Computer-implemented method, system and tangible non-transitory computerreadable medium storing instructions for generating probabilistic process window that accounts for measurement uncertainty

Abstract

A method, system, and computer-readable medium for configuring lithography tools to manufacture semiconductor devices. The method includes selecting a first variable; selecting a second variable; selecting at least one response variable that is a function of the first and second variables; determining a measurement uncertainty for each response variable; determining a plurality of probabilities based on a measurement of the response variable and the measurement uncertainty for the response variable, representing a plurality of indications for whether a plurality of points related to the lithography process meet specifications for each response variable, wherein the plurality of probabilities represent a process window; and configuring lithography tools to manufacture semiconductor devices based on the process window.

Description

Technical Field

[0001] This disclosure generally presents methods, systems, and computer-readable media for generating a probabilistic process window that takes into account measurement uncertainty.

[0002] Cross-referencing of related applications

[0003] This application is a continuation of U.S. Application No. 17 / 316,154, filed May 10, 2021, entitled "System and Method for Generating and Analyzing Roughness Measurements," which is a continuation of U.S. Application No. 16 / 730,393, filed December 30, 2019, entitled "System and Method for Generating and Analyzing Roughness Measurements," which is a continuation of U.S. Application No. 16 / 218,346 (now U.S. Patent No. 10,522,322), filed December 12, 2018, entitled "System and Method for Generating and Analyzing Roughness Measurements," which is a continuation of U.S. Application No. 15 / 892,080 (now U.S. Patent No. 10,176,966), filed February 8, 2018, entitled "Edge Detection System," and claims priority to it. This application further claims priority to U.S. Provisional Patent Application No. 62 / 739,721, filed October 1, 2018, entitled "System and Method for Generating and Analyzing Roughness Measurements," and U.S. Provisional Patent Application No. 62 / 678,866, filed May 31, 2018, entitled "System and Method for Removing Noise from Roughness Measurements." Furthermore, as a continuation of U.S. Application No. 16 / 218,346, this patent application claims priority to U.S. Provisional Patent Application Serial No. 62 / 602,152, filed April 13, 2017, entitled "Edge Detection System." All these applications are incorporated herein by reference as if reproduced in their entirety below. Prior Technology

[0004] Edge detection of pattern structures has been studied before. However, edge detection of pattern structures remains challenging in noisy images, such as those generated using scanning electron microscopes (SEMs) or other imaging devices that produce images containing unwanted noise. Therefore, this roughness measurement can be further improved as a function of process variation, and this analysis can be used to optimize the process and control process tools. Summary of the Invention

[0005] One aspect of this disclosure includes a computer-implemented method. The method may include selecting a first process variable, represented on a first axis of a graph. The method may also include selecting a second process variable, represented on a second axis of the graph. The method may also include selecting at least one response variable, which is a function of the first variable and the second variable. The method may also determine a measurement uncertainty for each response variable. The method may further include determining a plurality of probabilities based on a measurement of the response variable and the measurement uncertainty for the response variable, representing a plurality of indications of whether a plurality of points associated with a lithography process meet a specification requirement for each response variable, wherein the plurality of probabilities represent a process window. The method further includes configuring a lithography tool to manufacture a semiconductor device according to the process window.

[0006] Another aspect of this disclosure includes a system, in one embodiment comprising a lithography tool, a memory device storing instructions, and a processing device. The processing device is coupled to the memory device and the lithography tool. The processing device can execute the instructions to select a first variable, which can be represented on a first axis of a graph. The processing device can also execute the instructions to select a second variable, which can be represented on a second axis of the graph. The processing device can also execute the instructions to select a response variable, which is a function of the first variable and the second variable. The processing device can also execute the instructions to determine a measurement uncertainty for the response variable. The processing device can also execute the instructions to determine a plurality of probabilities based on a measurement of the response variable and the measurement uncertainty for the response variable, representing a plurality of indications of whether a plurality of points associated with a lithography process meet a specification requirement. The plurality of probabilities can represent a process window. The processing device can also execute the instructions to configure the lithography tool according to the process window to manufacture a semiconductor device.

[0007] Another aspect of this disclosure is a non-transitory, computer-readable medium containing an entity storing instructions that, when executed, cause a processing device to select a first variable represented on a first axis of a graph. The instructions may also cause the processing device to select a second variable represented on a second axis of the graph. The instructions may also cause the processing device to select a response variable, which is a function of the first and second variables. The instructions may also cause the processing device to determine a measurement uncertainty for the output response variable. The instructions may also cause the processing device to determine a plurality of probabilities based on a measurement of the response variable and the measurement uncertainty for the response variable, representing a plurality of indications of whether a plurality of points associated with a lithography process meet a specification requirement. The plurality of probabilities represent a process window. The instructions further cause the processing device to configure the lithography tool according to the process window to manufacture a semiconductor device. Simple Explanation of the Diagram

[0008] The accompanying drawings are merely exemplary embodiments of the present disclosure and are therefore not intended to limit its scope, as the concepts of the present invention are applicable to other equivalent and effective embodiments.

[0009] [Figure 1A] is a representation of a pattern structure that presents a parallel line feature with gaps between the lines.

[0010] [Figure 1B] is a representation of a pattern structure that includes the feature of contact holes.

[0011] [Figure 2] shows four different rough edges, all of which have the same standard deviation.

[0012] [Figure 3] is a representation of the power spectral density (PSD) relative to the frequency on a double log-log scale.

[0013] [Figure 4] is a graphical representation of the power spectral density (PSD) plotted relative to the frequency, and it depicts the roughness parameter PSD(0), correlation length, and roughness index.

[0014] [Figure 5] shows the power spectral density (PSD) of two individual edges corresponding to a feature on a patterned structure.

[0015] [Figure 6] is a graphical representation of the changes within a feature and the selection of changes from a feature to a feature as a function of line length.

[0016] [Figure 7] is a block diagram of a scanning electron microscope (SEM) coupled to an information processing system (IHS), which together form an embodiment of the disclosed edge detection device.

[0017] [Figure 8A] is a representation of a feature disposed on a substrate, depicting an electron beam striking the center of the feature.

[0018] [Figure 8B] is a representation of a feature disposed on a substrate, depicting an electron beam striking the feature near an edge close to the feature.

[0019] [Figure 9] shows a grayscale image representation above and a corresponding grayscale line scan drawn graphically along a horizontal section line directly below.

[0020] [Figure 10] shows an example of a patterned structure, which includes a feature on top of a substrate, wherein different numbers of electrons escape from the patterned structure depending on where the electron beam strikes the patterned structure.

[0021] [Figure 11] shows a predicted line scan of a photoresist step on a patterned structure, such as a silicon wafer.

[0022] Figure

[12] shows a pattern of photoresist lines on a silicon wafer and another representative predicted line scan of the gaps.

[0023] [Figure 13A] is a raw SEM image of a pattern structure without using the disclosed edge detection equipment and method.

[0024] [Figure 13B] is the same SEM image as Figure 13A, except that it utilizes the edge detection equipment and method disclosed.

[0025] [Figure 14] shows a raw (biased) linewidth roughness pattern relative to a critical value setting, which illustrates a result of a conventional technique (using a filter with a conventional critical value edge detection) and a result using no filter and a reverse line scan model (ILM).

[0026] [Figure 15A] is a graph of the power spectral density (PSD) relative to the frequency of a feature shown on the right and left edges before noise is subtracted.

[0027] [Figure 15B] is a graph of the power spectral density (PSD) relative to the frequency of a feature shown on the right and left edges after noise subtraction.

[0028] [Figure 16] shows a portion of three SEM images acquired at different SEM electron doses for the same nominal lithography features.

[0029] [Figure 17A] illustrates a typical line scan for a line feature on a wafer, where there are a very large number of electrons and the pixel noise is negligible.

[0030] [Figure 17B] shows the 1-standard deviation uncertainty at the edge detection location for a perfectly smooth feature, for three different X pixel sizes, in the presence of grayscale noise.

[0031] [Figure 17C] is an example of grayscale images using a simple threshold edge detection algorithm, where there is image filtering in the right image and no image filtering in the left image.

[0032] [Figure 18] is a graph of the relative frequency of linewidth roughness (LWR) PSD, which shows the effect of two different image filters on a set of 30 images.

[0033] [Figure 19] is a power spectral density map relative to frequency, which shows the noise reduction process of the disclosed edge detection device and method.

[0034] [Figure 20] shows a PSD of a specific type of photoresist feature on a given wafer, which is measured using the integration of different frames in the SEM.

[0035] [Figure 21] shows the deviation and no deviation values ​​of 3σ linewidth roughness (LWR), which is measured as a function of the number of frames integrated in the SEM.

[0036] [Figure 22A] shows the deviation of line width roughness (LWR) power spectral density (PSD) as a function of different pixel sizes and magnifications used in the SEM.

[0037] [Figure 22B] illustrates the unbiased linewidth roughness (LWR) power spectral density (PSD) as a function of the different pixel sizes and magnifications used in the SEM.

[0038] [Figure 23] is a flowchart depicting a representative overall process flow of the disclosed SEM edge detection system for detecting the edges of a pattern structure.

[0039] [Figure 24A] is a grayscale representation of a pattern structure of vertical lines and gaps analyzed by the disclosed measurement tool.

[0040] [Figure 24B] shows a single line scan at a Y pixel position.

[0041] [Figure 24C] shows the average line scan produced by averaging across all Y pixels.

[0042] [Figure 25A] is a PSD showing a spike artifact containing high frequency.

[0043] [Figure 25B] shows the PSD in which spike artifacts have been removed.

[0044] [Figure 26] shows a PSD containing mid-frequency spike artifacts and harmonics.

[0045] [Figure 27A] illustrates the impact of mid-frequency spike artifacts on the modeling and interpretation of the PSD.

[0046] [Figure 27B] illustrates the impact of removing mid-frequency spike artifacts on the modeling and interpretation of the PSD.

[0047] [Figure 28A] shows a PSD dataset that presents a type of raised feature.

[0048] [Figure 28B] shows an additional PSD dataset that presents a type of raised feature.

[0049] [Figure 29A] shows the model establishment and analysis of a low-frequency bulge of type I.

[0050] [Figure 29B] shows the model establishment and analysis of a low-frequency bulge of type II.

[0051] [Figure 30] is a flowchart depicting a representative process flow, used to detect unwanted spikes in a PSD dataset, remove the spikes from the PSD dataset, and obtain a roughness parameter for a specific feature.

[0052] [Figure 31] is a flowchart depicting another representative process flow, which is used to model the ridges in a PSD dataset and obtain unbiased roughness parameters for a specific feature.

[0053] [Figure 32] is a graph of an example of a Gaussian distribution of the mean.

[0054] [Figure 33] is a graph of an example of a heatmap, which depicts the probability of multiple points in a specification.

[0055] [Figure 34] is an alternative three-dimensional view of the heatmap of Figure 33.

[0056] [Figure 35] is a graph of an example of a heat map, which depicts a portion of the characteristics in the specification.

[0057] [Figure 36] is an alternative three-dimensional view of the heatmap of Figure 35.

[0058] [Figure 37] is a graph of an example of a curve for focal length error and exposure error.

[0059] [Figure 38] is a flowchart depicting a representative process flow, which is used to generate a probabilistic process window that takes into account measurement uncertainty.

[0060] [Figure 39A] is a graph of an example of a Poisson graph, which combines the effects of focal length and exposure dose on a CD.

[0061] [Figure 39B] is a chart of an example of a profile graph containing a dataset of a certain size, which has a profile with a fixed line width relative to the focal length and exposure.

[0062] [Figure 39C] is an example of a profile of CD (nominal + / -10%), 80-degree sidewall angle, and 10% light-blocking loss drawn on the same plot, which is a function of focal length (x-axis) and exposure dose (y-axis).

[0063] [Figure 40A] is a graphical example of a process window, showing two largest rectangles fitted within the process window.

[0064] [Figure 40B] is a graphical example of a process window, showing a largest rectangle and a largest ellipse fitted within the process window.

[0065] [Figure 41] is an example analysis of a process window that provides exposure latitude relative to focus depth.

[0066] [Figure 42] is an example of a process window for an overlapping line / gap pattern with two different spacings.

[0067] [Figure 43] illustrates the possible impact of measurement error on the geometric analysis of the process window size. Implementation

[0068] Measuring the roughness of a pattern is complex because noise in a measurement system is difficult to distinguish from the actual roughness being measured. A common approach is to use an imaging tool, such as a microscope, to create a detailed image of the object to be measured, and then analyze the information in that image to measure and describe the roughness characteristics of one or more features of the object. In this example, noise in the acquired image may appear to be the roughness of a feature in the image. Among other things, techniques are described below for separating noise in the image from the actual roughness of the feature, in order to produce a more accurate measurement of the roughness of the feature.

[0069] For example, scanning electron microscopy (SEM) is very useful for studying the characteristics of patterned structures, such as those of semiconductor devices. However, measuring the roughness of these structures is often challenging because noise is inherent in SEM images. Filtering (smoothing) of the SEM images is usually necessary to achieve accurate edge detection, but this filtering unintentionally alters the roughness of the measured features. An edge detection method is needed that reliably detects edges in highly noisy SEM images without using image filtering (or at least without any filtering that alters the roughness of the measured features).

[0070] Pattern roughness is a major problem in many fields. Many (if not all) techniques for creating patterns of various shapes create roughness at the edges of those patterns, at least close to the molecular scale (if not at larger scales). For example, in advanced lithography for semiconductor manufacturing, especially extreme ultraviolet (EUV) lithography, but also for other lithography methods, the roughness of printed and etched patterns can have many negative effects. Reduction in roughness requires a better understanding of the sources of random variation, thus necessitating better measurement and characterization of roughness characteristics. Conventional roughness measurement methods suffer from significant bias because noise in the image adds to the roughness on the wafer. This disclosure proposes a practical method to achieve unbiased roughness measurement through the use of a physical-based reverse line scan model. This enables accurate and robust measurement of roughness parameters across a wide range of SEM measurement conditions.

[0071] Before discussing the implementation of the disclosed techniques for solving the aforementioned SEM image noise problem, this disclosure first discusses the lithography of patterned structures and the frequency dependence of roughness.

[0072] 1. Random effects in microfilm

[0073] Advances in lithography and patterning have continued to advance Moore's Law by cost-effectively reducing the silicon area occupied by transistors in integrated circuits. In addition to the need for improved resolution, these lithography advancements should also allow for the creation of smaller features through improved control. Traditionally, lithography has focused on "global" sources of variation affecting pattern fidelity (e.g., exposure dose and focal length variations, hot plate temperature non-uniformity, scanner aberrations), attempting to minimize these sources and by developing processes with minimal sensitivity to these variations. However, today's small features also suffer from "local" variations caused by the fundamental randomness of patterning at near-molecular scales.

[0074] In lithography, light is used to expose a photosensitive material called photoresist. The resulting chemical reactions (including those occurring during baking after exposure) alter the solubility of the photoresist, enabling the development of a pattern and the creation of the desired critical dimension (CD). For a "large" volume of photoresist (in other words, a volume containing many photoresist molecules), the average amount of light energy per volume produces a certain amount of chemical change, which, on average, produces a certain amount of dissolution to create the pattern. The relationship between light energy, chemical concentration, and solubility can be described using deterministic equations that predict the output for a given set of inputs. These lithography models are extremely useful and are commonly used to understand and control lithography processes used in semiconductor manufacturing.

[0075] The deterministic view of lithography (that certain inputs always produce certain outputs) is only roughly true. The "mean-field theory" of lithography states that, on average, this deterministic model correctly predicts the lithography results. If we average over a large number of photons, then a single value (average) for the light energy is sufficient to describe that light energy. For a large volume of photoresist, the average concentration of a chemical species adequately describes its chemical state. However, for a very small volume, the number of atoms or molecules in that volume becomes random, even for a fixed "average" concentration. This randomness within a small volume (in other words, for a small number of photons or molecules, or the number of events) is generally called "shot noise" and is an example of random variation in lithography that occurs when the region of interest approaches the molecular scale.

[0076] A stochastic process is one in which the outcome is determined randomly. At the atomic / molecular level, virtually all processes are stochastic. For semiconductor patterning at nodes of 20 nm and below (where the smallest feature size is less than 40 nm), the size of interest is small enough that stochastic effects become significant and may even dominate the overall variation, influencing the size, shape, and arrangement of the fabricated patterns. For larger feature sizes, these stochastic effects may also be significant in certain situations.

[0077] The most noticeable manifestation of random variation in lithography (and etching and other parts of patterning processes) is that the resulting patterns are coarse rather than smooth (Fig. 1A). In the pattern structure shown in Fig. 1A, nominally parallel vertical lines are shown as bright vertical areas, while gaps are shown as dark vertical areas between the lines. The roughness of the edge of a feature is called line-edge roughness (LER), and the roughness of the width of a feature is called linewidth roughness (LWR). The roughness of the center line of the feature (at the midpoint between the left and right edges) is called pattern placement roughness (PPR). Another important result of these random variations is the random variation in the size, shape, and placement of features, which is particularly evident for contact hole features (Fig. 1B).

