KR20220041955A - Lithographic method - Google Patents

Abstract

A method for determining one or more optimized values of an operating parameter of a sensor system configured to measure a property of a substrate is disclosed, the method comprising: determining a quality parameter for a plurality of substrates; determining, for a plurality of values of the operating parameter, measurement parameters for a plurality of substrates obtained using the sensor system; comparing the substrate-to-substrate variation in the quality parameter with the substrate-to-substrate variation in the mapping of the measurement parameter; and determining one or more optimized values of the operating parameters based on the comparison.

Description

Lithographic method {LITHOGRAPHIC METHOD}

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to EP Application No. 17193637.0, filed on September 28, 2017.

technical field

The present invention relates to a lithographic method for manufacturing a device. More particularly, the present invention relates to a measuring method for the alignment of a substrate in a lithographic method.

Lithographic methods are used to apply a desired pattern onto a substrate, typically onto a target portion of the substrate. Lithography may be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device, also referred to as a mask or reticle, may be used to create a circuit pattern to be formed on individual layers of the IC. Such a pattern may be transferred onto a target portion (eg, comprising a portion of a die, one die, or several dies) on a substrate (eg, a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on a substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. A conventional lithographic apparatus consists of a so-called stepper in which each target portion is irradiated by exposing the entire pattern onto the target portion at once, and simultaneously scanning the pattern through a beam of radiation in a given direction (“scanning”-direction) parallel to this direction. or a so-called scanner in which each target portion is irradiated by scanning the substrate in antiparallel. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.

Generally, the integrated circuit being fabricated includes a plurality of layers comprising different patterns, each layer being created using an exposure process as described above. To ensure proper operation of the integrated circuit being fabricated, successively exposed layers need to be properly aligned with each other. To realize this, the substrate is typically provided with a plurality of so-called alignment marks (also referred to as alignment targets), whereby the positions of the alignment marks are used to determine or estimate the position of a previously exposed pattern. As such, prior to exposure of subsequent layers, the positions of alignment marks are determined and used to determine the positions of previously exposed patterns. Typically, to determine the position of such an alignment mark, an alignment sensor is applied, which can be configured to, for example, project a beam of radiation onto an alignment mark or target and determine the position of the alignment mark based on the reflected beam of radiation. . . In the scanner, the alignment markers are read by the scanner alignment system, which helps to achieve good positioning of each field on the substrate when subjected to the patterning step provided by the scanner. Ideally, the measured position of the alignment mark will coincide with the actual position of the mark.

However, various causes can cause deviations between the measured and actual positions of the alignment marks. In particular, the stated deviations may occur due to deformation of the alignment marks. Such deformations may be caused by, for example, processing of the substrate, such as etching, chemical mechanical polishing (CMP) or layer deposition, which leads to sub-optimal marker positioning. As a result, the layer may be projected or exposed in locations that do not match the previously exposed pattern, ie not aligned, resulting in so-called overlay errors.

According to one aspect the present invention comprises a method for determining one or more optimized values of an operating parameter of a sensor system configured to measure a property of a substrate. The method includes: determining a quality parameter for a plurality of substrates; determining, for a plurality of values of the operating parameter, a measurement parameter for the plurality of substrates obtained using the sensor system; comparing the substrate-to-substrate variation of the quality parameter with the substrate-to-substrate variation of the mapping of the measurement parameter; and determining one or more optimized values of the operating parameters based on the comparison.

The mapping may be a weighted sum, non-linear mapping or a trained mapping based on machine learning techniques.

The method may also include determining, based on the comparison, an optimal set of weighting coefficients for weighting the measurement parameter associated with the first value of the operating parameter and the measurement data associated with the second value of the operating parameter. .

The quality parameter may be an overlay or focus parameter.

The measurement parameter may be a location of a feature provided on the plurality of substrates or an out-of-plane deviation of a location on the substrate.

The operating parameter may be a parameter associated with the light source from the sensor system. The operating parameter may be a wavelength, a polarization state, a spatial coherence state, or a temporal coherence state of the light source.

The quality parameter may be determined using a metrology system. The quality parameter may be determined using a simulation model that predicts the quality parameter based on any of context information, measurement data, reconstructed data, or hybrid metrology data.

The optimized value of the operating parameter may include a first set of values associated with the first coordinates of the measurement parameter and a second set of values associated with the second coordinates of the measurement parameter.

The method may further include: determining a third coordinate parallel to the first preferential direction of the mark; determining a fourth coordinate parallel to a second preferred direction of the mark; determining a third set of optimized values of an operating parameter associated with a third coordinate and a fourth set of optimized values of an operating parameter associated with the fourth coordinate; determining transformations from the third and fourth coordinates to the first and second coordinates; and transforming the determined optimized values of the operating parameters at the third and fourth coordinates into optimized values of the operating parameters at the first and second coordinates, using the determined transforms.

The first value of the operating parameter may be optimized independently of the second value of the operating parameter.

In some embodiments, determining one or more optimized values of the operating parameter based on the comparison may be performed for different regions of the substrate. The different regions may include a region proximate to the edge of the substrate and a region proximate to the center of the substrate. Each zone may include one or more alignment marks applied to the substrate. Each zone may correspond to a respective one of a plurality of alignment marks applied to the substrate.

In some embodiments, the measurement parameter is a measured position of a mark and the quality parameter is a mark-to-device shift, and an optimized value of the operating parameter determines the quality parameter so that substrate-to-substrate variation is minimized. decided to optimize. An operating parameter is a parameter associated with a radiation source, radiation from the source is directed to a substrate, and an optimized value of the operating parameter is determined by applying a weight to adjust a measurement obtained using the operating parameter. Radiation from a source that is directed to the substrate may be received by the sensor system after targeting the substrate. Weighting may include the effect of heating a lens of a lens used to direct radiation to a substrate and/or to receive radiation by a sensor system. The method also sub-segmentation using measurements obtained from a substrate having sub-segmented marks to which an intentional mark-to-device shift has been applied to determine the sensitivity of the operating parameter to the mark-to-device shift. The method may further include determining a weight for an operating parameter for measuring the marked mark.

In some embodiments, such methods may be used to optimize operating parameters of a metrology system used to control processing of a substrate. The sensor system includes a first sensor system associated with a first measurement system configured to measure a first characteristic of the substrate prior to processing and a second sensor system associated with a second measurement system configured to measure a second characteristic of the substrate after processing may include The method may include: determining, for a plurality of values of the operating parameter, a first set of measurement parameters for the plurality of substrates obtained using the first sensor system; determining, for the plurality of values of the operating parameter, a second set of measurement parameters for the plurality of substrates obtained using the second sensor system; and comparing the substrate-to-substrate variation of the quality parameter with the substrate-to-substrate variation of the mapping of the measurement parameter to each of the first and second sets of the measurement parameter. Determining the one or more optimized values of the operating parameter may include simultaneously optimizing a first set of operating parameters associated with the first measurement system and a second set of operating parameters associated with the second measurement system. and the optimization mitigates the substrate-to-substrate variation of the second characteristic. The quality parameter may be an overlay determined from the measured second characteristic of the substrate after processing.

According to a second aspect, the present invention includes a method for determining a state of a semiconductor manufacturing process. The method comprises: determining an optimized value of an operating parameter according to a first aspect of the present invention; comparing the determined operating parameter with a reference operating parameter; and determining the status based on the comparison.

According to a third aspect, the present invention comprises a method of optimizing measurement data from a sensor system configured to measure a property of a substrate. The method includes acquiring overlay data for a plurality of substrates. The overlay indicates a deviation between the measured and expected positions of the alignment markers on the substrate and includes a plurality of measurements of the alignment marker positions made by a sensor system, each of the plurality of measurements using a different operating parameter of the sensor system. The method also includes combining, based on the obtained overlay data, and for each of the different operating parameters, weighted adjustments to measurements made by the sensor system for all of the different operating parameters such that overlay is minimized; The method further includes determining a weight for adjusting the obtained measurement using the operating parameter.

The operating parameter may be a parameter associated with the radiation source from the sensor system. The operating parameter may be a wavelength, a polarization state, a spatial coherence state, or a temporal coherence state of the light source.

According to another aspect, the present invention includes a method for aligning layers in an integrated circuit wafer. The method includes obtaining a plurality of position measurements of an alignment marker on the wafer using a sensor system, each of the plurality of measurements using a different operating parameter. For each of the plurality of alignment mark position measurements, a position deviation is determined as a difference between the expected alignment mark position and the measured alignment mark position, and the measured alignment mark position is determined based on the individual alignment mark position measurement. A set of functions is defined as possible causes for this positional deviation, the set of functions including a substrate deformation function representative of a deformation of the substrate and at least one mark deformation function representative of a deformation of one or more alignment marks. A matrix equation PD = M * F is generated, and a vector PD containing the position deviation is set equal to a weighted combination of a vector F containing a substrate deformation function and at least one mark transformation function, represented by a weighting factor matrix M and a weighting factor associated with the at least one mark deformation function depends on the applied alignment measure. Values for the weighting coefficients of the matrix M are determined based on overlays obtained for a plurality of substrates, the overlays representing the deviations between the measured and expected positions of the alignment markers, and using different operating parameters to a plurality of measurements of alignment marker positions made by the system, wherein the weights adjust the measurements obtained using different operating parameters such that weighted adjustments to the measurements can be combined to minimize overlay. An inverse or pseudo-inverse of the matrix M is determined to obtain a value for the substrate deformation function as a weighted combination of positional deviations. A value of the substrate strain function is applied to effect alignment of the patterned radiation beam with the target portion.

Exemplary embodiments are described herein with reference to the accompanying drawings:
1 shows a lithographic apparatus according to an embodiment of the present invention.
Figure 2 shows some possible alignment measurement results when applying different measurement parameters.
3 shows how different operating parameters of a sensor can be affected when performing measurements on a substrate.
4 is a graph showing how different operating parameters may be affected by mark deformation.
5 shows markers with different types of mark variants.
6A is a flowchart schematically illustrating the wafer alignment, exposure and overlay measurement process.
6B is a flowchart schematically illustrating another wafer alignment, exposure and overlay measurement process.
7A-C are graphs showing how product and mark shifts vary for different colors of radiation.
8 is a graph showing how the sensitivity to mark-to-device shift can be corrected.
9 is a plot showing alignment mark asymmetry across the wafer.
10A is a plot showing an on-product overlay on a wafer map when the active color is near infrared (NIR), and FIG. 10B shows an in-product overlay wafer map for the same wafer using two-color weighting. 10c shows the differences between the plots of FIGS. 10a and 10b.
11a and 11b are two graphs showing how the overlay error varies for two orthogonal directions according to different two-color weighting (TCW) combinations, one for the mark at the edge of the wafer and the other for the mark at the edge of the wafer. is for the center mark.
12 schematically shows a process for determining OCW for alignment correction using several different colors, models and layouts and determining overlay correction using several frequencies, models and layouts.
13 schematically shows a process for determining an optimal combination for both alignment correction and overlay correction.
14 shows an alignment mark comprising two sets of gratings.
15 is a block diagram illustrating a computer system that may be used to utilize embodiments described herein.

