Determining the characteristics of the exposure beam

Abstract

The apparatus includes an estimation system configured to determine a set of values ​​for the initial light beam based on a detected wavefront of the initial light beam, the set of values ​​including a first value and a second value. The estimation system is also configured to determine an estimate of a property of the exposure beam based on a nonlinear relationship including the first value and the second value. The exposure beam is formed by interacting the initial light beam with the optical system. The apparatus also includes a communication module coupled to the estimation system and configured to output the estimate of the property of the exposure beam.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Application No. 63 / 284,081, filed November 30, 2021, entitled DETERMINATION OF A PROPERTY OF AN EXPOSURE LIGHT BEAM, the entire contents of which are incorporated by reference into this specification. [Background technology]

[0002]

[0002] The present disclosure relates to determining characteristics of an exposure beam. The exposure beam can be generated based on an initial light beam emitted from a deep ultraviolet (DUV) light source.

[0003]

[0003] Photolithography is a process by which semiconductor circuits are patterned on a substrate, such as a silicon wafer. A light source generates deep ultraviolet (DUV) light that is used to expose photoresist on the wafer. The DUV light can include wavelengths, for example, from about 100 nanometers (nm) to about 400 nm. Often, the light source is a laser source (e.g., an excimer laser) and the DUV light is a pulsed laser beam. The DUV light from the light source interacts with projection optics, which projects the beam through a mask onto the photoresist on the silicon wafer. In this way, the layers of the chip design are patterned on the photoresist. The photoresist and wafer are then etched and cleaned. If necessary, the photolithography process is repeated with new photoresist. Summary of the Invention

[0004] In one aspect, the apparatus includes an estimation system configured to determine a set of values ​​for the initial beam based on a detected wavefront of the initial light beam, the set of values ​​including a first value and a second value. The estimation system is also configured to determine an estimate of a property of an exposure beam based on a nonlinear relationship including the first value and the second value. The exposure beam is formed by interacting the initial light beam with an optical system. The apparatus also includes a communication module coupled to the estimation system and configured to output the estimate of the property of the exposure beam.

[0005] Implementations may include one or more of the following features: The characteristic of the exposure beam may be a convolved bandwidth metric, the convolved bandwidth metric representing a width of a portion of the optical spectrum of the exposure beam at a wafer illuminated by the exposure beam, and the optical spectrum of the exposure beam including the intensity of the exposure beam as a function of wavelength.

[0006]

[0006] The detected wavefront of the initial light beam may include a fringe pattern generated from the initial light beam, the fringe pattern may include a plurality of fringes, the first value may include a first width of a first fringe in the plurality of fringes, and the second value may include a second width of a second fringe in the plurality of fringes. The first fringe in the plurality of fringes and the second fringe in the plurality of fringes may be the same fringe. The first width may be a width of the first fringe at a first percentage of a peak intensity of the fringe, and the second width may be a width of the second fringe at a second percentage of a peak intensity of the fringe. The first percentage and the second percentage may be different percentages. The multiple fringes may be concentric rings of light centered about a center point and separated by no light regions, and a fringe may be the fringe closest to the center point. The apparatus may also include an etalon configured to generate the fringe pattern.

[0007]

[0007] The non-linear relationship may be a quadratic relationship. One of the first value and the second value may be squared.

[0008]

[0008] The non-linear relationship may also include a plurality of calibration parameters. The estimation system may also be configured to determine a value for each of the calibration parameters by accessing a reference value of a property of the exposure beam and minimizing a difference between the estimate of the property and the reference value of the property. The reference value of the property may be obtained by a spectrometer.

[0009]

[0009] The apparatus may also include an optical system.

[0010]

[0010] The optical system may include a projection lens and a reticle.

[0011]

[0011] The apparatus may also include a detector configured to detect the wavefront and provide data related to the detected wavefront to the estimation system.

[0012]

[0012] In another aspect, a system includes a light source configured to emit a light beam including deep ultraviolet (DUV) light, an optical measurement system configured to generate a fringe pattern based on the light beam, a projection optical system configured to emit an exposure beam based on the light beam, and an estimation system configured to determine a first value and a second value from the fringe pattern and determine an estimate of a characteristic of the exposure beam based on the first value and the second value.

[0013]

[0013] Implementations may include one or more of the following features.

[0014] The projection optical system may include a projection lens and a reticle.

[0015]

[0015] The estimation system may be configured to determine an estimate of the characteristic based on a nonlinear relationship, where the nonlinear relationship may include a first value, a second value, and a plurality of calibration constants. The estimation system may also be configured to determine a value for each of the plurality of calibration constants based on minimizing a difference between the estimate of the characteristic and a reference value of the characteristic.

[0016] The optical measurement system may be an etalon.

[0017]

[0017] The light source may include a master oscillator configured to emit a seed light beam and a power amplifier configured to amplify the seed light beam to generate a light beam including DUV light.

[0018] In another aspect, a method includes sensing a wavefront of an initial light beam, determining a set of values ​​for the initial light beam based on the sensed wavefront, determining a relationship including at least two of the values ​​in the set of values, and determining an estimate of a property of an exposure beam based on the relationship. The exposure beam is generated by interacting the initial light beam with an optical system.

[0019]

[0019] The relational expression may be a non-linear relational expression.

[0020]

[0020] Implementations of any of the above techniques may include a system, a method, a process, a device, or an apparatus. Details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims. [Brief description of the drawings]

[0021] [Figure 1A]

[0021] FIG. 1 is a block diagram of an example system. [Figure 1B]

[0022] 1 shows an example of an interference pattern. [Figure 1C]

[0023] FIG. 1B is a block diagram of the image plane and output lens of the system of FIG. 1A. [Figure 2A]

[0024] FIG. 1 is a block diagram of an example of an optical measurement device. [Figure 2B]

[0025] Another example of an interference pattern. [Figure 2C]

[0025] Regarding another example of an interference pattern. [Diagram 3]

[0026] 1 is a flow chart of an example process for determining an estimate of a property of an exposure beam. [Figure 4]

[0027] 1 is an example of experimental data showing the estimation error of the convolutional bandwidth (CBW). [Diagram 5]

[0028] 1 is an example of experimental data showing the error in CBW estimated from the quadratic relationship as a function of the measured reference CBW. [Figure 6]

[0029] 1 is an example of experimental data showing the error in CBW estimated from the linear relationship as a function of the measured reference CBW. [Figures 7A-7B-7C]

[0030]

[0031]

[0032] Figure 7A shows simulated data of estimated critical dimension (CD) as a function of 95% integral width (E95) estimates for seven different exposure tools. Figure 7B shows simulated data of estimated critical dimension (CD) as a function of full width at half maximum (FWHM) estimates for seven different exposure tools. Figure 7C shows simulated data of estimated critical dimension (CD) as a function of CBW estimates for seven different exposure tools. [Figure 8]

[0033] 1 shows an example of a deep ultraviolet (DUV) optical system with which the optical measurement device can be used. [Figure 9]

[0034] This is an example of a projection optical system. [Figure 10]

[0033] An example of a deep ultraviolet (DUV) optical system with which the optical measurement device can be used is shown. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022]

[0035] FIG. 1A is a block diagram of a system 100. In FIG. 1A, dashed lines between elements represent optical paths along which light travels, and solid lines between elements represent signal paths along which information and / or data travels. The system 100 includes a light generating module 110 that generates an initial light beam 116. The initial light beam 116 interacts with an optical system 181 to generate an exposure beam 112. The optical system 181 includes a component 183, such as, for example, one or more lenses, mirrors, apertures, and / or reticles. The initial light beam 116 interacts with the component 183, such as, for example, by being reflected, refracted, and / or transmitted by the component 183, to generate the exposure beam 112. The exposure beam 112 exposes or irradiates the element 182 to form electronic features on the element 182. The element 182 can be, for example, a semiconductor wafer.