[0078] Random effects in patterning can degrade semiconductor device yield and performance in several ways: a) Roughness within a feature can affect the electrical characteristics of a device, such as wire resistance and transistor gate leakage current; b) Randomly induced feature-to-feature size variations (also known as local CD uniformity, LCDU) add to the total budget of CD variations, which can sometimes become a source of control issues; c) Randomly induced feature-to-feature pattern placement variations (also known as local pattern placement error, LPPE) add to the total budget of PPE, which can sometimes become a source of control issues; d) If the error distribution has fat tails, rare events leading to catastrophic bridging or outages are more likely to occur; and e) If those measurements do not properly account for random variations, decisions based on those measurements (including process monitoring and control, and calibration of optical proximity correction (OPC) models) can be of poor quality. For these reasons, proper measurement and characterization of randomly induced roughness is important.

[0079] Many other types of devices are also sensitive to characteristic roughness. For example, roughness along the edge of an optical waveguide can cause light loss due to scattering. Characteristic roughness in radio frequency microelectromechanical system (MEMS) switches can affect performance and reliability, and this is also true for other MEMS devices. Characteristic roughness can degrade the output of a light-emitting diode. Edge roughness can also affect characteristic mechanical and humidifying properties in microfluidic devices. Characteristic roughness in a linear grid polarizer can affect the efficiency and transmission of the polarizer.

[0080] However, conventional roughness measurements (such as linewidth roughness or line edge roughness measurements using a critical dimension scanning electron microscope, CD-SEM) are contaminated by measurement noise introduced by the measuring instrument. This results in biased measurements, where the measurement noise is added to the true roughness, leading to an overestimation of the true roughness. Furthermore, these biases are dependent on the specific measuring instrument used and its settings. These biases are also a function of the measured pattern. Attempts to provide unbiased roughness estimates using conventional techniques often fail in many modern applications due to smaller feature sizes and higher levels of SEM noise.

[0081] Therefore, a new method is needed to achieve unbiased roughness measurement that avoids the trial-and-error problems of conventional techniques and provides accurate and unbiased estimates of characteristic roughness. Furthermore, a good pattern roughness measurement method should have minimal dependence on measurement tool settings. For example, settings such as magnification, pixel size, average number of frames (equivalent to the total electron dose in the SEM), voltage, and current in a CD-SEM can significantly alter the roughness of the measured deviation. Ideally, unbiased roughness measurement would be largely independent of these settings.

[0082] 2. Frequency dependence of line edge roughness (LER), line width roughness (LWR), and pattern setting roughness (PPR)

[0083] Roughness is most often described by the standard deviation of edge location (for LER), linewidth (for LWR), or feature centerline (for PPR). However, the standard deviation alone is insufficient to fully describe roughness. Figure 2 shows four different rough edges, all with the same standard deviation. The visible significant differences on these edges clearly demonstrate that the standard deviation is insufficient to fully describe the characteristics of roughness. Instead, frequency analysis of roughness is necessary. The four randomly rough edges depicted in Figure 2 all have the same roughness standard deviation, but differ in the frequency parameters of correlation length (ξ) and roughness exponent (H). More specifically, regarding Figure 2, in case a) ξ=10, H=0.5; in case b) ξ=10, H=1.0; in case c) ξ=100, H=0.5; and in case d) ξ=0.1, H=0.5.

[0084] The standard deviation of a rough edge describes its variation relative to and perpendicular to an ideal straight line. In Figure 2, the standard deviation describes the vertical variation of the edge. However, this variation may spread differently along the length of the line (horizontally in Figure 2). This dependence on line length can be described using a correlation function, such as an autocorrelation function or a height-height correlation function.

[0085] Alternatively, the frequency f can be defined as the frequency along a length of the line (Figure 3). The frequency dependence of roughness can be characterized using the well-known power spectral density (PSD). The PSD is the variation of the edge per unit frequency (Figure 3) and is calculated as the square of the coefficients of the Fourier transform of the edge deviation. The low-frequency region of the PSD curve describes the edge deviation occurring on a long length scale, while the high-frequency region describes the edge deviation on a short length scale. Typically, the PSD is plotted on a double logarithmic scale as used in Figure 3.

[0086] The characteristic PSD defined by lithography generally has a shape similar to that shown in Figure 3. The low-frequency region of the PSD is flat (so-called "white noise" characteristic), and then above a certain frequency, it decreases by a power of that frequency (a statistically fractal behavior). The difference between these two regions is related to the correlation along the length of the characteristic. Points far apart along the edge are uncorrelated with each other (statistically independent), and the uncorrelated noise has a flat power spectral density. However, at short length scales, the edge deviation becomes correlated, which reflects a correlation mechanism in the generation of roughness, such as the acid-diffusion reaction used in a chemically amplified photoresist. The transition between uncorrelated and correlated behavior occurs over a distance called the correlation length.

[0087] Figure 4 illustrates a typical PSD curve that can be described using three parameters. PSD(0) is the zero-frequency value of the PSD. Although this value of the PSD may not be directly measurable (zero frequency corresponds to an infinitely long line), PSD(0) can be thought of as the value of the PSD in the flat, low-frequency region. The PSD begins to decrease near a frequency of 1 / (2πξ), where ξ is the correlation length. In the fractal region, we have what is sometimes called “1 / f” noise, and the PSD has a slope corresponding to a power of 1 / f (on the log-log plot). The slope is defined as 2H+1, where H is called the roughness exponent (or Hurst exponent). Typical H values ​​are between 0.5 and 1.0. For example, when a simple diffusion process causes the correlation, H = 0.5. As discussed in more detail below, each parameter of the PSD curve has an important physical meaning for a lithography definition. The variation in roughness is the area under the PSD curve and can be derived from the other three PSD parameters. The exact relationship between the variation and the other three PSD parameters depends on the exact shape of the PSD curve in the mid-frequency region (defined by the correlation length), but an approximate relationship can be used to show a general trend according to Equation 1 below: (1)

[0088] The differences observed in the four rough edges of Figure 2 can now be readily seen as differences in the PSD properties of the feature. Figure 5 shows two PSDs corresponding to edges a) and c) from Figure 2. Although these two edges have the same variation (the same area under the PSD curve), they have different values ​​for PSD(0) and associated length (in this example, the roughness index is kept constant). Although the standard deviation of the roughness of edges a) and c) is the same, these edges exhibit different PSD properties. As discussed below, for lithography features with finite lengths, the different PSD curves will result in different roughness properties.

[0089] 3. The influence of the frequency characteristics of roughness

[0090] The roughness of the lines and gaps in a patterned structure is characterized by measuring very long lines and gaps, long enough that the flat areas of the PSD become apparent. For a sufficiently long feature, the measured LWR (in other words, the standard deviation σ of the linewidth measured along the line) can be thought of as the LWR of an infinitely long feature, σLWR(∞). However, the patterned structure of a semiconductor device, for example, is made of features with various lengths L. For these shorter features, randomness will cause feature-to-feature variation in the roughness σLWR(L) within the feature, and in the feature-to-feature variation described by the standard deviation σCDU(L) of the average linewidth of the feature. This feature-to-feature variation is called the local critical size uniformity, LCDU, because it represents the CD (critical size) variation not caused by well-known "global" error sources (scanner aberrations, mask illumination nonuniformity, hot plate temperature variation, etc.).

[0091] For a line of length L, the variation within a feature and the variation from one feature to another can be related to the LWR of an infinitely long line (with the same nominal CD and spacing) by the roughness conservation principle given in Equation 2 below: (2)

[0092] The roughness conservation principle states that the variation of a very long line is divided into variations within a feature and variations from feature to feature by respect to a shorter line. How this division occurs is determined by the associated length, or more specifically by L / ξ. Using a basic model of the shape of the PSD as an example, it can be seen that: (3)

[0093] Therefore, Equations 1-3 demonstrate a measurement of PSD for a long line, and its description by the parameters PSD(0), ξ, and H enables us to predict random effects on a line of arbitrary length L. It should be noted that the LCDU is not determined by the roughness index, making H less important than PSD(0) and ξ. For this reason, it is useful to use an alternative set of three parameters: σLWR(∞), PSD(0), and ξ to describe the frequency dependence of roughness. It should be noted that these relationships also apply to LER and PPR.

[0094] It should also be noted that, examining Equation 3, the associated length is a length scale used to determine whether a line of length L acts as "long" or "short". For a long line, L >> ξ, therefore the characteristics of the local CDU are as follows: (4)

[0095] The result of this long line length provides a useful interpretation of PSD(0): it is the square of the LCDU for a given line multiplied by the length of that line. Decreasing PSD(0) by a factor of 4 decreases the LCDU by a factor of 2, while other PSD parameters remain unaffected (provided L >> ξ). Typically, photoresist produces an associated length on the order of one-quarter to one-half of the minimum half-pitch for its lithography. Therefore, when a feature is longer than approximately five times the minimum half-pitch of a technology node, it is roughly within the range of this long line length. For shorter line lengths, this associated length also begins to become important.

[0096] Equations 1–3 illustrate the variation within a feature and the variation from feature to feature as a function of line length. Figure 6 shows an example illustrating this relationship. For very long lines, LCDU is small, and the roughness within a feature is close to its maximum value. For very short lines, LCDU is dominant. However, due to the quadratic nature of the roughness conservation, σLWR(L) increases very rapidly with increasing L, but LCDU decreases very slowly with increasing L. Therefore, there is a wide range of line lengths where both feature roughness and LCDU are significant.

[0097] Since the principle of roughness conservation also applies to PPR, short features suffer not only from local CDU problems but also from local pattern setting error (LPPE). For the case of unrelated left and right edges of a feature, the PSD(0) of the LWR is typically twice that of the LER. Similarly, the PSD(0) of the LER is typically twice that of the PPR. Therefore, generally speaking, the LPPE is approximately half that of the LCDU. When the left and right feature edges are significantly correlated, these simple relationships no longer hold.

[0098] 4. Measurement of roughness of patterned structures using scanning electron microscopy (SEM)

[0099] A common method for measuring the roughness of small features is top-down critical size scanning electron microscopy (CD-SEM). Typical optical microscopes offer magnifications up to 1000x and resolutions down to hundreds of nanometers. Scanning electron microscopy uses electrons to create very small points (approaching 1 nm in width), which can be used to create high-resolution images, magnified over 20,000x. CD-SEM is a type of SEM optimized for measuring a wide range of features visible on semiconductor wafers. They can measure the average critical size of a rough feature with high precision, but have also proven useful for measuring LER, LWR, PPR, and their PSD. However, errors in the SEM images can have a large impact on the measured roughness and the roughness PSD, but a small impact on the measurement of the average CD. For this reason, the measurement methods required for PSD measurement may differ considerably from those commonly used for average CD measurement.

[0100] Figure 7 is a block diagram illustrating one embodiment of the disclosed edge detection system 700, which determines the roughness of the surface. The pattern structure 800 and the electron imaging optics (710, 715, 720, and 725) are located in a vacuum chamber 703, which is evacuated by a vacuum pump 702. Electrons are generated from a source, such as an electron gun 705, to form an electron beam 707. Common electron beam sources include heated tungsten filaments, lanthanum hexaboride (LaB6) crystals formed into thermionic emission guns, or sharp metal wires formed into field emission guns. The emitted electrons are accelerated and focused using electromagnetic focusing lenses 710, 715, and 720. The energy of the electrons impacting the pattern structure 800 is generally in the range of 200 eV to 40 keV in SEM, but more typically 300 eV to 800 eV for CD-SEM. The final focusing lens 720 utilizes a scanning coil 725 to provide an electric field that deflects the electron beam 707 into a focused spot toward the pattern structure 800. The scanning coil 725 passes the focused spot through the final lens aperture 735, scanning across the pattern structure 800 in a raster scan manner to expose a specific field of view on the pattern structure 800. The SEM 701 includes a backscattered electron detector 740 that detects backscattered electrons reflected from the pattern structure 800. As shown in Figure 7, the SEM 701 also includes a secondary electron detector 745. Before imaging the pattern structure 800, the user places the pattern structure 800 on a pattern structure receiver 732, which supports and positions the pattern structure 800 within the SEM 701. The SEM 701 includes a controller (not shown) that controls the raster scan of the pattern structure 800 during imaging.

[0101] Referring now to Figures 8A and 8B, the electrons of the electron beam 707 striking the patterned sample 800 undergo certain processes, depending on the energy of the electrons and the material properties of the sample. Electrons scattered from the atoms of the sample material release energy, change direction, and often generate cascades of secondary electrons by ionizing the sample atoms. Some of these secondary electrons 805 may escape from the patterned structure 800, while others may remain within the patterned structure. The patterned structure 800 includes a substrate 810, such as a semiconductor wafer. As shown in Figure 8A, a feature 815 is disposed on the top of the substrate 810. Feature 815 may be a metal line, a semiconductor line, a photoresist line, or other structure on the substrate 810. Feature 815 may have other shapes, such as a pillar or a hole, or more complex shapes. Feature 815 may be repetitive or isolated relative to other features on the patterned structure. The space surrounding feature 815 may be empty (vacuum or air) or may be filled with a different material. The pattern structure 800 can be a liquid crystal or other flat panel display, or other patterned semiconductor or non-semiconductor device. Feature 815 includes edges 815-1 and 815-2. The region in which the electron beam 707 interacts with feature 815 is the interaction volume 820, which is, for example, in a teardrop shape as depicted in Figure 8A.

[0102] Occasionally, electrons bounce back from the atomic nucleus and leave the sample (called backscattered electrons). Some lower-energy secondary electrons 805 may also escape from the sample 800 (often through a distinctive edge, as shown in Figure 8B). The SEM image is formed by detecting the number of secondary electrons and / or backscattered electrons escaping from the sample for each beam position.

[0103] As the electron beam is scanned across pattern structure 800 during a single-line scan, it "resides" at a specific point for a specific time. During this residence time, the number of electrons detected by the backscattered electron detector 740 or the secondary electron detector 745, or both, is recorded. The point is then moved to the next "pixel" position, and the process is repeated. The result is a two-dimensional pixel array (along the surface of the sample), where the electron count detected for each pixel is digitally recorded. The count is then typically normalized and represented as an 8-bit grayscale value between 0 and 255. This allows the detected electron count to be depicted as a grayscale "image," such as those shown in Figure 1. Although images from SEMs may remind the viewer of optical images perceived through the eye, it is important to note that these grayscale images are actually just a convenient depiction of the collected data.

[0104] CD-SEM uses the SEM image to measure the width of a feature. The first step in measuring the feature width is to detect the edges of the feature. For pixels close to an edge of a feature, a higher number of secondary electrons escape through the feature edge, resulting in bright pixels called "edge luminance" (see Figures 8B and 9). It is this bright edge luminance that allows the feature edges to be detected. For example, in the grayscale image representation of the upper part of Figure 9, this edge luminance is observed at edges 905 and 910 of feature 915. A line scan is essentially a horizontal section through a 2D SEM image, providing grayscale values ​​as a function of the horizontal pixel position on the feature, as shown in the lower half of Figure 9.

[0105] Data from pixels spanning a single horizontal column across the sample is referred to as a “line scan.” It is noted that the term line scan is used broadly enough here to encompass cases where an image is formed without scanning. The position of an edge of a feature can be detected from a single line scan or from a set of line scans representing, for example, the entire image shown in the upper portion of Figure 9. These edges appear as peaks 905' and 910' in the grayscale value relative to pixel position graph in the lower portion of Figure 9. Once the edge of a particular feature has been determined, the width of that particular feature is the difference between the positions of these two edges.

[0106] 5. Line scan model

[0107] Images are created through a physical process using a microscope or other imaging tool used to acquire an image of a structure. These images are typically two-dimensional arrays of data, which can be thought of as a set of data derived from the structure. A single one-dimensional cut through the image is called a line scan. A model of the imaging tool can predict the image of a given structure being imaged. For example, a model describing a scanning electron microscope can predict the image that will be obtained when imaging a given structure using a SEM.

[0108] CD-SEM converts a measured line scan or a series of measured line scans into a single-dimensional digital representation, i.e., the measured CD. To better understand how the line scan relates to the actual size of the feature being measured, it is important to understand how the SEM measurement tool's systematic response to the patterned structure affects the shape of the resulting line scan. For this purpose, rigorous 3D Monte Carlo simulations of SEM line scans can be extremely valuable, but they are often computationally too expensive for everyday use. Therefore, one approach is to develop a simplified analytical linescan model (ALM), which is computationally more suitable for rapidly predicting line scans. The ALM utilizes the physics of electron scattering and secondary electron generation, and each term in the model has physical significance. This analytical line scan representation can conform to rigorous Monte Carlo simulations to validate and calibrate its use.

