Methods for decoupling fluctuation sources related to semiconductor manufacturing

Abstract

Described herein is a method for determining process drift over time or outlier wafers in semiconductor manufacturing. The method involves obtaining data associated with a variation of a key performance indicator (KPI) characterizing the performance of a semiconductor process over time (e.g., LCDU) and a set of factors associated with the semiconductor process. A model of the KPI and the data are used to determine a contribution of a first set of factors to the variation of the KPI, the first set of factors exceeding a statistical threshold. The contribution from the first set of factors to the variation of the KPI is removed from the model to obtain a residual KPI variation. A residual value that exceeds a residual threshold is determined based on the residual KPI variation. The residual value is indicative of a process drift over time in the semiconductor process or an outlier wafer that corresponds to the residual value at a particular time.

Description

[Technical Field]

[0001] Cross-reference of related applications

[0001] This application claims priority to U.S. Patent Application No. 63 / 220,309, filed on 9 July 2021, which is incorporated herein by reference in its entirety.

[0002]

[0002] This disclosure relates to a method for improving the performance of a semiconductor manufacturing process. The method may be used in conjunction with a lithography apparatus or a metrology apparatus. [Background technology]

[0003]

[0003] A lithography apparatus is a machine that transfers a desired pattern to a target portion of a substrate. A lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that context, a patterning device, which may alternatively be called a mask or reticle, may be used to generate a circuit pattern corresponding to individual layers of the IC, and this pattern can be imaged onto a target portion (e.g., part of one or more dies) on a substrate (e.g., a silicon wafer) having a layer of radiation-sensitive material (resist). Generally, a single substrate includes a network of adjacent target portions that are exposed in succession. Known lithography apparatuses include a so-called stepper, where each target portion is irradiated by exposing the entire pattern to the target portion in a single pass, and a so-called scanner, where each target portion is irradiated by scanning the pattern in a certain direction ("scan" direction) using a beam, while simultaneously scanning the substrate synchronously parallel or counterparallel to this direction.

[0004]

[0004] Before transferring the circuit pattern from the patterning device to the substrate, the substrate may undergo various processes such as priming, resist coating, and soft baking. After exposure, the substrate may undergo other processes such as post-bake (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. These numerous processes are used as a basis for creating the individual layers of a device, such as an IC device. The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, and chemical mechanical polishing to produce the individual layers of the device. If several layers are required for the device, the entire procedure or variations thereof may be repeated for each layer. Finally, the device is present in each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, so that the individual devices can be mounted on a carrier, connected to pins, etc.

[0005]

[0005] Accordingly, the manufacture of semiconductor devices generally involves processing a substrate (e.g., a semiconductor wafer) using a number of fabrication processes to form various features and multiple layers of the device. Such layers and features are generally manufactured and processed using, for example, deposition, lithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices may be manufactured on multiple dies on a substrate and then separated into individual devices. Device manufacturing generally includes a patterning process. The patterning process includes a patterning step such as optical and / or nanoimprint lithography using a patterning device (e.g., a mask) in a lithography apparatus to transfer a pattern on a patterning device to a substrate, and generally (but optionally), includes one or more related pattern processing steps such as resist development with a developing apparatus, baking of the substrate with a baking tool, and etching using the pattern with an etching apparatus. [Overview of the project]

[0006]

[0006] Semiconductor manufacturing involves monitoring and controlling one or more processes and equipment used in manufacturing to accurately print nanoscale features of circuits onto substrates. For example, in a lithography process, processes and equipment are monitored to detect and flag process drift or excursions or outlier substrates by analyzing one or more key performance indicator (KPI) data (e.g., local critical dimension uniformity (LCDU), failure rate, etc.) that indicate process performance over time. Monitoring of these KPIs (e.g., local CD uniformity (LCDU), failure rate, etc.) is done by exposing substrates using a predetermined process at regular intervals, measuring these substrates, calculating KPI data, and monitoring trends in the KPI data over a period of time. For example, in a high-volume manufacturing (HVM) setting, a given process may employ multiple tools and reticles that are expected to contribute to the variation in KPIs over time, and other measurable process noises such as mean critical dimension (CD) or dose may also be present, which also affect the KPI being measured. To account for these variations, different tools and reticles can be monitored separately using distinct specification limits, and advanced process controls may be applied to ensure that the feature CD is as close as possible to the target CD.

[0007]

[0007] The present disclosure provides a mechanism for capturing process drift or outlier substrates that may be masked as meeting KPI-related specifications. The mechanism decomposes and filters contributions from a specific set of factors (such as tools and reticles) to the KPI variation and monitors the variation in residual KPIs. By removing contributions from various factors, the signal-to-noise ratio of the time-dependent variation in residual KPIs related to semiconductor processes is improved. The improved signal-to-noise ratio then advantageously helps in identifying process drift or outlier substrates in time.

[0008]

[0008] In embodiments, a method is provided for determining process drift over time or outlier wafers in semiconductor manufacturing. The method involves obtaining data associated with a set of factors associated with a key performance indicator (KPI) that characterizes the performance of a semiconductor process over time (e.g., LCDU) and the semiconductor process; determining the contribution of a first set of factors to the KPI variability using a model of the KPI and using the data as input to the model, wherein the first set of factors exceeds a statistical threshold; removing the contribution from the first set of factors to the KPI variability to obtain residual KPI variability; and determining residual values ​​that exceed a residual threshold based on the residual KPI variability, wherein the residual values ​​indicate outlier wafers corresponding to process drift over time or residual values ​​at a particular time.

[0009]

[0009] In the embodiment, the model is constructed based on a set of factors associated with semiconductor manufacturing. The model is applied to the data to determine the contribution of the set of factors to the variability in the KPI. In the embodiment, analysis of variance (ANOVA), analysis of covariance (ANCOVA), or other statistical or modeling techniques can be applied to the statistical model to determine the contribution of each factor in the set to the variability of the KPI.

[0010]

[0010] In embodiments, the factor set includes categorical variables, measurable parameters (e.g., dose, CD, focus, etc.) or combinations thereof. For example, a factor may include one or more first categorical variables for characterizing the contribution of multiple lithography devices to the variability of the KPI, second categorical variables for characterizing the contribution of multiple reticles to the variability in the KPI, third categorical variables for characterizing the contribution of multiple metrology tools to the variability of the KPI, and a fourth variable including measurable wafer parameters (e.g., mean CD) that contribute to the variability of the KPI.

[0011]

[0011] In embodiments, the method further includes detecting systematics (e.g., data patterns) in the variability of residual KPIs, determining root causes associated with the systematics in response to the detected systematics, and adjusting the model to include factors associated with the root causes as contributing factors to the variability of the KPIs. In embodiments, the root causes indicate that the variability of residual KPIs is caused by characteristics of downstream processes and / or upstream processes of the semiconductor process. Following the model adjustment, it is advantageous that the contribution of the detected systematics can be isolated from subsequent residual KPI monitoring, thereby further improving the signal-to-noise ratio of the variability of residual KPIs.

[0012]

[0012] Furthermore, in the embodiment, there is provided a non-temporary computer-readable medium containing instructions, the instructions, when executed by one or more processors, cause an operation including the steps of the method discussed above to be performed.

[0013]

[0013] Herein, an embodiment will be described as merely an example with reference to the attached drawings. [Brief explanation of the drawing]

[0014] [Figure 1]

[0014] A schematic diagram of a lithography apparatus according to an embodiment is shown. [Figure 2]

[0015] Examples of processing parameter categories according to the embodiment are shown below. [Figure 3]

[0016] This is a flowchart of a method for determining process drift over time in semiconductor manufacturing, according to an embodiment. [Figure 4]

[0017] This is a plot of local critical dimension uniformity (LCDU) and mean CD for different wafers patterned using different tools and reticles according to the embodiment. [Figure 5A]

[0018] Exemplary measured LCDUs for different wafers according to an embodiment are shown. [Figure 5B]

[0019] Exemplary modeled LCDUs for different wafers according to an embodiment are shown. [Figure 5C]

[0020] Exemplary residual LCDUs for different wafers according to an embodiment are shown. [Figure 5D]

[0021] Patterns in another exemplary residual LCDU for different wafers according to an embodiment are shown. [Figure 6A]

[0022] A histogram of LCDU according to an embodiment is shown. [Figure 6B]

[0023] A histogram of residual LCDU according to an embodiment is shown, and outliers are prominent due to an increased signal-to-noise ratio compared to the LCDU in FIG. 6A. [Figure 7]

[0024] A block diagram of an exemplary computer system according to an embodiment is shown. [Figure 8]

[0025] A diagram of an exemplary extreme ultraviolet (EUV) lithography projection apparatus according to an embodiment is shown. [Figure 9]

[0026] A more detailed diagram of the exemplary apparatus of FIG. 8 according to an embodiment is shown. [Figure 10]

[0027] A more detailed diagram of the source collector module of the apparatuses of FIGS. 8 and 9 according to an embodiment is shown.