[0023]

[0036] The system 100 includes an estimation system 150 that estimates a characteristic of the exposure beam 112. The characteristic of the exposure beam 112 may be, for example, a metric related to the spectral bandwidth of the exposure beam 112. Before describing the estimation system 150 in further detail, an overview of the system 100 is provided.

[0024]

[0037] The system 100 also includes a beam separator 117 that directs a portion 116' of the initial light beam 116 to the measurement system 160. The beam separator 117 can be, for example, a beam splitter that directs the portion 116' to the estimation system 150 and directs the remaining light in the initial light beam 116 to the optical system 181. In the example of FIG. 1A, the measurement system 160 includes an etalon 130 and a detector 140. The etalon 130 includes two parallel optical elements 133A, 133B separated by a distance 136 and an output lens 134. The output lens 134 has a focal length 163 and focuses the incident light at an image plane 137. The image plane 137 coincides with the active area 142 of the detector 140. FIG. 1C is a block diagram illustrating the image plane 137 and the output lens 134. The estimation system 150 is coupled to the measurement system 160. The estimation system 150 receives data from the detector 140 .

[0025]

[0038] 1B, the output of the etalon 130 is a fringe pattern or interference pattern 139 focused at an image plane 137. FIG. 1B shows the interference pattern 139 at the image plane 137. In the example of FIG. 1B, the interference pattern 139 is a plurality of concentric rings of light formed at the image plane 137. Although two fringes 139_1 and 139_2 are shown in FIG. 1B, the interference pattern 139 may include additional fringes. Fringe 139_1 is a primary fringe, fringe 139_2 is a secondary fringe, and the primary and secondary fringes 139_1, 139_2 are consecutive or adjacent fringes. In the configuration shown in FIG. 1, the spatial distribution of light in the interference pattern 139 depends at least in part on the spectral characteristics of the light in portion 116′ of the light beam 116.

[0026]

[0039] The initial light beam 116 and the exposure beam 112 each have an optical spectrum. The optical spectrum of a light beam contains information about how the optical energy, intensity, or power of the light beam is distributed over a range of wavelengths (or optical frequencies). An optical spectrum has a shape or profile as a function of wavelength. For example, the optical spectrum of the initial light beam 116 has an approximately Gaussian shape as a function of wavelength. The spectral bandwidth of a light beam represents the range of wavelengths in the light beam.

[0027]

[0040] Various metrics have been used to characterize spectral bandwidth. Specific metrics for spectral bandwidth include full width at half maximum (FWHM), which is the width of the optical spectrum at half the maximum intensity of the optical spectrum, and 95% integral width (E95), which is the interval of wavelengths that encompasses 95% of the total energy in the optical spectrum. Other metrics may also be used. For example, spectral bandwidth can be expressed as a value that represents the range of wavelengths between the minimum and maximum wavelengths of a light beam.

[0028]

[0041] Optical system 181 has a transfer function, which is a mathematical relationship that describes how optical system 181 responds to inputs of various wavelengths. The shape of the transfer function as a function of wavelength depends on the characteristics of components 183 (e.g., size, orientation, material, and / or shape) and the placement of the various components relative to each other.

[0029]

[0042] The optical system 181 affects the spectral content of the initial light beam 116 such that the exposure beam 112 does not have approximately the same optical spectrum as the initial light beam 116. Mathematically, the optical spectrum of the exposure beam 112 can be expressed as a convolution of the optical spectrum of the initial light beam 116 with the transfer function of the optical system 181. Convolution is a mathematical operation that expresses how the shape of a first function is modified by a second function to produce a third (or output) function. In this example, the optical spectrum of the exposure beam 112 is the optical spectrum of the initial light beam 116 modified by the transfer function of the optical system 181. In other words, the optical spectrum of the exposure beam 112 is the convolution of the optical spectrum of the initial light beam 116 with the transfer function of the optical system 181.

[0030]

[0043] Estimation system 150 estimates the spectral characteristics of exposure beam 112 based on fringe pattern 139. While some older techniques use interference patterns such as interference pattern 139 to determine properties of a light beam, estimation system 150 uses additional and / or different information than these older approaches and provides such information in an explicit manner.

[0031]

[0044] For example, some older systems use a direct spectral recovery technique to determine the optical spectrum of the initial light beam 116. The direct spectral recovery technique calculates the optical spectrum of the initial light beam 116 from the fringe pattern 139. However, the calculations involved in the spectral recovery technique are complex and difficult. For example, the direct spectral recovery technique involves inverting a matrix representing the transfer function of the etalon 130, which can be complex and can result in large errors and noise if the matrix contains small values. Complex calculations can be particularly undesirable if they need to be performed repeatedly during operation (e.g., periodically during the operation of the laser). They can lead to slow operating speeds or require excessive computational resources. Furthermore, the direct spectral recovery does not provide spectral information about the exposure beam 112 unless the calculated spectrum of the initial light beam 116 is convolved with a mathematical function representing the transfer function of the optical system 181. Additionally, in some older systems, spectral bandwidth metrics such as E95 and / or FWHM values ​​of the optical spectrum of the initial light beam 116 are estimated using information from the fringe pattern 139 and linear correlation techniques.

[0032]

[0045] On the other hand, the estimation technique implemented by the estimation system 150 provides a clear and accurate approach to estimate the characteristics of the exposure beam 112 based on information about the initial light beam 116. The convoluted bandwidth (CBW) is an example of a characteristic of the exposure beam 112. The CBW is the FWHM of the optical spectrum of the exposure beam 112. As shown in FIG. 7, the CBW has a strong correlation with the critical dimension (CD), which is the smallest feature size that can be printed on the wafer 120 by the system 100. To maintain product uniformity and quality, it is desirable to maintain a constant CD during use of the optical system 181 and also between many instances of the optical system 181. Knowledge of the CBW provides insight into the CD of a particular optical system 181. Furthermore, although each instance of the optical system 181 generates an exposure beam with unique characteristics, different exposure beams with the same CBW are generally associated with the same CD. Thus, the CBW is a robust metric that can be used to characterize the exposure beam 112 generated by the optical system 181. The CBW can also be a useful metric for exposure beams generated by different instances of optical system 181. Estimation system 150 estimates the CBW of exposure beam 112 based on information about initial light beam 116. The estimation can also be based on characteristics of optical system 181, such as the measured output through optical system 181, or a modeled or measured transfer function of optical system 181.