[0109] The general application of the ALM is a typical forward modeling problem: given material properties (for the feature and the substrate) and the geometric description of the feature (width, spacing, sidewall angle, apex rounding, footing, etc.), the ALM predicts the line scan that will be generated. The mathematical details of the ALM can be found in the following publications: Chris A. Mack and Benjamin D. Bunday, “Line Scan Model for SEM Measurement Analysis,” Proceedings of the XXIX Conference on Measurement, Inspection and Process Control of Micro-Etching, SPIE Vol. 9424, 94240F (2015), and Chris A. Mack and Benjamin D. Bunday, “Improvement of the Line Scan Model for SEM Measurement Analysis,” Proceedings of the XXIX Conference on Measurement, Inspection and Process Control of Micro-Etching, SPIE Vol. 9778, 97780A (2016), the contents of which are incorporated herein by reference in their entirety. Other models with similar inputs and outputs can also be utilized.

[0110] The line scan model (ALM) used in the analysis is briefly reviewed below. The mathematical model is established by assuming that the interaction of an electron beam with a flat sample of a given material produces an energy deposition profile with a double Gaussian form, having a forward scattering width and a portion of the energy deposited by the forward scattering, and a backscattering width and a portion of the energy deposited by those backscattered electrons. The model also assumes that the number of secondary electrons generated within the material is directly proportional to the energy deposited per unit volume, and that the number of secondary electrons escaping from the wafer (and detected by the SEM) is directly proportional to the number of secondary electrons near the very top of the wafer.

[0111] The secondary electrons arriving at the detector will leave the incident beam at a distance *r*. Based on the above assumptions, the number of detected secondary electrons will be a function of the following Equation 5: (5)

[0112] Where σf and σb are the forward and backscattering ranges, respectively, and a and b are the quantities of forward scattering and backscattering, respectively.

[0113] SEM detects surface configurations by observing the number of secondary electrons escaping when the beam is within the gap between features, compared to when the beam is at the top of the feature. Figure 10 illustrates that the number of secondary electrons escaping from a gap (especially if it is small) is doubled, making the gap appear quite dark. When an electron beam is focused at a point in a gap between lines, the scattered electrons interact with feature 815, absorbing some of the escaping secondary electrons. The detected secondary electron signal decreases as the beam approaches the edge of the feature within the gap.

[0114] A model can be built using the absorption of the step (i.e., feature 815) to predict the shape of the line scan in the gap region. If a large feature has a left edge 815-1 at x=0, where feature 815 is on the right (positive x), then the detected secondary electron signal as a function of position (SE(x)) will be given by the following Equation 6: (6)

[0115] Where αf is the fraction of forward-scattered secondary electrons absorbed by the step, and αb is the fraction of back-scattered secondary electrons absorbed by the step.

[0116] However, when the beam is at the top of feature 815, the interaction between the scattered electrons and the feature is very different, as considered in Equation 7 below. As illustrated in Figure 8, two phenomena occur when the beam is closer to the edge compared to when it is further away. First, secondary electrons from forward and backscattered electrons can escape more easily from the edge 815-1. This causes edge brightening as discussed above. To account for this effect, a positive term... An enhanced escape of forward-scattered secondary electrons is incorporated to account for this, where σe is very similar to the forward scattering range of the step material. Furthermore, the interaction volume itself decreases as the beam approaches the edge 815-1, resulting in fewer secondary electrons being generated. Therefore, the term where σv < σe... Subtracted to give in the following equation 7, which is a line scan representation of the top of the large feature 815: (7)

[0117] Figure 11 is an example showing the results for this model. More specifically, Figure 11 shows a predicted line scan (large feature, where the left edge 815-1 is at x=0) of a left-facing photoresist step 815 on a substrate, such as a silicon wafer. The calibrated model 1105 is overlaid on the rigorous Monte Carlo simulation result 1110. The calibrated model 1105 is so closely aligned with the Monte Carlo simulation result 1110 that the two curves together appear to be almost a single line.

[0118] The above discussion pertains to modeling an isolated left-facing edge 815-1. Adapting the model to include a right-facing edge involves translating and reversing the edge, as well as adding the resulting secondary components (i.e., secondary electrons). If the two edges are close enough to interact, some complexity arises, producing additional terms. Furthermore, the effects of non-perpendicular sidewalls and the rounded corners at the top and bottom of the characteristic edge can be incorporated into the model (Figure 12).

[0119] Figure 12 shows a representative predicted line scan of a pattern of photoresist lines and gaps on a silicon wafer. The calibrated model 1205 is overlaid on the rigorous Monte Carlo simulation result 1210. Similarly, the calibrated model 1205 is so closely aligned with the Monte Carlo simulation result 1210 that the two curves together appear almost as a single line. A final model (ALM) contains 15 parameters determined based on the material properties of the wafer and its features, as well as the beam voltage. To validate the model and calibrate these parameters, rigorous first-principles Monte Carlo simulations can be used to generate line scans for different materials and feature geometries. The ALM is then fitted to the Monte Carlo results, producing best-fit values ​​for the 15 unknown parameters.

[0120] 6. Reverse line scan model

[0121] Line scan or image modeling, such as the line scan model (ALM) analyzed above, predicts an image or shape of a line scan for a specific pattern structure (e.g., a feature on a wafer). The ALM solves a forward modeling problem, wherein the model receives geometric information for the specific feature as input and provides a predicted shape of another SEM line scan of the specific feature as output.

[0122] Compared to ALM, the disclosed edge detection system 700 includes a reversed model that receives "measured line scan information" as input from SEM 701, describing a specific feature on the wafer. In response to the measured line scan information describing the specific feature, the edge detection system 700 uses its reversed model to generate "feature geometry information" as output, which describes the feature geometry that will produce the measured line scan. Advantageously, the edge detection system 700 has been found to remain effective even when the measured line scan information from SEM 701 contains a considerable amount of image noise. In one embodiment, the output feature geometry information includes at least the feature width. In another embodiment, the output feature information includes the feature width and / or other geometric descriptors related to the geometry of the specific feature, such as sidewall angles, feature thickness, apex rounding, or bottom feet. It should be noted that a feature disposed on a semiconductor wafer is an example of a specific type of pattern structure to which the disclosed technology is applicable.

[0123] Like many imaging systems, the ALM (Aspect Ratio) is inherently nonlinear. To address the nonlinear nature of the ALM, the edge detection system 700 numerically inverts the ALM or a similar forward model and applies the resulting inverse line scan model to a measured line scan to detect feature edges (e.g., to estimate feature geometry on the wafer). The disclosed edge detection system apparatus and process include the functionality of detecting and measuring feature roughness. The disclosed apparatus and method can also be applied to other applications in general CD (Content Gravity) measurement of 1D or 2D features, such as the precise measurement of feature width (CD) and edge position or setting.

[0124] First, it should be noted that the ALM (and similar models) has two types of input parameters: material-dependent parameters and geometric parameters. Material-dependent parameters include, for example, forward and backscatter distances, while geometric parameters include, for example, feature width and spacing. In one embodiment, for a repetitive edge detection application, the material parameters will be fixed, and only the geometric parameters will vary. In the simplest case (in other words, for simple edge detection), it is assumed that only the edge position of the feature will change, such that sidewall angles, corner rounding, etc., are assumed to be fixed. Therefore, the use of a one-line scan model for edge detection in the edge detection system 700 involves two steps: 1) calibrating parameters assumed to be fixed across the entire image, and then 2) finding the edge position of the feature, which provides an optimal fit between the measured line scan and the line scan model for each measurement.

[0125] In one embodiment, in the first step, calibration is achieved by comparing the line scan model with a rigorous Monte Carlo simulation. The goal in this step is to identify the material parameters for the desired application range and ensure that the fit is sufficient for the range of desired characteristic geometry. When complete, this calibrated line scan model can serve as a starting point for generating an inverse line scan model (ILM). The inverse line scan model (ILM) should be calibrated to the specific SEM image to be measured. Since image grayscale values ​​are only proportional to the secondary electron signal, at least one mapping to grayscale values ​​is necessary. In real-world applications, the material properties in the experimental measurements will not be the same as those assumed in the Monte Carlo simulation, making some calibration of those parameters also necessary.

[0126] 7. Calibration of the reverse line scan model

[0127] Before using the ILM for edge detection, the ILM is calibrated. Certain parameters of the model (e.g., material-dependent parameters) are assumed to be constant across the entire image. However, geometric parameters such as the edge location, feature width, and spacing are assumed to vary for each line scan. The goal of ILM calibration is to determine parameters that are constant across the entire image, regardless of the exact location of the feature edges. A further goal of ILM calibration is to correctly determine these parameters in the presence of image noise. These goals are achieved by averaging along an axis of symmetry of the feature being measured, thus averaging out the image noise and the actual feature roughness.

[0128] By averaging the line scan along an axis of symmetry (e.g., a direction parallel to a long line or gap feature), information about the actual edge locations is lost, but information about the material parameters of the line scan model is retained. Furthermore, this method largely eliminates noise in the image. Calibrating the ILM to the averaged line scan produces a set of material parameters specific to this image (or any parameters assumed to be constant throughout the image).

[0129] Many features to be measured exhibit an axis of symmetry suitable for ILM calibration. For example, a vertical edge has a vertical axis of symmetry. Averaging all pixels in a vertical row from the image will average out all vertical variations, leaving only horizontal information in a direction perpendicular to the edge of the feature. The result of this averaging is a one-dimensional line scan, known as the average line scan. Similarly, a nominally circular contact hole or pillar is ideally radially symmetrical. Averaging by the polar angle around the center of the feature will produce an average line scan, which removes noise and roughness from the image. An elliptical hole shape can also be averaged by compressing or enlarging the pixel size in one direction proportional to the ratio of the major axis to the minor axis of the ellipse. Other axes of symmetry also exist in other features.

[0130] A measured image (e.g., a SEM image) may contain one or more features. For example, Figure 1A shows multiple vertical line features and multiple vertical gap features. Figure 1B shows multiple junction holes. In this case, each feature can be individually averaged along an axis of symmetry to form an average line scan for that feature. In the example of Figure 1A, the SEM image can be divided into vertical strips, each strip containing only one line feature, wherein the strip extends horizontally from approximately the center of one gap to approximately the center of the next gap. In the example of Figure 1B, the image can be divided into individual rectangular regions, each containing exactly one junction hole, wherein the center of the junction hole roughly coincides with the center of the rectangular region. An average line scan for the junction hole is then determined from that rectangular region of the image. Alternatively, each of the average line scans from each feature in an image can be averaged together to form a single average line scan applicable to the entire image.

[0131] For a repetitive edge detection application (e.g., detection of all edges on a single SEM image), the material parameters will be fixed, and only the geometric parameters will vary. In the simplest case (i.e., for simple edge detection), we can assume that only the edge location of the feature changes, and thus feature thickness, sidewall angles, corner rounding, etc., are assumed to be fixed. Therefore, the use of the ILM for edge detection involves two steps: calibrating once using the average line scan for the assumed fixed parameters (i.e., material and fixed geometric properties), and then finding the edge location of the feature that provides an optimal fit of the measured line scan to the line scan model for each line scan. Optionally, as previously described, calibration is first achieved by comparing the line scan model with a rigorous Monte Carlo simulation. The goal of this initial step is to find the material parameters for the desired application range and to ensure that the model is sufficient for the desired feature geometry. When completed, this partially calibrated line scan model must still be fully calibrated to the specific SEM image to be measured using the average line scan.

[0132] Once the ILM has been calibrated to a given SEM image or image set, it is then used to detect edges. Due to the nonlinear nature of the line-scan model of the ALM, for example, an inverse transformation of the values ​​is required, such as using nonlinear least-squares regression to find the optimal values ​​for fitting the model to the left and right edge positions of the data. For simpler line-scan models, linear least-squares fitting may be feasible. Other methods of "best fit" are also known in this art. The ILM as an edge detector allows for edge detection in a high-noise environment without the use of filters. Figures 13A and 13B demonstrate reliable edge detection for a very noisy image without the use of any filtering or image smoothing. More specifically, Figure 13A is a raw SEM image of a pattern structure before edge detection using an ILM, showing 18nm lines and gaps. Figure 13B is the same image after edge detection using an ILM.

[0133] Gaussian filters are common image smoothing filters designed to reduce noise in an image. Other filters, such as box filters and median filters, are also commonly used for this purpose. To illustrate the effect of image filtering on roughness measurements, Table 1 below shows the measured 3σ linewidth roughness (LWR) as a function of the x and y widths (in pixels) of the Gaussian filter. For each case, the ILM edge detection method is used, and therefore the difference in the resulting LWR is only a function of the image filter parameters. The range is almost a factor of 2, showing that many different roughness measurements can be obtained with arbitrary choices of filter parameters. In all cases, the ILM edge detection is used. If a conventional critical edge detection method is used, the range of the resulting 3σ roughness values ​​is much larger (Table 2). Similar results are obtained if other filter types (e.g., box or median) are used.

[0134] Table 1

[0135] The original (biased) 3σLWR (nm) is a function of the x and y widths (in pixels) of the Gaussian filter, which utilizes ILM edge detection. y-width = 1 y-width = 2 y-width = 3 y-width = 4 x width = 1 4.99 4.67 4.03 3.82 x width = 3 4.92 4.02 3.48 3.28 x width = 5 4.85 3.82 3.28 3.00 x width = 7 4.79 3.69 3.13 2.84 x width = 9 4.73 3.59 3.08 2.80 x width = 11 4.68 3.54 3.07 2.80

[0136] Table 2

[0137] The original (biased) 3σLWR (nm) is a function of the x and y widths (in pixels) of the Gaussian filter, which utilizes known critical value edge detection. y-width = 1 y-width = 2 y-width = 3 y-width = 4 x width = 1 11.17 8.52 7.28 x width = 3 9.58 5.22 4.02 3.72 x width = 5 8.12 4.62 3.83 3.49 x width = 7 7.44 4.50 3.78 3.42 x width = 9 7.03 4.45 3.77 3.41 x width = 11 6.77 4.44 3.77 3.41

[0138] While arbitrary choices of image filter parameters have a significant impact on the measurement of roughness of the patterned structure, the effect of the threshold value depends on the specific edge detection method used. For a simple threshold edge detection case after image filtering, there is a threshold value that minimizes the measured 3σ roughness, while other values ​​significantly alter the roughness (see Figure 14). For the ILM case, the choice of threshold value has almost no effect on the measured LWR (in Figure 14, as the threshold value changes from 0.25 to 0.75, the LWR changes from 5.00 nm to 4.95 nm). Therefore, for conventional edge detection methods, arbitrary choices of the threshold value can cause large variations in the measured roughness. For the ILM, there is no substantial effect from arbitrary choices on the roughness measurement.

[0139] Although the disclosed ILM system achieves correct edge detection in the presence of high-level noise, this noise still contributes to the measured roughness. For a line scan with a given edge slope, the uncertainty in the grayscale value near the line edge is directly converted into the uncertainty at the edge location. However, a major difference is that the effect of noise can be measured in the unfiltered case. The noise floor of an unfiltered image can be subtracted from the PSD (Power Spectral Density), thus producing an unbiased estimate of the PSD (and therefore the roughness). In the case of filtered images, the noise floor is largely erased, and therefore cannot be detected, measured, or removed.

[0140] Figures 15A and 15B show the LER power spectral density from many coarse features, where the right and left edges are individually combined. More specifically, Figure 15A shows the raw PSD after edge detection using the disclosed ILM technique, while Figure 15B shows the PSD after noise subtraction.

[0141] Considering the results shown in Figure 15A, where the line edge roughness (LER) for the left and right edges of a feature on a patterned structure is compared, the original PSD indicates that the two edges behave differently. However, these differences are an artifact of the SEM caused by an asymmetry in a scan direction (e.g., charging), which causes the right line scan slope to be lower than the left line scan slope. In fact, there is no difference between the right and left edges on the wafer for this sample. By individually measuring the noise floor for each edge and subtracting the noise, a common left / right LER is obtained (Figure 15B), which is an unbiased estimate of the true PSD.

[0142] Once the noise has been removed, reliable analysis of the PSD can lead to reliable estimates of important roughness parameters, such as the zero-frequency PSD(0), the correlation length ξ, and the roughness index H. The unbiased 3σ roughness can also be obtained. Extracting these parameters from empirical PSDs without removing the noise is problematic and prone to systematic errors.

[0143] 8. Unbiased measurement of PSD

[0144] The biggest obstacle to accurate coarseness measurement is noise in the CD-SEM image. Besides other sources of noise, SEM images suffer from shot noise, where the number of electrons detected for a given pixel varies randomly. For a expected Poisson distribution, the variation in the number of electrons detected for a given pixel in the image is equal to the expected number of electrons detected for that pixel. Since the number of detected electrons is proportional to the number of electrons striking the sample location represented by that pixel, the relative amount of noise can be reduced by increasing the electron dose received by the sample. For some types of samples, the electron dose can be increased with minimal consequences. However, for other types of samples (e.g., photoresist), a high electron dose can lead to sample damage (e.g., thinning of photoresist lines). Other types of samples, such as biological specimens, may also suffer from electron damage. Therefore, to avoid sample damage, the electron dose is kept as low as possible, with the lowest possible dose limited by the noise in the resulting image.