In order to facilitate understanding of the principles applied to the embodiments of the present invention, with reference to FIG. 1 , a lithographic apparatus and how such an apparatus is used will first be described.

1 schematically shows a lithographic apparatus according to an embodiment of the present invention. Such an apparatus is configured to support an illumination system (illuminator) IL, a patterning device (eg mask) MA, configured to condition a radiation beam B (eg UV radiation or any other suitable radiation). and a mask support structure (eg mask table) MT configured and coupled to a first positioning device PM configured to precisely position the patterning device according to specific parameters. The apparatus also holds a substrate (eg resist coated wafer) W and is connected to a substrate table (eg, a resist coated wafer) W connected to a second positioning device PW configured to accurately position the substrate according to specific parameters. wafer table) (WT) or "substrate support". The apparatus comprises a projection system (eg, comprising one or more dies) configured to project a pattern imparted to a beam of radiation B by a patterning device MA onto a target portion C (eg, comprising one or more dies) of a substrate W. For example, a refractive projection lens system (PS).

The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or combinations thereof, to direct, shape, or control radiation.

The mask support structure supports the patterning device, ie bears its weight. This holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions such as, for example, whether the patterning device is maintained in a vacuum environment. The mask support structure may hold the patterning device using mechanical, vacuum, electrostatic, or other clamping techniques. The mask support structure may be, for example, a frame or table, which may be fixed or movable as needed. The mask support structure may ensure that the patterning device is in a desired position relative to the projection system, for example. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device”.

As used herein, the term “patterning device” should be broadly interpreted to refer to any device that can be used to impart a pattern in a cross-section of a beam of radiation to create a pattern in a target portion of a substrate. It should be noted that the pattern imparted to the radiation beam may not exactly match the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so-called assist features. In general, the pattern imparted to the radiation beam will correspond to a particular functional layer of the device being created in the target portion, such as an integrated circuit.

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

As used herein, the term "projection system" refers to a refractive, reflective, catadioptric, magnetic , should be construed broadly to encompass any type of projection system, including electromagnetic and electrostatic optical systems, or any combination thereof. Any use of the term “projection lens” herein may be considered synonymous with the more general term “projection system”.

As shown, the device is transmissive (eg employing a transmissive mask). Alternatively, the apparatus may be of a reflective type (eg employing a programmable mirror array of the type as mentioned, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) or more substrate tables or “substrate supports” (and/or two or more mask tables or “mask supports”). In such "multi-stage" machines, additional tables or supports may be used in parallel, or preparatory steps may be performed on one or more tables or supports while using one or more other tables or supports for exposure.

Further, the lithographic apparatus may be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, for example water, in order to fill the space between the projection system and the substrate. The immersion liquid may also be applied to other spaces of the lithographic apparatus, for example between the mask and the projection system. Immersion techniques can be used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not mean that a structure, such as a substrate, must be submerged in liquid, but rather means that the liquid is located between the projection system and the substrate during exposure.

Referring to FIG. 1 , an illuminator IL receives a radiation beam from a radiation source SO. For example, where the radiation source is an excimer laser, the radiation source and the lithographic apparatus may be separate entities. In such a case, the radiation source is not considered to form part of the lithographic apparatus, and the radiation beam is transmitted to the radiation source SO with the aid of a beam delivery system BD comprising, for example, suitable directing mirrors and/or beam expanders. is transmitted to the illuminator IL. In other cases, for example if the radiation source is a mercury lamp, the source may be an integral part of the lithographic apparatus. The radiation source SO and the illuminator IL may optionally be referred to as a radiation system together with the beam delivery system BD.

The illuminator IL may comprise an adjuster AD configured to adjust the angular intensity distribution of the radiation beam. In general, at least outer and/or inner radial dimensions (generally referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components such as a collector IN and a collector CO. An illuminator may be used to condition the radiation beam to have a desired uniformity and intensity distribution in the cross-section.

The radiation beam B is incident on a patterning device (eg, mask MA) held on a mask support structure (eg, mask table MT) and is patterned by the patterning device. After passing through the mask MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioning device PW and a position sensor IF (eg an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT is positioned, for example, in the path of the radiation beam B It can be precisely moved to position the various target portions C. Likewise, a first positioning device PM and another position sensor (not explicitly shown in FIG. 1 ) are in the path of the radiation beam B, for example after mechanical retrieval from the mask library, or during a scan. It can be used to accurately position the mask MA with respect to In general, the movement of the mask table MT can be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) forming part of the first positioning device PM. . Similarly, movement of the substrate table WT or “substrate support” can be realized using a long-stroke module and a short-stroke module forming part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the mask table MT can only be connected or fixed to a short-stroke actuator. Mask MA and substrate W may be aligned using mask alignment marks M1 and M2 and substrate alignment marks P1 and P2. Substrate alignment marks as shown occupy dedicated target portions, but they may also be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations where two or more dies are provided on the mask MA, the mask alignment marks may be located between the dies.

The device shown can be used in at least one of the following modes:

In the step mode, the mask table MT or "mask support" and the substrate table WT or "substrate support" are substantially stationary, while the entire pattern imparted to the radiation beam is projected onto the target portion C at once. is maintained (single static exposure). The substrate table WT or “substrate support” is then shifted in the X and/or Y direction so that different target portions C can be exposed. In step mode, the maximum size of the exposure field limits the size of the target portion C imaged with a single static exposure.

In the scan mode, the mask table MT or “mask support” and the substrate table WT or “substrate support” are scanned synchronously while a pattern imparted to the radiation beam is projected onto the target portion C ( i.e. single dynamic exposure). The speed and direction of the substrate table WT or “substrate support” relative to the mask table MT or “mask support” may be determined by the magnification (reduction ratio) and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, while the length of the scanning operation determines the height (in the scanning direction) of the target portion.

In another mode, the mask table MT or “mask support” is held substantially stationary while holding the programmable patterning device, while the pattern imparted to the radiation beam is projected onto the target portion C of the substrate. The table WT is moved or scanned. In this mode, typically a pulsed radiation source is employed, and the programmable patterning device is updated as needed between successive radiation pulses during a scan or after each movement of the substrate table WT or “substrate support”. This mode of operation can be readily applied to maskless lithography using a programmable patterning device, such as a programmable mirror array of a type as described above.

Combinations and/or variations of the above-described modes of use or entirely different modes of use may also be employed.

Embodiments of the present invention will typically be used with lithographic apparatus as described above, which lithographic apparatus further comprises an alignment system AS configured to determine the position of one or more alignment marks present on the substrate. The alignment system is configured to perform a plurality of different alignment measurements to obtain a plurality of measured alignment mark positions for the alignment marks under consideration. In this regard, performing different alignment measurements on a particular alignment mark means performing the alignment measurements using different measurement parameters or properties. Such different measurement parameters or properties may include, for example, using different optical properties to perform alignment measurements. In one example, an alignment system applied to a lithographic apparatus according to the present invention comprises an alignment projection system configured to project a plurality of alignment beams having different characteristics or parameters to alignment mark positions on a substrate and an alignment position based on a beam reflected from the substrate. and a detection system configured to determine

After the wafer has been aligned and patterned during the exposure step, the wafer is calibrated to check the accuracy of the patterning, as described above. With reference to the position of the pattern within a previous layer on the wafer, the deviation between the actual (measured) position of the pattern and the desired position of the pattern is commonly referred to as overlay error or simply overlay. The overlay error associated with a process is a good indicator of the quality of the process. The overlay can therefore be considered as a quality parameter of the process. Overlay error is not the only relevant parameter indicative of process quality. When exposing a substrate (wafer), focus error is also important. The overlay error is typically related to the position error in the plane of the substrate and is therefore closely related to the performance of the alignment system. The focus error is associated with a position error perpendicular to the plane of the substrate and may be used in other measurement systems in a lithographic apparatus; It is closely related to the performance of the leveling system. Focus error can also be considered as a quality parameter of the process.

Quality parameters are typically measured by a metrology system (eg, a scatterometer used to determine overlay error). However, in addition to or alternatively to using a metrology system, prediction may be used to derive quality parameters. Context data (eg, knowledge of which processing apparatus was used to process the substrate of interest) and measurement data not directly related to quality data (eg, wafer shape data measured to predict overlay error) ), virtual metrology data representing directly measured quality parameter data can be reconstructed. This concept is often referred to as "hybrid instrumentation"; It is a method of combining various data sources and, if necessary, a simulation model to reconstruct metrology data associated with quality parameters of interest (overlay and/or focus error). Alternatively, a simulation model may be used to derive quality parameters based on context data and/or measurement data. For example, a simulation model can be used to mimic a lithography process based on pre-exposure measurements (leveling data, alignment data) and context data (reticle layout, process information). The simulation model itself can generate a map of the quality parameter data (in this case the predicted overlay).

Within the meaning of the present specification, the alignment system is operated with different operating parameters, including at least differences in the polarizations or differences in the wavelength (frequency) content of the alignment beams. Accordingly, the alignment system may use different operating parameters (eg, using alignment beams with different colors, ie, frequencies/wavelengths) to determine the position of the alignment marks. In general, the purpose of such alignment mark measurements performed by an alignment system is to determine or estimate the position of a target portion (eg, target portion C shown in FIG. 1 ) of a subsequent exposure process. Typically, the term “color” is used to refer to a beam having a particular measurement parameter or set of measurement parameters. These different “color” beams are not necessarily beams of different colors within the visible spectrum, but may have different frequencies (wavelengths) or other properties, such as polarization.

To determine these target portion positions, the positions of alignment marks, which may be provided, for example, in scribe lanes surrounding the target portion, are measured. When the measured alignment mark position deviates from the nominal or expected position, it can be assumed that the target portion on which the next exposure should be made also has a deviated position. Using the measured position of the alignment mark, it is possible to determine or estimate the actual position of the target portion, thus allowing the subsequent exposure to be performed at the appropriate position, thereby aligning the next exposure to the target portion.

If the measured alignment mark position deviates from the expected or nominal position, it is likely to be treated as due to deformation of the substrate. Such deformation of the substrate may be caused, for example, by various processes through which the substrate is subjected.

A plurality of measured alignment mark positions are available, and when a positional deviation, ie a deviation of an expected alignment mark position, is determined, this deviation can be approximated, for example, to a function to describe the deformation of the substrate. This can be, for example, a two-dimensional function that describes the deviation (Δx, Δy) as a function of (x, y) position. Using these functions, it is possible to determine or estimate the actual location of the target portion on which the pattern needs to be projected.