[0033]

[0046] FIG. 2A is a block diagram of another system 200. The system 200 includes an estimation system 250, which is an example of an implementation of the estimation system 150 (FIG. 1A), and a measurement system 260. The measurement system 260 includes an input lens 232, an etalon 230, an output lens 234 (or a focusing lens 234), and a detector 240. The portion 116' is diffused and passes through an aperture 235 of the measurement system 260. The portion 116' can be intentionally diffused by an optical diffuser (not shown) located in a plane 237 between the beam separator 117 and the aperture 235. The aperture 235 is in the focal plane of the input lens 232. The input lens 232 collimates the portion 116' before it enters the etalon 230. The output lens 234 has a focal length 263 and focuses the light to an image plane. The detector 240 is positioned so that the active area 242 of the detector 240 coincides with the image plane.

[0034]

[0047] In the example shown in FIG. 2A, the etalon 230 includes a pair of partially reflective optical elements 233A and 233B. The optical elements 233A and 233B are between the input lens 232 and the output lens 234. The optical elements 233A and 233B have respective reflective surfaces 238A and 238B spaced apart by a distance 236. The distance 236 can be a relatively short distance (e.g., millimeters to centimeters). The optical elements 233A and 233B are wedge-shaped to prevent the back surface (opposite the front surfaces 238A and 238B) from generating interference fringes. The back surface may have an anti-reflective coating. Other implementations of the etalon 230 are also possible. For example, in other implementations, the optical elements 233A and 233B are parallel plates and are not wedge-shaped. In yet another example, the etalon 230 may include only a single plate with two parallel partially reflective surfaces.

[0035]

[0048] Referring also to FIG. 2B, the etalon 230 interacts with the portion 116′ and outputs an interference pattern 239. FIG. 2B shows the interference pattern 239 at the image plane of the lens 234 at a time instance. The interference pattern 239 includes a plurality of fringes. Three of the plurality of fringes (239_1, 239_2, 239_3) are shown in FIG. 2B. The interference pattern 239 includes dark regions (relatively little or no light) created by the destructive interference of the portion 116′ and bright regions (relatively more light) created by the constructive interference of the portion 116′. The regions of constructive interference are fringes 239_1, 239_2, 239_3. The regions of no light are shown shaded gray and are between the regions of light. Fringes 239_1, 239_2, 239_3 are concentric rings of light at the image plane of output lens 234. Each ring of the set of fringes is an order (m) of the interference pattern, where m is an integer equal to or greater than 1. Fringe 239_1 is a first order fringe (m=1), fringe 239_2 is a second order fringe (m=2), and fringe 239_3 is a third order fringe (m=3). FIG. 2C is a graph of the intensity of interference pattern 239 as a function of distance from the center of interference pattern 239 along a path numbered as 244 in FIG. 2B. Path 244 extends in the X direction from the center of interference pattern 239. The FWHM of fringe 239_1 is numbered as 243 in FIG. 2C.

[0036]

[0049] The interference pattern 239 is detected in an active area 242 of a detector 240. The detector 240 can be any type of detector capable of detecting light in the interference pattern 239. For example, the active area 242 can be a linear photodiode array that includes multiple elements of the same size equally spaced along a single dimension within a package. Each element of the photodiode array is sensitive to the wavelength of the portion 116'. As another example, the detector 240 can be a two-dimensional sensor, such as a two-dimensional charge-coupled device (CCD) or a two-dimensional complementary metal-oxide semiconductor (CMOS) sensor.

[0037]

[0050] The detector 240 is connected to an estimation system 250 via a data connection 254. The estimation system 250 includes an electronic processing module 251, an electronic storage 252, and an I / O interface 253. The electronic processing module 251 includes one or more processors suitable for executing computer programs, such as general-purpose or special-purpose microprocessors, and any one or more processors of any type of digital computer. In general, the electronic processor receives instructions and data from a read-only memory, a random access memory (RAM), or both. The electronic processing module 251 may include any type of electronic processor. The electronic processor or processors of the electronic processing module 251 execute instructions and access data stored on the electronic storage 252. The electronic processor or processors may also write data to the electronic storage 252.

[0038]

[0051] The electronic storage 252 is any type of computer-readable or machine-readable medium. For example, the electronic storage 252 can be a volatile memory, such as a RAM, or a non-volatile memory. In some implementations, the electronic storage 252 includes non-volatile and volatile parts or components. The electronic storage 252 can store data and information used in the operation of the estimation system 250. The electronic storage 252 can also store instructions (e.g., in the form of a computer program) that cause the estimation system 250 to interact with the estimation system 250. For example, the instructions can be a number of instructions that together form the estimation module 231, which, when executed, causes the electronic processing module 251 to perform the process 300 described with respect to FIG. 3. The electronic storage 252 can also store initial values ​​for various calibration values ​​used by the process 300.

[0039]

[0052] The electronic storage 252 stores instructions that analyze data from the detector 240 to determine information about the initial light beam 116. For example, the electronic processing module 251 may be configured to determine values ​​or indicators related to characteristics of the initial light beam 116. In some implementations, the electronic processing module 251 is configured to determine these values ​​from the interference pattern 239. For example, the electronic storage 252 may store instructions that cause the electronic processing module 251 to determine a width of fringe 239_1 and a width of fringe 239_2, or two different widths of fringe 239_1 or fringe 239_2 or fringe 239_3, or other combinations. The width of fringe 239_1 may be determined by determining the FWHM 243 (FIG. 2C). Other widths of fringe 239_1 may also be determined. For example, a width of fringe 239_1 at 0.1, 0.2 or 0.9 of the maximum intensity of fringe 239_1 may be determined and stored as an indication and value for the initial light beam 116. As another example, a width that includes some percentage (e.g., 10%, 50%, 95%) of the total light of fringe 239_1 may be determined and stored as an indication and value for the initial light beam 116. In another example, the maximum intensity of each fringe 239_1, 239_2, 239_3 is determined and used as information about the initial light beam 116.

[0040]

[0053] Fringe 239_1 is the fringe closest to the center of fringe pattern 239 and generally has the widest radial extent of all fringes in fringe pattern 239. Thus, using data from fringe 231_1 can provide higher resolution and greater accuracy than data from other fringes in pattern 239. Additionally, while complete fringes are shown in fringe pattern 239, in some embodiments, the entire fringe pattern 239 does not fall within active area 242 and / or a central portion of active area 242 does not coincide with the center of fringe pattern 239. As a result of this configuration, active area 242 captures only some portions of the fringes, and partial fringes appear as partial rings in the data generated by detector 240. In these implementations, accuracy can be improved by obtaining data from one or more complete fringes.

[0041]

[0054] The electronic storage 252 also stores information about the etalon 230 or the optical system 181. For example, the electronic storage 252 may store a reference value of a characteristic of the exposure beam 112. In some implementations, the electronic storage 252 stores an actual or reference value of the CBW derived from an optical spectrum of the exposure beam 112 measured at the wafer 182 using a spectrometer (such as spectrometer 871 in FIG. 8 ) or other optical instrument. The actual or reference value may be a number directly representing the CBW, or may be an indication of the CBW, such as a first wavelength and a second wavelength representing the endpoints of the FWHM of the measured optical spectrum of the exposure beam 112.

