferred modes:

[0065] 1. In step mode, the support structure MT and substrate table WT are held substantially stationary while an entire pattern imparted to the radiation beam PB is projected at once onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C that is imaged in a single static exposure.

[0066] 2. In scan mode, the support structure MT and substrate table WT are scanned synchronously while a pattern imparted to the radiation beam PB is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PL. In scan mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0067] 3. In another mode, the support structure MT is held substantially stationary to hold the programmable patterning device, and the substrate table WT is moved or scanned whilst a pattern imparted to the beam PB 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 can be readily applied to maskless lithography, which makes use of a programmable patterning device (e.g. a programmable mirror array of the type indicated above).

[0068] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0069] Each patterned layer of the semiconductor substrate can be projected using a different lithography apparatus. Some lithography apparatuses can be designed to project very high-resolution patterns (e.g., having a critical dimension of less than 50nm, such as a critical dimension of less than 40nm, such as a critical dimension of less than 20nm). These lithography apparatuses can, for example, be used to form the first few layers on the substrate. Other lithography apparatuses can be designed to project patterns with lower resolutions (e.g., 100nm or greater (e.g., up to 300nm)). Such lithography apparatuses are typically used to project subsequent layers onto the substrate because these subsequent layers do not require as high a resolution as the previous layers (the subsequent layers can, for example, provide connections between transistors or other components formed by the previous layers). In one example, a lithography preparation plant may include a DUV lithography apparatus in which a liquid is provided between the projection lens and the substrate (referred to as an immersion lithography apparatus), and other DUV lithography apparatuses in which no liquid is present between the projection lens and the substrate (referred to as a dry lithography apparatus). An immersion lithography apparatus can be used to project the first few patterned layers onto the substrate, and a dry lithography apparatus can be used to project subsequent patterned layers. In another example, a lithography fabrication plant may include an EUV lithography apparatus, an immersion DUV lithography apparatus, and a dry DUV lithography apparatus.

[0070] It is expected that the lithographic apparatus projects a pattern onto a substrate without introducing aberrations into the projected pattern. However, in practice, the lithographic apparatus will not operate perfectly, but will introduce some aberrations into the projected pattern. The projection system of the lithographic apparatus can be adjusted to reduce this aberration, but residual aberrations will still remain. The aberrations caused by the projection system can be referred to as the aberration fingerprint of the lithographic apparatus. The aberration fingerprint of each lithographic apparatus will be different. This is applicable between lithographic apparatus of the same type (e.g., immersion lithographic apparatus). This also applies to different types of lithographic apparatus (e.g., between immersion and dry lithographic apparatus, and between EUV equipment and DUV equipment). Conventionally, attempts are made to reduce the aberration fingerprint of each lithographic apparatus to a minimum.

[0071] The aberration fingerprint of a lithographic apparatus can be expressed as a sum of Zernike polynomial functions. Zernike functions are often referred to as Zernikes for short and are identified using the nomenclature Z2, Z3, Z4, etc. For example, the aberration fingerprint of each lithographic apparatus can be reduced by minimizing the size of a particular aberration Zernike (e.g., Z2 or Z3). Alternatively, the aberration fingerprint can be reduced by minimizing the average taken over a series of Zernikes. Aberration fingerprints expressed as Zernikes are typically N-dimensional, where N exceeds 30 (e.g., 36, 64, or up to 100).

[0072] Figure 2The aberration fingerprints of five different lithographic apparatuses AE are schematically depicted.The lithographic apparatus is depicted on a graph showing the Zernike Z2 aberration on the horizontal axis and the Zernike Z3 aberration on the vertical axis. Figure 2 It is only schematic and no scale is set on the axis. It can be seen that each lithographic apparatus has an aberration fingerprint including a Z2 component and a Z3 component. This is a simplified example for illustrative purposes, and in practice, each lithographic apparatus may have an N-dimensional aberration fingerprint, where N is typically more than 30. The same applies to the other illustrated embodiments.