The alignment position measurements performed by the alignment system may be hampered by deformation or asymmetry of the alignment marks themselves. In other words, due to the deformation of the alignment mark, as compared to the situation in which the alignment mark is not deformed, an offset alignment mark position measurement can be obtained. If no action is taken, such an offset alignment mark position measurement may result in an erroneous alignment mark position determination. It has also been observed that this type of deviation, i.e., the deviation position measurement caused by alignment mark deformation, is dependent on the operating parameters used. For example, when alignment mark positions are measured using alignment beams with different frequencies, this may lead to different results, ie different measurement positions for alignment marks.

As such, when the positions of the alignment marks are measured using a plurality of different operating parameters, eg alignment beams having different frequencies, different results are obtained, eg a plurality of different alignment mark positions are based on these measurements. can be obtained by

As is evident from this, the result of the alignment measurement procedure should be an evaluation of the actual substrate deformation, ie an evaluation of the actual position of the alignment mark, which can be used to determine the actual position of the target portion for subsequent exposure.

Given the described effects, in particular the effects of alignment mark deformation, measured alignment mark positions (eg, commonly referred to as “measurement parameters”), i.e. derived from different measurements (i.e. using different operating parameters) The alignment mark position is affected by both the actual substrate deformation (unknown) and the mark deformation that occurred (unknown).

Both effects can lead to deviations between the expected and measured alignment mark positions. As such, when a positional deviation is observed, it may be caused by an actual substrate deformation or alignment mark deformation or a combination thereof.

Figure 2 schematically shows several possible scenarios; Assume that three measurements (M1, M2, M3) are performed to determine the position of the alignment mark (X). Fig. 2(a) schematically shows the nominal or expected positions E and the measurement positions M1, M2, M3 of the alignment marks. Fig. 2(a) also shows the actual position A of the alignment mark. As can be seen, none of the measurements performed provide an accurate representation of the actual position deviation (E-A).

Thus, the scenario shown in Fig. 2(a) involves an actual displacement of the alignment mark (actual alignment mark position (A) differs from expected position (E)) in combination with a mark deformation that results in an out-of-measure measurement.

Figure 2(b) shows an alternative scenario in which a difference is observed in measurements M1, M2, M3, where the measurement parameter (in this case the measured position) is different from the expected value of the measurement parameter (eg, position E), but the actual It is assumed that position A coincides with expected position E. In this scenario, the measurement would suggest that there is a positional deviation of the alignment mark, but in reality there is no positional deviation, ie the position of the alignment mark is not affected by the substrate deformation.

Fig. 2(c) schematically shows a third scenario in which all three measurements M1, M2, and M3 coincide with the actual location A. As shown in Figs. This scenario can occur when there is no alignment mark deformation affecting the measurement.

As is evident from the various scenarios shown, in order to arrive at an adequate estimate of the actual alignment mark position, it must be possible to distinguish the effect of mark deformation from the effect of substrate deformation.

The present invention provides a method for realizing the separation of these two effects. As an example, the lithographic apparatus may include a processing unit PU (see FIG. 1 ) for performing the operations necessary to separate the two effects. Therefore, such a processing unit (PU) may include a processor, a microprocessor, a computer, and the like.

3 illustrates the basic physical principle of the present invention (sometimes referred to as “optimal color weighting (OCW)” concept when the operating parameter of interest is the color of the alignment beam). As can be seen in the figure above, in an ideal situation all the colors used for multicolor measurements would produce the same alignment position marks 30 for the markers 32 on the geometrically perfect substrate 34, but in practice as described above. For some reason different colors result in different position indications 36 relative to the actual (ie not perfect) substrate 38 as shown in the figure below.

4 shows how different colors can be affected by mark deformation, and as shown in graph 40, the position error of each color can vary linearly with the degree of deformation (top tilt angle of the mark). It can be assumed that there is In this case, it may be possible to determine a single color as providing the best indication of the actual mark location. However, as shown in FIG. 5 , when there may be many different types of mark variations, no single color may provide the best approximation for all types of variations. In practice, it has been found that errors due to mark deformation scale differently for different colors (eg wavelength or polarization) as well as vary with layer thickness variations and the type of mark being measured. The OCW-based method aims to determine the optimal combination of all different colors used to minimize the effect of marker variations on the determined marker positions.

)이 정렬될 위치를 규정하도록 허용한다. '가중치'(wi)가 각각의 색상(xi)에 대해 추가되어, 프로세스에 대해 로버스트한 정렬된 위치(

)를 규정하기 위한 xi의 선형 조합에 도달하게 된다.Due to processing variations (PV), including mark variations, within wafers and from wafer to wafer (PV), variations in aligned position are shifted with respect to color ( i ). OCW solutions are far from the best single color, but all colors (

) to specify the position to be aligned. A 'weight' ( wi ) is added for each color ( xi ), so that the ordered position ( ) that is robust to the process (

) to arrive at a linear combination of xi to define

Accordingly, embodiments of the present invention solve the problem that alignment marks are deformed by wafer-to-wafer process variation (PV), resulting in in-product overlay errors. The OCW solution entails:

· Define the OCW position as a linearly weighted combination of alignment positions.

· Minimize the process sensitivity of y to process variations by taking optimal linear combinations such that wafer-to-wafer overlay errors are minimized.

· The optimal weight for each color/polarization is determined using training using overlay data.

· Preferably, the overlay data is obtained from measurements made on wafers that have undergone similar processing, and both measurement and processing are performed using the same or similar equipment.

)를 결정하는 데에 사용되는 수학적 원리는 다음과 같다.Color weights (

), the mathematical principle used to determine

)에 걸친 가중된 합계이다.OCW position y is the M measured color positions (

) is the weighted sum over

Given N measured marks,

를 최소화하기 위해 가중치를 최적화한다.Decorrected overlays

We optimize the weights to minimize

(Reverse Corrected Overlay = Overlay - Applied Wafer Alignment).

)는 다음의 식으로 구할 수 있다:· Then the color weight (

) can be obtained in the following way:

regular OCW

,

와 같은 좌표들의 세트일 수 있다.

,

좌표의 세트는 선형 좌표일 수 있고, 즉 이러한 좌표는 두 개의 축(

축과

축)으로 표현되며, 이들 축은 서로 평행하지 않은 상이한 방향을 가진다.

와

축의 방향은 각각

와

좌표의 방향으로 지칭될 수 있다.

,

좌표는 직교 좌표 또는 직교 정규 좌표일 수 있다.

와

의 축은 마크와 독립적으로 정렬될 수 있다. OCW는 이전에 획득된 정렬 및 오버레이 데이터에 대해 트레이닝될 수 있다. 색상 가중치 계수가

와

방향에 대해 독립적으로 트레이닝되어 적용될 수 있다. 대안적으로 색상 가중치 계수는 조합된

와

에 대해 트레이닝될 수 있지만, 독립적인 트레이닝을 통해 오버레이 성능이 향상된다.As mentioned above, OCW (Optimal Color Weighting) determines, for an alignment recipe, the optimal color weighting factor that can achieve minimal overlay variation of the pattern on the wafer. The OCW can be determined at multiple locations on the mark. A position on a mark can be described using a two-dimensional representation, which is, for example, a two-dimensional coordinate

,

It may be a set of coordinates such as

,

The set of coordinates may be linear coordinates, i.e. these coordinates are divided into two axes (

axis and

axes), and these axes have different directions that are not parallel to each other.

Wow

each axis direction

Wow

It can be referred to as the direction of the coordinates.

,

The coordinates may be Cartesian coordinates or Cartesian normal coordinates.

Wow

The axis of can be aligned independently of the mark. The OCW may be trained on previously obtained alignment and overlay data. color weighting factor

Wow

It can be trained and applied independently of the direction. Alternatively, the color weighting factor is

Wow

can be trained on, but the overlay performance is improved through independent training.

Mathematically, one implementation of the determination of color weights for two independent directions may be as follows:

및

는 오버레이 성능을 최적화하도록 결정되어, 그 결과 OCW 결정된 위치

및

가 된다. 예를 들어 공칭 마크 위치, 웨이퍼 로드 및 웨이퍼 변형이 가중치 계수에 의해 영향을 받지 않도록 하기 위해, 색상 가중치에 대해 하나 이상의 추가 제약이 가해질 수도 있다. 이는 모든 색상 가중치의 합이 1이 되어야 한다는 요건, 즉

와

의 두 독립적인 방향 모두에 대해 가중치의 합이 100 %가 되어야 한다는 요건을 추가함으로써 달성될 수 있다.weight factor in the above equation

and

is determined to optimize the overlay performance, resulting in the OCW determined position

and

becomes One or more additional constraints may be placed on the color weights, for example to ensure that nominal mark positions, wafer loads, and wafer deformations are not affected by the weighting factors. This is the requirement that the sum of all color weights equals 1, i.e.

Wow

This can be achieved by adding the requirement that the sum of the weights for both independent directions of

와

방향으로의 색상 가중치는 독립적으로 계산되지만, 위에서

와

에 대한 계산 세트의 표기법은 행렬 형식의 단일한 표기법으로 조합될 수 있다:in the above implementation

Wow

The color weights in the directions are calculated independently, but

Wow

The notations of the set of computations for can be combined into a single notation in matrix form:

,

은 고유한 가중치 행렬(

)을 얻게 되고, 여기서 각각의

는

와

방향 좌표 양자 모두에 대한 색상 가중치를 포함한다. 상기 계산에 의해 기술되는 OCW의 구현예에서, 각각의 가중치 행렬

는 대각 행렬이고, 이는 주된 대각선에 위치하지 않은 요소가 0임을 의미한다. 위의 행렬 방정식에서 알 수 있는 바와 같이,

의 계산은

에 의존하는 항을 포함하지 않으며, 마찬가지로

의 계산은

에 의존하는 항을 포함하지 않고, 따라서 이러한 OCW의 구현에서 색상 가중치의 계산은

와

방향에 대해 독립적이다.Each color in the matrix notation above

,

is the unique weight matrix (

), where each

Is

Wow

Contains color weights for both directional coordinates. In the implementation of OCW described by the above calculation, each weight matrix

is a diagonal matrix, which means that elements not located on the main diagonal are zero. As can be seen from the matrix equation above,

the calculation of

does not include a term dependent on

the calculation of

does not include a term that depends on

Wow

direction independent.

OCW by segment

,

좌표와 정렬되지 않은 경우, OCW는 상이한 각도들에 대해 상이한 효과들을 초래할 수 있고, OCW 결과는 상이한 웨이퍼들에 대해 일관성이 적어지며, 그 결과 웨이퍼-대-웨이퍼 (오버레이) 성능의 안정성을 감소시킨다.The alignment marks may include structures having one or more preferential directions. For example, the mark may be a sieve BF mark as shown in FIG. 14 , comprising two grids, the orientation of which may not be aligned with the coordinates used for OCW. Sub-segmentation of body BF marks, that is, their pitch and direction

,

If not aligned with the coordinates, OCW can lead to different effects for different angles, and the OCW result is less consistent for different wafers, resulting in reduced stability of wafer-to-wafer (overlay) performance .