[0042]

[0055] The I / O interface 253 is any type of interface that allows the estimation system 250 to exchange data and signals with an operator, other devices, and / or automated processes running on another electronic device. For example, in implementations in which data or instructions stored on the electronic storage 252 may be edited, the edits may be made through the I / O interface 253. In another example, the I / O interface 253 may be configured to output an estimate of a property of the exposure beam 112, or an indication of such an estimate. The I / O interface 253 may include one or more of a visual display, a keyboard, and a communication interface such as a parallel port, a universal serial bus (USB) connection, and / or any type of network interface, such as, for example, Ethernet. The I / O interface 253 may also enable communication without physical contact, for example, through an IEEE 802.11, Bluetooth, or Near Field Communication (NFC) connection.

[0043]

[0056] The estimation system 250 is coupled to various components of the measurement system 260 through a data connection 254. The data connection 254 is any type of connection that allows for the transmission of data, signals, and / or information. For example, the data connection 254 can be a physical cable or other physical data conduit (such as a cable that supports the transmission of data according to IEEE 802.3), a wireless data connection (such as a data connection that provides data via IEEE 802.11 or Bluetooth), or a combination of wired and wireless data connections.

[0044]

[0057] 3 is a flow chart of a process 300. Process 300 is used to determine an estimate of a characteristic of exposure beam 112. Process 300 may be performed by estimation system 250 (FIG. 2A). For example, process 300 may be performed by one or more electronic processors in processing module 251. Process 300 will be described with respect to estimation system 250 (FIG. 2A).

[0045]

[0058] A set of values ​​for the initial light beam 116 is determined (310). The set of values ​​is determined based on or from data generated by the detector 240. For example, the detector 240 may generate data indicative of a measured light intensity of a wavefront of the portion 116' incident on the active area 242. The data may be two-dimensional data that provides an indication of a distribution of light energy across the active area 242. For example, the data may include a plurality of intensity values ​​each associated with a spatial coordinate indicative of a portion of the active area 242. The data may include a representation of a fringe pattern formed from the portion 116', such as fringe pattern 239 (FIG. 2B).

[0046]

[0059] The set of values ​​includes two or more values ​​for the initial light beam 116. For example, in an implementation in which the set of values ​​is determined from data representing the fringe pattern 239, the set of values ​​may include the width of each of two or more of the fringes in the pattern 239. The width of a fringe is the spatial distance representing the extent of the fringe between two adjacent regions of no light, such as width 243 in FIG. 2C. The width may be expressed as the FWHM of each fringe, or the width of each fringe at a given percentage of the maximum intensity of the fringe. For example, the width of a fringe may be the width at 10% of the maximum intensity, or the width at 20% of the maximum intensity. Different percentages may be used to determine the width of each fringe, or the same percentage may be used to determine the width of some or all of the fringes.

[0047]

[0060] Further, one or more values ​​in the set of values ​​may be determined from the same fringe. For example, the set of values ​​may include two values, a first of the values ​​being the width of the primary fringe 239_1 at a first percentage of the maximum intensity of the fringe 239_1, and a second of the values ​​being the width of the primary fringe 239_1 at a second percentage of the maximum intensity of the fringe 239_1. The first and second percentages are different percentages. For example, the first percentage may be 10% and the second percentage may be 90%, or any other percentage between 0% and 100% not equal to 90%.

[0048]

[0061] The percentages used to determine the values ​​in the set can be stored on electronic storage 252. For example, in implementations that use fringe widths to determine the values ​​in the set, electronic storage 252 can store an array or collection of predefined percentage values, one of which is associated with each value in the set of values. In these implementations, if the set of values ​​includes two fringe widths, the predefined percentage values ​​can be stored in an array of two values ​​corresponding to the percentages used for each fringe measurement. In some implementations, the predefined percentage values ​​are input by a user via I / O interface 253.

[0049]

[0062] A relationship involving two or more values ​​in the set of values ​​is determined 320. In some implementations, the relationship is non-linear. The non-linear relationship can have a term for each of the two or more values, as shown in Equation 1.

number

[0050]

[0063] In some implementations, the relationship may be a more generalized non-linear relationship such as that shown in equation (1a).

number

[0051]

[0064] In some implementations, the relationship is a linear relationship such as shown in equation (2).

number

[0052]

[0065] A property of the exposure beam 112 is estimated (330) based on the relationship. The initial values ​​of cal, A, B,...X are used along with the values ​​in the set of values ​​in equation (1) or equation (2) to determine an estimate of the property P. Continuing with the example above where the relationship is a non-linear relationship and the set of values ​​includes two fringe width values ​​(one of which is the width of fringe 239_1 at 10% of maximum intensity and the other is the width of fringe 239_1 at 90% of maximum intensity), CBW is determined based on equation (3).

number

[0053]

[0066] The estimated properties of exposure beam 112 may be output by I / O interface 253. For example, the estimated properties of exposure beam 112 may be output as numerical values ​​that are visually presented on a display, a device remote from estimation system 250, and / or may be stored as values ​​in electronic storage 252.

[0054]

[0067] In some implementations, the process 300 ends after estimating the characteristics at (330). In some implementations, the process 300 returns to (310) after estimating the characteristics at (330) so that changes that may occur during operation of the system 200 are accounted for by estimating the characteristics of the exposure beam 112 during operation of the system 200.

[0055]

[0068] In some implementations, the estimated property is stored as an initial estimate and process 300 continues (340). A reference value for the same property is accessed (340). A reference value for a property is a measured or mathematically determined value of the property that is known to be accurate. For example, if the CBW of exposure beam 112 was estimated in (330), then a reference value for the CBW of exposure beam 112 is accessed. In this example, the optical spectrum is measured directly with a spectrometer positioned at wafer 182, and the reference value is a CBW value determined from the measured optical spectrum. The estimate and the reference value may be accessed from electronic storage 252 and / or may be received through I / O interface 253.

[0056]

[0069] The estimated property of the exposure beam 112 is compared to a reference value to determine how well the estimate matches the reference value (350). For example, the absolute value of the difference between the estimate of the property and the reference value can be determined and compared to a threshold. In this example, the threshold is a numerical value stored on electronic storage 252 and / or provided through I / O interface 253. The threshold can be any value equal to or less than zero.

[0057]

[0070] Based on the comparison, the acceptability of the estimated property is evaluated (360). If the absolute value of the difference is less than or equal to the threshold, the estimated value of the property is accepted and the process 300 ends or returns to (310) to continue monitoring the property of the exposure beam 112. If the absolute value of the difference is greater than the threshold, the estimated value of the property is not accepted and minimization and / or optimization techniques are initiated (370) to reduce the error in estimating the value of the property.

[0058]

[0071] In the example of FIG. 3, values ​​of the parameters A, B,..., X, and cal that minimize the difference between the initial estimated property and the reference value of the property, given the values ​​in the set of values, are determined (370) using an optimization or minimization technique. Any optimization and / or minimization technique can be used to determine the values ​​of the parameters that minimize the difference. For example, in an implementation where the set of values ​​includes two values ​​and the nonlinear relationship is a quadratic equation (as shown in Equation 3), a quadratic optimization can be used to determine the values ​​of A, B, and cal that minimize the difference between the estimated value of the property and the reference value. After determining the values ​​of the parameters A, B,..., X that minimize the difference, the process 300 ends or returns to (310) to continue estimating the property of the exposure beam 112.