[0073] In a conventional prior art approach, the projection system of each lithographic apparatus AE will be adjusted to reduce the aberrations Z2 and Z3 (in a simplified example) for each lithographic apparatus to as close to zero as possible. This can be done during the installation process when the lithographic apparatus is installed in the lithographic fabrication plant, which installation process may be referred to as setup. The result of this adjustment is Figure 3 It can be seen that for each lithographic apparatus, aberrations Z2 and Z3 have been reduced.

[0074] exist Figure 4 The results obtained using one embodiment of the present invention are schematically depicted in FIG. In this embodiment, instead of adjusting the aberrations Z2, Z3 to be as close to zero as possible, the aberrations Z2, Z3 are instead adjusted so that the aberrations Z2, Z3 are as similar to each other as possible for the five lithographic apparatus AEs. In other words, the spread of the Z2 and Z3 aberration values ​​is jointly reduced to a minimum. Figure 4 As schematically depicted in , five lithographic apparatuses AE have Z2 and Z3 aberration values ​​that are close to each other. The Z2 and Z3 aberration values ​​of at least some of the lithographic apparatuses are greater than the difference value in the case of trying to reduce these values ​​as close to zero as possible. However, the Z2 and Z3 values ​​are similar to each other. In general, the aberration fingerprints of the lithographic apparatuses AE are similar to each other. This is advantageous because it provides a better match between the aberrations of the patterns projected by the lithographic apparatuses AE, and as a result, the patterns are more accurately aligned to each other when they are projected onto the substrate. In other words, the overlay of the patterns is improved.

[0075] One method to achieve minimal spread of the aberration fingerprints for five lithography apparatuses AE is as follows:

[0076] • Setting up a first lithographic apparatus A and during the setup attempting to reduce the root mean square (RMS) of Z2 and Z3 to zero, thereby generating a residual aberration fingerprint AFA.

[0077] • Setting up a second lithographic apparatus B and during the setting up attempting to reduce the RMS of Z2 and Z3 of the second lithographic apparatus B to zero, thereby generating a second residual aberration fingerprint AFB.

[0078] • Compare AFA and AFB and use an algorithm to calculate adjustments to lithographic apparatus A and B that minimize the difference between AFA and AFB.

[0079] Applying the adjustment to the first lithographic apparatus A and the second lithographic apparatus B.

[0080] • Setting up a third lithographic apparatus C and during the setting up attempting to minimize Z2 and Z3 of the third lithographic apparatus C to zero, thereby generating a third aberration fingerprint AFC.

[0081] • The aberration fingerprints AFA, AFB, AFC are compared and an algorithm is used to calculate adjustments of the lithographic apparatus A, B and C to minimize the differences between the aberration fingerprints.

[0082] • Applying the adjustment to the first lithographic apparatus A, the second lithographic apparatus B and the third lithographic apparatus C.

[0083] Repeat the above three steps for the fourth lithography apparatus D and the fifth lithography apparatus E.

[0084] The above method may be considered to comprise a moving average, since each time a new lithographic apparatus is added to the set of lithographic apparatuses, the average aberration fingerprint will change. The algorithm for minimizing the difference between the aberration fingerprints AFA-E of the lithographic apparatuses attempts to minimize a merit function which is a measure of the average (or cumulative) distance between the aberration fingerprints of different lithographic apparatuses AE. For all lithographic apparatuses AE, the merit function may be, for example, the root mean square of the difference between the Zernike Z2 values ​​and the average, and the difference between the Zernike Z3 values ​​and the average. Other merit functions may be used.

[0085] In one embodiment, the distance between Zernike values ​​up to a given value may be minimized (instead of minimizing only the distance between Z2 values, and the distance between Z3 values). The distance between Zernike values ​​may be minimized, for example, for 30 Zernikes or more (e.g., up to Z36, up to Z64, or up to Z100 or more). The merit function may, for example, be the root mean square of the distance between the Zernike value for each lithographic apparatus in the lithographic apparatus AE and the average Zernike value determined for each Zernike. Other merit functions may be used.