,

좌표와 정렬되지 않은 우선적인 방향(예컨대, 마크 구조체에 있어서 지배적인 방향)을 갖는 경우, 새로운 대안적인 좌표 세트를 사용하는 OCW를 수행하여 색상 가중치를 결정하는 것이 바람직할 수 있으며, 여기서 새로운 좌표 방향은 마크의 하나 이상의 우선적인 방향과 일치한다. 예를 들어, 체형 BF 마크의 경우, 도 14에 도시된 격자 방향은 새로운 좌표

,

를 결정하기 위해 우선적인 방향으로 사용될 수 있다. 따라서, 일부 구현예에서, OCW를 수행하는 것은 새로운 좌표 세트

,

를 결정하는 것을 포함할 수 있고, 여기서

,

방향은 마크의 우선적인 방향, 예를 들어 체형 BF 마크의 피치 방향에 정렬될 수 있다. 새로운 좌표

,

는 종전의 좌표

,

와 독립적으로 선택될 수 있다. 세그먼트별 OCW 라 지칭될 수 있는 이러한 구현예에서, 새로운 좌표는 위에서 정규 OCW 방법에 대해 설명된 바와 같이 OCW를 수행하기 위해 사용된다. 종전의 좌표 세트

,

에서 하나 이상의 결정된 OCW 위치 및 색상 가중치의 수식이 필요한 경우, 색상 가중치가 결정된 후에 새로운 세트

,

로부터 이전 세트

,

로의 좌표 변환이 수행될 수 있다.alignment mark

,

If you have a preferred orientation that is not aligned with the coordinates (eg, a dominant orientation in a mark structure), it may be desirable to perform an OCW using a new alternative set of coordinates to determine the color weights, where the new coordinate orientation coincides with one or more preferential directions of the mark. For example, in the case of a body type BF mark, the grid direction shown in FIG. 14 is a new coordinate

,

can be used in the preferential direction to determine Thus, in some implementations, performing OCW is a new set of coordinates.

,

may include determining, where

,

The direction may be aligned with the preferential direction of the mark, for example the pitch direction of the body shape BF mark. new coordinates

,

is the previous coordinates

,

can be selected independently of In this implementation, which may be referred to as segment-by-segment OCW, the new coordinates are used to perform OCW as described for the regular OCW method above. old coordinate set

,

If a formula for one or more determined OCW positions and color weights is required in

,

from the previous set

,

A coordinate transformation into .

The mathematical principles used to determine color weights based on overlay data using segment-by-segment OCW are as follows:

방향에 대해 상대적인, 새로운 방향

및

의 법선의 각도를 φ₁ 및 φ₂ 라 한다. 각도 φ₁ 및 φ₂ 는 동일하지 않을 수도 있고, 서로간에 180 °의 각도를 형성하지 않을 수도 있으며, 즉

과

방향은 평행하지 않을 수도 있다. 각도 φ₁ 및 φ₂ 는 직교할 수도 있고, 서로 간에 다른 각도를 형성할 수도 있다.positive in coordinates

relative to direction, new direction

and

Let the angles of the normal to φ ₁ and φ ₂ be. The angles φ ₁ and φ ₂ may not be equal and may not form an angle of 180° with each other, i.e.

class

The directions may not be parallel. The angles phi ₁ and phi ₂ may be orthogonal, and may form different angles with each other.

The relationship between the new coordinates and the old coordinates can be expressed as:

과

를 사용하여 위에서 설명한 방법으로 수행되는데, 여기서

과

에 대한 색상 가중치는 서로 독립적으로 계산된다.OCW is a new set of coordinates

class

This is done in the way described above using

class

The color weights for are calculated independently of each other.

로

과

를 표현하기 위해, 새로운 좌표계로부터 종전의 좌표계로의 변환이 다음 식에 따라 수행된다:coordinate set

as

class

To express , the transformation from the new coordinate system to the old coordinate system is performed according to the following equation:

This leads to the following equation.

좌표로 표현되는

는 다음과 같다.from this

expressed in coordinates

is as follows

로 두 방향에 대해 독립적으로 결정된다. 새로운 좌표

로 표현될 때 OCW 위치

및

가 서로 독립적이라는 것은,

가

가중치 또는

위치에 의존하지 않으며,

가

가중치 또는

위치에 의존하지 않음을 의미한다. 결정된 OCW 위치가 종전의 좌표

로 표현될 때(여기서,

및

는

및

함수로 표현됨), 최적화된 위치

및

양자 모두는

와

두 방향에서 그리고 두 색상 가중치

과

로 색상의 가중된 조합으로 표현될 수 있다. 좌표

에 대해 가중치 합의 제약이 충족되는 경우, 좌표

로 표현된 해당 색상 가중치에 대한 제약도 충족된다: With segment-by-segment OCW, the color weights are assigned to the new coordinates.

is determined independently for both directions. new coordinates

OCW position when expressed as

and

are independent of each other,

go

weight or

location independent,

go

weight or

This means that it is not dependent on location. The determined OCW position is the previous coordinates

When expressed as (here,

and

Is

and

expressed as a function), the optimized position

and

both are

Wow

in two directions and two color weights

class

can be expressed as a weighted combination of colors. coordinate

If the weight sum constraint is satisfied for

The constraint on the corresponding color weight, expressed as , is also satisfied:

방향이 0 °이고

방향이 90 ° 인 것으로 기술될 수 있다. 이러한 특정 예의 경우, 위에서 설명한 세그먼트별 OCW 알고리즘에 따르면, 좌표

와

로 표현되는 색상 가중치 행렬이 다음과 같이 표현될 수 있다:An example of such segment-specific OCW for a body BF mark with a preferred orientation with angles φ ₁ = - 45° and φ ₂ = 45° is provided below. The previous coordinates were

direction is 0°

The direction can be described as being 90°. For this particular example, according to the segment-by-segment OCW algorithm described above, the coordinates

Wow

The color weight matrix represented by , can be expressed as:

와

로 표현되는 OCW 위치는 다음과 같이 표현될 수 있다:From this color weight matrix determined for the new coordinates based on the transformed coordinate angles of ϕ ₁ = - 45 ° and ϕ ₂ = 45 °,

Wow

The OCW position represented by , can be expressed as follows:

Extended OCW

좌표에 기초하는 정규 OCW의 예에서,

와

방향에 대한 색상 가중치

및

는 서로 독립적으로 결정된다. 세그먼트별 OCW에서는, 색상 가중치

및

이

좌표를 사용하여 서로 독립적으로 결정되지만, OCW 위치를 종전의 좌표

로 표현할 때,

및

는 나머지 방향과 관련되는 가중치

및

그리고 색상

및

에 무관하지 않다. 두 방법 모두, 독립적으로 두 방향으로 색상 가중치를 결정함으로써 최적의 색상 가중치를 결정할 때 2의 자유도를 제공한다.

In the example of normal OCW based on coordinates,

Wow

color weight for direction

and

are determined independently of each other. In OCW by segment, color weighting

and

this

Although determined independently of each other using coordinates, the OCW location is

When expressed as

and

is the weight relative to the rest of the direction

and

and color

and

is not irrelevant to Both methods provide two degrees of freedom in determining the optimal color weights by independently determining the color weights in two directions.

In some implementations of OCW, the degree of freedom used to determine the OCW location is further increased to be greater than 2 for every color. This can be achieved by adding an additional coefficient to the color weights to determine the OCW location. Specifically, the increase in degrees of freedom may be determined by adding a separate color weighting element at one or more positions of the color weighting matrix that are not on the main diagonal. The resulting color weight matrix contains three or more distinct color weights independent of each other. Color weights are independent because the value of one color weight does not depend on the value of any one or more of the other distinct color weights.

및

의 함수로서 상호 연결된다.This approach differs from segment-by-segment OCW, which may have non-zero color weight matrix elements in locations other than the dominant diagonal, but each color weight matrix element contains only two separate independent color weights.

and

are interconnected as a function of

An implementation of OCW with 3 or more degrees of freedom is extended OCW, where two independent additional color weights are added to each color weight matrix to determine the OCW.

과

가 결정된다. 네 가지 별개의 색상 가중치

가 모두 서로 독립적으로 결정될 수 있다. 위의 행렬은 확장된 OCW에서 OCW 위치

,

를 계산하는 데에 사용된다:In extended OCW, the color weight matrix above is used

class

is decided Four distinct color weights

can all be determined independently of each other. The above matrix is the OCW position in the extended OCW

,

is used to calculate:

In extended OCW, the weight sum constraint may also be applied, ie the following set of equations, expressed here in matrix form, may have to be satisfied by the color weights.

In non-matrix form, the extended OCW equation can be expressed as

와

방향으로 또는

과

방향으로 피처를 가질 수 있으며, 이는 대응하는 및/또는 상관되는 변형에 의해 영향을 받은 것이다. 이러한 경우, 최적화된 색상 가중치 위치가 양 방향의 색상 위치에 의존하도록 하면 보다 정확한 결과를 얻을 수 있으므로, 확장된 OCW에 의해 최적화가 증대 및 개선되고 오버레이가 향상될 수 있다.Where the mark includes one, two or more, or all features spanning a plurality of directions, formed as part of the same process layer, a deformation occurring in that process layer affects the features in some or all of these plurality of directions. can affect For example, the mark is

Wow

in the direction or

class

It may have features in a direction, which are affected by corresponding and/or correlated deformations. In this case, more accurate results can be obtained by making the optimized color weight position depend on the color position in both directions, so the optimization can be increased and improved by the extended OCW and the overlay can be improved.

The above method in which linear weighting is applied to measurement parameters (alignment data) can be generalized to a mapping of measurement parameters. As noted above, this mapping is typically a linearly weighted sum of measurement parameters. However, the present invention is not limited to linear weighted sums, and trained mappings such as those used in machine learning algorithms may be used.

The above method for optimal color weighting is not limited to the use of color as an operating parameter of interest, and different polarization modes lead to different measurement parameters, such as those measured by an alignment sensor system (measuring mark positions) for example. may be used to In addition, the degree of coherence may be considered as an operating parameter (if the degree of coherence is adjustable, temporal and/or spatial coherence may be adjusted, for example, by adjusting the laser characteristics). Also, different measurement parameters may be considered, for example where the operating parameter is color and the sensor system is a level sensor, the measurement parameter may be a focus value associated with the substrate being the target of the level sensor measurement. A quality parameter associated with the level sensor measurement is the focus error generated during exposure of the substrate.

6A is a flowchart schematically illustrating the wafer alignment, exposure and overlay measurement process. As shown, in step 601 a wafer alignment scan is performed using a number of different colors (operating parameters of the sensor system). In step 602, the color recipe is used to determine how the different color measurements should be applied to determine wafer marker positions for aligning the wafer. In step 603 the wafer (or layer) is aligned by the device using the marker positions determined from the previous step. In step 604, adjustments to wafer positioning are made based on data provided from measurements made on the wafer at a previous stage (ie, after the underlying layers of the wafer have been processed). In step 605 the wafer is exposed to a processing stage (as described above with reference to FIG. 1 ). In step 606, overlay measurements are performed and the overlay data is provided to a training data processor (APC). In step 607, the APC evaluates the overlay data to determine any deviations from the expected positions, which are used to provide corrections for the next wafer/layer alignment.