[0059]

[0072] Aspects of process 300 can also be used to determine a predetermined percentage value that is applied to data from detector 240 to determine the set of values ​​at (310). As discussed above, the set of values ​​may be a collection of fringe widths, each fringe width measured at a particular percentage of the maximum intensity of the fringe. The predetermined percentage value is determined before process 300 is performed, and the predetermined percentage value may be a percentage that is known to produce best or acceptable results through empirical and / or mathematical analysis.

[0060]

[0073] For example, the predetermined percentage can be a percentage known or predicted to provide the best estimate of the CBW. To determine the predetermined percentage value, the CBW is estimated using equation (1) or equation (2) using initial values ​​of A, B,..., X, and cal, and fringe width values ​​(V1, V2,..., VN) based on many possible percentage values. For each possible percentage value, the error between the estimated CBW and the reference CBW is determined, and the percentage or percentages that result in the smallest error are selected and stored as the predetermined percentage value. The process 300 is then performed using the predetermined percentage value, and the values ​​of A, B,..., X, and cal are optimized at (360).

[0061]

[0074] FIG. 4 is an example of a CBW estimation error of a second-order nonlinear relationship (as shown in Equation (3)) for many different fringe width percentage values. The data shown in FIG. 4 is experimental data generated using a two-stage master oscillator power amplifier (MOPA) such as the light-generating module 1010 shown in FIG. 10. The parameters of the light-generating module 1010 were changed to scan the CBW over its full operating range. The timing of the excitation of the electrodes in the master oscillator (MO) 1012_1 relative to the timing of the excitation of the electrodes in the power amplifier (PA) 1012_2, the repetition rate, and the angle of the prism in the line narrowing module 1095 were changed to obtain a full range of CBW values. In FIG. 4, the y-axis is the first fringe width percentage value, the x-axis is the second fringe width percentage value, and the contour lines represent the minimum mean square error in the CBW estimation as a function of the first and second fringe width percentage values. The fringe width percentage value that corresponds to the smallest CBW error is selected. In the illustrated example, the CBW error is minimized by setting the first fringe width percentage value to about 50% and the second fringe width percentage value to about 10%. The point corresponding to the percentage value is numbered as 490 in FIG. 4. After selecting the predetermined percentage value, the process 300 is performed.

[0062]

[0075] Other approaches are possible for setting the predetermined percentage value prior to performing process 300. For example, the predetermined percentage value can be random or set to a particular initial value, such as 50%. In these implementations, the error in the initial CBW estimate is reduced by performing 370 an optimization as part of process 300.

[0063]

[0076] FIG. 5 shows the error in CBW estimation (in femtometers) as a function of the measured reference CBW (in femtometers) when a quadratic relationship such as shown in Equation (3) is used to estimate the CBW, where FW1 is the fringe width at 10% intensity of the fringe closest to the center of the ring of fringes and FW2 is the fringe width at 40% intensity of the fringe closest to the center of the ring of fringes. The reference CBW was measured using an external spectrometer. FIG. 6 shows the error in CBW estimation (in femtometers) as a function of the measured reference CBW (in femtometers) when a linear relationship such as shown in Equation (2) is used to estimate the CBW. The error in the CBW estimated using the quadratic relationship (FIG. 5) has a smaller maximum value and a smaller standard deviation compared to the error in the CBW estimated using the linear relationship (FIG. 6). For example, the maximum error in the CBW error in the quadratic approach is about 4, and the maximum error in the linear approach is about 6. Although the CBW can be estimated using a linear relationship, Figures 5 and 6 show that the quadratic relationship (Figure 5) provides a more accurate estimate of the CBW with only a slight increase in complexity. The maximum error and standard deviation of the error in the CBW estimation can be further reduced by using a higher order polynomial (e.g., n=3 or n=4 in Equation 1).

[0064]

[0077] Each figure in Figures 7A-7C shows simulated data of estimated CD as a function of estimated spectral bandwidth metric (in femmeters (fm)) for seven different exposure tools. Figure 7A shows CD as a function of FWHM metric. Figure 7B shows CD as a function of E95 metric. Figure 7C shows CD as a function of CBW. As shown in Figure 7C, CBW and CD are linearly correlated for all seven exposure tools. Furthermore, when CBW is the metric, the characteristics of the linear correlation (e.g., when plotted as a function of CBW, the slope of the line matches the CD value) were similar for all seven exposure tools. CD is linearly correlated with FWHM metric (Figure 7A) and E95 metric (7B), but the characteristics of the correlation between CD and FWHM and E95 metrics change among different exposure tools. Figures 7A-7C show that CBW has the best correlation with CD across different exposure tools. Thus, the CBW is a robust metric that can be used to monitor and / or tune performance on different machines.

[0065]

[0078] 8 and 10 are examples of deep ultraviolet (DUV) optics with which measurement system 160 or 260 may be used. In the examples that follow, measurement system 260 is shown as being used with DUV optics.

[0066]

[0079] 8 and 9, system 800 includes a light generation module 810 that provides an exposure beam (or output light beam) 816 to a scanner apparatus 880 that includes a projection optics 881. In various implementations, the transfer function of the optics 181 can be the transfer function of the scanner apparatus 880 or the transfer function of one or more parts of the scanner apparatus, such as the projection optics 881. The light generation module 810 and the projection optics 881 are implementations of the light generation module 110 and the optics 181 (FIG. 1A), respectively.

[0067]

[0080] System 800 also includes a beam separator 117, a measurement system 260, and an estimation system 250. Beam separator 117 directs a portion of exposure beam 816 to measurement system 260, which is used to measure the wavelength of exposure beam 816. Estimation system 250 is coupled to measurement system 260. In the example of Figure 8, estimation system 250 is also coupled to light generating module 810 and various components associated with light generating module 810.

[0068]

[0081] The light generating module 810 includes an optical oscillator 812. The optical oscillator 812 generates an output light beam 816. The optical oscillator 812 includes a discharge chamber 815 that surrounds a cathode 813a and an anode 813b. The discharge chamber 815 also includes a gas gain medium 819. A potential difference between the cathode 813a and the anode 813b creates an electric field in the gas gain medium 819. The potential difference can be created by controlling a voltage source 897 to apply a voltage to the cathode 813a and / or the anode 813b. The electric field provides sufficient energy to the gas gain medium 819 to cause a population inversion and enable the generation of pulsed light via stimulated emission. Repeated creation of such a potential difference creates a train of pulses that are emitted as a light beam 816. The repetition rate of the pulsed light beam 816 is determined by the rate at which a voltage is applied to the electrodes 813a and 813b.