[0086] Other examples of merit functions are minimizing the root mean square of the distances between the aberrations of the lithographic apparatuses AE. In one approach, this can be done by generating a sum comprising the following terms, and trying to minimize the sum, the sum comprising the differences between the lithographic apparatuses AE for each Zernike.

[0087] When performing a method according to an embodiment of the invention, each Zernike in the evaluation function may be given the same weight. Alternatively, different weights may be given to different Zernikes in the evaluation function. For example, Zernikes (phase differences) that primarily affect overlap, such as Z2 and Z3, may be given a greater weight than Zernikes that primarily affect focus, such as Z4. In one embodiment, the method may include modifying the weights given to the different Zernikes in the evaluation function. This may be done using an optimization algorithm that also attempts to minimize the evaluation function (e.g., as described below in conjunction with Figure 5 further described).

[0088] An example of an alternative evaluation function is to use Figure 1 ) is minimized. The target portion C may also be referred to as an exposure field.

[0089] The optimization algorithm for minimizing the difference between the aberration fingerprints of the lithographic apparatus may use artificial intelligence, such as an evolutionary algorithm, a genetic algorithm, or simulated annealing. Alternatively, an algorithm that does not use artificial intelligence may be used. For example, a conventional lens model that models the effect of adjustments to the aberration fingerprint may be used.

[0090] In one embodiment, the model used during the setup of the lithographic apparatus AE may be a quadratic programming method. The quadratic programming method may optimize aberrations in the exposure field of the lithographic apparatus AE, and constraints caused by manipulators that may be used to adjust the lithographic apparatus (e.g., manipulators used to adjust the lens of the projection system). A combined setup model may be generated that includes all manipulators of all lithographic apparatuses and corresponding merit functions.

[0091] Using the evaluation function for each lithographic apparatus, the lithographic apparatus AE can be steered toward the target performance. During this process, the key performance indicators (KPIs) of the set of lithographic apparatus AE can be determined. The key performance indicators can be generated using the following function, which receives the Zernike value as input and outputs the root mean square, maximum value, minimum value, maximum value on the exposure field, or some other value. The key performance indicator can be the Zernike value itself. The evaluation function can be the sum of "terms", each of which has a parameter, and the higher the parameter, the more important the term is in the evaluation function. The parameters of the separate evaluation function can be selected in part by the user, for example. For example, the user can select Zernike Z3 as particularly important, Zernike Z2 as less important, etc. Other parameters of the evaluation function can be selected by an evolutionary algorithm. An optimization algorithm such as an evolutionary algorithm can adjust the weights of the parameters applied to the evaluation function. By viewing the changes in the corresponding KPI when adjusting the weights of the parameters applied to the separate evaluation function, the optimization algorithm can search for the best set of weight parameters to achieve the best match of the KPI of the set across the lithographic apparatus. In this way, the optimization of each lithographic apparatus retains the original setup model with the adjusted merit function, while the collection of lithographic apparatuses is optimized via adjustments to the merit functions of the individual lithographic apparatuses.

[0092] In embodiments described herein, an optimization algorithm may be used to minimize the difference between aberration fingerprints of a lithographic apparatus. The optimization algorithm may be an artificial intelligence algorithm. The optimization algorithm may, for example, be an evolutionary algorithm, a genetic algorithm, or a simulated annealing algorithm. The optimization algorithm may include an algorithm involving, for example, techniques such as quadratic programming.

[0093] Figure 5 It is a flow chart of an optimization algorithm that can be used. In step S11, the algorithm receives or generates an initial population of individuals. Each individual represents a possible set of values, which can be used as a solution to the proposed problem. For example, if the problem proposed is to find a set point fingerprint that allows the lithographic device to reach the minimum value of a given evaluation function, each individual is a different set point fingerprint expressed as a weight of a Zernike polynomial. Individuals can include other values ​​or combinations of values. For example, an individual can include both a set of set point fingerprints and a set of numerical weights present in the evaluation function considered. An individual can include values ​​of reference different lithographic devices. For example, if the spread of Z2 and Z3 of three lithographic devices is to be minimized, the set point fingerprint for each of the three devices is changed independently, then each individual is a set of three set point fingerprints (one set point fingerprint for each lithographic device).