Mode for Carrying Out the Invention

[0015]

[0028] While this text may contain specific references to the use of lithography equipment in IC manufacturing, it should be understood that the lithography equipment described herein may also have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memory, liquid crystal displays (LCDs), and thin-film magnetic heads. Those skilled in the art will recognize that in the context of such alternative applications, the terms “wafer” or “die” used herein can be considered synonymous with the more general terms “substrate” or “target portion,” respectively. The substrates described herein may be processed before or after exposure, for example, with a track (generally a tool for coating a layer of resist onto the substrate and developing the exposure resist) or a metrology or inspection tool. Where applicable, the disclosures herein may apply to the above and other substrate processing tools. Furthermore, the substrate may be processed two or more times, for example, to produce a multilayer IC, and therefore the term “substrate” as used herein may also refer to a substrate that already contains multiple processed layers.

[0016]

[0029] As used herein, the terms “radiation” and “beam” encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5 to 20 nm), as well as particle beams such as ion beams or electron beams.

[0017]

[0030] As used herein, the term “patterning device” is broadly interpreted to refer to a device that can be used, for example, to impart a patterned beam to a cross-section in order to generate a pattern on a target portion of a substrate. It should be noted that the pattern imparted to the beam may not precisely match the desired pattern on the target portion of the substrate. Generally, the pattern imparted to the beam corresponds to a specific functional layer within the device being generated on the target portion, such as an integrated circuit.

[0018]

[0031] Patterning devices 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, Levenson (alternating) phase shift, and halftone (attenuated) phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect the incident radiation beam in a different direction, thus patterning the reflected beam.

[0019]

[0032] A support structure holds the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithography apparatus, and other conditions such as whether the patterning device is held in a vacuum environment. The support can use mechanical clamping, vacuum, or other clamping techniques such as electrostatic clamping under vacuum conditions. The support structure may be, for example, a frame or table that can be fixed or movable as needed and can ensure that the patterning device is in a desired position relative to the projection system. The use of the terms “reticle” or “mask” herein can be considered synonymous with the more general term “patterning device.”

[0020]

[0033] As used herein, the term “projection system” shall be broadly interpreted to encompass various types of projection systems, including refractive optics, reflective optics, and reflective-refractive optics, appropriately depending on the exposure radiation used, or other factors such as the use of immersion liquid or vacuum. The use of the term “projection lens” herein may be considered synonymous with the more general term “projection system.”

[0021]

[0034] Illumination systems may also include various types of optical components, including refraction, reflection, and refractional optical components for guiding, shaping, or controlling the radiant beam, and such components may be referred to collectively or individually as “lenses” below.

[0022]

[0035] Figure 1 schematically depicts a lithography apparatus according to one embodiment. This apparatus is

[0036] - Illumination system (illuminator) IL for adjusting the radiation beam PB (e.g., UV radiation or DUV radiation).

[0037] - A support structure MT is connected to a first positioning device PM for supporting a patterning device (e.g., a mask) MA and for precisely positioning the patterning device relative to an item PL.

[0038] - A substrate table (e.g., wafer table) WT connected to a second positioning device PW for holding a substrate (e.g., a resist-coated wafer) W and for accurately positioning the substrate relative to an item PL, and

[0039] - A projection system (e.g., a refractive projection lens) PL configured to image the pattern applied to the radiation beam PB by a patterning device MA onto a target portion C of the substrate W (e.g., including one or more dies), Includes.

[0023]

[0040] As depicted here, the device is transmissive (for example, using a transmissive mask). Alternatively, the device may be reflective (for example, using a programmable mirror array of the type described above).

[0024]

[0041] The illuminator IL receives the radiation beam from the radiation source SO. The radiation source and lithography apparatus may be separate entities, for example, when the radiation source is an excimer laser. In such cases, the radiation source is not considered to form part of the lithography apparatus, and the radiation beam is delivered from the radiation source SO to the illuminator IL using a beam delivery system BD, for example, including appropriate guide mirrors and / or beam expanders. In other cases, the radiation source may be an integrated part of the apparatus, for example, when the radiation source is a mercury lamp. The radiation source SO and illuminator IL, together with the beam delivery system BD if necessary, may be referred to as a radiation system.

[0025]

[0042] The illuminator IL can modify the beam intensity distribution. The illuminator may be positioned to limit the radial range of the emitted beam so that the intensity distribution is non-zero within an annular region within the pupil plane of the illuminator IL. Additionally or alternatively, the illuminator IL may be operable to limit the distribution of the beam within the pupil plane so that the intensity distribution is non-zero in multiple equally spaced sectors within the pupil plane. The intensity distribution of the emitted beam within the pupil plane of the illuminator IL may be referred to as the illumination mode.

[0026]

[0043] The illuminator IL may include an adjuster AM configured to adjust the beam intensity distribution. Generally, at least the outer and / or inner radial ranges of the intensity distribution within the pupil plane of the illuminator (usually called σ-outer and σ-inner, respectively) can be adjusted. The illuminator IL may also be operable to change the angular distribution of the beam. For example, the illuminator may be operable to change the number and angular range of sectors within the pupil plane in which the intensity distribution is non-zero. Different illumination modes may be achieved by adjusting the beam intensity distribution within the pupil plane of the illuminator. For example, by limiting the radius and angular range of the intensity distribution within the pupil plane of the illuminator IL, the intensity distribution may have a multipolar distribution, such as a dipole, quadrupole, or hexapole distribution. The desired illumination mode may be obtained, for example, by inserting an optical component that provides that illumination mode into the illuminator IL, or by using a spatial light modulator.

[0027]

[0044] The illuminator IL may be operable to change the polarization of the beam, and may be operable to adjust the polarization using an adjuster AM. The polarization state of the radiated beam across the pupil plane of the illuminator IL may be called the polarization mode. The use of different polarization modes can enable the achievement of greater contrast in the image formed on the substrate W. The radiated beam may be unpolarized. Alternatively, the illuminator may be configured to linearly polarize the radiated beam. The polarization direction of the radiated beam may differ across the pupil plane of the illuminator IL. The polarization direction of the radiation may differ in different regions within the pupil plane of the illuminator IL. The polarization state of the radiation may be selected based on the illumination mode. In the case of a multipole illumination mode, the polarization of each pole of the radiated beam may be approximately perpendicular to the position vector of that pole within the pupil plane of the illuminator IL. For example, in the case of a dipole illumination mode, the radiation may be linearly polarized in a direction approximately perpendicular to the line bisecting the two opposing sectors of the dipole. The radiated beam may be polarized in one of two different orthogonal directions, which may be called the X-polarization state and the Y-polarization state. In the quadrupole illumination mode, the radiation in each pole sector may be linearly polarized in a direction approximately perpendicular to the line bisecting that sector. This polarization mode may be called XY polarization. Similarly, in the hexapole illumination mode, the radiation in each pole sector may be linearly polarized in a direction approximately perpendicular to the line bisecting that sector. This polarization mode may be called TE polarization.

[0028]

[0045] Furthermore, the illuminator IL generally includes various other components such as the integrator IN and the capacitor CO. The illuminator provides a regulated radiant beam PB with the desired uniformity and intensity distribution in cross-section.

[0029]

[0046] The radiating beam PB is incident on a patterning device (e.g., a mask) MA held on a support structure MT. After the beam PB traverses the patterning device MA, it passes through a lens PL that focuses the beam onto a target portion C of the substrate W. A second positioning device PW and a position sensor IF (e.g., an interferometer) can be used to precisely move the substrate table WT to position, for example, different target portions C within the beam PB path. Similarly, a first positioning device PM and another position sensor (not clearly shown in Figure 1) can be used to precisely position the patterning device MA relative to the beam PB path, for example, after or during a machine search of a mask library. Generally, the movement of the object tables MT and WT is achieved using long-stroke modules (coarse positioning) and short-stroke modules (fine positioning) that form part of the positioning devices PM and PW. However, in the case of a stepper (as opposed to a scanner), the support structure MT may be connected only to short-stroke actuators or may be fixed. The patterning device MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0030]

[0047] The projection system PL has an optical transfer function that can be non-uniform (which can affect the pattern projected onto the substrate W). For unpolarized radiation, such effects can be fairly well represented by two scalar maps that describe the transmission (apodization) and relative phase (aberration) of radiation emitting from the projection system PL as functions of its position in the pupil plane. These scalar maps, sometimes called transmission maps and relative phase maps, can be expressed as a linear combination of a complete set of basis functions. A particularly useful set is the Zernike polynomials, which form a set of orthogonal polynomials defined on the unit circle. Determining each scalar map may involve determining the coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients may be determined by sequentially calculating the inner product of each Zernike polynomial and the measured scalar map, and dividing this by the square of the norm of the Zernike polynomial.