[0145] Figure 16 shows partial SEM images of three images acquired under different electron doses for the same nominal lithography characteristics. More specifically, Figure 16 shows partial SEM images of the same nominal photoresist characteristics with integration of 2, 8, and 32 frames (from left to right). Doubling the integration of frames doubles the electron dose per pixel. Since the dose is increased by a factor of 4 in each case, the noise is reduced by a factor of 2.

[0146] SEM image noise is the actual roughness of the pattern added to the wafer, resulting in a higher deviation in the measured roughness. Typically, we obtain a roughness with a deviation as given by Equation 8A. (8A)

[0147] Where σbiased is the roughness measured directly from the SEM image, σunbiased is the unbiased roughness (i.e., the true roughness of the wafer feature), and σnoise is the random error at the detected edge location (or linewidth) caused by noise in the SEM imaging and edge detection. Equation 8A assumes that the noise is statistically independent of the roughness on the feature being measured. If this is not the case, a more complex noise model can be used, as further described below. Since an unbiased estimate of the feature roughness is desired, the measured roughness can be corrected by subtracting an estimate of the noise term.

[0148] The pixel noise in the SEM is edge detection noise created based on the expected shape of the line scan for the feature. For example, Figure 17A shows a typical line scan (grayscale value relative to the horizontal position g(x)) for a line feature on a wafer, where the pixel noise is negligible when there is a very large number of electrons. The result is the "expected" line scan, i.e., the expected value of the line scan signal from a statistical point of view. The edge position can be determined by defining a critical grayscale level. However, noise in the grayscale value will result in noise at the detected edge position. For a given grayscale noise σgray, the edge position uncertainty σnoise will depend on the slope dg / dx of the line scan at the edge. For small-level noise, (8B) Therefore, the level of edge detection noise is a function of the pixel grayscale noise and the slope of the line scan at the characteristic edge.

[0149] Equation 8B is strictly only valid for small levels of noise and infinitesimally small pixel sizes. To explore the effects of larger amounts of noise and non-zero pixel sizes, simulations of SEM images were employed. Perfectly smooth lines and gaps (25 nm width, 50 nm spacing) were used as input to the line scan model for the analysis to create composite SEM images. The grayscale values ​​generated for each pixel (ranging from 0 to 255) were then treated as the average of a normal distribution with a given standard deviation (σgray), and a random grayscale number was assigned to each pixel drawn from this normal distribution. These SEM images were then used as experimental SEM images and measured using a reverse line scan model to detect the edge positions of each feature. The LER of 1 standard deviation measured from these images is the uncertainty in the detected edge positions caused by the grayscale pixel noise. Figure 17B shows the uncertainty of 1 standard deviation in the edge detection positions for these perfectly smooth features in the presence of grayscale noise. In this figure, for simulated synthetic SEM images (an average of 100 images, each with 20 dense line / gap features 25nm wide and 50nm spaced), edge detection noise for three different X-pixel sizes is depicted as a function of grayscale noise. Edge detection using a reverse line scan model and the resulting line edge roughness of the aforementioned features are considered as edge detection noise. The result is slightly non-linear, where higher-level pixel noise produces increasingly larger edge detection noise. Furthermore, smaller X-pixel sizes produce lower-level edge detection noise. In fact, for low-level grayscale noise, the edge detection variation... It is directly proportional to the size of the X pixels.

[0150] Pixel noise is not the only source of edge detection noise. During operation, the electron beam is scanned from left to right using beam control electronics. Errors in this beam control can place the beam in an incorrect position, resulting in an edge error. The charging of the sample during electron exposure can deflect the beam to an incorrect position. While some charging effects will be systematic, there will also be random or pseudo-random components that will appear randomly varying in the detected edge locations.

[0151] Although several methods for estimating and subtracting noise at the SEM edge locations have been proposed in the prior art, these methods have not been proven successful for today's small feature sizes and high-level SEM image noise. The problem is a lack of robustness in edge detection in the presence of high image noise. More specifically, when the noise level is high, edge detection algorithms often fail to find the edges. The solution to this problem is usually to defilter the image and smooth out high-frequency noise. For example, if a Gaussian 7x3 filter is applied to the image, then for each rectangular region of the image that is 7 pixels wide and 3 pixels high, the grayscale value of each pixel is multiplied by a Gaussian weight and then averaged together. The result is assigned to the center pixel of the rectangle. Box (averaging) filters and median filters can also be used and produce similar results. When image noise is high, this smoothing makes edge detection significantly more robust. Figure 17C shows an example of an edge detection algorithm using a simple threshold, where there is image filtering in the right image and no image filtering in the left image. Without image filtering, the edge detection algorithm mostly detects noise in the image and therefore cannot reliably find the edges.

[0152] Image filtering can have a significant effect on the resulting PSD and the measured roughness. Figure 18 illustrates the effect of two different image filters on the PSD obtained from a set of 30 images, each containing 12 features. All images were measured using a reverse line scan model for edge detection. The power spectral density is averaged from these 360 ​​roughness features, where the images were pre-processed using a 7x2 or 7x3 Gaussian filter, or were completely unfiltered, as indicated in the figure. As can be seen, high-frequency regions are significantly affected by filtering. Even the low-frequency regions of the PSD show significant changes when a smoothing filter is used. Filtering in the y-direction smooths out high-frequency roughness. Filtering in the x-direction reduces the slope of the line scan, which may affect the measured low-frequency roughness. As will be described below, the use of image filtering makes the measurement and subtraction of image noise impossible.

[0153] If edge detection without image filtering is achievable, then noise measurement and subtraction can be achieved by comparing the PSD characteristics of the noise with those of the actual wafer features. We anticipate that photoresist features (and etched features) have a PSD characteristic as shown in Figure 19 as the "true PSD" (and was also shown earlier in Figure 4). The correlation along the length of the feature edge is a reduction in high-frequency roughness, thus making the roughness very small over a very short length scale. On the other hand, SEM image noise can generally be assumed to be white noise, thus the noise PSD is flat across all frequencies. Other models of SEM image noise are also possible, for example, using line-scan to line-scan correlations to describe the noise, as further described below. Therefore, at a sufficiently high frequency, the measured PSD will be dominated by image noise, rather than the actual feature roughness (the so-called "noise floor"). Given a grid size (Δy) along the length of the line, the white noise detected by SEM edge detection affects the PSD according to the following Equation 9: (9)

[0154] Therefore, the measurement of the high-frequency PSD (without any image filtering) provides a measurement of the SEM edge detection noise. Figure 19 illustrates this method for a white SEM noise model. Clearly, this method for noise reduction cannot be used on PSDs from already filtered images because such filtering removes the high-frequency noise floor (see Figure 18).

[0155] Equation 9 assumes a white noise model in which noise found in any pixel of the image is independent of noise found in any other pixel. This may not always be the case. For example, noise in each pixel may be slightly related to its nearest neighbor, affecting σgray in Equation 8B. Instead, the grayscale slope in Equation 8B may be correlated from one column of pixels to the next, which may be caused by the interaction volume of the electrons, as shown in Figure 8. If a correlation model is assumed or measured, a suitable noise expression for the PSD can be used to replace Equation 9, as further described below.

[0156] Figure 19 illustrates one embodiment of the noise subtraction procedure of the disclosed edge detection apparatus and method. In the disclosed edge detection method, the method first detects the position of the edge using the ILM (e.g., using a reverse line scan method) without using any image filtering. From these detected edges, a biased PSD is obtained, which is the sum of the actual wafer roughness PSD and the SEM noise PSD. Using a model for the SEM image noise (e.g., a fixed white noise PSD), the amount of noise is determined by measuring the noise floor in the high-frequency portion of the measured PSD. The true (unbiased) PSD is obtained by subtracting the noise level from the measured (biased) PSD. The key to the method of using the above noise subtraction to obtain an unbiased PSD (and thus an unbiased estimate of the parameters σLWR(∞), PSD(0), and ξ) is robust edge detection without the use of image filtering. This can be achieved using a reverse line scan model. A reverse line scan model is used to generate the filterless PSD data shown in Figure 18.

[0157] An exemplary method for subtracting white noise will now be described. First, edges are detected from a SEM image without any image filtering (e.g., using a reverse line scan model). The power spectral density of one or more edges is calculated in a conventional manner. Since the PSD of a single edge is quite noisy, it is extremely valuable to measure many edges and average the PSD. Typically, hundreds or thousands of edges are measured, and their PSDs are averaged. This averaged PSD is called the biased PSD. From the averaged biased PSD, the highest frequency is examined to determine whether a flat noise floor is observed. This noise floor is observed whenever the y-pixel size is sufficiently smaller than the correlation length of the true roughness. Typically, a y-pixel size that is 20% or less of the correlation length is sufficient. If a noise floor is observed, the average PSD value in the flat region is calculated. This is the noise floor. This amount is then subtracted from the biased PSD at each frequency to produce an unbiased PSD. The PSD of the deviation is our best estimate of the true PSD of the roughness on the wafer.

[0158] Other SEM errors can also affect the measurement of roughness PSD. For example, SEM field distortion may artificially increase the low-frequency PSD for LER and PPR, although it has a small effect on LWR. Background intensity variations in the SEM can also cause an increase in the measured low-frequency PSD, including LWR, LER, and PPR. If these variations are measurable, they can potentially be subtracted, thus producing the best possible unbiased estimate of the PSD and its parameters. By averaging the results of many SEM images, where the only common feature of these measurements is the SEM used, the judgment of SEM image distortion and background intensity variations can be made.

[0159] 9. Sensitivity settings for measurement tools

[0160] Not all noise in a measured PSD is white noise. White noise occurs when measurement noise from the edge positions of each line scan is completely independent of all other line scans (and especially of its nearest neighbor). White noise occurs when there is no correlation between the error in one line scan and the error in the adjacent line scan. Any small correlation along the edge error along the length of the line will cause "pink noise," a noise characteristic that is not perfectly flat across the entire frequency range.

[0161] The settings of the SEM measurement tools may affect the measured roughness of a feature in a pattern structure. These settings include the SEM 701 magnification and pixel size. These two parameters can be changed independently by altering the number of pixels in the image (e.g., from 512×512 to 2048×2048). Furthermore, the number of integrated frames (the electron dose) when capturing an SEM image can be adjusted. To investigate the effect of this setting, the number of integrated frames can be changed, for example, from 2 to 32, which represents a 16-fold change in electron dose.

[0162] The total electron dose is directly proportional to the number of integrated frames. Therefore, shot noise and its impact on edge detection noise are expected to be proportional to the square root of the number of integrated frames. Figure 20 shows a PSD of a specific photoresist feature type on a given wafer, measured using different numbers of integrated frames. In this example, the PSD corresponds to 18nm photoresist lines and gaps, where only the number of integrated frames is varied. The SEM conditions used are 500eV, 49 images per condition, 21 features per image, pixel size = 0.8nm², and image size = 1024 × 1024 pixels. The integration of 8 or more frames produces a PSD exhibiting a fairly flat high-frequency noise region. For integration of 2 and 4 frames, the noise region is significantly skewed. Therefore, the assumption of white SEM noise is only approximately true and becomes a more accurate assumption as the number of integrated frames increases and the noise level decreases. This observation has been confirmed in other cases: high noise conditions are more likely to present a non-flat noise floor.

[0163] Figure 21 shows the deviation and undevised values ​​of the 3σ linewidth roughness as a function of the number of frames measured as integration. All conditions are the same as described in Figure 20, and the error bars represent 95% confidence interval estimates. The deviation roughness varies from 8.83 nm for integration of two frames to 5.68 nm for eight frames and 3.98 nm for 32 frames. On the other hand, the undevised roughness is fairly stable after integration of six frames, varying from 5.25 nm for integration of two frames to 3.25 nm for eight frames and 3.11 nm for 32 frames. Although the deviation roughness is 43% higher for eight frames compared to 32 frames, the undevised roughness is only 4% higher for eight frames compared to 32 frames. Since the assumption of white SEM noise is not very accurate in the integration of 2 and 4 frames, the unbiased measurement using a white noise model to subtract noise from the integration of these very few frames is not entirely successful. A relevant noise model, particularly for the integration of these few frames, can produce better noise subtraction, as described in more detail below. Although the results shown are for LWR, similar results are obtained for measurements of Line Edge Roughness (LER) and Pattern Setting Roughness (PPR).

[0164] One possible cause of the correlation in edge noise is the correlation in pixel noise. To test this possibility, isolated edges were measured using the CD-SEM. The edges allow the SEM to perform its imaging function in a typical manner, but at a distance to the left or right of the edge, the field is flat and featureless. In this region, the only variation in pixel grayscale values ​​comes from image noise. The correlation coefficients between adjacent pixels can then be calculated. Performing these calculations, the average correlation between adjacent pixels in the x-direction is 0.12, but the average correlation in the y-direction is only 0.01, practically zero. These correlation coefficients were determined for edges measured in integration of 2 to 32 frames. There is only a small variation in pixel-to-pixel correlation as a function of the number of integrated frames. Therefore, the associated pixel noise is not the cause of the pink noise observed in integration of fewer frames. However, the line scan slope in Equation 8B may be the cause of the noise correlation.

[0165] One possible cause of noise correlation in the line scan slope is the interaction between the beam and the sample. Electrons striking the sample undergo a process that depends on the energy of the electrons and the material properties of the sample. Electrons scatter from the atoms of the sample material, release energy, change direction, and typically generate secondary electrons through a cascade, usually by ionizing the sample atoms. Occasionally, electrons bounce back from the atomic nuclei and leave the sample (called backscattered electrons). Some lower-energy secondary electrons may also escape from the sample (typically through a distinctive edge, as seen in Figures 8A and 8B). A SEM image is formed by detecting the number of secondary electrons and / or backscattered electrons escaping the sample for each beam position.

[0166] When an image is formed using a SEM, a small electron resides at a specific point on the sample (i.e., a pixel), while the number of escaping secondary electrons is counted by the secondary electron detector. As in Figure 8A, when the point is a long distance away from a feature edge, the number of detected secondary electrons 805 is small (and therefore the pixel is dark). As in Figure 8B, when the point is close to a feature edge, secondary electrons 805 from the interacting volume easily escape from the feature edge, resulting in a bright pixel.

[0167] The electron interaction volume can range from one to tens of nanometers in diameter, depending on the beam voltage and the properties of the sample material. This interaction volume represents the influence of the sample shape over a range determined by the interaction volume on an electron striking a point on the sample. Therefore, whenever the radius of the interaction volume is greater than y pixels, the slope of the line scan in a column of pixels will not be independent of the slope of the line scan in adjacent pixels. This dependence may be the cause of correlation in the noise, where the noise correlation length is affected by the electron beam interaction volume.

[0168] 10. Detection and removal of spikes from power spectral density

[0169] Besides noise interference affecting the signal in a typical image with rough characteristics, other errors may also exist in the image, exhibiting very different frequency characteristics compared to white or pink noise and compared to the roughness being measured. Some of these errors produce large but narrow spikes in a PSD. Figure 25A illustrates an example of a high-frequency "spike," which is intermittently visible in the dataset. One cause of such spikes may be electrical interference in the scanning electronics of the imaging tool. If the interference is within a frequency range permissible for one or more interference events within a complete scan of the image, this interference may produce slight but regular "jitter" in the scanning beam position. For highly accurate scans, even a single nanometer of jitter can produce one or more large spikes in the measured PSD. According to this mechanism, such interference spikes may exist in the Line Edge Roughness (LER) and Pattern Setting Roughness (PPR) PSDs, but not in the Line Width Roughness (LWR) PSDs. Alternatively, the interference may cause spikes at the same frequency in all three PSDs.

[0170] For example, when the measurement tool captures images at a standard “TV” scan rate or a small multiple of this rate, electrical interference at a frequency of 50 Hz or 60 Hz may cause significant spikes in the measured PSD. Furthermore, electrical interference in normal audio may cause spikes visible at higher PSD frequencies in typical measurement tool images.

[0171] The presence of spikes in the PSD may be undesirable for several reasons, depending on their number, amplitude, and frequency. In the case of high-frequency spikes, as seen in Figure 25A, these spikes may affect the aforementioned noise removal process, resulting in an overestimation of the amount of white or pink noise in the image.

[0172] PSD spikes can be caused by phenomena other than electrical interference within the imaging tool. The object being measured may contain periodic or semi-periodic structures other than the roughness features to be measured. For example, a set of vertically oriented roughness features of the object may be at the top of a set of periodic horizontal features, resulting in a surface configuration beneath the roughness features being slightly visible in the image. This underlying surface configuration may generate a mid-frequency spike to the PSD (where higher-frequency harmonics are also possible). Figure 26 is an example illustrating this phenomenon.

[0173] Another phenomenon that could cause spikes in the PSD is the presence of a small range of particles within the material of the object being measured. Particles of similar size tightly packed together could produce an almost periodic appearance, resulting in a spike in the measured PSD.