6B is a flowchart schematically illustrating another wafer alignment, exposure and overlay measurement process. The same steps described above with respect to FIG. 6A have the same reference numerals in FIG. 6B . One difference is that in step 602', which occurs in the same place as step 602 in FIG. 6A, an optimal color weight is used to determine the marker positions for aligning the wafer, instead of applying the same color recipe each time. that it will be Another difference is that in step 607', instead of simply determining the alignment correction determined from the overlay, more data is used as training data. This data includes alignment measurement data 608 for each color obtained in step 601 and overlay data from previous wafer measurements (step 606). Any other relevant data, such as stack data 611 , may also be used for training data. The training data then updates 609 the optimal color weights used in step 602', as well as providing wafer positioning alignment corrections in step 604, and the substrate used in step 603 used to update 610 the grid model.

As can be seen from FIG. 6B , while learning as the system is used, the weights for the OCW measurement and alignment procedure are continuously updated. Accordingly, a major advantage of the method described above is that any local device-specific variations in the operating parameters of the employed sensor system can be accounted for and corrected. The more sensor systems and devices used, the better the alignment will be.

The optimal color weighting (OCW) technique described herein combines alignment information from all wavelengths simultaneously measured and optimal set weights to be used for linear combinations of colors, such that the measured alignment positions are minimally responsive to mark deformation. to calculate However, the properties of the stack in which the marker is etched or the stack overlying the mark may change over time. When these changes affect the optical properties (eg refractive index) of the stack(s), the mark's response to various operating parameters (color, polarization state) may also change accordingly. What this change in stack characteristics means is that the particular optimal set of weights to be used for the linear combination of operating parameters may no longer be optimal.

Additionally, mark deformation may change over time, due to, for example, changes in the characteristics of processing equipment (such as CMP tools and deposition equipment). The mark deformation may be, for example, a change in the sidewall angle of the mark as it is etched into the substrate and/or a change from a bottom tilt-like deformation to a top tilt deformation. A consequence of the change in mark deformation properties is that the previously determined optimal set of weights associated with the linear combination of colors is no longer optimal (e.g., suboptimal alignment of the substrate may result in overlay quality being an issue). exist) can be.

Herein, it is proposed to periodically determine an optimal set of weights that provides the least amount of overlay variation between substrates. If the calculated substrate-to-substrate variation in a quality parameter based on the determined set of weights deviates significantly from previously observed wafer-to-wafer variation in such quality parameter, a change in one or more processes within the semiconductor manufacturing process occurs. there is a possibility that Alternatively speaking: the likelihood that one or more process changes within the semiconductor manufacturing process have occurred if the new set of weights determined based on the newly observed substrate-to-substrate variation of the quality parameter deviates significantly from the previously determined set of weights. There is this.

In one embodiment, the state of the semiconductor manufacturing process is determined by a) determining an optimized value of the operating parameter (eg, a new set of weights associated with the color of the alignment), and b) setting the determined operating parameter as a reference operating parameter (eg, for example, by comparing it to a previously determined set of weights associated with the color of the alignment, and c) determining a state based on this comparison.

For a previously determined set of weights associated with the color of the alignment sensor, the reference operating parameter may be expressed as a vector. For example, when the optimal weight for red is +1 and the optimal weight for green is -1, the reference operation parameter may be expressed as a vector <1, -1>. Such vectors have no components parallel to their orthogonal complement<1,1>. For example, the component vector <1, -1> is associated with the top tilt deformation of the (etched) alignment mark and the component vector <1,1> is associated with the sidewall angle deformation of the (etched) mark. For process variations, the new optimal set of weights for red could be 1.2 and 0.6 for green. The new optimized value of the operating parameter can now be expressed as the vector 1.2 * <1, -1> + 0.6 * <1,1>. Clearly the vector <1,1> is more relevant, indicating that the etched alignment marks are (also) deformed according to the sidewall angle profile. A semiconductor manufacturing process can be monitored by monitoring a vector representation of an optimal operating parameter.

In one embodiment, the optimal set of weights is initially determined based on quality parameter (substrate-to-substrate) fluctuations and sensitivity to fluctuations in operating parameters. The subsequently measured substrate may be further characterized by a set of orthogonal (or orthonormal) vectors representing the ratio of operating parameters present within the substrate-to-substrate variation of the measurement data. For example, if the alignment data associated with red exhibits a wafer dependent variation f(w_i) (a function of wafer "w_i") and the alignment data associated with green exhibits -f(w_i), the vector representation < 1, -1> It can be said that it exists in this measurement data. When process changes occur, changes in alignment data may change; For example, red may exhibit a wafer-dependent variation 3*g(w_i), while green may exhibit a wafer-dependent variation g(w_i), the vector representation of which is <3,1>. The vector <3,1> can be expressed as 1 * <1, -1,> projected onto <1, -1> and 2 * <1,1,> projected onto <1,1> (<1, 1> is the orthogonal complement of <1, -1>). Therefore, due to the process change, the component <1,1> was introduced into the variation of the measurement data that was not previously present. The optimal set of weights can now be optimized to suppress the strongest component (the vector with the largest amplitude) observed in the corresponding measurement data set. It is proposed to periodically project the newly measured operating parameters onto an orthogonal basis image corresponding to the original calibration moment of the optimal set of weights. If the amplitude distribution across the vector changes, it is possible that a process change has occurred.

In one embodiment, the state of the semiconductor manufacturing process is monitored by: a) obtaining an optimized value of the operating parameter as determined by an embodiment of the present invention (the optimized value of the operating parameter is represented by a first vector with respective operating parameters as basis); b) obtaining a variation across operating parameters of a substrate-to-substrate variation of the measurement data; c) determining a new value of the operating parameter associated with the expected minimum substrate-to-substrate variation of the measurement data, the new value of the operating parameter being represented by a second vector having the respective operating parameters as a basis; and determining a state of the semiconductor manufacturing process based on the comparison of the first vector and the second vector.

In an embodiment, the following steps are performed: a) measurement data for a plurality of substrates and a plurality of operating parameters are obtained; b) a set of vectors representing a linear combination of operating parameters present in the measurement data is determined, c) optionally: if a previously determined optimal set of weights for the operating parameter is available, the previously determined optimal set of weights is determined. The projection of the vector set into the space defined by Vectors associated with singular values , which are particularly important, represent combinations of operating parameters that do not contain information about mark transformations). f) a so-called "zero kernel" is computed based on a vector associated with a singular value that is near zero It is a linear vector space representing).

In one embodiment, outliers are ranked and all outliers that exceed a threshold are filtered out. A zero kernel is determined based on the vector associated with the unfiltered singular value.

The change in processing state may be captured by projection of the newly determined operating parameter data (associated with one or more substrates) onto the determined zero kernel. When the properties of the mark deformation and/or the stack properties change, the projection of the new operating parameter data to the zero kernel changes, so that the zero kernel can be used in a method of monitoring and/or determining changes in the processing state.

In one embodiment, an initial set of vectors representing variations in measurement data and/or performance data is determined for a plurality of operating parameters. The vector represents a linear combination of operating parameters associated with reduced substrate-to-substrate variation in measurement and/or quality parameters. The procedure for determining the vector set is repeated for a plurality of different mark variants and/or stack properties. As such, the entire vector set describes the optimally chosen operating parameters (combinations) for a standard set of mark deformation and/or stack characteristics. New measurement data is acquired periodically for a new substrate and a number of operating parameters. The newly acquired measurement data is used to obtain a new vector representation associated with the new optimal operating parameter. The newly acquired vector representation is projected onto an initial set of vectors, and the relative weights associated with the projections to each of the sets of vectors are computed. Relative weights are then ranked and relative weights below a threshold are considered zero (eg, components below a certain relevance are filtered out). In one embodiment, an optimal operating parameter is monitored and its vector representation is decomposed into vectors belonging to the initial vector set. Ranking of the components and application of threshold values is then performed. The relative intensity of non-zero components can be considered a KPI of the semiconductor manufacturing process, how the mark etched from these components (vectors) is affected (eg top tilt, sidewall angle change, etc.) As a result, it is possible to estimate which process step has changed. For example, a significant change in the relevance of the vector <1, -1> may indicate a change in the top tilt characteristic of the alignment mark, which is typically associated with drift in the CMP process step.

One application for implementing the above principle is in correcting the so-called mark-to-device offset (MTD). This is the effect if the shift to the nominal of the alignment mark is different from the surrounding product features. This effect is caused by the presence of product features having pitches (ie, feature widths or spacing between features) significantly smaller than the alignment marks, so that exposure light passes through different portions of the projection lens. In the case of lens aberrations due to lens heating, for example, this results in a pitch-dependent shift. These effects are not stable from wafer to wafer or lot to lot as they depend on the history of product features and lighting settings on a particular scanner, and therefore cannot be fully corrected by the APC system.

Proposed solutions to this problem include mark design and computation MTD (c-MTD). Mark design is limited by design rules, detectability and aberration sensitivity, whereas cMTD does not consider processing influences.

Another method involves the use of sub-segmented marks. Here, additional marks with a finer pitch (similar to the pitch of product features) are included on the substrate. So-called sub-segmented marks consist of coarse pitch marks (used for alignment) and fine pitch marks (to comply with product design rules). Exposure light for illuminating fine pitch marks passes through the same projection lens portion as exposure light for product features. Pitch dependent shifts or MTDs caused by lens aberrations result in litho-induced mark asymmetry. This mark asymmetry results in differences in alignment positions for different colors of the alignment sensor.

Although the OCW principle can be applied to sub-segmented marks to determine weights for different colors (operating parameters) for sub-segmented marks, in this case the tolerance for effects of lens aberrations for different colors can be set. The training data used to determine the color weights is taken from the product overlay data.

It should be noted that OCW is generally applied to minimize the effect of process-induced mark asymmetry, and is particularly suitable for layers where processing issues are expected (mainly back-end optical lithography - BEOL). However, MTD is primarily a matter of front-end optical lithography - FEOL where extreme lighting setups are used.

7 illustrates the MTD shift effect in three scenarios. In Fig. 7(a), the effect of lens aberration Z on the perceived overlay error (OVL) for smaller pitches of device (product) features is denoted as ΔD, which is substantially linearly proportional to lens aberration Z, ΔD = m1 + SdZ, where m1 is a constant offset and Sd is the device aberration sensitivity. In Fig. 7(b), the larger pitch alignment marker exhibits a shift ΔM in the detected marker position (APD), which is again substantially linearly proportional to Z and independent of the illuminating radiation (color), thus lyso-induced color asymmetry. there will be no In this case ΔM = m2 + SmZ, where m2 is a constant offset and Sm is the principal marker aberration sensitivity. Since the illumination radiation is passing through different parts of the projection lens, ΔM does not have the same relationship as ΔD (ie, the gradient of the graph).