[0031]

[0048] The transmission map and relative phase map are field and system dependent. That is, generally, each projection system PL has a different Zernike expansion for each field point (i.e., for each spatial position in its image plane). The relative phase of the projection system PL in the pupil plane may be determined, for example, by projecting radiation from a point radiation source in the objective plane of the projection system PL (i.e., the plane of the patterning device MA) through the projection system PL, and by measuring the wavefront (i.e., the locus of points with the same phase) using a shearing interferometer. The shearing interferometer is a common-path interferometer and therefore, advantageously, does not require a secondary reference beam for wavefront measurement. The shearing interferometer may include a diffraction grating (e.g., a two-dimensional grid) in the image plane of the projection system (i.e., the substrate table WT) and a detector positioned to detect interference patterns in a plane conjugate to the pupil plane of the projection system PL. The interference pattern is related to the derivative of the phase of radiation with respect to coordinates in the pupil plane in the shearing direction. The detector may include, for example, an array of sensing elements such as a charge-coupled device (CCD).

[0032]

[0049] The diffraction grating may be sequentially scanned in two perpendicular directions, either coinciding with the axes (x and y) of the coordinate system PL of the projection system, or forming an angle such as 45 degrees with respect to these axes. The scan may be performed over an integer grating period, such as one grating period. The scan allows for averaging the phase variation in one direction and reconstructing the phase variation in the other direction. This allows the wavefront to be determined as a function of both directions.

[0033]

[0050] The projection system PL of state-of-the-art lithography apparatus LA does not generate visible fringes, and therefore, wavefront determination accuracy can be improved using phase stepping techniques, such as moving the diffraction grating. Stepping can be performed in the plane of the diffraction grating, perpendicular to the scanning direction of the measurement. The stepping range can be one grating period, and at least three (uniformly distributed) phase steps can be used. For example, three scanning measurements can be performed in the y-direction, with each scanning measurement performed for a different position in the x-direction. This stepping of the diffraction grating effectively converts phase variations into intensity variations, thereby enabling the determination of phase information. To calibrate the detector, the grating can be stepped in a direction perpendicular to the diffraction grating (z-direction).

[0034]

[0051] The transmission (apodization) of the projection system PL within the pupil plane may be determined, for example, by projecting radiation from a point radiation source within the objective plane of the projection system PL (i.e., the plane of the patterning device MA) through the projection system PL, and by measuring the intensity of radiation in a plane conjugate to the pupil plane of the projection system PL using a detector. The same detector used for wavefront measurements to determine aberrations may be used. The projection system PL may include a plurality of optical (e.g., lens) elements and further include an adjustment mechanism PA configured to adjust one or more of the optical elements to correct aberrations (phase variations across the pupil plane of the entire field). To achieve this, the adjustment mechanism PA may be operable to operate one or more optical (e.g., lens) elements within the projection system PL in one or more different ways. The projection system may have a coordinate system in which the optical axis extends in the z direction. The adjustment mechanism PA may be operable to perform any combination of the following: displacing one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. The displacement of the optical element may be in any direction (x, y, z, or a combination thereof). The tilt of the optical element is generally deviated from the plane perpendicular to the optical axis by rotating around an axis in the x or y direction (rotation around the z axis may be used for non-rotationally symmetric aspherical optical elements). The deformation of the optical element may include both low-frequency shapes (e.g., astigmatism) and high-frequency shapes (e.g., free-form aspherical). The deformation of the optical element may be performed, for example, by applying force to one or more sides of the optical element using one or more actuators, and / or by heating one or more selected regions of the optical element using one or more heating elements. In general, it may not be possible to adjust the projection system PL to correct apodization (transmission variation across the pupil plane). A transmission map of the projection system PL may be used when designing a patterning device (e.g., mask) MA for a lithography apparatus LA. Using computer lithography techniques, the patterning device MA may be designed to correct apodization at least partially.

[0035]

[0052] Parameters in a lithography process are sometimes called "processing parameters." Lithography can include processes upstream and downstream of the actual exposure. Figure 2 shows examples of categories of processing parameters. The first category may be parameters of the lithography apparatus or any other apparatus used in the lithography process. Examples of this category include parameters of the source, projection optics, and substrate stage of the lithography apparatus. The second category may be parameters of any procedure performed in the lithography process. Examples of this category include focus, dose, bandwidth, exposure duration, development temperature, and the chemical composition used for development. The third category may be parameters of the design layout. Examples of this category may include the shape and location of assist features, as well as adjustments applied by resolution enhancement techniques (RET). The fourth category may be parameters of the substrate. Examples include the properties of the structure beneath the resist layer, the chemical composition, and the physical dimensions of the resist layer. The fifth category may be the properties of the temporal variation of some parameters of the lithography process. For example, processing parameters may include characteristics of high-frequency stage movement (e.g., frequency, amplitude, etc.), high-frequency laser bandwidth changes (e.g., frequency, amplitude, etc.), and / or high-frequency laser wavelength changes. These high-frequency changes or movements exceed the response time of the mechanism for adjusting basic parameters (e.g., stage position and laser intensity). A sixth category may be characteristics of downstream processes of exposure, such as PEB, development, etching, deposition, doping, and packaging.

[0036]

[0053] Some or all of the processing parameters can be determined by appropriate methods. For example, these values ​​may be determined from data obtained using various substrate metometry tools. These values ​​may also be obtained from various sensors on the lithography apparatus. Alternatively, these values ​​may be obtained from the operator of the lithography process.

[0037]

[0054] Existing techniques monitor semiconductor manufacturing processes based on one or more KPIs. For example, monitoring KPI variability can enable the detection and flagging of process drift or excursions to trigger root cause analysis of process performance degradation over time. As an example, KPI monitoring is performed by exposing wafers using a predetermined process at regular intervals, measuring these wafers, calculating KPI variability, and analyzing KPI variability over time. For example, in mass production settings, multiple lithography tools and reticles may be employed in the semiconductor manufacturing process, and other measurable process noises such as average CD or dose may also be present, which also affect KPI variability. To account for KPI variability resulting from differences in tools and reticles, different tools and reticles can be monitored separately using distinct specification limits. As soon as a violation of the specification limits is detected, corrective actions can be applied (e.g., via advanced process control) to bring the KPI within the desired limits. For example, corrective actions may be applied to control the printing process so that the printed wafer CD is as close as possible to the target CD. However, in KPI-based monitoring and process control, specific wafer or process drift may be masked as meeting the KPI specifications.

[0038]

[0055] This disclosure provides a mechanism for capturing process drift or outlier substrates that may be masked as meeting KPI-related specifications. In embodiments, the cause of the relevant process drift can be more accurately determined when process drift is detected. The mechanism monitors the variation in residual KPIs by decomposing and filtering contributions from various factors (such as tools and reticles) to the variation in KPIs. By removing contributions from various factors, the signal-to-noise ratio of the residual variation over time related to the semiconductor process is improved. This improvement in the signal-to-noise ratio then helps in identifying process drift or outlier substrates in time. The mechanism described herein is explained using the KPI of local CD uniformity (LCDU), which can be affected by categorical independent variables (such as reticle, tool, and continuous independent variable mean CD). However, this disclosure is not limited to LCDU, and the same mechanism can be applied using other KPIs (such as CD, exposure tolerance (EL), or depth of field (DOF)) and other combinations of independent variables.

[0039]

[0056] Figure 3 is a flowchart of an exemplary method for determining process drift over time in semiconductor manufacturing according to embodiments of the present disclosure. The method involves determining the contribution of selected variables or a set of factors (e.g., tools, reticles, etc.) to the variation of a KPI. In some embodiments, these factors are measurable and quantifiable causes of the KPI variation. Thus, once these contributions are removed, the remaining KPI variation may be a better indicator of process drift or excursion of concern than the original KPI. Below, exemplary implementations of Method 300 are discussed with respect to processes P301, P303, P305, and P307. Method 300 can be implemented as instructions on one or more processors (e.g., 104 in Figure 7).

[0040]

[0057] Process P301 involves obtaining data 301 of variability in key performance indicators (KPIs) that characterize the performance of a semiconductor process over time, and a set of factors associated with the semiconductor process. In embodiments, the semiconductor manufacturing process may include a patterning process, a metronome process, a pre-patterning process (e.g., CMP), and a post-patterning process (e.g., etching), or other semiconductor manufacturing-related processes performed by one or more lithography apparatuses.

[0041]

[0058] In the embodiment, the KPI may be at least one of the following: LCDU associated with the pattern imaged onto the substrate via the patterning process, edge placement error associated with the pattern imaged onto the substrate via the patterning process, overlay associated with the pattern imaged onto the substrate via the patterning process, or any other suitable KPI related to process monitoring or characterization. In the embodiment, the KPI data may be obtained over a period of time and may employ multiple lithography devices, pre / post-patterning process devices, multiple reticles, multiple metronome tools, and / or one or more measurable parameters during the semiconductor manufacturing process.

[0042]

[0059] In embodiments, the set of factors contributing to KPI variability may be categorical variables, measurable parameters (see, for example, Figure 2), or a combination thereof. For example, the set of factors may be at least one of a first categorical variable characterizing the contribution of multiple lithography devices to KPI variability, a second categorical variable characterizing the contribution of multiple reticles to KPI variability, a third categorical variable characterizing the contribution of multiple metronome tools to KPI variability, and a fourth variable including measurable substrate parameters contributing to KPI variability. In embodiments, the measurable parameters may include at least one of the mean critical dimension (CD) of the pattern printed on the substrate or a portion of the substrate, the dose of the lithography device, and the focus of the lithography device. Additional examples are shown in Figure 2.