[0094] Processing enters step S12 from step S11. The optimization algorithm includes a fitness function, which may alternatively be referred to as an optimization function. In the context of the optimization algorithm, the term "evaluation function" is sometimes used to replace the fitness function, but in order to avoid confusion with the existing usage of the term "evaluation function" in this document, the term "evaluation function" is not used in this document. The fitness function determines the appropriateness (or "fitness") of an individual for solving the proposed problem. The proposed problem may be, for example, how to minimize the spread of Z2 and Z3 in a set of lithographic equipment. In step S12, the fitness function provides a score for each individual of the initial population, which reflects the goodness of the solution of each individual to the proposed problem according to the fitness function. The specific operation mode of the fitness function will depend on the nature of the problem to be solved by the evolutionary algorithm. In an exemplary embodiment, the fitness function in step S12 can determine the goodness of the Z2 and Z3 spread of three lithographic equipment by evaluating the spread of a fixed evaluation function.

[0095] In step S13, the score of the best individual in the initial group assigned to by the fitness function is evaluated to check whether it is satisfactory. If the score of the best individual assigned to the group is satisfactory, then the best individual is the desired solution to the problem being raised. If the score of the best individual assigned to the initial group is not satisfactory, a new group (as described below) is produced. Whether the score is satisfactory can be determined by comparing with a predetermined score. Alternatively, the optimization algorithm can output the best individual of the group after a predetermined time or after a predetermined number of individuals have been produced or after the group generation process of a predetermined number has been applied to the group. The optimization algorithm can output the best individual of the group after reaching any desired restriction and / or obtaining any desired result.

[0096] In step S14, a new colony of individuals is generated. The optimization algorithm may be, for example, an evolutionary algorithm, in which case the evolutionary algorithm "evolves" the colony of individuals via known processes (e.g., replication, mutation, recombination, and selection). For example, individuals with the highest scores may be selected to replicate each other to produce new individuals. Alternatively, some individuals may be stored without participating in replication. New individuals may be produced by undergoing random changes, i.e. mutations, of existing individuals. New individuals may be produced via recombination between more than one parent individual. The evolutionary algorithm repeats these processes until the colony of the next generation of individuals is produced. The process may be repeated for a predetermined amount of time. The process may be repeated until a predetermined number of processes are reached. The process may be repeated until a predetermined number of colonies have been generated.

[0097] The optimization algorithm can be, for example, a simulated annealing algorithm, in which case the simulated annealing algorithm uses an operation similar to the mutation or crossover in the evolutionary algorithm and moves to the adjacent individual in the search space. In this way, a new individual colony is generated. In simulated annealing, the probability density function can be a Boltzmann (Boltzman) probability density function, or can be some other probability density functions. The annealing algorithm can include rapid annealing, Boltzmann annealing or some other form of annealing. The temperature update function of the annealing algorithm can be a rapid update function, a Boltzmann update function, an exponential update function or some other update function. Adaptive simulated annealing (ASA) can be used. If adaptive simulated annealing is used, reannealing (reannealing) can occur after a predetermined number of iterations, can occur after the current state has been replaced for a predetermined number of times, or can occur according to some other predetermined intervals.

[0098] In step S15, the fitness function provides a score for each individual in the population of new individuals. For example, this can be achieved using an evaluation function determined by an evolutionary algorithm, where the output is evaluated using a fitness function.

[0099] In step S16, the score assigned to the best individual in the group by the fitness function is evaluated to see if it is satisfactory. If the score assigned to the best individual in the group is not satisfactory, the process returns to step S14. The group is evolved again, or simulated annealing is used to generate a new group.

[0100] If the score assigned to the best individual of the group is satisfactory, the process proceeds to step S17, and the best individual is output as a desired solution to the posed problem.