In Fig. 7(c) the effect on the sub-segmented mark is shown. There is a color (wavelength) dependence, which results in a lyso-induced asymmetry (different measures for different colors). where ΔM = m3 + SmZ + K(λ) [Sm-Ss] Z , where Ss is the segmented mark sensitivity and K(λ) is the stack sensitivity. However, as discussed above, by using the principle of OCW, where different colors are weighted differently, it is possible to determine a color-weighted measure that closely approximates the true overlay error, which takes into account lens aberration effects that cause MTD shifts. will be.

To correct the color weights to be insensitive to MTD, the correction set may include a lens heating effect. If marks with intentional MTD shifts are used to calculate for each color the sensitivity of the alignment position to the MTD, calibration data may be obtained from measurements performed using designer segmented marks (DSM). . An exemplary calibration is schematically illustrated in FIG. 8 . Another possibility is to calculate the sensitivities of different colors using computational methods.

The same principle can be applied to metrology marks used to measure overlay, since such marks can also be sub-segmented and will suffer from similar mark-to-device offsets.

Another problem that can be solved by the OCW principles described herein relates to the strain that can occur across a substrate or wafer. So far, wafer alignment settings such as mark layout, color(s) and mark type are used for the entire wafer. However, mark asymmetry typically varies across the wafer in different regions. Using the same color settings for wafer alignment of the entire wafer can result in greater wafer-to-wafer variation as it does not account for changing mark asymmetry. For example, in situations where wafer edge mark asymmetry is large, it is current practice to ignore marks at the wafer edge if an unacceptably large error occurs.

Accordingly, embodiments may provide for optimization by the use of OCW such that wafer alignment is applied across a wafer surface area by applying different color weights to different areas or regions of the wafer. Thus, different color weights can reduce overlay errors in regions where the mark asymmetry is greater than the rest of the wafer, or in regions where the mark asymmetry is different from the rest of the wafer. It also provides greater flexibility in optimizing the wafer alignment layout if accurate color weighting is applied per region/region (ie edge-to-center).

9 shows an alignment mark asymmetry plot across the wafer. This plot shows the variation between the four colors for an array of alignment marks on the wafer. The larger the arrow associated with the mark, the greater the degree of mark asymmetry. The mark asymmetry is clearly greater at the edge of the wafer. A similar effect can be seen in Figure 10, where plot (a) shows a product overlay wafer map with the active color near infrared (NIR). Plot 10(b) shows an in-product overlay wafer map for the same wafer using two-color weighting. Plot 10(c) shows the difference between plots 10(a) and 10(b), it is clear that there is a significant difference between NIR and TCW. This difference is most significant in the area distributed around the edge of the wafer. This demonstrates that the effect of mark asymmetry varies across the wafer. To investigate this behavior, TCW analysis was performed on the edge of the wafer and the center of the wafer to determine the best color weights for the two regions on the wafer.

The improvement in wafer alignment performance can be shown by applying two-color weighting (TCW) with reference to only two colors. There are two graphs in Fig. 11, one for the mark at the edge of the wafer and the other for the mark at the center. Each graph shows how the overlay error varies for two orthogonal directions parallel to the wafer surface (X-Overlay and Y-Overlay) as a function of different two-color weighting combinations. The two colors in this case are green (ie visible light at approximately 510 nm) and near infrared (NIR). The two-color weights are -1 to 2 for green and 2 to -1 for NIR. The sum of the weights is always 1.

11 shows that the optimal color weights (when the overlay error is minimal) are different for the edge and center of the wafer. For the edge of the wafer, the combination of green with weight -1 and NIR with weight 2 gives the best performance, whereas for the center of the wafer, the combination of green with weight -0.4 and NIR with weight 1.4 gives the best performance. provides performance. The difference between the weights is 20%.

It will be appreciated that greater improvements can be realized by using more colors/color weights.

Applying color weighting to different regions of the wafer (ultimately per mark) reduces the effect of mark asymmetry at the edges as well as at the center of the wafer. There are different color settings (colors, weights) for each region of the wafer to which this method can be applied. In this way, the user can optimize the wafer alignment strategy for different regions of the wafer and make fine adjustments to the wafer alignment to reduce wafer-to-wafer variation during the process.

In the wafer processing method described above, two sets of overlay corrections that affect overlay wafer-to-wafer variation are applied. One correction is due to alignment. Before the wafer is exposed, alignment marks on that wafer are measured with a scanner alignment sensor and a set of corrections are calculated for the alignment measurements using a predefined alignment model. A correction is then applied to the wafer during exposure. The remaining corrections are wafer-by-wafer overlay process corrections. After exposure of the wafer, it is sent to an overlay metrology tool to measure the overlay marks. The measured overlay is used to calculate the correction set used to set the subsequent exposure. This correction can be performed on a wafer-by-wafer basis.

Each of the two correction methods has advantages and disadvantages. Alignment is always wafer-by-wafer and is a real-time correction, but the limited measurement time limits the number of alignment marks and can be adversely affected by alignment mark asymmetry. Per-wafer overlay correction has more correction capability - it can measure many overlay marks per wafer - Correction is usually not done in 'real time': for example, a time filter is used for run-to-run control .

Alignment and wafer-by-wafer overlay correction have the same goal of reducing overlay wafer-to-wafer variation. The setup of the two methods is performed separately: in the case of alignment correction, the setup is based on the optimization of the alignment model, sampling and color; In the case of overlay correction, on the other hand, the setup is based on optimization of the overlay model, sampling, measurement frequency, etc. However, these independent setups do not take into account the interaction between alignment and overlay. So the setups may not be optimal.

This is schematically illustrated in FIG. 12 . The figure above shows the process of determining the OCW for alignment correction using several different colors, models and layouts. Overlay measurements are used to evaluate the optimal combination of color, model and layout, and, as described above, optimal color weights are determined for the alignment correction process. The diagram below shows the corresponding process for correcting the overlay using different frequencies, models and layouts. Overlay measurements are used to evaluate the optimal combination of frequency, model, and layout, and in turn optimal color weights are determined for the alignment correction process. The optimal color weights will be different for the two correction procedures.

In an embodiment of the present invention, as shown in FIG. 13 , an evaluation of the overlay is used to provide one evaluation that determines the best combination for both alignment correction and overlay correction. Thus, by simultaneously evaluating settings based on the same overlay measurements, a single combination of alignment and overlay setting parameters that is optimal for the combination of alignment and overlay correction is determined, but only one or the other of the alignment and overlay corrections. It may turn out to be different from the setting determined for the bay.

The OCW (Optimal Color Weighting) method described above is a very effective way to minimize the effect of processing artifacts on the control of the lithographic apparatus (eg, affecting the marks). However, it is not always necessary to use the OCW method in all cases. a) processing-induced wafer-to-wafer quality parameter (eg overlay) variations may be small or non-correctable (in which case processing-induced variations will not be present in the final result) and/or b ) mark is sufficiently robust to processing artifacts and reading the mark (or stack in the case of a level sensor reading) for any selected operating parameter may provide similar results. An assessment of the merits of OCW may have to be performed for each layer on the substrate that is subjected to the semiconductor manufacturing process. As an embodiment, for a set of layers of interest, i) wafer-to-wafer variation in correctable error associated with a quality parameter, and ii) wafer-to-wafer variation in measurement data variation across operating parameters are determined. do. Layers that have wafer-to-wafer variations in measurement data variations and/or wafer-to-wafer variations in correctable errors below certain thresholds may be excluded from the OCW framework.

In one embodiment, a layer associated with a substrate comprises: a) a first substrate-to-substrate variation in a quality parameter associated with such layer; and b) an evaluation of a second substrate-to-substrate variation of variation between measurement parameters associated with this layer across the selected operating parameters.

As an embodiment, this layer is selected for application of the OCW algorithm when the first substrate-to-substrate variation and the second substrate-to-substrate variation exceed thresholds.

In one embodiment, the first substrate-to-substrate variation and the second substrate-to-substrate variation are configured as KPIs of the semiconductor process. These KPIs are monitored in a timely manner, for example by displaying them in one plot (x-axis is the value of the first KPI associated with the first substrate-to-substrate variation and the y-axis is the second substrate-to-substrate variation) value of the second KPI associated with ).

If both the first and second KPIs exceed the threshold, a decision may be made to determine a new OCW recipe by recalculating an optimal operating parameter configured to yield a minimum substrate-to-substrate variation in the quality parameter. As fluctuations in quality parameters and variability in measurement data across operating parameters are combined, it is evident that a) measurements are clearly affected by changes in processing, and b) as a result performance (expressed as quality parameters) becomes an issue. conclusions can be drawn. Thus, recalculation of the optimal operating parameters will probably improve performance (eg, reduce first substrate-to-substrate variation) and probably make sense.

Alternatively, the first and second KPIs may be combined into a single KPI. In this case, a decision can be made to determine a new OCW recipe when a single KPI exceeds a threshold.

If only the second KPI exceeds the threshold, the mark may be affected by the change in processing, but the performance is not significantly degraded. It may be concluded that the current OCW settings (recipes containing optimal operating parameter settings) are suitable for controlling the changed processing.

Process-induced mark deformation and/or stack characteristic changes are not responsible for the observed change in quality parameter variability if only the first KPI exceeds the threshold. Therefore, recalculating the optimal operating parameters becomes less meaningful.

Further embodiments of the invention are presented in the following numbered list of clauses:

1. A method for determining one or more optimized values of an operating parameter of a sensor system configured to measure a property of a substrate, the method comprising:

determining a quality parameter for the plurality of substrates;

determining, for a plurality of values of the operating parameter, a measurement parameter for the plurality of substrates obtained using the sensor system;

comparing the substrate-to-substrate variation of the quality parameter with the substrate-to-substrate variation of the mapping of the measurement parameter; and

A method for determining one or more optimized values of an operating parameter of a sensor system comprising determining one or more optimized values of the operating parameter based on the comparison.

2. The method of clause 1, wherein the mapping is a weighted sum, a non-linear mapping or a trained mapping based on machine learning techniques.

3. The method of clause 1, further comprising determining an optimal set of weighting factors for weighting a measurement parameter associated with a first value of an operating parameter and a measurement parameter associated with a second value of the operating parameter based on the comparison. A method for determining one or more optimized values of an operating parameter of a sensor system, comprising:

4. Method according to any of clauses 1 to 3, wherein the quality parameter is an overlay or focus parameter.

5. The sensor system according to any one of clauses 1 to 4, wherein the measurement parameter is a position of a feature provided on the plurality of substrates or an out-of-plane deviation of a position on the substrate. A method for determining one or more optimized values of an operating parameter.

6. A method for determining one or more optimized values of an operating parameter of a sensor system according to any one of clauses 1 to 5, wherein the operating parameter is a parameter associated with a light source from the sensor system.