[0043]

[0060] Returning to Figure 3, process P303 involves determining the contribution of a first set of factors 302 to the variability of the KPIs, using a model of the KPIs and data 301 as input to the model. In embodiments, the first set of factors 302 refers to factors that have statistical values ​​above a statistical threshold. For example, values ​​associated with the first set of factors 302 can be considered statistically significant (e.g., p-value greater than 0.9). In embodiments, factors whose contribution is not statistically significant are not removed from the model. In other words, contributions from factors that are not statistically significant can be included as part of the residuals in the model.

[0044]

[0061] In embodiments, the model may be a statistical model configured to decompose the variability of KPIs into a function of a factor set and residual terms. In embodiments, the model may be a linear or regression model configured to decompose the variability of KPIs into a function of a factor set and residual terms. In embodiments, the machine learning model is configured to receive data 301 related to a factor set as input and to produce the variability of residual KPIs 304 as output. Other models configured to decompose KPI variability may also be within the scope of this disclosure.

[0045]

[0062] In embodiments, determining a first set of factors 302 involves constructing a model based on a set of factors associated with semiconductor manufacturing (e.g., patterning processes). The model is applied to data 301 associated with the set of factors to determine the contribution of each of the set of factors to the variability of the KPIs. For example, determining the first set of factors 302 may involve applying an analysis of variance (ANOVA) or analysis of covariance (ANCOVA) technique to the statistical model to determine the contribution of each of the set of factors to the variability of the KPIs. This disclosure is not limited to any particular technique for determining contributions. Other techniques may also be applied.

[0046]

[0063] For example, the contributions and statistical significance of three sources of KPI variability (e.g., variability of LCDU) can be considered. For example, ANOVA or ANCOVA can be used. LCDU = μ + α i +β j +γ * CD ijk +ε ijk Statistical models of KPIs such as (e.g., LCDDU) can be used and applied to the dataset.

[0047]

[0064] In the LCDU model above, i refers to the reticle, j refers to the tool, and α i and β j These terms represent the contributions from the reticle and tool categorical variables, respectively. The CD term refers to the CD data of the k-th substrate, which is processed using reticle i and tool j. ε ijk The term refers to the variability of the residual KPI. In the embodiment, ANCOVA generates a p-value to indicate whether there is a statistically significant difference between the reticle-based LCDU and the tool-based LCDU after considering the continuous covariate mean CD.

[0048]

[0065] Figure 4 shows an exemplary scatter plot of LCDU versus average CD in a series of monitored substrates. Each point represents the measured CD and LCDU in a single substrate, and the shape and pattern of the data points indicate the tools and reticles used to process the particular substrate. For example, the tool can be T1 or T2, and the reticle can be R1 or R2. The plot shows that a significant amount of the variation in the measured LCDU can be explained by the average CD. ANCOVA using the above LCDU model shows that much of the variation in LCDU can be accounted for by three variables (tool, reticle, and average CD).

[0049]

[0066] Returning to FIG. 3, process P305 involves removing the contribution from the first set of factors 302 to the variation in the KPI in order to obtain the variation 304 in the residual KPI. For example, referring to the above LCDU equation, after the contributions of the tool, reticle, and average CD have been quantified (e.g., by applying ANOCVA), their contributions can be removed from the data set associated with the set of factors. For example, removing from the data set can be accomplished by subtracting the modeled KPI value from the measured KPI value, or by any other mathematical or computational technique or operation. The residual (ε ijk ) variation in the KPI is the remaining variation not accounted for by differences between tools, differences between reticles, and / or average CD. In other words, the variation in LCDU is decomposed into (i) a component accounted for by the tool, reticle, and average CD and (ii) a residual component representing the variation caused by one or more processes and process drift over time. If the contribution from a factor is not statistically significant, such a factor and its contribution are not removed from the data set and can be included as part of the variation 304 in the residual KPI.

[0050]

[0067] Process P307 involves determining a residual value 320 that exceeds a residual threshold based on the variability 304 of the residual KPI. The residual value 320 indicates an outlier substrate corresponding to process drift over time in the semiconductor process or a residual value 320 at a specific time. For example, to identify outliers, the variability 304 of the residual KPI can be analyzed over time as a trend instead of the original KPI. An outlier indicates that the variability 304 of the residual KPI is increasing above a threshold at a particular time, and therefore, the substrate corresponding to that time or outlier residual value 320 requires further analysis and problem resolution so that appropriate control adjustments can be made to the process. As another example, an outlier residual value 320 may indicate that the residual value 320 is increasing due to some process drift occurring over a period of time. Therefore, once a drift begins relative to a preceding residual value, the process parameters or events causing the drift can be monitored and appropriate measures taken. For example, cleaning the reticle, activating the mask cooling system, or monitoring other changes in the patterning process settings can cause drift or specific patterns in the variability of residual KPIs. Other examples of patterns in residuals may include changing the resist batch or altering upstream or downstream processes (such as cleaning or etching).

[0051]

[0068] Figures 5A–5C show exemplary trend charts for the measured LCDDU 510, modeled LCDDU 520, and residual LCDDU 530 over time. The modeled LCDDU 520 may be the LCDDU estimated from ANCOVA for a given tool, reticle, and mean CD. The residual LCDDU 530 may be the remaining variability after the contributions from the tool, reticle, and mean CD have been removed. Each point in the trend chart corresponds to a substrate (e.g., W2 and W7). As can be seen from the chart, different substrates can be flagged as outliers in the residual LCDDU 530 compared to the trend chart of the measured LCDDU 510, based on the threshold limits assigned to LCDDU 510, modeled LCDDU 520, and residual LCDDU 530. However, as mentioned above, since certain measurable causes of variability (e.g., those not related to process drift of concern) have been removed, the residual may be a better indicator of process drift or excursion of concern. For example, in LCDU 510, wafers W2 and W7 do not exceed the outlier threshold TH1 assigned to the LCDU trend chart. However, residual LCDU 530 shows that wafers W2 and W7 are outliers because the residual values ​​corresponding to these wafers W2 and W7 exceed the residual threshold Rth1. Therefore, wafers W2 and W7 are masked as being problem-free, but residual LCDU indicates that this is not the case.

[0052]

[0069] In embodiments, method 300 may further include detecting systematics (e.g., data patterns) in the variability of residual KPIs 304, determining root causes associated with the systematics in response to the detected systematics, and adjusting the model based on the root causes. For example, in the variability of residual KPIs 304, data patterns may evolve over time. Root causes associated with such data patterns can be considered as factors that can be added to the model. For example, during reticle cleaning, the variability of residual KPIs 304 may include a level change from a first range of values ​​to a second range of values ​​(see, for example, Figure 5D). For example, in Figure 5D, the variability of residual KPIs associated with a series of substrates L1 is at the first level, and the variability of residual KPIs associated with a second series of substrates L2 is at the second level. Such a level change may occur due to reticle cleaning. Therefore, to quantify the impact of reticle cleaning and potentially remove its contribution from KPI variability, reticle cleaning can be included as a categorical variable in the model. For example, other causes could be reticle or pellicle degradation or replacement.

[0053]

[0070] In the embodiment, root cause analysis shows that outliers or process drift detected using residual KPI variability 304 are caused by characteristics of a downstream process in the semiconductor manufacturing process, for example, downstream of substrate exposure. In the embodiment, root cause analysis shows that residual KPI variability 304 is caused by characteristics of an upstream process in the semiconductor manufacturing process, for example, upstream of substrate exposure. In the embodiment, detecting systematics involves identifying a shift in the level of residual KPI variability 304 over a period of time. In the embodiment, detecting systematics involves running a statistical model configured to identify systematics (e.g., data patterns) in residual KPI variability 304.

[0054]

[0071] In embodiments, method 300 may further involve capturing new data 301 related to a set of factors associated with the semiconductor manufacturing process at regular intervals or continuously, and updating the variability 304 of residual KPIs based on the captured data 301. In embodiments, the model may be updated based on the captured data and the detected systematics.

[0055]

[0072] In this embodiment, the variability of the residual KPI 304 includes a higher signal-to-noise ratio compared to the signal-to-noise ratio in the measured KPI. For example, Figure 6 shows the histogram 610 of the measured LCDDU and the histogram 620 of the residual LCDDU. These histograms clearly show outliers 621 in the residual LCDDU histogram 620, while in the LCDDU histogram 610, these outliers are hidden within the noise 611. These histograms demonstrate that the residual LCDDU 620 shows improved signal / noise over time with respect to process variations.