[0069]

[0082] The gain medium 819 is pumped by applying a voltage to the electrodes 813a and 813b. The duration and repetition rate of the pulses in the pulsed light beam 817 are determined by the duration and repetition rate of the application of the voltage to the electrodes 813a and 813b. The repetition rate of the pulses may range, for example, between about 500-6000 Hz. In some implementations, the repetition rate may be greater than 6000 Hz, and may be, for example, 12000 Hz or greater. Each pulse emitted from the optical oscillator 812 may have a pulse energy of, for example, approximately 1 millijoule (mJ).

[0070]

[0083] The gas gain medium 819 can be any gas suitable for producing a light beam at the wavelength, energy, and bandwidth required for the application. The gas gain medium 819 can include one or more types of gas, with the various gases referred to as gas components. In the case of an excimer source, the gas gain medium 819 can include a noble gas, such as argon or krypton, or a halogen, such as fluorine or chlorine. In implementations where a halogen is the gain medium, the gain medium also includes traces of xenon, as well as a buffer gas, such as helium.

[0071]

[0084] The gas gain medium 819 may be a gain medium that emits light in the deep ultraviolet (DUV) range. DUV light may include wavelengths from about 100 nanometers (nm) to about 400 nm, for example. Examples of gas gain medium 819 include argon fluoride (ArF), which emits light at a wavelength of about 193 nm, krypton fluoride (KrF), which emits light at a wavelength of about 248 nm, or xenon chloride (XeCl), which emits light at a wavelength of about 351 nm.

[0072]

[0085] A resonator is formed between a spectral conditioner 895 on one side of the discharge chamber 815 and an output coupler 896 on a second side of the discharge chamber 815. The spectral conditioner 895 may include a diffractive optic, such as a grating and / or a prism, that finely tunes the spectral output of the discharge chamber 815. The diffractive optic may be reflective or refractive. In some implementations, the spectral conditioner 895 includes multiple diffractive optical elements. For example, the spectral conditioner 895 may include four prisms, some of which are configured to control the center wavelength of the light beam 816 and others of which are configured to control the spectral bandwidth of the light beam 816.

[0073]

[0086] The spectral characteristics of the light beam 816 can be adjusted in other ways. For example, the spectral characteristics of the light beam 816, such as the spectral bandwidth and center wavelength, can be adjusted by controlling the pressure and / or gas concentration of the gas gain medium in the chamber 815. For implementations in which the light-generating module 810 is an excimer source, the spectral characteristics (e.g., the spectral bandwidth or center wavelength) of the light beam 816 can be adjusted by controlling, for example, the pressure and / or concentration of fluorine, chlorine, argon, krypton, xenon, and / or helium in the chamber 815.

[0074]

[0087] The pressure and / or concentration of the gas gain medium 819 can be controlled using a gas supply system 890. The gas supply system 890 is fluidly coupled to the interior of the discharge chamber 815 via a fluid conduit 889. The fluid conduit 889 is any conduit capable of carrying a gas or other fluid with no or minimal fluid loss. For example, the fluid conduit 889 may be a pipe made of or coated with a material that does not react with the fluid or fluids carried in the fluid conduit 889. The gas supply system 890 includes a chamber 891 configured to contain and / or receive a supply of the gas or gases used in the gain medium 819. The gas supply system 890 also includes devices (such as pumps, valves, and / or fluidic switches) that allow the gas supply system 890 to remove gas from or inject gas into the discharge chamber 815.

[0075]

[0088] The optical oscillator 812 also includes a spectrum analyzer 898. The spectrum analyzer 898 is a measurement system that can be used to measure or monitor the wavelength of the light beam 816. In the example shown in FIG. 8, the spectrum analyzer 898 receives light from the output coupler 896. In some implementations, the spectrum analyzer 898 is part of the measurement system 260.

[0076]

[0089] The light generation module 810 may include other components and systems. For example, the light generation module 810 may include a beam preparation system 899. The beam preparation system 899 may include a pulse stretcher that stretches in time each pulse that interacts with the pulse stretcher. For example, the beam preparation system may also include other components that can act on the light, such as reflective and / or refractive optical elements (e.g., lenses and mirrors) and / or filters. In the illustrated example, the beam preparation system 899 is positioned in the path of the exposure beam 816. However, the beam preparation system 899 may be located elsewhere in the system 800.

[0077]

[0090] The system 800 also includes a scanner apparatus 880. The scanner apparatus 880 exposes a wafer 882 to a shaped exposure beam 816A. The shaped exposure beam 816A is formed by passing the exposure beam 816 through a projection optics 881. The scanner apparatus 880 may be an immersion system or a dry system. The scanner apparatus 880 includes the projection optics 881 through which the exposure beam 816 passes before reaching the wafer 882, and a sensor system or metrology system 870. The wafer 882 is held or received on a wafer holder 883. The scanner apparatus 880 may also include temperature control devices, such as (air conditioning devices and / or heating devices), and / or power sources for various electronic components.

[0078]

[0091] Metrology system 870 includes sensor 871. Sensor 871 may be configured to measure characteristics of shaped exposure beam 816A, such as bandwidth, energy, pulse duration, and / or wavelength. Sensor 871 may be, for example, a camera or other device capable of capturing an image of shaped exposure beam 816A at wafer 882, or an energy detector capable of capturing data representative of the amount of optical energy at wafer 882 in the xy plane. Sensor 871 may also be a spectrometer that determines the optical spectrum of exposure beam 816A.

[0079]

[0092] Referring also to FIG. 9, the projection optical system 881 includes a slit 884, a mask 885, and a projection objective including a lens system 886. The lens system 886 includes one or more optical elements. The exposure beam 816 enters the scanner device 880 and impinges on the slit 884, and at least a portion of the output light beam 816 passes through the slit 884 to form a shaped exposure beam 816A. In the example of FIGS. 8 and 9, the slit 884 is rectangular and shapes the exposure beam 816 into an elongated rectangular shaped light beam, which is the shaped exposure beam 816A. The mask 885 includes a pattern that determines which portions of the shaped light beam are transferred by the mask 885 and which portions are blocked by the mask 885. Microelectronic features are formed on the wafer 882 by exposing a radiation-sensitive photoresist material layer on the wafer 882 to the exposure beam 816A. The design of the pattern on the mask is dictated by the particular microelectronic circuit features desired.

[0080]

[0093] 8 is an example configuration for a DUV system. Other implementations are possible, and the estimation system 250 can be used with other implementations of the light-generating module 810.

[0081]

[0094] For example, the light generation module 810 may include N instances of optical oscillators 812 arranged in parallel, where N is an integer greater than 1. In these implementations, each optical oscillator 812 is configured to emit a respective light beam towards a beam combiner that forms an exposure beam 816 from beams emitted by one or more of the N oscillators.

[0082]

[0095] 10, the light-generating module 810 can be configured as a multi-stage laser system. For example, the light-generating module 810 can include a master oscillator (MO) that provides a seed light beam to a power amplifier (PA), which amplifies the seed light beam to generate the output light beam 816. Such a laser system may be referred to as a MOPA laser system.

[0083]

[0096] Figure 10 shows another example configuration of a DUV system. Figure 10 is a block diagram of a photolithography system 1000 including a light generation module 1010 that generates a pulsed light beam 1016 that is provided to a scanner device 880. The photolithography system 1000 also includes a beam separator 117, a measurement system 260, and an estimation system 250. The estimation system 250 is coupled to the measurement system 260, various components of the light generation module 1010, and the scanner device 1080, and controls various operations of the system 1000. In the example of Figure 10, the beam separator 117 directs a portion of the output light beam 1016 to the measurement system 260.