[0101] The use of an optimization algorithm is advantageous because it provides a reasonable balance between good optimization and computational resources (determined by the number of calculations that need to be performed). In one embodiment, the merit function of each lithographic device may include about 4000 aberration data points that vary according to about 200 manipulators. Making a single model of, for example, 10 lithographic devices will produce a problem including 40,000 aberration data points that vary according to about 2000 manipulators. In some cases, using such a large combination of data points and manipulators to generate optimization may require certain stability and may require a large amount of computational resources. However, the use of optimization algorithms such as genetic algorithms, evolutionary algorithms, or simulated annealing is relatively light in computation and inherently stable. The optimization algorithm is very suitable for finding the optimal weights of the merit function parameters of a set of stable setting models (for example, for 10 lithographic devices).

[0102] The evaluation function used by an embodiment of the present invention can be defined as the distance of the worst performing lithography apparatus from the average aberration fingerprint of all lithography apparatuses or a subset thereof in the manufacturing plant (the average includes the worst performing lithography apparatus). The model calculates the adjustment to be applied to the worst performing lithography apparatus to reduce its distance from the average aberration fingerprint. The effect of the adjustment is calculated, and the aberration fingerprint of the calculated worst performing lithography apparatus is updated. The average aberration fingerprint will also be recalculated. A new calculation is then performed, which determines the worst performing lithography apparatus from the recalculated average aberration fingerprint. The worst performing lithography apparatus may be the same lithography apparatus as before, or may be a different lithography apparatus. The model again calculates the adjustment to be applied to the worst performing lithography apparatus to reduce its distance from the average aberration fingerprint. The aberration fingerprint of the calculated worst performing lithography apparatus will change, and the calculated average aberration fingerprint will also change. The iterative process is repeated. The iteration can be repeated until no further improvement in the distance of the aberration fingerprint from the average aberration fingerprint is seen by the model. The method can be considered as an iterative process, where the goal of optimization changes over time. In some embodiments (such as embodiments using evolutionary algorithms), the evaluation function can be changed during the iterative process.

[0103] In the above example, the algorithm drives the “worst” performing lithography equipment toward other lithography equipment. Figure 5 The embodiment depicted in accommodates the situation if the "worst" lithographic apparatus cannot be improved further. The average population is driven towards different averages so that the overall spread of the system is minimized. In some embodiments, the aberrations of the lithographic apparatus may be measured between iterations, for example using a sensor S provided in the substrate table. In doing so, the worst performing lithographic apparatus may be identified using the measurements, and the model may then calculate adjustments to be applied to that lithographic apparatus to reduce its distance from the average aberration fingerprint. In such an embodiment, the average aberration fingerprint will change between measurements, and may be referred to as a moving average.

[0104] In another example, specific optical or imaging properties (e.g., overlay) to be achieved by different lithographic apparatuses AE may be selected as the basis for the evaluation function. Different weights may be given to different Zernikes. For example, Zernikes that primarily affect overlay (aberrations, such as Z2 and Z3) and / or other odd Zernikes may be given greater weight than Zernikes that primarily affect focus (such as Z4).

[0105] After the lithographic apparatus is set up, some properties of the lithographic apparatus may drift over time. For example, the shape of a substrate table of the lithographic apparatus may change very slowly due to wear of the substrate table. In another example, properties of the projection system of the lithographic apparatus may drift over time because the lens moves slowly in its mechanical support due to drift of the glue. As a result of the drift, the aberration fingerprint AFA-AFE of the lithographic apparatus AE will change over time and the distance between the aberration fingerprints will increase. Figure 6 This is schematically depicted in , where it can be seen that the distance between the aberration fingerprints is greater than Figure 4 The distance in.

[0106] In one embodiment, the aberration fingerprint is measured periodically to compensate for changes in the aberration fingerprint AFA-AFE. An algorithm is then used to calculate adjustments to the lithographic apparatus AE to minimize the distance between the aberration fingerprint AFA-AFE, and these adjustments are subsequently applied. The results are in Figure 7 A schematic diagram is given in Figure 7 In, with Figure 6 . The distance between the aberration fingerprints AFA-AFE has been reduced compared to the distance shown in . For at least some of the lithography apparatuses AE, reducing the distance between the aberration fingerprints AFA-AFE increases the value of the Z2 aberration. This may seem undesirable, but the advantages gained by having a reduced distance between the aberration fingerprints outweigh the disadvantages of increasing the Z2 aberration. This is because all lithography apparatuses AE apply similar Z2 aberrations, resulting in a good overlap between patterns projected by different lithography apparatuses.