[0056]

[0073] It can be understood that the mechanisms discussed herein are not limited to a specific KPI or set of factors contributing to the variability of a KPI. In some embodiments, a KPI such as LCDU may be measured for a single dose and focus condition. In the case of this KPI, the mean CD of the pattern printed on the substrate can be used as a continuous covariate to account for variability in substrate centering due to noise in the exposure dose or other factors. In some embodiments, other KPIs such as exposure tolerance and depth of field may be calculated based on data collected from multiple dose and focus conditions across a focus exposure matrix (FEM) used to print the substrate. In the case of these “substrate-based” KPIs, control for variability in substrate centering may not be necessary. Therefore, only categorical variables for the exposure tool and reticle may be used in the model. Accordingly, as discussed herein, once ANOVA is performed, the contributions from the reticle and exposure tool are determined and can subsequently be removed to calculate the variability of the residual KPI.

[0057]

[0074] In some embodiments, KPIs may be process condition-based metrics, substrate-based metrics, or other semiconductor-related metrics. In embodiments, condition-based KPIs may be determined by a single focus and dose condition (e.g., nominal conditions) for the substrate. For example, LCDU may be determined as the average of 3 sigma of CD measurements per image or field of view (FOV) under nominal conditions. As another example, CDU may be determined as 3 sigma of CD measurements across all images / FOVs under nominal conditions. As yet another example, a modeled failure rate can be modeled by process window metrology under nominal conditions. In models of these KPIs, categorical variables may correspond to multiple lithography tools, reticles, or other tools used in semiconductor manufacturing. In embodiments, some KPIs may include common categorical variables, such as those for reticles, while other KPIs may have different categorical variables. The selection of categorical variables may depend on the amount of KPI variability to which a particular categorical variable contributes. In embodiments, categorical variables may be selected based on heuristic experience.

[0058]

[0075] In the embodiment, the substrate-based KPI may be determined based on all focus and dose condition data measured on the substrate. For example, the first KPI (referred to as CDPW_EL) may be exposure tolerance determined from the maximum area of ​​an ellipse that fits within the CD process window. The ellipse may be constrained by a fixed depth of focus. In the case of the first KPI, the categorical variable may correspond to the reticle, rather than the lithography tool. The second KPI (indicated as CDPW_DoF) may be depth of focus determined from the maximum area of ​​an ellipse that fits within the CD process window. The ellipse may be constrained by a fixed exposure tolerance. In the case of the second KPI, the categorical variable may correspond to the reticle, rather than the lithography tool. The third KPI may be the maximum area of ​​an ellipse that fits within the CD process window. In the case of the third KPI, the categorical variables may correspond to the reticle and the lithography tool. The fourth KPI (indicated as FRPW EL) may be exposure tolerance determined from the maximum area of ​​an ellipse that fits within the failure rate process window. The ellipse may be constrained by a fixed depth of field. The fifth KPI (indicated as FRPW DoF) may be depth of field determined from the maximum area of ​​an ellipse that fits within the failure rate process window. The ellipse may be constrained by a fixed exposure tolerance. The sixth KPI (indicated as FRPW Maximum Ellipse Area) may be the maximum area of ​​an ellipse that fits within the failure process window. The seventh KPI may be exposure tolerance determined from the maximum area of ​​an ellipse that fits within the overlapping CD and failure rate process window. The ellipse may be constrained by a fixed depth of field. The eighth KPI may be depth of field determined from the maximum area of ​​an ellipse that fits within the overlapping CD and failure rate process window. The ellipse may be constrained by a fixed exposure tolerance. The ninth KPI may be the maximum area of ​​an ellipse that fits within the overlapping CD and failure process window. The tenth KPI could be the dose required to obtain the target CD, which can be calculated from the CD model, a function of the dose. The eleventh KPI could be the dose sensitivity at the highest energy or the highest focus.Dawes sensitivity can be calculated as the change in CD with a change in Dawes, calculated from the CD model at the highest energy / highest focus. The twelfth KPI may be the minimum failure rate across all focus and Dawes conditions, as modeled by process window metronome techniques. While categorical variables for each KPI are not specified in the above list of KPIs, they will be understood by those skilled in the art. Each categorical variable may be appropriately based on the likely contributions from specific lithography tools, reticles, metronome tools, etc. It can be understood that one or more of the aforementioned KPIs can be used, as discussed herein, and that the variability of the corresponding residual KPIs can be determined.

[0059]

[0076] Figure 7 is a block diagram showing an exemplary computer system 100 configured to assist in carrying out the methods and flows disclosed herein according to embodiments of the present disclosure. The computer system 100 includes a bus 102 or other communication mechanism for communicating information and a processor 104 (or a plurality of processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes main memory 106 coupled to the bus 102 for storing information and instructions executed by the processor 104, such as random access memory (RAM) or other dynamic storage device. The main memory 106 may also be used to store temporary variables or other intermediate information during the execution of instructions executed by the processor 104. The computer system 100 further includes read-only memory (ROM) 108 or other static storage device coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0060]

[0077] The computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT), flat panel, or touch panel display, for displaying information to the computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 to communicate information and command selections to the processor 104. Another type of user input device is a cursor control unit 116, such as a mouse, trackball, or cursor directional keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. This input device generally has two degrees of freedom (a first axis (e.g., x) and a second axis (e.g., y)) that allow the device to be positioned in a plane. A touch panel (screen) display may be used as an input device.

[0061]

[0078] According to one embodiment, a portion of the process may be performed by the computer system 100 in response to a processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as a storage device 110. The execution of the sequence of instructions contained in main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multiprocessing configuration may be used to execute the sequence of instructions contained in main memory 106. In one alternative embodiment, hardwired circuitry may be used instead of, or together with, software instructions. Thus, the description herein is not limited to any particular combination of hardware circuitry and software.

[0062]

[0079] As used herein, the term “computer-readable medium” refers to any medium involved in providing instructions to the processor 104 for execution. Such mediums can take many forms, but are not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks such as storage device 110. Volatile media include dynamic memory such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers (including wires including bus 102). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, and other magnetic media, CD-ROMs, DVDs, and other optical media, punch cards, paper tapes, and other physical media having perforation patterns, RAM, PROMs, and EPROMs, FLASH-EPROMs, and other memory chips or cartridges, carrier waves as described below, or other media that can be read by a computer.

[0063]

[0080] Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially reside on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send them over a telephone line using a modem. A modem local to computer system 100 can receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 can receive the data carried by the infrared signal and load that data onto bus 102. Bus 102 transports the data to main memory 106, from which the processor 104 reads and executes the instructions. Instructions received by main memory 106 may optionally be stored in a storage device 110 before or after execution by the processor 104.

[0064]

[0081] The computer system 100 also preferably includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides bidirectional data communication coupled to a network link 120 connected to a local network 122. For example, the communication interface 118 may be an Integrated Digital Network (ISDN) card or modem that provides data communication connectivity to a corresponding type of telephone line. Alternatively, the communication interface 118 may be a local area network (LAN) card that provides data communication connectivity to a compatible LAN. A wireless link may also be implemented. In such an implementation, the communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0065]

[0082] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide connection to data equipment operated by a host computer 124 or an Internet service provider (ISP) 126 through a local network 122. The ISP 126 then provides data communication services via the World Wide Packet Data Network (now commonly referred to as the "Internet" 128). Both the local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals to carry digital data streams. Signals across various networks, and signals on the network link 120 and through the communication interface 118, carrying digital data to and from the computer system 100, are examples of carrier wave forms that carry information.

[0066]

[0083] The computer system 100 can send messages and receive data, including program code, through one or more networks, network links 120, and communication interfaces 118. In an internet example, server 130 may send request code for an application program through the internet 128, ISP 126, local network 122, and communication interfaces 118. Such a downloaded application could, for example, provide lighting optimization as described in the embodiment. The received code may be executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 may obtain application code in carrier form.

[0067]

[0084] Figure 8 shows another exemplary lithography projection apparatus 1000 according to an embodiment of the present disclosure. Apparatus 1000 is - Source collector module SO for providing radiation, - An illumination system (illuminator) IL configured to adjust the radiated beam B (e.g., EUV radiation) from the source collector module SO, - A support structure (e.g., a mask table) MT is constructed to support a patterning device (e.g., a mask or reticle) MA and is connected to a first positioner PM configured to precisely position the patterning device. - A substrate table (e.g., wafer table) WT connected to a second positioner PW constructed to hold a substrate (e.g., a resist-coated wafer) W and configured to precisely position the substrate, - A projection system (e.g., a reflection projection system) PS configured to project a pattern applied to the radiation beam B by a patterning device MA onto a target portion C of a substrate W (e.g., including one or more dies) and Includes.

[0068]

[0085] As shown herein, the apparatus 1000 is reflective (for example, employing a reflective mask). Note that since most materials are absorbent in the EUV wavelength range, the patterning device may have a multilayer reflector containing, for example, a multilayer stack of molybdenum and silicon. In one example, the multilayer reflector has 40 layers of molybdenum and silicon, with each layer having a thickness of a quarter wavelength. Even smaller wavelengths can be produced by X-ray lithography. Since most materials are absorbent in EUV and X-ray wavelengths, a thin piece of absorbent material patterned on the topography of the patterning device (e.g., a TaN absorber on the multilayer reflector) defines where features are printed (positive resist) or where they are not printed (negative resist).