7. The method of clause 5, wherein the operating parameter is a wavelength, a polarization state, a spatial coherence state, or a temporal coherence state of the light source.

8. A method for determining one or more optimized values of an operating parameter of a sensor system according to any one of clauses 1 to 7, wherein the quality parameter is determined using a metrology system.

9. The quality parameter according to any one of clauses 1 to 6, wherein the quality parameter is determined using a simulation model that predicts the quality parameter based on any of context information, measurement data, reconstructed data, hybrid metrology data. A method for determining one or more optimized values of an operating parameter of a sensor system.

10. A method for determining a state of a semiconductor manufacturing process, comprising:

determining an optimized value of the operating parameter according to clause 1;

comparing the determined operating parameter with a reference operating parameter; and

determining the condition based on the comparison.

11. A method of optimizing measurement data from a sensor system configured to measure a property of a substrate, the method comprising:

obtaining overlay data for a plurality of substrates, wherein the overlay represents a deviation between a measured position and an expected position of the alignment marker on the substrate and comprises a plurality of measurements of alignment marker positions made by the sensor system; each measurement uses a different operating parameter of the sensor system;

using an operating parameter, based on the obtained overlay data and such that for each of the different operating parameters, a weighted adjustment to the measurements made by the sensor system for all the different operating parameters is combined so that the overlay is minimized. and determining a weight for adjusting the obtained measurement.

12. The method of clause 11, wherein the operating parameter is a parameter associated with a radiation source from the sensor system.

13. A method for determining one or more optimized values of an operating parameter of a sensor system according to clause 12, wherein the operating parameter is a wavelength, a polarization state, a spatial coherence state, or a temporal coherence state of the light source.

14. The method according to any one of clauses 1 to 9, wherein determining one or more optimized values of the operating parameter based on the comparison is performed for different regions of the substrate.

15. The method of clause 14, wherein the different regions include a region proximate to an edge of the substrate and a region proximate to a center of the substrate.

16. The method of clauses 14 or 15, wherein each zone comprises one or more alignment marks applied to the substrate.

17. The method of clauses 14 or 15, wherein each zone corresponds to a respective one of a plurality of alignment marks applied to the substrate.

18. The method according to any one of clauses 1 to 9, wherein the measurement parameter is a measured position of a mark and the quality parameter is a mark-to-device shift, and the optimized value of the operating parameter is substrate-to-device. A method for determining one or more optimized values of an operating parameter of a sensor system, the method being determined to optimize the quality parameter so that substrate variation is minimized.

19. The operating parameter of clause 18, wherein the operating parameter is a parameter associated with the radiation source, radiation from the source is directed to the substrate, and an optimized value of the operating parameter is weighted to adjust the measurement obtained using the operating parameter. determined by the method.

20. The method of clause 19, wherein radiation from a source directed to the substrate is received by the sensor system after targeting the substrate.

21. The method of clause 19, wherein the weighting comprises the effect of heating a lens of a lens used to direct radiation to a substrate and/or to receive radiation by a sensor system.

22. The sub-segmented mark according to any one of clauses 18 to 21, wherein an intentional mark-to-device shift is applied to determine the sensitivity of the operating parameter to the mark-to-device shift. The method further comprising: determining a weight for an operating parameter for measuring the sub-segmented mark using the measurement obtained from the substrate.

23. The sensor system of any of clauses 1-9, wherein to optimize an operating parameter of a metrology system used to control processing of the substrate, the sensor system is configured to measure a first characteristic of the substrate prior to processing. a first sensor system associated with a first measurement system configured and a second sensor system associated with a second measurement system configured to measure a second characteristic of the substrate after processing, the method comprising:

determining, for a plurality of values of the operating parameter, a first set of measurement parameters for the plurality of substrates obtained using the first sensor system;

determining, for the plurality of values of the operating parameter, a second set of measurement parameters for the plurality of substrates obtained using the second sensor system; and

comparing the substrate-to-substrate variation of the quality parameter with the substrate-to-substrate variation of the mapping of the measurement parameter to each of the first and second sets of the measurement parameter;

wherein determining the one or more optimized values of the operating parameter comprises simultaneously optimizing a first set of operating parameters associated with the first measurement system and a second set of operating parameters associated with the second measurement system; , wherein the optimization mitigates substrate-to-substrate variation of the second characteristic.

24. The method of clause 23, wherein the quality parameter is an overlay determined from a measured second characteristic of the substrate after processing.

25. The method of clause 1, wherein the quality parameter and the measurement parameter are associated with a particular layer associated with a plurality of substrates.

26. The method of clause 25, wherein a particular layer comprises: i) a first substrate-to-substrate variation of the quality parameter associated with the particular layer; and ii) an evaluation of a second substrate-to-substrate variation in variation between the measurement parameters associated with the particular layer.

27. The method of clause 26, wherein the particular layer is selected if the first substrate-to-substrate variation and the second substrate-to-substrate variation exceed thresholds.

A method for determining a state of a semiconductor manufacturing process, comprising:

obtaining an optimized value of the operating parameter using the method according to any one of clauses 1 to 27;

obtaining, for a plurality of values of the operating parameter, a measurement parameter for an additional substrate obtained using the sensor system;

determining a new value of the operating parameter associated with an expected minimum substrate-to-substrate variation of the measurement data; and

and determining a state of a semiconductor manufacturing process based on a comparison of the new value with the optimized value of the operating parameter.

29. The sensor of clause 1, wherein the optimized value of the operating parameter comprises a first set of values associated with a first coordinate of the measurement parameter and a second set of values associated with a second coordinate of the measurement parameter. A method for determining one or more optimized values of an operating parameter of a system.

30. Clause 29,

determining a third coordinate parallel to the first preferred direction of the mark;

determining a fourth coordinate parallel to a second preferred direction of the mark;

determining a third set of optimized values of the operating parameter associated with the third coordinate and a fourth set of optimized values of the operating parameter associated with the fourth coordinate;

determining transformations from the third and fourth coordinates to the first and second coordinates; and

transforming the determined optimized values of the operating parameter at the third and fourth coordinates into optimized values of the operating parameter at the first and second coordinates using the determined transform.

31. The method of clause 29, wherein the first value of the operating parameter is optimized independently of the second value of the operating parameter.

15 is a block diagram illustrating a computer system 100 that may be helpful in implementing the methods and flows disclosed herein. Computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or several processors 104 and 105) coupled with bus 102 for processing information. The computer system 100 includes a main memory 106, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 may also be used to store temporary variables or other intermediate information during execution of instructions to be executed by the processor 104. The computer system 100 provides static information for the processor 104. and a read only memory (ROM) 108 or other static storage device for storing instructions coupled to the bus 102. A storage device such as a magnetic disk or an optical disk for storing information and instructions. A 110 is provided and coupled to the bus 102 .

Computer system 100 may be coupled via bus 102 to a display 112 , such as a cathode ray tube (CRT) or flat panel or touch panel display, for displaying information to a computer user. An input device 114 comprising alphanumeric keys and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104 . Another type of user input device is a cursor control 116 , such as a mouse, trackball, or cursor direction keys, for communicating pointing information and command selections to the processor 104 and for controlling cursor movement on the display 112 . . Such input devices typically have two degrees of freedom in two axes, a first axis (eg, x) and a second axis (eg, y), allowing the device to specify a position in a plane. A touch panel (screen) display may be used as the input device.

Portions of the process may be performed by computer system 100 in response to processor 104 executing one or more sequences of one or more instructions stored in main memory 106 , according to one embodiment. These instructions may be read into main memory 106 from another computer-readable medium, such as storage device 110 . Executing the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. To execute the sequence of instructions contained in main memory 106, one or more processors in the multiprocessing device may be employed. In other embodiments, wired circuitry may be used instead of or in combination with software instructions. Accordingly, the description herein is not limited to any particular combination of hardware circuitry and software.

The term “computer-readable medium” as used herein refers to any tangible medium that participates in providing instructions to the processor 104 for execution. Such media may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks such as storage device 110 . Volatile media includes dynamic memory, such as main memory 106 . Transmission media includes coaxial cables including wires including bus 102 , copper wiring, and fiber optics. Transmission media may take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, and any other magnetic media, CD-ROM, DVD, any other optical media, punch card, paper. tape, any other physical medium having a pattern of holes, RAM, PROM, and EPROM, FLASH EPROM, any other memory chip or cartridge, a carrier wave as described below, or any other computer readable medium.

Various forms of computer-readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially be held on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and transmit the instructions over a telephone line using a modem. A modem local to computer system 100 receives data from the telephone line and uses an infrared transmitter to convert this data into infrared signals. An infrared detector coupled to bus 102 may receive data carried in the infrared signal and place such data on bus 102 . Bus 102 carries data to main memory 106 from which processor 104 retrieves and executes instructions. Instructions received by main memory 106 may optionally be stored in storage device 110 before or after execution by processor 104 .

Computer system 100 preferably further includes a communication interface 118 coupled to bus 102 . Communication interface 118 provides a two-way data communication coupling to network link 120 coupled to local network 122 . For example, communication interface 118 may be an Integrated Information Network (ISDN) card or modem to provide a data communication connection to a corresponding type of telephone line. As another example, communication interface 118 may be a LAN card to provide a data communication connection to a compatible local area network (LAN). A wireless link may be implemented. In any such implementation, communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

Network link 120 typically provides data communications over one or more networks to other data devices. For example, network link 120 may provide a connection via local network 122 to data equipment operated by host computer 124 or Internet service provider (ISP) 126 . ISP 126 now provides data communication services over a world-wide packet data communication network, now commonly referred to as "Internet 128". Both the local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals to carry digital data streams. Signals traversing various networks that carry digital data to or from computer system 100 and signals via communication interface 118 over network link 120 are exemplary forms of carriers that carry information.

Computer system 100 may send messages and receive data, including program code, via network(s), network link 120 , and communication interface 118 . In the example of the Internet, the server 130 may transmit the requested code for the application program over the Internet 128 , the ISP 126 , the local network 122 , and the communication interface 118 . One such downloaded application may provide for example lighting optimization of an embodiment. The received code may be executed by the processor 104 when received and/or stored in the storage device 110 , or other non-volatile storage for later execution. In this way, the computer system 100 may obtain the application code in the form of a carrier wave.

Embodiments of the present specification may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the present disclosure may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (eg, a computing device). For example, machine-readable media may include read-only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory device; electrical, optical, acoustic, or any other form of propagated signal (eg, carrier wave, infrared signal, digital signal, etc.); and the like. Also, firmware, software, routines, and instructions may be described herein as performing specific operations. It should be appreciated, however, that this description is for convenience only, and that such operations may actually result from a computing device, processor, controller, or other device executing firmware, software, routines, instructions, or the like.