[0107] When compensating for drift of the lithographic apparatus AE, one attempt might be to return the aberration fingerprints AFA-AFE to their previous values ​​(i.e., to try to return them to the values ​​as in Figure 4 ). However, due to drift in the properties of the lithographic apparatus AE, it is not possible to restore the aberration fingerprints AFA-AFE completely to those values. As a result, the distances between the aberration fingerprints AFA-AFE will not be minimized. The spread of the aberration fingerprints will increase, and this will have an adverse effect on the accuracy with which the patterns are projected onto each other (the overlap will not be as good as that obtained using this embodiment). By instead using an algorithm to calculate an adjustment of the lithographic apparatus AE, which provides a new aberration fingerprint AFA-AFE with minimized differences, a tighter clustering of the aberration fingerprints can be achieved. This improves the accuracy with which the patterns can be projected onto each other (overlay is improved). This is an example of a moving average, as the average of the aberration fingerprints AFA-AFE is changed to a different average when the method is applied.

[0108] In one embodiment, one or more reference substrates may be passed through the lithographic apparatus AE periodically (e.g., after every three days or some other time period). The reference substrates are exposed and developed. The developed substrates allow the aberrations caused by each lithographic apparatus AE to be determined (i.e., allow the aberration fingerprint AFA-AFE to be measured). This information can then be used to calculate adjustments to be applied to each lithographic apparatus that minimize the spread of the aberration fingerprints of the lithographic apparatus.

[0109] Periodic adjustment of the lithographic apparatus AE to compensate for drift may take several minutes (eg, less than 10 minutes), may take several seconds (eg, less than 10 seconds), may take less than a second, or may take less than 500 milliseconds.

[0110] The adjustments applied can be selected based on the time available to apply those adjustments. For example, adjustments that take a few minutes can be applied after measurements have been performed using a reference substrate (e.g., at intervals of 1 day or more). An example of such an adjustment is the z-direction movement of a lens element of a projection system.

[0111] In another example, adjustments that take a few seconds (e.g., 10 seconds or less) can be made during normal production of the lithographic apparatus without affecting throughput. Such adjustments can be made between so-called lots of substrates, or when the lithographic apparatus exchanges a substrate that has already been patterned for a substrate that is to be patterned. Examples of such adjustments are x- or y-direction movement of a lens element or mirror, and rotation of a lens element or mirror (e.g., about the x, y, or z axis).

[0112] In another example, an adjustment that takes less than 50 milliseconds can be made between exposures of consecutive target areas. The time it takes for the lithographic apparatus to move between consecutive target areas can be about 50 milliseconds. An example of such an adjustment is to tilt a selected lens element of the projection system (the selected lens element is provided with an actuator that is capable of moving the lens element within 50 milliseconds). Adjustments that are relatively fast (e.g., about 100 milliseconds or less) but slower than the time it takes to move between consecutive target areas can be performed in stages. A first part of the adjustment can be made during a first movement between consecutive target areas, and the adjustment can be completed during a second movement between further consecutive target areas. The adjustment can typically be performed in stages, for example, between several exposures or between exposures of several substrates.

[0113] The lens of a lithographic apparatus may be replaced (for example, if it is determined that the existing lens is not functioning properly). The new lens will have a different aberration fingerprint than the old lens. A two-step process can be used to minimize the distance between the aberration fingerprints of the lithographic apparatus. This is done in Figure 8 and Fig. 9 The lens of the lithographic apparatus C is replaced.

[0114] In a first step, during the setup of the lithographic apparatus C with the new lens, adjustments are applied to the lithographic apparatus which minimize the difference between Z2 and Z3 of the lithographic apparatus and the average of Z2 and Z3 of the other lithographic apparatuses A, B, D, E. Figure 8 The results are schematically depicted in , where it can be seen that the aberration fingerprint AFC of the lithography apparatus C with the new lens is an outlier compared to the aberration fingerprints AFA, AFB, AFD, AFE of the other lithography apparatuses.