[0069]

[0086] Referring to Figure 8, the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. One such method, often called laser-generated plasma ("LPP"), can generate plasma by irradiating a fuel, such as droplets, streams, or clusters of material having a line-emitting element, with a laser beam. The source collector module SO may be part of an EUV radiation system that includes a laser (not shown in Figure 8) for providing the laser beam to excite the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector located in the source collector module. For example, when a CO2 laser is used to provide the laser beam for fuel excitation, the laser and the source collector module may be separate entities.

[0070]

[0087] In such cases, the laser is not considered to form part of the lithography apparatus, and the radiation beam is delivered from the laser to the source collector module using a beam delivery system that includes, for example, appropriate guidance mirrors and / or beam expanders. In other cases, for example, when the radiation source is a discharge-generated plasma EUV generator (often called a DPP radiation source), the radiation source may be integrated with the source collector module.

[0071]

[0088] An illuminator (IL) may include adjusters for adjusting the angular intensity distribution of the radiated beam. Generally, the intensity distribution at the pupil plane of the illuminator can be adjusted by at least the outer and / or inner diameter ranges (usually called σ-outer and σ-inner, respectively). In addition, an illuminator (IL) may include various other components (such as facet fields and pupil mirror devices). The illuminator can be used to adjust the radiated beam so that it has desired uniformity and intensity distribution in the cross-section of the radiated beam.

[0072]

[0089] A radiating beam B is incident on a patterning device (e.g., a mask) MA held on a support structure (e.g., a mask table) MT, and a pattern is formed by the patterning device. After reflection from the patterning device (e.g., a mask) MA, the radiating beam B passes through a projection system PS, which focuses the beam onto a target portion C on the substrate W. By using a second positioner PW and a position sensor PS2 (e.g., an interference device, a linear encoder, or a capacitive sensor), the substrate table WT can be precisely moved so that, for example, different target portions C are positioned along the path of the radiating beam B. Similarly, the patterning device (e.g., a mask) MA can be precisely positioned relative to the path of the radiating beam B using a first positioner PM and another position sensor PS1. The patterning device (e.g., a mask) MA and the substrate W can be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0073]

[0090] The device 1000 shown can be used in at least one of the following modes: 1. In step mode, the support structure (e.g., mask table) MT and substrate table WT are kept essentially stationary (i.e., one static exposure) while the entire pattern applied to the radiation beam is projected onto the target portion C at once. The substrate table WT is then shifted in the X and / or Y directions to allow exposure to different target portions C. 2. In scanning mode, the support structure (e.g., mask table) MT and the substrate table WT are scanned synchronously (i.e., one dynamic exposure) while the pattern applied to the radiation beam is projected onto the target portion C. The speed and direction of the substrate table WT relative to the support structure (e.g., mask table) MT can be determined by the expansion (reduction) and image inversion characteristics of the projection system PS. 3. In another mode, while the pattern applied to the radiation beam is projected onto the target portion C, the support structure (e.g., mask table) MT is kept essentially stationary, holding the programmable patterning device, while the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is generally employed, and the programmable patterning device is updated as needed between continuous radiation pulses after each movement or scan of the substrate table WT. This mode of operation can be readily applied to maskless lithography utilizing programmable patterning devices such as the type of programmable mirror array mentioned above.

[0074]

[0091] Figure 9 shows the apparatus 1000, including a source collector module SO, an illumination system IL, and a projection system PS, in more detail. The source collector module SO is constructed and positioned to maintain a vacuum environment within the enclosed structure 220 of the source collector module SO. The EUV radiation emission plasma 210 can be formed by a discharge-generated plasma radiation source. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor) to generate a very hot plasma 210 to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is generated, for example, by a discharge that produces at least a partially ionized plasma. To efficiently generate radiation, a partial pressure (e.g., 10 Pa) of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In embodiments, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0075]

[0092] Radiation emitted by the high-temperature plasma 210 is passed from the source chamber 211 to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (sometimes also called a contaminant barrier or foil trap) located within or behind the opening of the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 further described herein includes at least a channel structure, as is known in the art.

[0076]

[0093] The collector chamber 212 may include a radiation collector CO, which may be a so-called oblique incidence collector. The radiation collector CO has an upstream radiation collector 251 and a downstream radiation collector 252. Radiation crossing collector CO is reflected by the grating spectral filter 240 and focused to a virtual source point IF along the optical axis indicated by the dotted line "O". The virtual source point IF is generally called the intermediate focus, and the source collector module is positioned such that the intermediate focus IF is located at or near the aperture 221 of the closed structure 220. The virtual source point IF is an image of the radiant emission plasma 210.

[0077]

[0094] Subsequently, the radiation crosses the illumination system IL, which may include a faceted field mirror device 22 and a faceted pupil mirror device 24, positioned to provide a desired angular distribution of the radiation beam 21 in the patterning device MA and to provide a desired uniformity of radiation intensity in the patterning device MA. As soon as the radiation beam 21 is reflected in the patterning device MA held by the support structure MT, a patterning beam 26 is formed, and the patterning beam 26 is imaged by the projection system PS onto the substrate W held by the substrate table WT via reflective elements 28, 30.

[0078]

[0095] In general, the illumination optical system unit IL and projection system PS may contain more elements than those shown. Depending on the type of lithography apparatus, a grating spectral filter 240 may be optionally present. Furthermore, more mirrors than those shown in the figure may be present; for example, 1 to 6 additional reflective elements may be present in the projection system PS in addition to those shown in Figure 9.

[0079]

[0096] As shown in Figure 9, the collector optical system CO is shown as a nested collector with oblique incidence reflectors 253, 254, and 255, as just one example of a collector (or collector mirror). The oblique incidence reflectors 253, 254, and 255 are arranged symmetrically in the axial direction around the optical axis O, and this type of collector optical system CO is preferably used in combination with a discharge-generated plasma radiation source.

[0080]

[0097] Alternatively, the source collector module SO may be part of an LPP emission system as shown in Figure 10. The laser LAS is positioned to store laser energy in a fuel such as xenon (Xe), tin (Sn), or lithium (Li) to generate a highly ionized plasma 210 with an electron temperature of several tens of eV. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal incident collector optical system CO, and focused at an aperture 221 of a closed structure 220.

[0081]

[0098] The concepts disclosed herein can simulate or mathematically model general imaging systems for imaging subwavelength features and may be particularly useful for new imaging techniques capable of generating increasingly smaller wavelengths. New techniques already in use include EUV (extreme ultraviolet) lithography, capable of generating wavelengths as low as 193 nm using ArF lasers and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate wavelengths in the range of 20–5 nm, which is achieved by using a synchrotron or by bombarding a material (solid or plasma) with high-energy electrons to generate photons in this range.

[0082]

[0099] The concepts disclosed herein can be used for imaging on substrates such as silicon wafers, but it should be understood that the disclosed concepts can be used in any type of lithography imaging system, including, for example, those used for imaging on substrates other than silicon wafers.

[0083]

[0100] While specific references may be made in this text to the use of embodiments in the manufacture of ICs, it should be understood that the embodiments herein may also have many other possible applications. For example, embodiments herein can be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memory, liquid crystal displays (LCDs), thin-film magnetic heads, micromechanical systems (MEMs), and the like. Those skilled in the art will understand that in the context of such alternative applications, the use of the terms “reticle,” “wafer,” or “die” herein can be considered synonymous with or interchangeable with the more general terms “patterning device,” “substrate,” or “target portion,” respectively. Substrates referred to herein may be processed before or after exposure, for example, with a track (typically a tool for coating a layer of resist onto a substrate and developing the exposure resist) or with a metronome or inspection tool. Where applicable, the disclosure herein can be applied to such and other substrate processing tools. Furthermore, a substrate may be processed multiple times, for example, to produce a multilayer IC, and as a result, the term substrate as used herein may also refer to a substrate that already contains multiple processed layers.

[0084]

[0101] In this document, the terms “radiation” and “beam” as used herein encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having wavelengths of about 365, about 248, about 193, about 157, or about 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having wavelengths in the range of 5 to 20 nm), as well as particle beams such as ion beams or electron beams.

[0085]

[0102] As used herein, the terms “optimize” and “optimize” refer to or mean adjusting a patterning apparatus (e.g., a lithography apparatus), a patterning process, etc., so that the result and / or process has more desirable characteristics (e.g., higher accuracy of projection of the design pattern onto the substrate, a larger process window, etc.). Accordingly, as used herein, the terms “optimize” and “optimize” refer to or mean the process of identifying one or more values ​​for one or more parameters that provide an improvement (e.g., a local optimal) in at least one related metric compared to an initial set of one or more values ​​for one or more parameters. “Optimal” and other related terms should be interpreted accordingly. In embodiments, the optimization step may be applied iteratively to provide further improvements in one or more metrics.