In the block diagrams, the illustrated components are shown as discrete functional blocks, but embodiments are not limited to an organized system in which the functionality described herein is illustrated. Functions provided by each of the components may be provided by software or hardware modules organized differently from those shown in the drawings, for example, such software or hardware may be intermixed, jointly combined, duplicated, separated, distributed (eg, eg within a data center or geographically), or otherwise organized. The functionality described herein may be provided by one or more processors of one or more computers executing code stored on a tangible, non-transitory, machine-readable medium. In some cases, a third party content delivery network may host some or all of the information communicated across the networks, in which case the extent to which the information (eg, content) is said to be supplied or otherwise provided. , this information may be provided by sending a command to retrieve the information from the content delivery network.

Unless expressly stated otherwise, descriptions utilizing terms such as “processing,” “computing,” “compute,” “determining,” and the like, throughout this specification, as apparent from this specification, refer to or use such terms as a dedicated computer or similar dedicated electronic processing/computing device. It is understood that it refers to an operation or process of a particular device.

The reader should understand that this invention describes several inventions. Rather than separating such inventions into multiple separate patent applications, Applicant has grouped these inventions into a single document because the subject matter associated therewith may itself be economical in the filing process. However, the separate advantages and aspects of these inventions should not be combined. In some instances, while embodiments address all of the deficiencies pointed out herein, such inventions are useful independently, and some embodiments solve only a subset of these problems, or will become apparent to one of ordinary skill in the art upon review of this specification. It should be understood that it provides other advantages not mentioned. Because of cost constraints, some inventions disclosed herein are not currently claimed, but may be claimed in subsequent applications, such as continuation applications, or by amending the present claims. Likewise, due to space constraints, the Contents section and Abstract of this specification should not be considered as an extensive recitation of all such inventions or all aspects of such inventions.

The detailed description and drawings are not intended in any way to limit the present invention to the specific form disclosed, on the contrary, the present invention is intended to cover all modifications, equivalents, and substitutions falling within the spirit and scope of the invention as defined by the appended claims. It should be understood that it is intended to cover examples.

Modifications and alternative embodiments of various aspects of the invention will become apparent to those skilled in the art upon reference to this specification. Accordingly, these detailed description and drawings are by way of example only and are to be interpreted as indicating a general manner of carrying out the invention to those skilled in the art. It is to be understood that the forms of the invention shown and described herein are to be regarded as examples of embodiments. As will be apparent to one of ordinary skill in the art upon reading this description of the invention, elements and materials may be substituted for those illustrated and described herein, and parts and processes may be reversed, reordered, or omitted, and Features may be utilized independently, and embodiments or features of embodiments may be combined. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as set forth in the appended claims. The annotations herein are for organizational purposes only and are not intended to be used to limit the scope of the present invention.

As used throughout this specification, the word "may" is used in a permissive sense (ie, it is possible) rather than in a coercive sense (ie, meaning must). The words "comprising", "comprising", and "comprises" and the like mean including, but not limited to. As used throughout this specification, the singular forms "a", "an" and "the" and the like include plural referents unless the context clearly indicates otherwise. Thus, for example, reference to an element "an" or "a" element is, notwithstanding the use of different terms and phrases for one or more elements, such as "one or more", two or more elements. Combinations of the above elements are included. The term “or” is non-exclusive, ie, encompasses both “and” and “or”, unless indicated otherwise. Terms that describe conditional relationships, such as "in response to X, Y is", "if X, then Y", "if X, then Y," "if X, then Y", etc. It encompasses causal relations in which an outcome is a necessary causal condition, or an antecedent is a sufficient causal condition, or a causal condition in which an antecedent contributes to an outcome, e.g., "state X occurs when condition Y is achieved" It is a generic term for "X occurs only in the case of" and "X occurs in the case of Y and Z". These conditional relationships are not limited to the consequences immediately following the fulfillment of the antecedents, since some results may be deferred, and in conditional statements, the antecedent is linked with that result, e.g., the antecedent is the result related to the likelihood of occurrence. A statement that a plurality of attributes or functions maps to a plurality of objects (eg, one or more processors performing steps A, B, C, and D) is, unless otherwise indicated, all such attributes or functions both that it is mapped to an object and that a subset of an attribute or function is mapped to a subset of an attribute or function (eg, that all processors each perform step AD, and that processor 1 performs step A and , processor 2 performs part of step B and step C, and processor 3 performs part of step C and part D). Furthermore, unless otherwise indicated, a statement that one value or action is "based on" another condition or value is a statement where the condition or value is the only factor and when the condition or value is one of several factors. covers both Unless otherwise indicated, a statement that "each" instance of some set has some property is not to be construed as excluding instances where the same or similar elements of some or the same or similar elements of a larger set do not have such property, and , that is, each does not necessarily mean each and all.

To the extent that certain U.S. patents, U.S. patent applications, or other documents (eg, articles) are incorporated by reference, the content of such U.S. patents, U.S. patent applications, and other documents is incorporated herein by reference and to To the extent that there is no conflict between the drawings, the drawings are incorporated herein by reference. In the event of such a conflict, any such conflicting material in these US patents, US patent applications, and other documents which are incorporated herein by reference is not specifically incorporated herein by reference. Although specific embodiments of the invention have been described above, it will be understood that such embodiments may be practiced otherwise than as described.

Claims (21)

A method for determining one or more optimized values of an operating parameter of a sensor system configured to measure a property of a substrate, the method comprising:
obtaining a first value of a quality parameter for a plurality of substrates;
obtaining a second value of a measurement parameter for the plurality of substrates, the second value of the measurement parameter being a measured value obtained by using the sensor system for the plurality of values of the operating parameter;
comparing, by a hardware computer system, the substrate-to-substrate variation of the first value with the substrate-to-substrate variation of the mapping of the second value; and
and determining one or more optimized values of the operating parameter based on the comparison. A non-transitory computer readable medium comprising computer readable instructions that, when executed by a computer system, cause the computer system to at least:
obtain a first value of a quality parameter for the plurality of substrates;
obtain a second value of a measurement parameter for the plurality of substrates, wherein the second value of the measurement parameter comprises: using the sensor system for a plurality of values of an operating parameter of a sensor system configured to measure a characteristic of the substrate; is the measured value obtained;
compare the substrate-to-substrate variation of the first value with the substrate-to-substrate variation of the mapping of the second value;
and determine one or more optimized values of the operating parameters based on the comparison. 3. The method of claim 2,
wherein the mapping is a weighted sum, a non-linear mapping, or a trained mapping based on machine learning techniques. 3. The method of claim 2,
The instructions further cause the computer system to determine, based on the comparison, an optimal set of weighting coefficients for weighting a measurement parameter associated with the first value of the operating parameter and a measurement parameter associated with a second value of the operating parameter. configured, non-transitory computer-readable medium. 3. The method of claim 2,
wherein the first value of the quality parameter is determined using a simulation model that predicts the quality parameter based on one or more selected from context information, measurement data, reconstructed data, and/or hybrid metrology data. possible medium. 3. The method of claim 2,
The measurement parameter includes a measured position of a mark and the quality parameter includes a mark-to-device shift, and the optimized value of the operating parameter optimizes the quality parameter so that substrate-to-substrate variation is minimized. A non-transitory computer-readable medium determined to 7. The method of claim 6,
The instructions cause the computer system to use measurements obtained from a substrate having sub-segmented marks to which an intentional mark-to-device shift has been applied to determine the sensitivity of the operating parameter to the mark-to-device shift. and determine a weight for an operating parameter for measuring the sub-segmented mark. 3. The method of claim 2,
wherein the first value of the quality parameter and the second value of the measurement parameter are associated with a particular layer associated with a plurality of substrates. 9. The method of claim 8,
The particular layer comprises: i) a first substrate-to-substrate variation between first values of the quality parameter associated with the particular layer; and ii) an evaluation of a second substrate-to-substrate variation between second values of the measurement parameter associated with the particular layer. 10. The method of claim 9,
and the particular layer is selected when the first substrate-to-substrate variation and the second substrate-to-substrate variation exceed thresholds. 3. The method of claim 2,
wherein the at least one optimized value of the operating parameter comprises a first set of values of the operating parameter associated with the first coordinate of the measurement parameter and a second set of values of the operating parameter associated with the second coordinate of the measurement parameter; A transitory computer readable medium. 12. The method of claim 11,
The instructions cause the computer system to:
determine a third coordinate parallel to the first preferred direction of the mark;
determine a fourth coordinate parallel to the second preferred direction of the mark;
determine a third set of optimized values of the operating parameter associated with the third coordinate and a fourth set of optimized values of the operating parameter associated with the fourth coordinate;
determine transformations from the third and fourth coordinates to the first and second coordinates;
and convert the determined optimized values of the operating parameter at the third and fourth coordinates to optimized values of the operating parameter at the first and second coordinates using the determined transform. 12. The method of claim 11,
wherein the first set of values of the operating parameter is optimized independently of the second set of values of the operating parameter. 3. The method of claim 2,
wherein the quality parameter comprises an overlay or focus parameter. 3. The method of claim 2,
wherein the measurement parameter comprises an out-of-plane deviation of a location on or on a location of a feature provided on the plurality of substrates. 3. The method of claim 2,
and wherein the instructions are configured to cause a computer system to determine one or more optimized values of the operating parameter based on the comparison to be performed for different regions of the substrate. 17. The method of claim 16,
wherein the different regions include a region proximate to an edge of the substrate and a region proximate to a center of the substrate. A method of optimizing measurement data from a sensor system configured to measure a property of a substrate, the method comprising:
obtaining overlay data for a plurality of substrates, the overlay indicating a deviation between a measured position and an expected position of an alignment marker on the substrate and comprising a plurality of measurements of alignment marker positions made by a sensor system; wherein each of the measurements of R uses a different value of and/or a different operating parameter of the sensor system;
Based on the obtained overlay data and for different values and/or different operating parameters of the operating parameters, respectively, by the sensor system for different values and/or different operating parameters of all operating parameters so that overlay is minimized. optimizing measurement data from a sensor system, comprising determining weights for adjusting measurements obtained using different values of the operating parameters and/or different operating parameters such that weighted adjustments to measurements made are combined method. A non-transitory computer readable medium comprising computer readable instructions that, when executed by a computer system, cause the computer system to at least:
acquire overlay data for a plurality of substrates, wherein the overlay indicates a deviation between the measured and expected positions of the alignment markers on the substrates and comprises a plurality of alignment marker positions achieved by a sensor system configured to measure a characteristic of the substrate. a measurement, wherein each of the plurality of measurements uses a different value and/or a different operating parameter of an operating parameter of the sensor system;
Based on the obtained overlay data and for different values and/or different operating parameters of the operating parameters, respectively, by the sensor system for different values and/or different operating parameters of all operating parameters so that overlay is minimized. and determine weights for adjusting measurements obtained using different values of the operating parameters and/or different operating parameters such that weighted adjustments for measurements made are combined. 20. The method of claim 19,
wherein the operating parameter comprises a parameter associated with a radiation source of the sensor system. 20. The method of claim 19,
wherein the operating parameter comprises a wavelength, a polarization state, or a spatial or temporal coherence state of the measurement radiation.

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