[0084]

[0097] The light generation module 1010 is a two-stage laser system that includes a master oscillator (MO) 1012_1 that provides a seed light beam 1018 to a power amplifier (PA) 1012_2. The PA 1012_2 receives the seed light beam 1018 from the MO 1012_1 and amplifies the seed light beam 1018 to generate a light beam 1016 for use in the scanner device 880. For example, in some implementations, the MO 1012_1 can emit a pulsed seed light beam with a seed pulse energy of approximately 1 millijoule (mJ) per pulse, and these seed pulses can be amplified by the PA 1012_2 to approximately 10-15 mJ, although other energies may be used in other examples.

[0085]

[0098] The MO 1012_1 includes a discharge chamber 1015_1 having two elongated electrodes 1013a_1 and 1013b_1, a gain medium 1019_1 which is a gas mixture, and a fan (not shown) for circulating the gas mixture between the electrodes 1013a_1, 1013b_1. A resonator is formed between a line narrowing module 1095 on one side of the discharge chamber 1015_1 and an output coupler 1096 on a second side of the discharge chamber 1015_1.

[0086]

[0099] The discharge chamber 1015_1 includes a first chamber window 1063_1 and a second chamber window 1064_1. The first and second chamber windows 1063_1 and 1064_1 are on opposite sides of the discharge chamber 1015_1. The first and second chamber windows 1063_1 and 1064_1 transmit light in the DUV range and allow the DUV light to enter and exit the discharge chamber 1015_1.

[0087]

[0100] The line narrowing module 1095 may include one or more diffractive optics, such as a grating or prism, that finely tune the spectral output of the discharge chamber 1015_1. The light generation module 1010 may also include a line center analysis module 1068 that receives the output light beam from the output coupler 1096, and beam combining optics 1069. The line center analysis module 1068 is a measurement system that may be used to measure or monitor the wavelength of the seed light beam 1018. The line center analysis module 1068 may be located elsewhere in the light generation module 1010 or at the output of the light generation module 1010.

[0088]

[0101] The gas mixture, which is the gain medium 1019_1, can be any gas suitable for generating a light beam at the wavelength and bandwidth required for the application. In the case of an excimer source, the gas mixture may include traces of xenon as well as noble gases, e.g., argon or krypton, halogens, e.g., fluorine or chlorine, and buffer gases, e.g., helium. Examples of gas mixtures include argon fluoride (ArF), which emits light at a wavelength of about 193 nm, krypton fluoride (KrF), which emits light at a wavelength of about 248 nm, or xenon chloride (XeCl), which emits light at a wavelength of about 351 nm. Thus, in this embodiment, the light beams 1016 and 1018 include wavelengths in the DUV range. The excimer gain medium (gas mixture) is pumped with short (e.g., nanosecond) current pulses in a high-voltage electrical discharge by application of a voltage to the elongated electrodes 1013a_1, 1013b_1.

[0089]

[0102] PA 1012_2 includes beam combining optics 1069 that receive the seed light beam 1018 from MO 1012_1 and direct the seed light beam 1018 through discharge chamber 1015_2 to beam turning optics 1092, which modifies or changes the direction of the seed light beam 1018 so that it is transmitted back into discharge chamber 1015_2. The beam turning optics 1092 and beam combining optics 1069 form a circular and closed loop optical path in which the input to the ring amplifier meets the output of the ring amplifier at beam combining optics 1069.

[0090]

[0103] The discharge chamber 1015_2 includes a pair of elongated electrodes 1013a_2, 1013b_2, a gain medium 1019_2, and a fan (not shown) for circulating the gain medium 1019_2 between the electrodes 1013a_2, 1013b_2. The gas mixture forming the gain medium 1019_2 may be the same as the gas mixture forming the gain medium 1019_1.

[0091]

[0104] The discharge chamber 1015_2 includes a first chamber window 1063_2 and a second chamber window 1064_2. The first and second chamber windows 1063_2 and 1064_2 are on opposite sides of the discharge chamber 1015_2. The first and second chamber windows 1063_2 and 1064_2 transmit light in the DUV range and allow the DUV light to enter and exit the discharge chamber 1015_2.

[0092]

[0105] When the gain medium 1019_1 or 1019_2 is pumped by applying a voltage to the electrodes 1013a_1, 1013b_1, or 1013a_2, 1013b_2, respectively, the gain medium 1019_1 and / or 1019_2 emits light. When a voltage is applied to the electrodes at regular time intervals, the light beam 1016 is pulsed. Thus, the repetition rate of the pulsed light beam 1016 is determined by the rate at which the voltage is applied to the electrodes. The repetition rate of the pulses may range between about 500-6000 Hz for various applications. In some implementations, the repetition rate may be greater than 6000 Hz, and may be, for example, 12000 Hz or greater, although other repetition rates may be used in other implementations. Additionally, a controller (which may be implemented as part of the estimation system 250) controls the timing of the application of voltage to electrodes 1013a_1, 1013b_1 relative to the application of voltage to electrodes 1013a_2, 1013b_2 to ensure that the gain medium 1019_2 is excited at the appropriate time and the seed light beam 1018 is amplified.

[0093]

[0106] The output light beam 1016 can be directed through a beam preparation system before reaching the scanner device 880. The beam preparation system 1099 can include a bandwidth analysis module that measures various parameters (such as bandwidth or wavelength) of the beam 1016. The beam preparation system 1099 can also include a pulse stretcher that stretches each pulse of the output light beam 1016 in time. For example, the beam preparation system 1099 can also include other components that can act on the beam 1016, such as reflective and / or refractive optical elements (e.g., lenses and mirrors), filters, and optical apertures (including automatic shutters).

[0094]

[0107] The DUV light generation module 1010 also includes a gas management system 1090 that is fluidly connected to the interior 1078 of the DUV light generation module 1010 .

[0095]