[0115] In a second step, the aberration fingerprints AFA-AFE of all lithographic apparatuses are compared and an algorithm is used to calculate adjustments to the lithographic apparatus AE to minimize the differences between the aberration fingerprints. Fig. 9 The result is schematically depicted in . In this example, the Z3 aberration of the lithography apparatus C with the new lens has changed slightly, but the Z3 aberrations of the other lithography apparatuses A, B, D, E have changed significantly and become larger for at least some of the lithography apparatuses. In general, when minimizing the difference between the aberration fingerprints of the lithography apparatus that has been in operation and the lithography apparatus with the new lens, the aberration fingerprint of at least one lithography apparatus may deteriorate. This is another example of a moving average, because the average value of the aberration fingerprint AFA-AFE becomes a different average value when the method is applied.

[0116] In an alternative, instead of using the two-step method described above, a single-step method can be used. In the single-step method, when setting up a lithography apparatus C with a replacement lens, an aberration fingerprint AFA-AFE that minimizes the difference between aberration fingerprints for all lithography apparatuses can be determined and used as part of the setup process. This may be more difficult to implement than the two-step method because the lithography apparatus C being set up may have a relatively large range of potentially achievable ways to reduce aberration values ​​using lithography apparatus adjustments. It may be difficult to accommodate these in an algorithm together with a smaller range of potentially achievable aberration value reductions using lithography apparatus adjustments for lithography apparatus A, B, D, E that have been operated. This is another example of a moving average.

[0117] If a new lithography apparatus is installed in a fabrication plant, a method equivalent to that described above may be used. This is another example of a moving average.

[0118] Although embodiments of the present invention have been described with reference to five lithographic apparatuses, the present invention can be implemented for any number of lithographic apparatuses (e.g., all lithographic apparatuses in a manufacturing plant). The lithographic apparatus to which the method is applied can be referred to as a set of lithographic apparatuses. The term "set" is not intended to limit the number of lithographic apparatuses to any specific number of lithographic apparatuses, and can be interpreted as covering two or more lithographic apparatuses. In some embodiments, the set of lithographic apparatuses can be a plurality of lithographic apparatuses all located in the same semiconductor manufacturing plant. In some embodiments, the set of lithographic apparatuses can be a plurality of lithographic apparatuses used to prepare a specific integrated circuit. In other words, different lithographic apparatuses in the set of lithographic apparatuses can be used to project different layers onto the same substrate.

[0119] The above description refers to adjusting the projection system of the lithographic apparatus to reduce the difference between the aberrations of the lithographic apparatus. Other properties of the lithographic apparatus may also be adjusted to reduce the aberrations. For example, the spacing between the substrate table WT and the projection system PL may be adjusted, the substrate table may be rotated, etc. In another example, the spacing between the patterning device MA and the projection system PL may be adjusted, the patterning device may be rotated, etc.

[0120] In some embodiments, the method may be performed using predicted aberrations. For example, a model may be made in which the lens manipulators of a collection of lithographic apparatus are misaligned, and the method is then used to direct the modeled lithographic apparatus relative to each other such that the difference between the aberration fingerprints is minimized.

[0121] In some embodiments, during a given step of the method, only some of the aberrations of the lithographic apparatus are measured. This may be referred to as a partially measured set of aberrations. Optimization of the lithographic apparatus may be determined using the partially measured set of aberrations, as well as using previously measured aberrations. The previously measured aberrations are modified to take into account the effects of adjustments that have been applied to the lithographic apparatus after the aberrations are measured and before they are applied to the optimization.

[0122] Measurement data from all lithographic apparatuses (or a subset of lithographic apparatuses) in a fabrication plant can be stored in a central location along with the current position of the manipulators of the lithographic apparatuses. This data can be periodically sent from the lithographic apparatuses to the central location and / or can be sent upon request from the central location. The central controller can perform optimization for all lithographic apparatuses and output manipulator adjustments to be applied to the lithographic apparatuses. Manipulator adjustments can be automatically received and applied by the lithographic apparatuses.