[0174] Roughness measurements can also be performed on an image taken from a photomask feature used in a lithography process. The photomask is typically fabricated using a direct-write lithography tool, which has, for example, a non-zero address grid and rectangular exposure constraints to form the image. For some features, for example, oriented at a 45-degree angle relative to the writing grid of the tool used to print the photomask, the result will be small, regularly spaced protrusions along the edge of the photomask feature. These protrusions will produce a spike (or a main spike plus harmonic spikes) in the PSD of the measured photomask roughness.

[0175] For example, the spikes visible in Figure 26 can be very detrimental to the measurement of roughness parameters, as they are not part of the biased or unbiased PSD. Figure 27A illustrates how a PSD with spikes can alter the model fitted to the unbiased PSD, including modeling parameters such as PSD(0), correlation length, and roughness index. Conversely, Figure 27B illustrates how a PSD with spikes removed can affect the model fitted to the unbiased PSD, including modeling parameters such as PSD(0), correlation length, and roughness index.

[0176] For these and other reasons, when the cause of those spikes is believed to be a mechanism different from the mechanism that produces the roughness of the feature being measured, it is desirable to remove the spikes from the PSD. In other words, it is desirable to separate PSD artifacts caused by one mechanism (e.g., spikes caused by electrical interference) from PSD artifacts caused by other mechanisms (e.g., random effects that cause roughness). This can be very similar to the noise removal described above, accomplished by identifying the different frequency characteristics of the different mechanisms.

[0177] As mentioned above, white noise (or pink noise) can be separated from the true (unbiased) roughness PSD because the frequency characteristics of the noise (flat or nearly flat at high frequencies) are very different from the frequency characteristics of the true roughness (a power-law reduction at high frequencies). Similarly, these so-called spikes in the PSD have frequency characteristics very different from the frequency characteristics of the characteristic roughness itself. In particular, a so-called spike has a high amplitude over a very narrow frequency range.

[0178] A procedure for detecting and removing spikes will now be described. First, a “spik” can be defined as a frequency response that rises and falls within a frequency range below a threshold (“critical range”) and has a height above a threshold (“critical height”).

[0179] Next, a baseline can be established as the best estimate of the PSD in the absence of the spike. For example, the critical range for spike detection can be set as three frequency increments in the PSD data (which is typically sampled at a fixed frequency increment). Other critical ranges are also possible. A baseline can be determined by smoothly connecting PSD values ​​spaced apart from the critical range plus an increment (e.g., using a straight line on a linear or logarithmic scale, or by using a model for the expected PSD characteristics). This baseline is then subtracted from the actual PSD data within this critical range to obtain an estimate of the non-baseline PSD characteristics within this frequency range. If the non-baseline PSD characteristics rise to a value greater than the critical height (expressed as an absolute value or a multiple of the baseline PSD value), a spike has been identified. To remove the spike, the calculated baseline characteristics can be used instead of the actual PSD values ​​within the critical range. If desired, the spike search can cover the entire PSD frequency range.

[0180] The critical range can be selected in such a way that it only detects (and may remove) spikes that occur due to a specific type of mechanism. For example, interference at exactly a single frequency is likely to cause a spike in the PSD, which is at most two frequency increments wide (because the spike is unlikely to be at a frequency that exactly coincides with the sampling frequency of the PSD). In detecting such "single-frequency" interference events, a critical range of two to three frequency increments wide would be effective. A wider critical range would detect other interference events across a wider frequency band.

[0181] The threshold height can also be adjusted according to the mechanism to be detected. However, the minimum threshold height is also a function of the overall noise in the PSD. Since a PSD is, by definition, a measurement of randomness in a random, coarse sample, PSD measurements are inherently noisy. It is well known that the PSD of a single measured feature has 100% statistical uncertainty (1 standard deviation). In other words, for a measurement of a single feature, the statistical uncertainty in any given PSD value at any given frequency is 100%. For this reason, many features are usually measured and averaged together, and thus the uncertainty in the PSD can be reduced by one square root of the number of features being measured.

[0182] However, for any given quantity of features being measured and averaged, the PSD will have an inherent statistical uncertainty in terms of sample size. The critical height for spike detection should be chosen to be significantly higher than the inherent noise level of the PSD. Otherwise, spike detection will often be triggered by noise in the PSD data rather than by the physical spike. Alternatively, the critical height can be chosen to be a multiple (e.g., 5 times) of the measured or calculated PSD noise.

[0183] Figure 25A shows several PSDs (linewidth roughness (LWR PSD 2502), line edge roughness (LER PSD 2504), and pattern setup roughness (PPR PSD 2506) exhibiting several high-frequency spikes (spiking artifacts 2507). Figure 25B shows the same PSDs (e.g., LWR PSD 2502 is LWR PSD 2508, LER PSD 2504 is LER PSD 2510, and PPR PSD 2506 is PPR PSD 2512), where the spikes are removed using the procedure outlined in the previous paragraphs. For this removal, the critical range is set to three frequency increments, and the critical height is set to three times the baseline PSD value. Effective spike removal is achieved using these settings.

[0184] Figures 27A and 27B illustrate another scenario of spike removal, this time for mid-frequency spikes. Figure 27A on the left shows the PSD (biased and unbiased) before spike removal. The presence of the spikes has a detrimental effect on modeling the PSD and extracting the measured PSD values. Figure 27B on the right shows the same PSD, where the spikes are removed using the procedure outlined in the previous paragraphs. For this removal, the critical range is set to three frequency increments, and the critical height is set to three times the baseline PSD value. Effective spike removal is achieved using these settings. The resulting PSD model and PSD measurements more accurately reflect the characteristic roughness PSD properties, excluding the mechanisms causing the spikes.

[0185] An alternative procedure for removing spikes will now be described. Spikes can be removed from a PSD by passing it through a low-pass filter. Using well-known techniques, the PSD can be Fourier transformed, multiplied by a low-pass frequency filter, and then subjected to an inverse Fourier transform. The cutoff frequency of the low-pass filter can be set to filter out only spikes narrower than a predetermined limit. Other low-pass filtering methods known in the art can also be applied.

[0186] Other methods for detecting and removing spikes based on the different frequency characteristics of a spike compared to the more slowly changing true roughness PSD will be known to those skilled in the art.

[0187] Referring to Figure 7, the information processing system (IHS 750) can be modified to include the detection and / or removal of spikes utilizing one of the methods described herein. Information regarding each detected spike, such as its center frequency, amplitude, area, and / or width, can be recorded and output to the output device 770. This information may be part of a process that includes mechanisms for identifying the root cause of the spike formation and thus can help reduce or eliminate such root cause.

[0188] 11. Detection and measurement of PSD bulges

[0189] Other phenomena may cause a "bulge" characteristic in the PSD, which originally had the typical shape shown in Figure 3. This bulge generally occurs at relatively low frequencies. These bulges are distinguished from a pulse by covering a relatively wide frequency range, compared to the narrow frequency limitation of a pulse. Figures 28A and 28B show two examples of this so-called bulge characteristic in a PSD, labeled as Bulge Type I and Bulge Type II.

[0190] Type I bulge (Fig. 28A) is a large rise in the low-frequency PSD characteristics, extending beyond the flat low-frequency region typically considered characteristic of the PSD(0). Several mechanisms can cause this bulge, such as the presence of mask roughness, which is subsequently transferred to the wafer during a lithography step. Uncompensated field distortion in the imaging tool used to capture the image being measured can also cause this type of bulge. Other mechanisms are also possible.

[0191] Type II bulges (Fig. 28B) occur at low to medium frequencies, such that PSD characteristics at frequencies above and below the bulge are as expected (e.g., as seen in Fig. 3). When this type of PSD bulge is present in the line edge roughness PSD but not in the line width roughness PSD, the effect is sometimes referred to as a "wiggle" because it can be a significant wiggle in the features of the image. This wiggle can be caused, for example, by stress or tension in the film used to form the feature. Lithography and subtractive etching of the film used to form the feature may relieve stress, thus allowing the remaining film to wiggle. Other mechanisms that cause wiggles are also possible.

[0192] Bulges in the PSD, such as white noise and spikes, are thought to occur through a mechanism that separates them from the random mechanisms that generate the rest of the PSD. Therefore, it is desirable to separate the effect of the bulges from the rest of the PSD. It is possible to detect and remove bulges using a procedure similar to spike detection and removal. However, this method becomes problematic when the width of the bulge is large, as defining a baseline PSD characteristic over a large frequency range is difficult. While the large frequency range of the bulge indicates that distinguishing between bulges and spikes is possible, it also suggests that different procedures for detecting and measuring bulges may be necessary.

[0193] One technique for detecting, measuring, and removing bumps involves the use of a model for the bump. For example, white noise and pink noise, the bump model is directly added to a typical PSD with the characteristic roughness. Therefore, the bump model can be fitted to the PSD simultaneously with a typical PSD model that does not include bump characteristics.

[0194] A useful form for a bulge model is given in the following Equation 10: (10)

[0195] Where A is the amplitude of the bulge, fc is the center frequency of the bulge, and σw is the width of the bulge. For a type I bulge (Fig. 28A), the center frequency can be zero. Other models can also be used. Alternative parameterizations of the model can also be used, such as the area of ​​the bulge and the center frequency.

[0196] As determined, for example, from the best-fit model, the area of ​​the bulge above the baseline PSD is a useful measure of the magnitude of the phenomenon causing the bulge. For example, in the case of oscillation (an example of bulge type II, Figure 28B), the area represents the variation of the oscillation added to the variation caused by random roughness. In other words, this method for bulge detection and measurement allows the total variation of the feature to be separated into an oscillation variation, plus a random roughness variation.

[0197] Referring to Figure 7, the IHS 750 can be modified to include the detection and / or removal of bulges utilizing one of the methods described herein. Information about each detected bulge, such as its center frequency, amplitude, area, and / or width, can be recorded and output to the output device 770. This information can be used to identify the root cause of the bulge formation and thus can help reduce or eliminate such root cause mechanisms. By subtracting the bulge characteristics from the total PSD, the remaining PSD can be characterized (e.g., using parameters such as PSD(0), correlation length, and roughness index), thus this remaining PSD more accurately reflects the mechanism that generates the PSD that eliminates the bulge mechanism.

[0198] Referring now to FIG30, a method 3000 for detecting unwanted spikes in a PSD dataset and for removing examples of spikes in a PSD dataset is depicted. The method 3000 begins (block 3002) and utilizes an imaging device to generate a set of one or more images, each image in the set containing an instance of a feature within a different pattern structure, each image containing measured line scan information corresponding to the pattern structure including noise (block 3004). The method then proceeds to detecting the edges of the feature within the pattern structure of each image in the set without filtering the images (block 3006) and generating a power spectral density (PSD) dataset representing the geometric information of the feature corresponding to the edge detection measurements of the images in the set (block 3008). If desired, an unbiased PSD dataset can be generated from the biased PSD dataset by subtracting SEM noise. Next, the method defines a critical range and a critical height (block 3010), and generates a baseline for a portion of the PSD dataset by smoothly connecting a first PSD value to a second PSD value of that portion of the PSD dataset, wherein the first PSD value and the second PSD value are separated by the critical range (block 3012). It is determined that a difference between a third PSD value of that portion of the PSD dataset and the baseline is greater than a critical height (block 3014), and the portion of the PSD dataset is replaced with the baseline for that portion of the PSD dataset (block 3016). The method then ends (block 3018).

[0199] Referring now to Figure 31, a method 3100 for modeling an example of a bulge in a PSD dataset is depicted. The method 3100 begins (block 3102) and utilizes an imaging device to generate a set of one or more images, each image in the set containing an instance of a feature within a different pattern structure, each image containing measured line scan information corresponding to the pattern structure including noise (block 3104). The method then proceeds to detecting the edges of the feature within the pattern structure of each image in the set without filtering the images (block 3106) and generating a biased power spectral density (PSD) dataset representing the feature geometry information corresponding to the edge detection measurements of the images in the set (block 3108). If desired, an unbiased PSD dataset can be created from the biased PSD dataset by subtracting SEM noise. A first bulge is evaluated in the PSD dataset to generate a bulge model (block 3110); and a typical PSD model and the bulge model are fitted to the PSD dataset to create a best-fit model (block 3112). The method then ends (block 3114).

[0200] The flowcharts of Figures 30 and 31 include steps that can be performed using the edge detection system 700 depicted in Figure 7. These steps include some that can be performed by the SEM 701, and others that can be performed by the IHS 750 and its included processor 755 and storage 760, as described in detail herein. Instructions can be stored in storage 760, and when executed by the processor, they cause the processor to perform the methods disclosed herein and described by the flowcharts of Figures 30 and 31 in a manner similar to other instructions stored in storage 760 that implement the reverse line scan model measurement tool 765 described herein.

[0201] 12. The impact of pixel size and magnification

[0202] Regarding the pixel size and magnification used in SEM 701, Figures 22A and 22B respectively illustrate the bias and unbiased power spectral density (PSD) of a 16nm line and gap pattern for different magnifications and pixel sizes, assuming a white noise model. For a given number of frames, changing the pixel size changes the electron dose per unit wafer area and the noise in the SEM image. Under these conditions, the biased LWR changes by 0.63nm (14%), while the unbiased LWR changes by only 0.07nm (2%). The unbiased LWR is substantially unaffected by these measurement tool settings. Similar results were obtained for measurements of LER and PPR.

[0203] Figures 22A and 22B illustrate the power spectral density as a function of pixel size and magnification. More specifically, Figure 22A shows the LWR PSD with the aforementioned bias, and Figure 22B shows the unbiased LWR PSD after noise has been measured and subtracted. The SEM conditions used for these results were a landing energy of 500 eV, 3 images per condition, and 16 nm photoresist lines and gaps.

[0204] Table 3 below shows the measured PSD parameters for the PSDs shown in Figures 22A and 22B.

[0205] Table 3

[0206] The biased and unbiased 3σLWR (nm) measurements are a function of pixel size and magnification. 0.8nm pixel 82kX 0.8nm pixel 164kX 0.5nm pixel 130kX 0.5nm pixel 264kX 0.37nm pixel 180kX LWR of the bias (3-standard deviation, nm) 5.10 4.99 4.67 4.61 4.47 Unbiased LWR (3-standard deviation, nm) 3.66 3.65 3.70 3.67 3.63 Unbiased LWR PSD(0) (nm 3) 15.95 16.18 17.2 16.25 16.35 LWR correlation length (nm) 5.08 5.05 5.31 5.11 5.38

[0207] It has been found that the difference between the biased and unbiased LWRs is not fixed, but varies with the measurement tool settings, feature size, and process. Similarly, the ratio between the biased and unbiased LWRs also varies with the measurement tool settings, feature size, and process. Table 4 below shows the difference and ratio of the biased to the unbiased LWRs for various conditions. For these conditions, the ratio of the biased to the unbiased LWRs varies from 1.09 to 1.66. In this specific example, the difference between the biased and unbiased LWRs changes from 0.32 nm to 2.19 nm.

[0208] Table 4

[0209] The relationship between LWR with and without deviation for various processes. process 3σ LWR: Deviation-biased / Unbiased 3σ LWR (nm): Biased – Unbiased 193i micro-lithography, 84nm pitch, 500V, 512 rectangular pixels 1.20 0.76 193i etching, 84nm pitch, 800V, 512 rectangular pixels 1.14 0.43 EUV lithography, 32nm pixel pitch, 500V, 2048 0.8nm pixel. 1.39 1.44 EUV lithography, 32nm pixel pitch, 500V, 1024 0.8nm pixels 1.37 1.34 EUV lithography, 32nm pixel pitch, 500V, 2048 0.5nm pixel. 1.26 0.97 EUV lithography, 32nm pixel pitch, 500V, 1024 0.5nm pixels 1.26 0.94 EUV lithography, 32nm pixel pitch, 500V, 1024 0.37nm pixels 1.23 0.84 EUV lithography, 36nm pixel pitch, 500V, 1024 0.8nm pixel resolution 1.52 1.86 EUV lithography, 32nm pixel pitch, 500V, 1024 rectangular pixels 1.66 2.19 EUV etching, 32nm pitch, 800V, 1024 rectangular pixels 1.09 0.32

[0210] 13. Implementation methods for edge detection

[0211] Figure 23 is a flowchart depicting a representative overall process flow of the disclosed SEM edge detection system for detecting the edges of a pattern structure. For discussion purposes, the process described in the flowchart of Figure 23 is the sample 2400 applied to Figure 24A. Sample 2400 is a pattern structure, which may also be referred to as pattern structure 2400. The flowchart of Figure 23 includes steps performed by a reverse line scan model measurement tool 765 to determine the edges of the pattern structure.

[0212] The process flow begins at the start block 2300 of Figure 23. As can be seen in Figure 7, the IHS 750 is coupled to the SEM 701 to receive SEM line scan image information from the SEM 701. The IHS 750 includes a processor 755 and a storage unit 760 coupled thereto. The storage unit 760 may include volatile system memory and non-volatile permanent memory, such as a hard disk drive, solid-state storage device (SSD), and the like, which permanently stores applications and other information. The storage unit 760 stores the reverse line scan model (ILM) measurement tool 765 disclosed herein and described by the flowchart of Figure 23. The SEM 701 includes a controller (not shown) that instructs the IHS 750 to perform image acquisition on the pattern structure 800 and to provide line scan information from the SEM 701 to the IHS 750.