[0108] Implementations and / or embodiments may be further described using the following clauses. 1. determining a set of values ​​for an initial light beam based on a detected wavefront of the initial light beam, the set of values ​​including a first value and a second value; determining an estimate of a characteristic of an exposure beam based on a non-linear relationship including the first value and the second value, the exposure beam being formed by interacting the initial light beam with an optical system; an estimation system configured to: a communication module coupled to the estimation system and configured to output an estimate of the property of the exposure beam; An apparatus comprising: 2. The apparatus described in clause 1, wherein the characteristics of the exposure beam include a convolved bandwidth metric, the convolved bandwidth metric representing a width of a portion of the optical spectrum of the exposure beam at a wafer illuminated by the exposure beam, and the optical spectrum of the exposure beam includes the intensity of the exposure beam as a function of wavelength. 3. The apparatus of clause 1, wherein the detected wavefront of the initial light beam includes a fringe pattern generated from the initial light beam, the fringe pattern including a plurality of fringes, the first value includes a first width of a first fringe in the plurality of fringes, and the second value includes a second width of a second fringe in the plurality of fringes. 4. The apparatus of claim 3, wherein the first fringe in the plurality of fringes and the second fringe in the plurality of fringes are one and the same fringe. 5. The apparatus of clause 4, wherein the first width is a width of a fringe at a first percentage of a peak intensity of the fringe, and the second width is a width of a fringe at a second percentage of a peak intensity of the fringe. 6. The apparatus of claim 5, wherein the first percentage and the second percentage are different percentages. 7. The apparatus of clause 6, wherein the plurality of fringes are concentric rings of light centered about a central point and separated by no light areas, one fringe being the fringe closest to the central point. 8. The apparatus of claim 1, wherein the nonlinear relationship includes a quadratic relationship. 9. The apparatus of claim 8, wherein one of the first value and the second value is squared. 10. The apparatus of claim 1, wherein the nonlinear relationship further includes a plurality of calibration parameters. 11. The estimation system accessing a reference value of a characteristic of an exposure beam; determining a value for each of the calibration parameters by minimizing a difference between an estimate of the characteristic and a reference value of the characteristic; 11. The apparatus of claim 10, further configured to: 12. The apparatus according to claim 11, wherein the reference value of the characteristic is obtained by a spectrometer. 13. The apparatus described in clause 1, further comprising an optical system. 14. The apparatus of claim 1, wherein the optical system comprises a projection lens and a reticle. 15. The apparatus of claim 3, further comprising an etalon configured to generate the fringe pattern. 16. The apparatus of clause 1, further comprising a detector configured to detect a wavefront and provide data relating to the detected wavefront to the estimation system. 17. A light source configured to emit a light beam including deep ultraviolet (DUV) light; an optical measurement system configured to generate a fringe pattern based on the light beam; a projection optical system configured to emit an exposure beam based on the light beam; determining a first value and a second value from the fringe pattern; determining an estimate of a characteristic of the exposure beam based on the first value and the second value; an estimation system configured to: A system comprising: 18. The system of claim 17, wherein the projection optics comprises a projection lens and a reticle. 19. The system of clause 17, wherein the estimation system is configured to determine an estimate of the characteristic based on a nonlinear relationship, the nonlinear relationship including a first value, a second value, and a plurality of calibration constants. 20. The system of clause 19, wherein the estimation system is further configured to determine a value for each of a plurality of calibration constants based on minimizing a difference between the estimate of the characteristic and a reference value of the characteristic. 21. The system of claim 17, wherein the optical measurement system comprises an etalon. 22. The system of clause 17, wherein the light source includes a master oscillator configured to emit a seed light beam and a power amplifier configured to amplify the seed light beam to generate a light beam including DUV light. 23. Detecting a wavefront of an initial light beam; determining a set of initial light beam values ​​based on the detected wavefront; determining a relationship involving at least two of the values ​​in the set of values; determining an estimate of a characteristic of an exposure beam based on a relationship, the exposure beam being generated by interacting an initial light beam with an optical system; A method comprising: 24. The method according to clause 23, wherein the relational expression is a nonlinear relational expression.

[0096]

[0109] Other implementations are within the scope of the claims.

Claims

1. determining a set of values ​​for the initial light beam based on the detected wavefront of the initial light beam, the set of values ​​including a first value and a second value; determining an estimate of a characteristic of an exposure beam based on a non-linear relationship including the first value and the second value, the exposure beam being formed by interacting the initial light beam with an optical system; and an estimation system configured to: a communications module coupled to the estimation system and configured to output the estimate of the property of the exposure beam; An apparatus comprising:

2. 2. The apparatus of claim 1, wherein the characteristics of the exposure beam include a convolved bandwidth metric that represents a width of a portion of the optical spectrum of the exposure beam at a wafer illuminated by the exposure beam, and the optical spectrum of the exposure beam includes an intensity of the exposure beam as a function of wavelength.

3. 2. The apparatus of claim 1, wherein the detected wavefront of the initial light beam comprises a fringe pattern generated from the initial light beam, the fringe pattern comprising a plurality of fringes, the first value comprising a first width of a first fringe in the plurality of fringes, and the second value comprising a second width of a second fringe in the plurality of fringes.

4. The apparatus of claim 3 , wherein the first fringe in the plurality of fringes and the second fringe in the plurality of fringes are one and the same fringe.

5. 5. The apparatus of claim 4, wherein the first width is a width of the one fringe at a first percentage of a peak intensity of the one fringe and the second width is a width of the one fringe at a second percentage of the peak intensity of the one fringe.

6. The apparatus of claim 5 , wherein the first percentage and the second percentage are different percentages.

7. 7. The apparatus of claim 6, wherein the fringes are concentric rings of light centered about a central point and separated by no light areas, and the one fringe is the fringe closest to the central point.

8. The apparatus of claim 1 , wherein the nonlinear relationship comprises a quadratic relationship.

9. The apparatus of claim 8 , wherein one of the first value and the second value is squared.

10. The apparatus of claim 1 , wherein the nonlinear relationship further comprises a plurality of calibration parameters.

11. The estimation system comprises: accessing a reference value of said characteristic of said exposure beam; determining a value for each of the calibration parameters by minimizing a difference between the estimate of the characteristic and the reference value of the characteristic; The apparatus of claim 10 , further configured to:

12. The apparatus of claim 11 , wherein the reference value of the property is obtained by a spectrometer.

13. The apparatus of claim 1 further comprising the optical system.

14. The apparatus of claim 1 , wherein the optical system comprises a projection lens and a reticle.

15. The apparatus of claim 3 , further comprising an etalon configured to generate the fringe pattern.

16. The apparatus of claim 1 , further comprising a detector configured to detect the wavefront and provide data related to the detected wavefront to the estimation system.

17. a light source configured to emit a light beam comprising deep ultraviolet (DUV) light; an optical measurement system configured to generate a fringe pattern based on the light beam; a projection optical system configured to emit an exposure beam based on the light beam; determining a first value and a second value from the fringe pattern; determining an estimate of a characteristic of the exposure beam based on the first value and the second value; an estimation system configured to: A system comprising:

18. The system of claim 17 , wherein the projection optics comprises a projection lens and a reticle.

19. 20. The system of claim 17, wherein the estimation system is configured to determine the estimate of the characteristic based on a non-linear relationship, the non-linear relationship including the first value, the second value, and a plurality of calibration constants.

20. 20. The system of claim 19, wherein the estimation system is further configured to determine a value for each of the plurality of calibration constants based on minimizing a difference between the estimate of the characteristic and a reference value of the characteristic.

21. The system of claim 17 , wherein the optical measurement system comprises an etalon.

22. 20. The system of claim 17, wherein the light source comprises a master oscillator configured to emit a seed light beam and a power amplifier configured to amplify the seed light beam to produce the light beam comprising DUV light.

23. Sensing a wavefront of an initial light beam; determining a set of initial light beam values ​​based on the detected wavefront; determining a relationship that includes at least two of the values ​​in the set of values; determining an estimate of a characteristic of an exposure beam based on the relationship, the exposure beam being generated by interacting the initial light beam with an optical system; The method includes:

24. The method of claim 23 , wherein the relationship is a non-linear relationship.

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