[0086]

[0103] Embodiments of the present invention can be implemented in any convenient form. For example, embodiments can be implemented by one or more suitable computer programs that can be carried on a suitable carrier medium, which may be a tangible carrier medium (e.g., a disk) or an intangible carrier medium (e.g., a communication signal). Embodiments of the present invention can be implemented using a suitable device that may take the form of a programmable computer running a computer program configured to carry out a method as described herein. Accordingly, embodiments of the present disclosure can be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may be implemented as instructions stored on a machine-readable medium that can be read and executed by one or more processors. The machine-readable medium may include a mechanism for storing or transmitting information in a form that can be read by a machine (e.g., a computing device). For example, the machine-readable medium may include read-only memory (ROM), random access memory (RAM), magnetic disk storage medium, optical storage medium, flash memory device, electrical, optical, sound, or other forms of propagating signals (e.g., carrier waves, infrared signals, digital signals, etc.). Furthermore, firmware, software, routines, and instructions may be described in this specification as performing certain actions. However, such descriptions are for convenience only, and it should be understood that such actions actually result from computing devices, processors, controllers, or other devices that execute firmware, software, routines, instructions, etc.

[0087]

[0104] In block diagrams, the illustrated components are depicted as discrete functional blocks, but embodiments are not limited to systems in which the functionalities described herein are organized as illustrated. Functionalities provided by each component may also be provided by software or hardware modules organized differently from those currently depicted, for example, such software or hardware may be mixed, combined, duplicated, divided, distributed (e.g., within a data center or geographically), or organized differently. Functionalities described herein may also be provided by one or more processors of one or more computers executing code stored in tangible, non-temporary machine-readable media. In some cases, a third-party content distribution network may host some or all of the information transmitted over the network, in which case the information (e.g., content) may be provided by sending commands to read that information from the content distribution network to the extent that the information is supplied or said to be provided.

[0088]

[0105] Unless otherwise stated, as is evident from the above description, throughout this specification, any use of terms such as “process,” “calculate,” “operate,” and “determine” is understood to refer to the operation or process of a specific device, such as a dedicated computer or similar dedicated electronic processing / calculating device.

[0089]

[0106] The reader should recognize that this application describes several inventions. Rather than dividing these inventions into multiple separate patent applications, they are combined into a single document because their related subject matter is suitable for the economics of the filing process. However, the different merits and aspects of such inventions cannot be combined into one. In some cases, embodiments address all of the shortcomings described herein, but it should be understood that these inventions are useful independently, and some embodiments address only some of such problems or provide other unmentioned merits that will be obvious to a person skilled in the art who examines this disclosure. Due to cost constraints, some inventions disclosed herein may not be claimed at present and may be claimed in subsequent applications, such as continuation applications, or by amendments to the current claims. Similarly, due to space constraints, neither the abstract nor the summary section of this document should be considered to contain a comprehensive list of all of the above inventions or all aspects of them.

[0090]

[0107] This specification and drawings are not intended to limit the disclosure to any particular form disclosed, but rather to include all modifications, equivalent forms, and alternative forms that fall within the spirit and scope of the invention as defined by the appended claims.

[0091]

[0108] Various modifications and alternative embodiments of the present invention will be apparent to those skilled in the art in view of this specification. Accordingly, this specification and drawings should be considered merely illustrative and are intended to teach those skilled in the art general modes of carrying out the invention. It should be understood that the embodiments of the present invention illustrated and described herein should be considered examples of embodiments. Elements and materials may be used instead of those illustrated and described herein, parts and processes may be reversed or deleted, certain features may be used independently, and multiple embodiments or features of multiple embodiments may be combined, as will be apparent to those skilled in the art after benefiting from this specification of the present invention. Modifications to the elements described herein may be made without departing from the spirit and scope of the invention as set forth in the following claims. The headings used herein are for illustrative purposes only and are not intended to limit the scope of this specification.

[0092]

[0109] Throughout this application, the word “may” is used in an impermissible sense (i.e., “may”) rather than an obligatory sense (i.e., “must”). Words such as “include,” “including,” and “includes” mean “to include without limitation.” Throughout this application, the singular forms “a,” “an,” and “the” include multiple referents unless the content clearly indicates otherwise. Thus, for example, a reference to an “an” element or an “a” element includes a combination of two or more elements, despite the use of other terms and phrases for one or more elements, such as “one or more.” The term “or” is non-exclusive unless otherwise indicated, i.e., encompassing both “and” and “or.” For example, terms expressing conditional relationships such as "in response to X, Y," "on X, Y," "if X, Y," and "when X occurs" encompass causal relationships where the antecedent is a causal condition that requires an antecedent, where the antecedent is a sufficient causal condition, or where the antecedent is a causal condition that contributes to the result (for example, "on the acquisition of condition Y, state X occurs" encompasses "X occurs only on Y" and "X occurs on Y and Z"). Such conditional relationships are not limited to results acquired immediately following the antecedent, as some results may be delayed; in conditional sentences, the antecedent is related to those results, for example, the antecedent is related to the possibility of the result occurring. A statement in which multiple attributes or functions are associated with multiple objects (for example, one or more processors perform steps A, B, C, and D) includes, unless otherwise indicated, both cases in which all such attributes or functions are associated with all such objects, and in which a subset of attributes or functions is associated with a subset of attributes or functions (for example, each of all processors performs steps A through D, and processor 1 performs step A, processor 2 performs part of steps B and C, and processor 3 performs part of step C and step D).Unless otherwise indicated, a statement that one value or action "based on" another condition or value includes both cases where the condition or value is the sole factor and cases where the condition or value is one of several factors. Unless otherwise indicated, a statement that "each" example of a group has a certain characteristic should not be interpreted as excluding cases where otherwise identical or similar members of a larger group do not have that characteristic; that is, "each" does not necessarily mean "all." A reference to selection from a range includes the endpoints of the range.

[0093]

[0110] In the above description, any process, description, or block in the flowchart should be understood as representing a module, segment, or portion of code containing one or more executable instructions for performing a particular logical function or step of the process, and as will be understood by those skilled in the art, alternative implementations are included within the scope of exemplary embodiments of the present invention, and functions may be performed in an order other than those shown or discussed, including substantially simultaneously or in reverse order, depending on the functionality involved.

[0094]