[0213] According to block 2305, SEM 701 transmits an SEM image of pattern structure 800 to IHS 750, and IHS 750 loads this SEM image into system memory within storage 760 in response. According to block 2310, IHS 750 preprocesses the pattern structure image from SEM 701. For example, this preprocessing of the loaded SEM image may include adjusting grayscale values ​​and subtracting background tilt of intensity levels. Optionally, according to block 2315, IHS 750 may perform filtering on the loaded image, although this is generally not preferred.

[0214] In a pattern structure of vertical lines and gaps, such as that seen in pattern structure 2400 of Figure 24A, according to block 2320, the reverse line scan model measurement tool 765 vertically averages along the axis of symmetry to produce an average line scan. An average line scan can be a grayscale value as a function of a horizontal position, where all vertical pixels have been averaged together. This averaging removes most of the SEM noise contained in the SEM image and produces a line scan, which further represents the physical process of producing a line scan without noise. Figure 24B shows a single line scan at a Y pixel position. Figure 24C shows an averaged line scan, which is produced by averaging over all Y pixels.

[0215] Although the examples shown here pertain to vertical lines and gaps, any pattern with an axis of symmetry can be treated in this way to produce an average line scan. For example, long lines, long gaps, or long isolated edges can be treated in this way whenever the length of the lines is sufficient to allow for adequate averaging. Connecting holes or pillars with circular or elliptical symmetry can also be averaged in a radial direction to produce an average line scan.

[0216] According to block 2325, tool 765 calibrates the reverse line scan model to the average line scan obtained in the manner described above. It should be noted that the line scan model contains two types of parameters: 1) parameters determined by the properties of the material and the SEM, and 2) parameters determined by the geometry of the features on the sample. Tool 765 can calibrate all of these parameters. According to block 2325, tool 765 finds the best fit of the model to the average line scan of Figure 24C. The values ​​of the best-fit parameters of the model are then the calibrated values.

[0217] The calibrated model is applied to a single-line scan as shown in Figure 24B. The best fit of the model to the single-line scan of Figure 24B is determined; however, in this example, the reverse-line scan model measurement tool 765 keeps all parameters related to the material and the SEM imaging tool fixed. In this scenario, tool 765 only changes the geometric parameters related to the characteristics of the pattern structure to find the best fit of the calibrated model to the single-line scan.

[0218] In a simplified scenario, the only parameter changed in block 2330 would be the position of the feature's edge. In one embodiment, it is assumed that the vertical dimension of the feature has a preset thickness, and only the position of the feature's edge is variable. Next, according to block 2330, the calibrated reverse line scan model is fitted to a single horizontal section line passing through each 2D image of the feature. We obtain the pixels of the top horizontal column, and then the pixels of the next column below the next pixel, and then the pixels of the next horizontal column below, and so on. An example of this single line scan is shown in Figure 24B. The resulting best-fit edge position is the detected edge.

[0219] After the edges of the features described above are detected, tool 765 may detect that the sample was slightly rotated during image acquisition, resulting in parallel skewed lines (i.e., imperfectly vertical lines). This skew or rotation may contribute to the inaccuracy of the detected edges by altering the average line scan and thus the calibrated ILM. Image rotation can be detected by fitting all edges in the image to a set of parallel lines and determining their slope relative to vertical. If the slope is sufficiently different from the vertical case, the rotation should be removed. A possible criterion would be comparing the pixel positions of the best-fit lines at the top and bottom of the image. If these pixel positions differ by a certain threshold, such as two pixels, the image rotation is considered sufficiently large, and its removal is necessary.

[0220] If such tilt / rotation is detected, according to block 2335, the previous calibration is considered a first pass calibration, and the calibration is repeated. More specifically, according to block 2345, if such tilt / rotation is detected, the rotation is subtracted by shifting certain columns of pixels to bring the edge to a vertical alignment, and a new average line scan is calculated. The calibration of the model is then repeated according to blocks 2350 and 2325. According to block 2330, another fitting is also performed. Finally, tool 765 outputs geometric feature information (e.g., edge position) that describes the geometry corresponding to the features of the line scan image information provided to tool 765.

[0221] Similar to image rotation, the roughness of the feature itself contributes inaccuracies to the ILM calibration. Optionally, after a first edge detection, the pixels in each column can be shifted to subtract not only image rotation but also the feature roughness. The final result of shifting the pixels in each column is a vertical edge, where the change in edge position from a perfect vertical line is less than one pixel. These shifted pixel columns can then be vertically averaged to produce a more accurate average line scan for ILM calibration.

[0222] In practical implementation, the IHS 750 may include an interface 757, or other user interface, coupled between the processor 755 and an output device 770, such as a display or printer, so that the user can observe characteristic edges determined by the reverse line scan model measurement tool 765. The interface 757 may be a drawing interface, a printer interface, a network interface, or other hardware interface suitable for a specific type of output device 770.

[0223] Although the above embodiments are based on measurements of structures visible on semiconductor wafers, i.e., as used by manufacturers of semiconductor devices, the present invention is not limited to these applications. This disclosure can be usefully employed to measure the roughness of characteristic edges visible on flat panel displays, microelectromechanical systems, microfluidic systems, optical waveguides, photonic devices, and other electronic, optical, or mechanical devices. Furthermore, the present invention can be used to measure characteristic edge features of, for example, naturally occurring structures of crystals or minerals, or artificial structures such as nanoparticles or other nanostructures. Moreover, the present invention can also be used to measure characteristic edge features of biological samples.

[0224] Although the above embodiments refer to measurements using a scanning electron microscope, the present invention is not limited to this imaging tool. Other imaging tools, such as optical microscopes, stimulated emission and depletion (STED) microscopes, X-ray microscopes, transmission electron microscopes (TEM), focused ion beam microscopes, and helium ion microscopes, can also be used. Other types of microscopes, such as scanning probe microscopes (atomic force microscopes) (AFM) and scanning near-field optical microscopes (SNOM), can also be used.

[0225] 14. Methods for using conventional techniques to determine process windows

[0226] In lithography, two key variables are frequently adjusted to maintain the final printed characteristics: exposure dose (also known as exposure energy, which is the product of light intensity and exposure time) and focal length (often described as the position of the optimal focal plane of the projected image relative to the top surface of the photoresist when coated on the wafer). These process variables can be altered using lithography projection imaging tools (such as steppers, scanners, or step-scan tools) employed to print these characteristics. Other lithography techniques, such as direct-write patterning, proximity lithography, and electron beam lithography, also allow for adjustment of exposure dose and focal length, or equivalents.

[0227] To achieve optimal lithography results, it is desirable to set the exposure dose and focal length of the lithography tool to optimal values, sometimes referred to as optimal dose and optimal focal length. The meaning of "optimal" can vary depending on the objectives of the lithography process. A common objective would be to ensure that the average feature size of a specified set of printed patterns on one or more wafers matches a target value for that feature size within a certain tolerance. Another objective would be to minimize the variation in feature size across a set of features. Yet another objective would be to improve the pattern fidelity of the printed patterns. Still another objective would be to minimize the sensitivity of the printed feature size or fidelity across a set of features to process variations.

[0228] The feature set to be inspected may include features printed at different points in the imaging field (or, in the case of scanning lithography, different points within the scanner slit area), different points across the manufactured wafer, across the wafer, and different points across different wafers or different batches of wafers. The feature set to be inspected may also include features printed at different times. The feature set to be inspected may also include different feature types, features with different proximity relative to other features, and features with different target feature sizes.

[0229] In many lithography processes, feature size varies monotonically with exposure dose. For example, over a small range of doses, the feature size can vary approximately linearly with the dose. For some processes, the feature size can be approximately proportional to one-fifth of the exposure dose. With respect to focal length, the feature size typically varies approximately squared with the focal length. Furthermore, focal length and dose largely interact to create variations in the printed pattern. The effect of dose on a feature depends on the focal length setting of the exposure tool, and the effect of focal length on a feature depends on the exposure dose setting of the exposure tool.

[0230] The characteristics depicting the effects of focal length and exposure dose on printed patterns are largely achieved through the use of a focus-exposure matrix (FEM). Explanations of the FEM can be found in prior art, for example in the textbook "Fundamentals of Optical Lithographics: The Science of Microfabrication" by Chris A. Mack, John Wiley & Sons (London: 2007).

[0231] Generally, depth of focus (DOF) can be thought of as the range of focal length errors that a process can tolerate while still providing acceptable lithography results. A change in focal length will have two main effects on the final lithography result: changes in the photoresist profile (including its dimensions) and changes in the process's sensitivity to other processing errors. Typically, the photoresist profile is described using parameters such as the linewidth (or critical dimension CD), edge setting error, sidewall angle of the profile, final height of the feature, line edge or linewidth roughness, and other measures known in the art. These parameters, along with variations in focal length, can be determined using various measurement methods for any given set of conditions. For example, CD can be measured using a scanning electron microscope.

[0232] Furthermore, when an image is out of focus, the process becomes more sensitive to changes in other processing variables, such as exposure dose, post-exposure baking time and temperature, development time, developer concentration and temperature, underlying film stacking properties, and so on. Exposure dose is typically chosen to represent these other process responses. The effect of focal length on the sensitivity of patterning to exposure dose can be characterized by varying both exposure dose and focal length, each set within a certain range, and measuring characteristics of the printed pattern, such as CD, line width roughness, etc.

[0233] One way to show the effect of the combination of focal length and exposure dose on CD is using a so-called Poisson plot, as can be seen in Figure 39A. Not shown in Figure 39A is experimental error (or experimental uncertainty), which is always present in the experimental data. Experimental error / uncertainty (often expressed as a multiple of the standard error of the measured value, for example, twice the standard error) can be one to several percentages of the CD at optimal focal length and exposure, but when out of focus, the error can be much higher. To better analyze focal length-exposure CD data, a common approach in this technique is to fit the data to a reasonable empirical equation to reduce data noise and eliminate fly-offs (also known as outliers). A drawback of this method is that the choice of the empirical expression adds a degree of arbitrariness to the resulting analysis.

[0234] The output of a function for two inputs can be plotted in several different ways. For example, the Poisson curve can also be depicted as an exposure latitude curve (linewidth relative to exposure dose) for different focal length settings. Another very useful way to plot this two-dimensional dataset is as a profile plot, i.e., a profile with fixed linewidths relative to focal length and exposure (Figure 39B). For noisy experimental data, it is also common to plot a smoothed version of the data in these profile plots. For example, as mentioned above, curve fitting can be used to smooth the data, and then the profile is drawn based on the plotted curve fit, rather than drawing the profile from the original data.

[0235] The visualization of data in the form of contour plots is particularly useful for establishing the limits of exposure and focal length that allow the final image to conform to certain specifications. Instead of drawing the entire contour of a fixed CD, we can draw only two CDs, corresponding to the outer limits of acceptability, i.e., the smallest and largest CDs permissible according to CD specifications. Due to the nature of contour plots, other variables can also be plotted on the same plot. Figure 39C shows an example of drawing the contour of a CD (nominal + / - 10%), with an 80-degree sidewall angle and 10% photoresist loss, all on the same plot. The result is a process window, i.e., the area where the final printed image remains within all applicable specifications in terms of focal length and exposure.

[0236] Many different measurements can be combined into a single process window. For instances where random variations are significant, such as feature size and lithography processes, stochastically related results can be plotted on the outline of the process window. For example, linewidth roughness can be plotted using a single specification, i.e., the maximum permissible LWR. Defect rate can also be used as a stochastic metric.

[0237] The focal length-exposure process window is useful because it shows how exposure and focal length work together to affect linewidth and / or other metrics used to evaluate print results. The process window can be thought of as a process function, i.e., how the process responds to changes in focal length and exposure. Analysis of the sources of error in focal length and exposure within a given process will establish process requirements. If the process function exceeds these requirements, the yield of the device being manufactured will be high. However, if the process requirements are too large to fit the process function, yield or device performance may suffer.

[0238] It is often useful to assess the maximum range of focal length and exposure that can fit within the process window (in other words, the maximum process requirements). A simple way to investigate this problem is to graphically represent the errors in focal length and exposure as a rectangle on the same graph for the process window. The width of the rectangle represents the built-in focal length error of the process, and the height represents the built-in dose error. The problem then becomes finding the largest rectangle that fits within the process window.

[0239] There may be many possible rectangles with different widths and heights that are 'largest', meaning they cannot become larger in any direction without extending beyond the process window (Figure 40A). Each largest rectangle represents a possible trade-off between the tolerance for focal length error and the tolerance for exposure error. If the exposure error is minimized, a larger DOF can be obtained. Similarly, if the focal length error is small, the exposure latitude can be improved. The result is a trade-off between exposure latitude and DOF.

[0240] If all focal length and exposure errors are systematic, then a graphical (or geometric) representation of those errors would be a rectangle. The width and height would represent the total range of the individual errors. However, if the errors are randomly distributed, then a probability distribution function would be needed to describe them. It is commonly assumed that random errors in exposure and focal length are caused by the summation of many small error sources; therefore, according to the central limit theorem, the overall probability distribution for focal length and exposure would be approximately Gaussian (a normal distribution).

[0241] To graphically represent focal length and exposure errors, we should describe a surface with fixed probabilities of occurrence. All errors in focal length and exposure within this surface will have a probability of occurrence greater than the established cutoff frequency. For a bigaussian distribution (a Gaussian distribution for two independent variables), the surface with fixed probabilities is an ellipse (Figure 40B).

[0242] Using a rectangle for systematic errors or an ellipse for random errors, the magnitude of the tolerable error for a given process window can be estimated using this geometric method. Taking the rectangle as an example, we can find the largest rectangle that will fit within the process window. Figure 41 shows the analysis of the process window, where each largest rectangle is identified, and its height (the exposure latitude) is plotted relative to its width (depth of focus). Similarly, assuming Gaussian errors in focal length and exposure, each largest ellipse that fits within the process window can be identified. The horizontal width of the ellipse can represent six standard deviations of error in focal length (a change relative to the optimal focal length plus or minus three standard deviations), while the vertical height of the ellipse will give six standard deviations of error in exposure. Plotting the height of all the largest ellipses relative to their widths gives the second curve of exposure latitude versus DOF ​​in Figure 41.

[0243] The definition of depth of focus naturally leads to the determination of the optimal focal length and optimal exposure. The DOF value corresponding to a point on the exposure latitude relative to the DOF curve corresponds to the largest rectangle or ellipse fitted within the process window. The center of this rectangle or ellipse will then correspond to the optimal focal length and exposure for the desired operating point. Knowing the optimal focal length and dosage values ​​is important for being able to use the entire process window. If the process focal length and dosage settings deviate from these optimal values, the tolerable range of focal length and dosage errors will be reduced.

[0244] While the results above all describe the focal length and exposure response of a single important feature, in reality, several masking features must be printed simultaneously. For example, features with different nominal sizes and spacings, or different proximity to other features, may exist within the same design. In such cases, the overall process window will be an overlap of process windows for each feature size or type considered. The focal length and dosage settings within these overlapping process windows will allow each feature type and / or size to meet specifications. More important than the DOF of each individual feature is the DOF of the overlapping features.

[0245] Just as in Figure 39C multiple profile measurements are overlapped to form an overlapping process window, process windows from different features can be overlapped to determine which DOFs are used to print multiple features simultaneously. Figure 42 shows such an example for a line / gap pattern with two different spacings. Ideally, process windows for all important feature sizes and spacings would be overlapped.

[0246] In patterning, a systematic variation of a field position as a function can also be taken into account using overlapping process windows. If the same feature is printed at different points in the lithography tool's image field (typically the center and four corners of the field are sufficient), process windows can be overlapped to create a usable process window for that feature. The resulting depth of focus is sometimes referred to as the usable depth of focus (UDOF).

[0247] FEM analysis can also be utilized in other ways. One possible output of process window analysis is the isofocus deviation. Generally, there is an exposure dose that minimizes the sensitivity of a printing characteristic to changes in focal length. This dose is called the isofocus dose. At this dose, the printed CD will generally differ from the target or desired CD. This difference is called the isofocus deviation. The process window can be used to evaluate this isofocus deviation.

[0248] The conventional geometric methods used for process window determination and analysis, as described above, have several problems. First, measurement errors or measurement uncertainties are not considered. The outlines drawn in Figures 39C or 40A depict clearly defined boundaries, separating the area within the process window from the area outside. This clear boundary creates a hard cutoff between the area considered "good" (within the process window) and the area considered "bad" (outside the process window). In reality, due to measurement uncertainties, the boundary between good and bad is blurred.