[0123] Embodiments of the invention may use a moving average. For example, the average aberration fingerprint around which the aberration fingerprints of the lithographic apparatus are grouped may vary over time. This provides improved performance (e.g., improved overlay) compared to schemes in which the average aberration fingerprint is fixed and does not change, around which the aberration fingerprints of the lithographic apparatus are grouped. Improved performance is achieved because drift of the lithographic apparatus over time caused by, for example, wear of the substrate table or gradual movement of the lens is taken into account.

[0124] Embodiments of the present invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include a read-only memory (ROM); a random access memory (RAM); a disk storage medium; an optical storage medium; a flash memory device; an electrical, optical, acoustic, or other form of propagation signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), and others. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such descriptions are merely for convenience, and such actions are actually caused by a computing device, processor, controller, or other device that executes firmware, software, routines, instructions, etc.

[0125] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. This description is not intended to limit the invention.

Claims

1. A method for adjusting a lithographic apparatus, comprising: determining an aberration caused by each lithographic apparatus in a set of lithographic apparatuses; calculating an adjustment for the lithographic apparatus that minimizes a difference between the aberrations caused by each of the lithographic apparatus; as well as The adjustment is applied to the lithographic apparatus such that the calculated adjustment increases an average aberration caused by the at least one lithographic apparatus relative to an average aberration caused by the at least one lithographic apparatus before the adjustment is applied.

2. The method of claim 1, wherein calculating the adjustment of the lithographic apparatus uses a merit function. The method of claim 2 , wherein calculating the adjustment of the lithographic apparatus uses an optimization algorithm. The method according to claim 3 , wherein the optimization algorithm is an evolutionary algorithm, a genetic algorithm or a simulated annealing algorithm.

5. The method according to claim 3 or 4, wherein the optimization algorithm modifies the merit function during calculation of the adjustment.

6. The method of any one of the preceding claims, wherein calculating an adjustment of the lithographic apparatus comprises: Calculating an average value of aberrations caused by all of the lithographic apparatuses; determining the lithographic apparatus with the worst performance; and then calculating an adjustment for the lithographic apparatus with the worst performance, wherein the adjustment for the lithographic apparatus with the worst performance brings the aberrations caused by the lithographic apparatus with the worst performance closer to the average value.

7. A method according to any of the preceding claims, wherein the method is applied during setup of the lithographic apparatus, and wherein the aberrations are determined via measurements performed during setup of the lithographic apparatus.

8. A method according to any one of the preceding claims, wherein the method is applied periodically.

9. A method according to claim 8, wherein the method uses a moving average of the aberrations caused by the lithographic apparatus.

10. A method according to claim 8 or 9, wherein the method is applied between production exposures of a substrate and wherein the aberrations are measured periodically.

11. A method according to any preceding claim, wherein the aberrations are measured using a sensor located within the lithographic apparatus.

12. A method according to any preceding claim, wherein the method comprises minimizing differences between the lithographic apparatuses for the selected Zernikes. The method of claim 12 , wherein weights are applied to the Zernike.

14. A collection of lithographic apparatuses, each lithographic apparatus comprising: an irradiation system for providing a radiation beam; a support structure for supporting a patterning device for imparting a pattern to the radiation beam in a cross-section of the radiation beam; a substrate table for holding a substrate; as well as a projection system for projecting the patterned radiation beam onto a target portion of the substrate; in Each lithographic apparatus is adjustable to adjust for aberrations caused by the lithographic apparatus when projecting a pattern; and wherein The device also includes a processor configured to: determine the aberration caused by each lithographic device in the set of lithographic devices; calculate an adjustment for the lithographic device, the adjustment for the lithographic device minimizing the difference between the aberrations caused by each lithographic device in the lithographic devices; and apply the adjustment to the lithographic device such that the calculated adjustment increases the average aberration caused by the at least one lithographic device relative to the average aberration caused by the at least one lithographic device before the adjustment is applied.

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