[0111] Embodiments can be further described using the following clauses. 1. A non-temporary computer-readable medium on which instructions are recorded, wherein when the instructions are executed by one or more processors, a method for determining process drift over time in semiconductor manufacturing is carried out, and the method is To obtain data relating to the variability of key performance indicators (KPIs) that characterize the performance of semiconductor processes over time, and to associate them with factor sets associated with semiconductor processes, The objective is to determine the contribution of a first set of factors to the variability of KPIs, using a KPI model and data as input to the model, and to determine whether the first set of factors exceeds a statistical threshold. To obtain the variability of the residual KPI, we remove the contribution from the first set of factors to the variability of the KPI, The determination of residual values ​​exceeding a residual threshold based on the variability of residual KPIs, wherein the residual values ​​indicate outlier substrates corresponding to process drift over time in semiconductor processes or residual values ​​at a specific time. A medium that includes 2. Determining the first set of factors is Constructing a model based on a set of factors associated with semiconductor manufacturing, To determine the amount of contribution from a factor set to the variability in KPIs, we apply a model to the data and The media described in Clause 1, including the media described in Clause 1. 3. The model is A statistical model configured to decompose KPIs into a function of a set of factors and residual terms, and A machine learning model configured to receive data related to a factor set as input and generate the variability of residual KPIs as output. A medium as described in Clause 1 or 2, including one of the following. 4. Determining the first set of factors is Applying analysis of variance (ANOVA) or analysis of covariance (ANCOVA) techniques to a statistical model to determine the contribution of each factor set to the variability of KPIs. The media described in Clause 3, including the media described in Clause 3. 5. KPIs are, Local critical dimension uniformity (LCDU) associated with the pattern imaged onto the substrate via the patterning process, Edge placement error associated with the pattern imaged onto the substrate via the patterning process, and Overlay associated with a pattern formed on the substrate via a patterning process. A medium which is at least one of the media specified in any one of the clauses 1 to 4. 6. A medium described in any one of Clauses 1 to 5, in which the variability of the KPI is obtained by using multiple lithography devices, multiple process devices, multiple reticles, multiple metronome tools and / or one or more measurable parameters. 7. The factor set is A first categorical variable to characterize the contribution of multiple lithography devices to KPI variability, A second categorical variable to characterize the contribution of multiple reticles to variability in KPIs, A third categorical variable to characterize the contribution of multiple metronome tools to KPI variability, and A fourth variable, including measurable wafer parameters that contribute to KPI variability. A medium as described in any one of the clauses 1 to 6, including at least one of the following. 8. The medium described in Clause 7, wherein the measurable parameters include at least one of the mean critical dimension of the pattern, the dose of the lithography apparatus, and the focus of the lithography apparatus. 9. The above instruction is, To detect the systematics in the variability of residual KPIs, In response to the detected systematics, determine the underlying causes associated with the systematics, Adjust the model to include factors associated with root causes as contributing factors to KPI variability. The media described in any one of the clauses 1 to 8, including, further. 10. The root cause is the medium described in Clause 9, which indicates that the variability in residual KPIs is caused by the characteristics of the downstream processes in the semiconductor process. 11. The root cause is the medium described in Clause 9, which indicates that the variability in residual KPIs is caused by the characteristics of the upstream process in the semiconductor process. 12. Detecting systematics is Identifying shifts in the level of variability of residual KPIs over a certain period of time. The media described in Clause 9, including the media described in Clause 9. 13. Detecting systematics is Run a statistical model configured to identify the systematics in the variability of residual KPIs. The media described in any one of clauses 9 to 12, including the media described in any one of clauses 9 to 12. 14. The above instruction is, To capture data related to a set of factors associated with semiconductor processes at regular intervals or continuously, Update the variability of residual KPIs based on the captured data. The media described in any one of clauses 1 to 13, including, further. 15. A medium described in any one of clauses 1 to 14, wherein the variability of the residual KPI includes a higher signal-to-noise ratio compared to the signal-to-noise ratio in the measured KPI. 16. A method for determining process drift over time in semiconductor manufacturing, To obtain data relating to the variability of key performance indicators (KPIs) that characterize the performance of semiconductor processes over time, and to associate them with factor sets associated with semiconductor processes, The objective is to determine the contribution of a first set of factors to the variability of KPIs, using a KPI model and data as input to the model, and to determine whether the first set of factors exceeds a statistical threshold. To obtain the variability of the residual KPI, we remove the contribution from the first set of factors to the variability of the KPI, The determination of residual values ​​exceeding a residual threshold based on the variability of residual KPIs, wherein the residual values ​​indicate outlier substrates corresponding to process drift over time in semiconductor processes or residual values ​​at a specific time. Methods that include... 17. Determining the first set of factors is Constructing a model based on a set of factors associated with semiconductor manufacturing, To determine the amount of contribution from a factor set to the variability in KPIs, we apply a model to the data and The method described in Article 16, including the method described in Article 16. 18. The model is, A statistical model configured to decompose KPIs into a function of a set of factors and residual terms, and A machine learning model configured to receive data related to a factor set as input and generate the variability of residual KPIs as output. The method described in Article 16 or 17, including one of the following. 19. Determining the first set of factors is Applying analysis of variance (ANOVA) or analysis of covariance (ANCOVA) techniques to a statistical model to determine the contribution of each factor set to the variability of KPIs. The method described in Article 18, including the method described in Article 18. 20. KPIs are Local critical dimension uniformity (LCDU) associated with the pattern imaged onto the substrate via the patterning process, Edge placement error associated with the pattern imaged onto the substrate via the patterning process, and Overlay associated with a pattern formed on the substrate via a patterning process. The method described in any one of the provisions 16-19, which is at least one of the following. 21. The method according to any one of clauses 16 to 20, wherein the variability of the KPI is obtained by using multiple lithography devices, multiple process devices, multiple reticles, multiple metronome tools and / or one or more measurable parameters. 22. The factor set is A first categorical variable to characterize the contribution of multiple lithography devices to KPI variability, A second categorical variable to characterize the contribution of multiple reticles to variability in KPIs, A third categorical variable to characterize the contribution of multiple metronome tools to KPI variability, and A fourth variable, including measurable wafer parameters that contribute to KPI variability. A method described in any one of the provisions 16 to 21, including at least one of the following. 23. The method according to Clause 22, wherein the measurable parameters include at least one of the mean critical dimension of the pattern, the dose of the lithography apparatus, and the focus of the lithography apparatus. 24. To detect systematics in the variability of residual KPIs, In response to the detected systematics, determine the underlying causes associated with the systematics, Adjust the model to include factors associated with root causes as contributing factors to KPI variability. The method described in any one of the clauses 16 to 23, further including the method described in any one of the clauses 16 to 23. 25. The method of Clause 24, wherein the root cause is that the variability in residual KPIs is caused by the characteristics of a downstream process in the semiconductor process. 26. The method of Clause 24, wherein the root cause is that the variability in residual KPIs is caused by the characteristics of the upstream process of the semiconductor process. 27. The ability to detect systematics Identifying shifts in the level of variability of residual KPIs over a certain period of time. The method described in Clause 24, including the method described in Clause 24. 28. Detecting systematics Run a statistical model configured to identify the systematics in the variability of residual KPIs. The method described in any one of the clauses 24 to 27, including the method described in any one of the clauses 24 to 27. 29. To capture data related to a set of factors associated with semiconductor processes at regular intervals or continuously, Updating the variability of residual KPIs based on captured data and The method described in any one of the clauses 16 to 28, further including the method described in any one of the clauses 16 to 28. 30. The method according to any one of clauses 16 to 29, wherein the variability of the residual KPI includes a higher signal-to-noise ratio compared to the signal-to-noise ratio at the measured KPI.

[0095]

[0112] While specific embodiments have been described, these embodiments are presented merely as examples and are not intended to limit the scope of this disclosure. In fact, the novel methods, apparatuses and systems described herein can be embodied in a variety of other forms, and various omissions, substitutions, and modifications can be made to the forms of the methods, apparatuses and systems described herein, without departing from the spirit of this disclosure. The appended claims and their equivalents are intended to cover such forms or modifications, as they fall within the scope and spirit of this disclosure.

Claims

1. A non-temporary computer-readable medium on which instructions are recorded, wherein when the instructions are executed by one or more processors, a method for determining process drift over time in semiconductor manufacturing is performed, and the method is To obtain data relating to the variability of key performance indicators (KPIs) that characterize the performance of semiconductor processes over time, and to associate them with a set of factors associated with the semiconductor process, Determining the contribution of a first set of factors to the variability of the KPIs using the KPI model and the data as input to the model, wherein the first set of factors exceeds a statistical threshold. In order to obtain the variability of the residual KPI, the contribution from the first set of factors to the variability of the KPI is removed, Based on the variability of the residual KPI, determine a residual value that exceeds a residual threshold, wherein the residual value indicates an outlier substrate corresponding to the process drift over time in the semiconductor process or the residual value at a specific time. A medium that includes

2. Determining the first set of factors is The model is constructed based on the set of factors associated with the semiconductor manufacturing process, In order to determine the amount of contribution from the factor set to the variability in the KPI, the model is applied to the data. The medium according to claim 1, including the following:

3. The aforementioned model, A statistical model configured to decompose the KPI into a function of the factor set and a residual term, and A machine learning model configured to receive the data related to the aforementioned factor set as input and to generate the variability of the residual KPI as output. The medium according to claim 1, comprising one of the following.

4. Determining the first set of factors is The medium according to claim 3, comprising applying analysis of variance (ANOVA) or analysis of covariance (ANCOVA) techniques to the statistical model to determine the contribution of each of the factor set to the variability of the KPI.

5. The aforementioned KPIs are, Local critical dimension uniformity (LCDU) associated with the pattern imaged onto the substrate via the patterning process, The edge placement error associated with the pattern imaged on the substrate via the patterning process, and The medium according to claim 1, which is at least one overlay associated with the pattern imaged on the substrate via the patterning process.

6. The medium according to claim 1, wherein the variation of the KPI is obtained by using multiple lithography devices, multiple process devices, multiple reticles, multiple metronome tools and / or one or more measurable parameters.

7. The aforementioned set of factors A first categorical variable for characterizing the contribution of the multiple lithography devices to the variation in the KPI, a second categorical variable for characterizing the contribution of the multiple reticles to the variation in the KPI, A third categorical variable for characterizing the contribution of the multiple metronome tools to the variability of the KPIs, and The medium according to claim 1, comprising at least one fourth variable, which includes a measurable wafer parameter that contributes to the variability of the KPI.

8. The medium according to claim 7, wherein the measurable parameters include at least one of the mean critical dimension of the pattern, the dose of the lithography apparatus, and the focus of the lithography apparatus.

9. The aforementioned instruction is, To detect the systematics in the variability of the residual KPI, In response to the detected systematics, determine the root cause associated with the systematics, The medium according to claim 1, further comprising adjusting the model to include factors associated with the root cause as contributing factors to the variability of the KPI.

10. The medium according to claim 9, wherein the aforementioned root cause indicates that the variation in the residual KPI is caused by the characteristics of a process downstream of the exposure process.

11. The medium according to claim 9, wherein the aforementioned root cause indicates that the variation in the residual KPI is caused by the characteristics of an upstream process of the exposure process.

12. The detection of the aforementioned systematics is The medium according to claim 9, comprising identifying a shift in the level of variation of the residual KPI over a certain period of time.

13. The detection of the aforementioned systematics is The medium according to claim 9, comprising running a statistical model configured to identify systematics in the variability of the residual KPI.

14. The aforementioned instruction is, To capture data related to the set of factors associated with the semiconductor process at regular intervals or continuously, The variability of the residual KPI is updated based on the captured data. The medium according to claim 1, further comprising:

15. The medium according to claim 1, wherein the variation in the residual KPI includes a higher signal-to-noise ratio compared to the signal-to-noise ratio in the measured KPI.

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