[0249] A second problem with the conventional geometric method is that the measurement data needs to be curve-fitted or smoothed before the process window is constructed. Even a single anomalous data point near the edge of the process window can cause a large deviation in the contour position (Figure 43). This can result in a very significant difference in the DOF determined from this process window, and / or a large difference in the optimal focal length and exposure.

[0250] The use of smoothing or curve fitting on the original data increases the degree of arbitrariness in the analysis of the data. There is no prior correct amount of smoothing or a correct fitting function to use, and therefore different choices produce different results.

[0251] A third problem is the choice between rectangles, ellipses, or some other geometry to represent the probability of focal length and exposure dose errors related to optimal focal length and dose values. As shown in Figure 41, different choices produce different results. Furthermore, using geometry to represent these probabilities and then finding the largest shape that fits within the process window indicates that only a few points in the process window shape affect the results. As shown in Figure 40B, the inscribed ellipses and rectangles only touch the process window at a few points. This makes the size of those inscribed shapes particularly sensitive to measurement errors that may only affect those few points of the contour-based process window.

[0252] All of the above problems are exacerbated when there are more measures of the size, fidelity, or roughness of the overlapping patterns, or when the overlapping comes from process windows with different characteristics.

[0253] One consequence of geometric process window analysis is inaccurate and / or imprecise measurement of exposure latitude and depth of focus. Inaccurate or imprecise measurement of exposure latitude or depth of focus results in poor optimization of the patterning process. Typically, material selection (different photoresists, different underlying layers beneath the photoresist, etc.) is made based on (or taking into account) which material, for example, provides the maximum depth of focus. Furthermore, process tooling settings, such as the size and shape of the illumination used for optical projection tools, are taken into account the resulting depth of focus.

[0254] Optical proximity correction (OPC) is used to modify the wafer design when it is represented on a photomask to improve the fidelity of the final printed pattern. Sometimes, this OPC takes into account the impact of these photomask modifications on the process window. Therefore, inaccurate or imprecise judgments or analyses of the process window can have a detrimental effect on the OPC results.

[0255] Another consequence of geometric process window analysis is inaccurate and / or imprecise measurement of optimal focal length and optimal exposure. The outputs of optimal focal length and optimal exposure from the process window analysis can be used during manufacturing to control the lithography tool. The measured values ​​of optimal focal length and dose are transmitted to the lithography tool and used to adjust the tool's dose and focal length settings for subsequent use in manufacturing product wafers. Therefore, inaccurate and / or imprecise measurement of optimal focal length and optimal exposure can negatively impact device yield or device performance.

[0256] Furthermore, the exposure settings of a lithography tool can affect its throughput. Generally, a lower exposure dose results in a higher throughput for the exposure tool. For this reason, it is desirable to reduce the exposure dose as much as possible while still maintaining sufficient exposure latitude and depth of focus as determined by the process window analysis. Inaccurate and / or imprecise measurements of the process window make it difficult to achieve such improvements in throughput without compromising device yield or performance.

[0257] Another application of process window analysis is for process monitoring. Optimal focal length, optimal exposure, exposure latitude, and depth of focus can all be monitored over time using standard statistical techniques such as trend tabulation or statistical process control (SPC). The current characteristics of the tabulated variables can be flagged as deviations from their historical characteristics for further investigation or other actions. Inaccuracies and / or imprecise measurements of the process window and its associated measurements can reduce the effectiveness of trend tabulation or other forms of process control.

[0258] Furthermore, the conventional geometric process window method does not generate uncertainty estimates for various analytical outputs, such as optimal focal length, optimal exposure, depth of focus, and exposure latitude. Without uncertainty estimates, the usefulness of these outputs is reduced. For example, if a change is greater than the uncertainty estimate for the optimal dose and / or focal length for the process window, then controlling the dose and focal length settings of a scanner during manufacturing using values ​​that are the optimal dose and focal length determined from the process window analysis should only result in that change in the scanner settings.

[0259] For these and other reasons, it is desirable to find a different method for process window measurement and analysis that addresses one or more of the problems related to the conventional process window methods.

[0260] 15. Probability Process Window

[0261] A novel method embodiment for process window measurement and analysis, and its use in process optimization and control, will now be described. This novel method embodiment, referred to as the Probabilistic Process Window (PPW), addresses many problems of conventional techniques (such as the geometric process window) as described above. This PPW method can be used when two or more interacting process variables are changed to determine their impact on one or more outputs. In the main examples used below, two process variables will be discussed. Furthermore, the main examples below will utilize two process variables: exposure dose and focal length during the lithography patterning process step. However, the PPW method is generally sufficient to handle more than two process variables related to lithography, etching, deposition, or other processing steps.

[0262] In some implementations, among other things, a probability process window is used to consider the uncertainty in the measurement to determine where the probability of an associated indication within a lithography process meets a specification requirement. For example, instead of the ILM measurement tool 765 (or an additional one), the system 700 may include a probability process window tool (not shown). A two-dimensional (2D) design of experiment (DoE) may include a table listing... The values ​​(possibly irregularly spaced) represent a first DoE factor, increasing in an ordered manner. This first DoE factor will be a process variable, intentionally altered to determine its impact on one or more outputs. The 2D DoE may also include a table of values. The value (which may be irregularly spaced) represents a second DoE factor, which increases in an ordered manner. This second DoE factor will also be a process variable, which is deliberately altered to determine its impact on one or more outputs.

[0263] The 2D DoE may also include a set of specifications. (It has a minimum and / or maximum acceptable value), which is applied to a process response or output. For example, in a lithography process, an output might be a critical dimension (CD) of a printed characteristic. A specification on this output would describe the minimum acceptable value for that output, and / or the maximum acceptable value for that output. For example, the specification on the CD could be a target (desired) value + / - 10%. For a target value of 20nm for the CD, the specifications (minimum and maximum, respectively) could be set to 18nm and 22nm.

[0264] For each specification For some points Furthermore, the 2D DoE may also include a z-value (a measurement result) and a standard error corresponding to that z-value (an expression for measurement uncertainty). In other words, the measurement data can be obtained through two methods... The index is represented by a three-dimensional array, one for the z-value and the other for the standard error. To determine a point... Within specifications, a process can be used to generate a probabilistic process window. In some implementations, the process may comprise two main steps. In a first step, each given z-value is actually within specifications. The probability of success is determined using the standard error (or other measurement of uncertainty) for that point, as further described below. In a second step, given... and Some errors, spanning the center of the field generated in the first step, at certain test points (x) A bivariate probability distribution (value) is applied to determine the probability that the test point is within the specification, as further described below.

[0265] The experimental part of PPW (Pressure Process Width) determination involves changing two or more process variables in a matrix. Two process variables (here referred to as x-inputs and y-inputs) are considered, such as exposure dose and focal length. Each of the exposure dose and focal length is varied within a certain range, for example, using a fixed step size for both dose and focal length. Variable step sizes for dose and focal length can also be used. The pattern is printed on one or more wafers using the input values ​​of this two-dimensional matrix. Those wafers are then measured to determine one or more measurement outputs (here referred to as z-outputs). For example, CD (Cutoff), unbiased roughness, defect rate, local CDU (Cutoff Duct Size), a measure of pattern shape or fidelity, or other measures of the process output can be measured.

[0266] In most cases, a measurement of, for example, CD output includes an estimate of the measurement uncertainty for that output. For example, a single SEM image of a wafer may contain, for example, 20 lines and gaps. In this case, it is common to generate the average CD as a measurement output, which is the desired output, i.e., the average of the CDs for each other line in the image. The standard error of the average can then be used as an estimate of the measurement uncertainty of the average CD. Other measures of the uncertainty of the average, as known in the field of statistics, can also be used. Sometimes a multiple of the standard error (e.g., 2 times) is used as an estimate of the uncertainty. Other estimates of the total measurement uncertainty can also be used.

[0267] Sometimes, for various reasons, one or more data points that are functions of the input values ​​may be missing from the output array. Therefore, before the first step in the PPW decision process, the missing data points can be filled in (with approximate values), for example, by interpolation. For example, Tables 5 and 6 below contain the measured values ​​with missing data points. Other methods for handling missing data points may also be employed.

[0268] Table 5

[0269] Moving average CD (Specification 1). x value = 1 x value = 2 x value = 3 x value = 4 x value = 5 y value = 10 20.8 22.2 23.6 25 26.9 y value = 9 20.6 21.9 23.4 24.8 26.7 y value = 8 20.4 21.6 24.6 26.5 y value = 7 20.2 21.3 23.2 24.4 26.3 y value = 6 20 twenty one twenty three 24.2 26

[0270] Table 6

[0271] Unbiased LER average (Specification 2). x value = 1 x value = 2 x value = 3 x value = 4 x value = 5 y value = 10 9 11 13 15 17 y value = 9 8 10 10.5 11 15 y value = 8 7 7.5 9 14 y value = 7 6 7 8 9 10 y value = 6 5 5.5 6 6.5 7

[0272] In the first step of the process, as many cells as possible are filled for each specification, for example, values ​​that can be determined by interpolation, to determine whether an output value conforms to its specification (in other words, the value is referred to as "within specification" or "in the specification"). In a first part of the first step of the process, for each measurement output (average z-value) and for the uncertainty of that output (e.g.) That is, the standard error of the average z-value), and for each specification s, the probability that the output is actually within the specification is determined. For example, we can assume that the distribution of the output follows a normal (i.e., Gaussian) distribution. Other probability distributions are also possible. The calculation of the probability that the output is actually within the specification will now be described.

[0273] Given an average output value The standard error of the average and a specification (Minimum and maximum specification values, for example) and We want to determine the average value of the measurements. The probability in the specification. For example, assuming the average value... The above is a Gaussian distribution, and the area under the normal curve can be... as well as Below, from to It is calculated so that it can be judged. The true value is The probability of being in the middle. The typical normal cumulative distribution function (CDF) is given in the following equation 11: normal distribution (11)

[0274] in It is a well-known error function. The definition of the error function is given in the following Equation 12: (12)

[0275] The probability that a z-value is within the specification can be determined using the following equation 13: (13)

[0276] If there is no largest specification value, the first term equals 1. Furthermore, if there is no smallest specification value, the second term equals 0. Figure 32 is an example illustrating the area under the probability density curve below which the measured value corresponds to the probability in the specification.

[0277] In the traditional process window approach, without considering the uncertainty of the measurement, an output value is either in or out of specification. In other words, a 1 has the probability of being an output that is in specification, while a 0 has the probability of being an output that is out of specification.

[0278] In the second part of the first step, the output is a probability within the entire specification range. The output of the first step may be referred to as a "probability process window." Given for each point (pair of input values)... of The probability of each point falling within all specifications is determined. For example, based on the assumption that each P is independent (in other words, the measurement uncertainty for one output response is independent of the measurement uncertainty for a second output response), all probabilities for all specifications are multiplied together, as given in Equation 14 below: (14)

[0279] After determining the probability of |s| cells being in the specification, the final result of the first step is the probability of one cell being in the specification. In some embodiments, the processor 755 of system 700 is configured to present one or more graphical elements of a graph on a user interface (e.g., on the output device 770) to display the plurality of probabilities. For example, Figure 33 is an example of a heatmap representing a final result of the first step. The outlines contained in the heatmap depicted in Figure 33 represent the conventional (geometric) process window and are drawn for comparative purposes. An alternative view of the three-dimensional final result heatmap is depicted in Figure 34.

[0280] In the second step of the process, using the probabilities from the grid in the first step, a bivariate probability distribution of the input values ​​is obtained using a certain average. and a certain error And is applied to the grid. The average This represents the process setpoint, that is, the nominal values ​​of the input variables x and y used in the process. The error... This represents the variation in the input variables present in the process, such as variations across the scanner field, across the wafer, across the die, or from wafer to wafer. Typically, for the purpose of generating the bivariate probability distribution, the two input variables x and y (e.g., focal length and exposure dose) can be considered independent variables, but this is not a requirement. Using a certain average... and a certain error The bivariate distribution represents the probability density that the two input variables x and y will have specific values.

[0281] In the first part of the second step, for each grid cell between points, at the center at a certain average... and a certain error The volume under a bivariate distribution is determined. Then, the determined volume is the output of a function weighted and fitted to the probability of the corner points of the current lattice cell generated in the first step of the process. For example, using a Gaussian distribution, the volume can be determined using the following Equation 14: (14)

[0282] Next, all the values ​​in the cells are summed to determine the average. as well as The overall probability. For example, all the values ​​in the lattice can be summed using the following equation 15: (15)

[0283] In the second part of the second step, the first part of the second step is repeated for different purposes. The value is used to determine the average probability of having the center at that point within the specification. For example, using the original grid from the first step depicted in Figures 33 and 34, Each value is determined, although there is no requirement. The values ​​are set to the values ​​of the original input data cells. Figure 35 shows the first part of the second step being repeated. Here is an example of a graph. Each square depicted in Figure 35 represents a bivariate Gaussian centered at that point. An alternative graph view of the graph depicted in Figure 35 is shown in Figure 36.

[0284] In a third step of the process, a standard nonlinear optimization algorithm (e.g., Nelder-Mead or Gauss-Newton) is used to optimize a given error. , determine the one with the highest probability This represents the "optimal" values ​​for the process settings of the input variables x and y. Here, the error is given. Built into the process, "optimal" will represent the process setting (the value). This is the highest-level characteristic produced in the specifications. For an FEM process window, this will be the optimal focal length and optimal exposure. Setting the lithography tool to use this focal length and exposure dosage will produce the best printing results.

[0285] In the fourth step of the process, one relatively The curve is generated. Used for The step size is selected. When When incremented, The method was adjusted, and the search method in the third step was repeatedly used to determine the method used for... The optimal value (where 'optimal value', for example, represents the lowest probability exceeding a certain cutoff frequency, such as a point of 99.73%). When there is no When the cutoff frequency standard is met, the increment is It was stopped. The determined points were plotted to produce the... relatively Curve. In some implementations, It focuses on depth, and It refers to exposure latitude. Figure 37 is an example. relatively An example of a curve. A traditional process window analysis can be based on geometry, finding the largest rectangle or ellipse that fits within the process window. A similar but more rigorous curve can be generated using the probabilistic process window, following the steps outlined above.

[0286] Once a probability process window is determined for a dataset with certain specifications, it can be combined with any number of other probability process windows, provided that the two or more input process variables are identical and have similar boundaries. These other probability process windows may have different underlying output values, feature types, and specifications, but are still combined due to the dimensionless nature of probability. To combine probability process windows, a test point on each window can be evaluated, and the resulting probabilities are multiplied together to determine the probability of a combination spanning the probability process windows.

[0287] Referring now to Figure 38, an exemplary method 3800 is proposed to generate a probabilistic process window that takes into account measurement uncertainty. Method 3800 begins (block 3802) and selects a first variable, which is represented on a first axis of a graph (3804). Then, method 3800 proceeds to select a second variable, which is represented on a second axis of a graph (block 3806). In some embodiments, the first variable and the second variable are associated with a stochastic process window. In some embodiments, the first variable includes the exposure dose, and the second variable includes the focal length of a scanning lithography process. In alternative embodiments, the first variable includes the etching time, and the second variable includes the wafer temperature. Many other combinations of process variables are possible.

[0288] Next, method 3800 proceeds (block 3808) to select at least one response variable (or output response variable) that is a function of the first variable and the second variable. These output response variables are measured as a function of the first and second variables. Each output response variable can be plotted as a function of the first and second variables. For each output response variable, a specification is set for a value of the output response that is considered acceptable.

[0289] Next, method 3800 proceeds to determining a measurement uncertainty for each of the output response variables (block 3810). Next, method 3800 proceeds (block 3812) to determine a plurality of probabilities, representing a plurality of indications related to a lithography process, whether these probabilities meet a plurality of indications for a specification requirement for each output response variable, based on a measurement of the one or more output response variables and the measurement uncertainty for the at least one output response variable (block 3810). The plurality of probabilities represent a process window. Next, method 3800 proceeds to configuring a lithography tool to manufacture a semiconductor device according to the process window.

[0290] In some implementations, a third input variable is selected. In some implementations, the third variable is temperature. Furthermore, based on a measurement that the output response is a function of the third variable combined with changes in the first and second variables, a second plurality of probabilities representing whether a second plurality of points related to the lithography process meet the specifications are determined. The second plurality of probabilities represent a second process window.

[0291] The plurality of probabilities can be modified to achieve the desired cost optimization for manufacturing a semiconductor device. For example, in some embodiments, one or more graphical elements are presented, configured such that a user can change the first and / or second variables instantly or nearly instantly to modify the plurality of probabilities. Instantaneous can mean less than or equal to 2 seconds. Nearly instantaneous can mean any interaction of a sufficiently short duration to allow two people to engage in a conversation through such a user interface, and will generally be less than 10 seconds (or any suitable approximate difference between two different times), but greater than 2 seconds.

[0292] In some embodiments, the process range variation is selected for the first and second variables. Given a setting for each of the first and second variables and a process range, a portion of the characteristics conforming to a specification requirement is determined. Based on the portion of the characteristics conforming to a specification requirement, a determination can be made of the setting of the first and second variables that produces the largest portion of the characteristics conforming to the specification requirement.

[0293] 16. Utilizing the aforementioned probability process window in process control

[0294] Controlling focal length and dosage is a crucial part of maintaining critical dimensions of the printed pattern during semiconductor manufacturing. As discussed above, the first step in understanding how focal length and dosage are controlled is to utilize the focal length-exposure process window to characterize the response of important features to variations. Appropriate analysis of the CD (and other output responses) relative to focal length and dosage data allows for the calculation of the process window, the measurement of the process window size to generate the exposure latitude-DOF plot, and the determination of a single value for the depth of focus. As discussed above, the optimal analytical method utilizes the probabilistic process window.

[0295] The optimal focal length and dosage are also determined using this analysis, based on the process settings that maximize the tolerance for focal length and dosage errors according to the PPW. Once the optimal focal length and dosage are determined, the next goal is to maintain the process center at this optimal focal length and dosage condition as the wafer passes through the lithography unit. Since almost all errors occurring in lithography act as an effective dosage error or an effective focal length error, appropriately adjusting the dosage and focal length after an appropriate interval can provide tighter patterning control. Thus, improved patterning control can lead to higher manufacturing yields and better performance of the device being manufactured.

[0296] Typically, the dose and focal length variables, as well as other process variables that may be used in a probabilistic process window analysis, are monitored and controlled using well-known Advanced Process Control (APC) methods. These APC methods include feedforward and feedback loops for controlling process tools. These process control methods will be enhanced by replacing the traditional process window analysis with the more rigorous and precise PPW analysis described above.

[0297] Process window analysis can also be used for wafer handling purposes. Wafer handling involves obtaining the output of a process window analysis and determining whether a wafer represented by the process window should proceed to the next process or be rejected due to anticipated poor printing patterns. If rejected, these wafers can be reprocessed or scrapped. Incorrect decisions during wafer handling can be very costly, as they may allow defective wafers to proceed to subsequent processing or reject good wafers. For example, improving the accuracy of process window analysis in the PPW process described above can improve the accuracy of wafer handling.

[0298] One approach for process control utilizes machine learning. A machine learning algorithm seeks to make predictions, such as those related to yield or device performance, based on process variables used in the manufacture of the device. A predictive machine learning model is first trained using a function (the process variables and intermediate results, such as the CD of a specific characteristic at a specific step in the process) as input to the measurement output (the thing to be predicted). The machine learning algorithm can utilize process window information for both training and prediction. In this regard, improved accuracy and precision of the PPW method can lead to improved machine learning predictions.

[0299] Although the above-described embodiments measure edge roughness by referring to a top-view image of a nominal planar patterned structure, this disclosure is not limited to such patterned geometry. Three-dimensional structures, non-planar structures, curved surfaces, or inclined structures can be measured using this invention. In addition to edge roughness, surface roughness can be measured and analyzed using techniques similar to those described in this disclosure.

[0300] Although the above-described embodiments refer to the measurement of roughness, this disclosure can also be used for other measurements. For example, the accurate determination of the height of the edge of a pattern structure can be used in the measurement of feature width, feature setting, edge setting, and other similar measurements. The profile of the measured feature can be used for many purposes, such as modeling or controlling the performance of the measured device. By collecting and statistically averaging many samples of measurements, even higher accuracy (lower uncertainty) can be obtained.

[0301] Consistent with the foregoing disclosure, the examples of systems and methods listed in the following clauses are explicitly conceived and intended as a set of non-limiting examples.

[0302] Clause 1. A computer-implemented method comprising: Choose a first variable, which is represented on a first axis of a graph; Choose a second variable, which is represented on a second axis of the graph; Choose at least one response variable, which is a function of the first variable and the second variable; For each response variable, determine a measurement uncertainty; Based on a measurement of the response variable and the measurement uncertainty of the response variable, a plurality of probabilities are determined, representing whether a plurality of points associated with a lithography process meet a plurality of indications for a specification requirement for each output, wherein the plurality of probabilities represent a process window; and Configure a lithography tool according to the process window to manufacture a semiconductor device.

[0303] Clause 2. The method implemented by the computer as claimed in claim 1, wherein the configuration includes sending a control signal to the lithography tool to set a first operating parameter according to the first variable and to set a second operating parameter according to the second variable.

[0304] Clause 3. A method implemented by a computer as described in any of the clauses herein, further comprising presenting the plurality of graphic elements that are probabilities of being the graphic on a user interface of a computing device.

[0305] Clause 4. The method implemented by a computer as described in any of the clauses herein, wherein the presentation of the plurality of probabilities is a heatmap, 3D graph, or outline on the user interface.

[0306] Clause 5. The method implemented by a computer as described in any of the clauses herein, wherein the measurement uncertainty of the one or more response variables is represented by a Gaussian normal probability distribution.

[0307] Clause 6. The method implemented by a computer as described in any of the clauses herein, wherein the first and second variables are related to a random process window.

[0308] Clause 7. A computer-implemented method as described in any of the clauses herein, wherein the first variable includes an exposure dose and the second variable includes a focal length of a scanning lithography process.

[0309] Clause 8. A method implemented by a computer as described in any of the clauses herein further includes presenting one or more graphical elements configured such that a user can change the nature of the first variable, the second variable, or both in real time or near real time to modify the plurality of probabilities.

[0310] Clause 9. A method implemented by a computer as described in any of the clauses herein further includes presenting one or more graphical elements configured such that a user can change the nature of the first variable, the second variable, or both in real time or near real time to modify the plurality of probabilities, wherein the modification of the plurality of probabilities is related to a desired cost optimization in manufacturing the semiconductor device.

[0311] Clause 10. A system comprising: A short film tool; A memory device that stores instructions; and A processing device coupled to the memory device and the lithography tool, the processing device executing the instructions to: Choose a first variable, which is represented on a first axis of a graph. Choose a second variable, which is represented on a second axis of the graph. Choose a response variable, which is determined based on the first and second variables. Determine the measurement uncertainty for the response variable. Based on a measurement of the response variable and the measurement uncertainty of the response variable, a plurality of probabilities are determined, representing a plurality of indications of whether a plurality of points related to a lithography process meet a specification requirement, wherein the plurality of probabilities represent a process window, and Configure the lithography tool according to the process window to manufacture a semiconductor device.

[0312] Clause 11. The system as described in any of the clauses herein, wherein the configuration includes sending a control signal to the lithography tool to set a first operating parameter according to the first variable and to set a second operating parameter according to the second variable.

[0313] Clause 12. In any of the clauses herein, the processing device is further configured to present the plurality of graphical elements that are probabilities of the graphic on a user interface of a computing device.

[0314] Clause 13. As in any of the clauses herein, the presentation of the plurality of probabilities is a heatmap on the user interface.

[0315] Clause 14. As in any of the clauses herein, the measurement uncertainty of the said response variable is a Gaussian normal probability distribution.

[0316] Clause 15. As in any of the clauses herein, the first and second variables are associated with a random process window.

[0317] Clause 16. As in any of the clauses herein, the first variable includes the exposure dose, and the second variable includes the focal length of a scanning lithography process.

[0318] Clause 17. As in any of the clauses herein, the processing apparatus is further configured to: Select the process range variation for the first and second variables. For each of the first and second variables, given a setting and process range, determine a portion of the characteristics that meet a specification requirement. The setting of the first and second variables is determined based on the portion that conforms to a specification requirement, which determines the largest portion of the characteristics that conform to a specification.

[0319] Clause 18. A non-transitory computer-readable medium storing instructions, which, when executed, causes a processing device to: Choose a first variable, which is represented on a first axis of a graph; Choose a second variable, which is represented on a second axis of the graph; Choose at least one response variable, which is a function of the first variable and the second variable; For each response variable, determine a measurement uncertainty; Based on a measurement of the response variable and the measurement uncertainty of the response variable, a plurality of probabilities are determined, representing a plurality of indications of whether a plurality of points related to a lithography process meet a specification requirement, wherein the plurality of probabilities represent a process window; and Configure the lithography tool according to the process window to manufacture a semiconductor device.

[0320] Clause 19. Computer-readable media as in any of the clauses herein, wherein the configuration includes sending control signals to the lithography tool to set a first operating parameter according to the first variable and a second operating parameter according to the second variable.

[0321] Clause 20. As in any of the computer-readable media herein, wherein the processing device is further configured to present the plurality of graphical elements that are probabilities of the graphic on a user interface of a computing device.

[0322] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this disclosure. As used herein, unless the context clearly indicates otherwise, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well. It will further be understood that the terms “comprising” and / or “including” as used in this specification indicate the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0323] It should be noted that not all activities described in the general description or examples above are necessary; a portion of a particular activity may not be necessary; and one or more further activities may be performed in addition to those described. Furthermore, the order in which activities are listed is not necessarily the order in which they are performed.

[0324] It may be advantageous to define certain words and phrases used throughout this patent document. The term "communication" and its derivatives include both direct and indirect communication. The terms "comprising" and "including" and their derivatives indicate unrestricted inclusion. The term "or" includes, meaning and / or. The term "related" and its derivatives may mean including, being contained in, interconnected, contained, being included in, connected to or connected with, coupled to or coupled with, communicable with, cooperating with, interleaved, juxtaposed, proximate, linked to or connected with, having, having one of the properties, having a relationship to or having a relationship with, or similar. When the term "at least one of" is used in a list of items, it indicates that one or more different combinations of the listed items are available, and only one item in the list may be required. For example, "at least one of the following: A, B and C" is any combination of the following: A, B, C, A and B, A and C, B and C, and A and B and C.

[0325] The descriptions in this disclosure should not be construed as implying that any particular element, step, or function is an essential or critical element that must be included within the scope of the claim. The scope of the subject matter of the granted patent is defined solely by the granted claim. Furthermore, none of the appended claims or claim elements invoke 35 U.S.C. §112(f) unless the exact words “means (apparatus) for” or “steps for” are explicitly used in the specific claim, followed by a participle identifying a function. For example, the use of terms such as (but not limited to) “mechanism,” “module,” “apparatus,” “unit,” “component,” “element,” “part,” “device,” “machine,” “system,” “processor,” or “controller” within a claim is understood and intended to refer to structures known to those skilled in the art, i.e., as further modified or enhanced by the characteristics of the claim itself, and therefore does not invoke 35 U.S.C. §112(f).

[0326] The benefits, other advantages, and solutions to the problem have been described above with respect to the specific implementation. However, the benefits, advantages, solutions to the problem, and any features that may make any benefit, advantage, or solution occur or become more significant are not intended to be construed as any or all of the claimed items as a critical, necessary, or essential feature.

[0327] Upon reading this specification, those skilled in the art will recognize that certain features are described herein in the context of individual embodiments for clarity, but may also be presented in combination within a single embodiment. Conversely, various features described herein in the context of a single embodiment for brevity may also be presented individually or in any sub-combination. Furthermore, reference to values ​​stated as ranges is to each value contained within the range.

[0328] All functional means or step elements in the following claims refer to corresponding structures, materials, actions, and equivalents intended to include any structure, material, or action used to perform the function in combination with other elements as expressly claimed. The description in this disclosure has been presented for illustrative purposes but is not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of this disclosure. The embodiments described have been chosen and described to best explain the principles of this disclosure and its practical applications, and to enable others skilled in the art to understand that this disclosure can be used in various embodiments with various modifications as suited to the particular purpose conceived.

[0329] 700: Edge Detection System 701:SEM 702: Vacuum Pump 703: Vacuum Chamber 705: Electron Gun 707: Electron Beam 710, 715, 720: Condensing Lens 725: Scanning coil 732: Patterned Receiver 735: Lens aperture 740: Backscattered Electron Detector 745: Secondary Electronic Detector 750: Information Processing Systems (IHS) 755: Processor 757: Interface 760: Storage 765: Reverse Line Scan Model Measurement Tool 770: Output device 800: Pattern Structure 805: Secondary Electron 810:Substrate 815: Features 815-1, 815-2: Edge 820: Interaction Volume 905: Edge 905': Peak 910: Edge 910': Peak 915: Features 1105: The calibrated model 1110: Monte Carlo simulation results 1205: The calibrated model 1210: Monte Carlo simulation results 2300-2350: Block 2400: Sample 2502:LWR PSD 2504:LER PSD 2506: PPR PSD 2507: Sharp Pulse Artifact 2508:LWR PSD 2510:LER PSD 2512: PPR PSD 3000: Method 3002-3018: Blocks 3100: Method Blocks 3102-3114 3800: Method Blocks 3802-3812

Claims

1. A computer-implemented method for generating a probabilistic process window that considers measurement uncertainty, comprising: Choose a first variable; Choose a second variable; Choose at least one response variable, which is a function of the first variable and the second variable; For each response variable, a measurement uncertainty is determined, wherein the first variable includes an exposure dose and the second variable includes a focal length of a scanning lithography process; based on a measurement of the response variable and the measurement uncertainty for the response variable, a plurality of probabilities are determined, representing whether a plurality of points related to a lithography process meet a plurality of indications for a specification requirement for each response variable, wherein the plurality of probabilities represent a process window; and a lithography tool is configured according to the process window to manufacture a semiconductor device.

2. The method implemented by the computer as claimed in claim 1, wherein the configuration includes sending a control signal to the lithography tool to set a first operating parameter according to the first variable and to set a second operating parameter according to the second variable.

3. The computer-implemented method of claim 1, further comprising a graphical element that presents the plurality of probabilities as a graphic on a user interface of a computing device.

4. The computer implementation method of claim 3, wherein the presentation of the plurality of probabilities is a heatmap, a three-dimensional graph, or a contour map on the user interface.

5. The computer-implemented method of claim 1, wherein the measurement uncertainty of the response variable is represented by a Gaussian normal probability distribution.

6. The method implemented by the computer as claimed in claim 1, wherein the first variable is represented on a first axis of the graph, and the second variable is represented on a second axis of the graph.

7. The computer-implemented method of claim 1, further comprising presenting one or more graphical elements configured such that a user can change the nature of the first variable, the second variable, or both in real time or near real time to modify the plurality of probabilities.

8. The computer implementation of claim 1, further comprising presenting one or more graphical elements configured such that a user can change the properties of the first variable, the second variable, or both in real time or near real time to modify the plurality of probabilities, wherein the modification of the plurality of probabilities is related to cost optimization for manufacturing the semiconductor device.

9. A system for generating a probabilistic process window that takes into account measurement uncertainty, comprising: A short film tool; A memory device that stores instructions; The device includes a processing unit coupled to the memory device and the lithography tool, the processing unit executing the instructions to: select a first variable; select a second variable; select a response variable based on the first and second variables, wherein the first variable includes an exposure dose and the second variable includes a focal length for a scanning lithography process; determine a measurement uncertainty for the response variable; determine a plurality of probabilities based on the measurement of the response variable and the measurement uncertainty for the response variable, representing whether a plurality of points related to a lithography process meet a plurality of indications for a specification requirement for each response variable, wherein the plurality of probabilities represent a process window; and configure the lithography tool to manufacture a semiconductor device according to the process window.

10. The system of claim 9, wherein the configuration includes sending a control signal to the lithography tool to set a first operating parameter according to the first variable and to set a second operating parameter according to the second variable.

11. The system of claim 9, wherein the processing device is further configured to present the plurality of probabilities as graphical elements of a graph on a user interface of a computing device.

12. The system of claim 11, wherein the presentation of the plurality of probabilities is a heatmap on the user interface.

13. The system of claim 9, wherein the measurement uncertainty of the response variable is a Gaussian normal probability distribution.

14. The system of claim 9, wherein the first variable is represented on a first axis of the graph, and the second variable is represented on a second axis of the graph.

15. The system of claim 9, wherein the processing apparatus is further configured to: select a process range variation for the first and second variables; give a setting and a process range for each of the first and second variables; determine a portion of the characteristics that meet the specification requirements; and, based on the portion of the characteristics that meet the specification requirements, determine the setting of the first and second variables that generates the largest portion of the characteristics that meet the specification requirements.

16. A physically non-transitory computer-readable medium for generating stored instructions for a probabilistic process window that considers measurement uncertainty, wherein, when the instructions are executed, they cause a processing device to: select a first variable; select a second variable; select at least one response variable that is a function of the first variable and the second variable, wherein the first variable includes an exposure dose and the second variable includes a focal length of a scanning lithography process; determine a measurement uncertainty for each response variable; determine a plurality of probabilities based on a measurement of the response variable and the measurement uncertainty for the response variable, representing a plurality of indications for whether a plurality of points related to a lithography process meet a specification requirement for each response variable, wherein the plurality of probabilities represent a process window; and configure a lithography tool to manufacture a semiconductor device according to the process window.

17. The computer-readable media of claim 16, wherein the configuration includes sending control signals to the lithography tool to set a first operating parameter according to the first variable and to set a second operating parameter according to the second variable.

18. The computer-readable media of claim 16, wherein the processing device is further configured to present the plurality of probabilities as a graphical element of a graph on a user interface of a computing device.

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