Method for determining a stressor applied to a substrate and related devices - Patent Application 20070122997

Abstract

Disclosed is a method for determining the presence of a stressor on a substrate, the method comprising: acquiring substrate position data describing positions of structures on the substrate within a substrate plane; acquiring substrate shape data describing a shape of the substrate; determining a first warp value from the substrate position data, the first warp value describing a bow of the substrate; determining a second warp value from the substrate shape data, the second warp value describing a bow of the substrate; and determining the presence of a stressor on a back surface of the substrate based on the first warp value and the second warp value.

Description

[Technical Field]

[0001] (CROSS-REFERENCE TO RELATED APPLICATIONS)

[0001] This application claims priority to European Application No. 23160853.0 filed March 9, 2023 and European Application No. 23165332.0 filed March 30, 2023, which applications are incorporated by reference in their entireties into this specification. [Background technology]

[0002] (Technical field) The present invention relates to control apparatus and methods that can be used to maintain performance in the manufacture of devices by patterning processes such as lithography, and further to methods of manufacturing devices using lithographic techniques. The present invention still further relates to computer program products for use in implementing such methods.

[0003] (Related Technology)

[0003] A lithography process is one in which a lithography apparatus applies a desired pattern to a substrate, usually to a target portion of the substrate, and then various processing chemicals and / or physical processing steps process the pattern to create functional features of a complex product. Precise placement of the pattern on the substrate is a major challenge for reducing the size of circuit components and other products that can be produced by lithography. In particular, the challenge of precisely measuring features already placed on the substrate is a key step in being able to overlay and position successive layers of features with sufficient accuracy to produce working devices with high yields. So-called overlay should generally be achieved within tens of nanometers for today's submicron semiconductor devices, and down to a few nanometers for the most critical layers.

[0004]

[0004] Modern lithographic apparatus therefore involve extensive measurement or "mapping" operations prior to the step of actually exposing or otherwise patterning the substrate at the target location. So-called advanced alignment models have been and continue to be developed to more precisely model and correct for non-linear distortions of the wafer "grid" caused by processing steps and / or by the lithographic apparatus itself.

[0005]

[0005] Stresses and in-plane strains in a substrate can result from the application of one or more stress-inducing layers to the substrate, and it would be desirable to determine the presence of such stressors and / or to quantify the effects of such stressors. Summary of the Invention

[0006] According to a first aspect of the present invention, there is provided a method for determining the presence of a stressor on a substrate, the method comprising: acquiring substrate position data describing positional information of structures on the substrate within a substrate plane; acquiring substrate shape data describing a shape of the substrate; determining a first warp value from the substrate position data, the first warp value describing a bow of the substrate; determining a second warp value from the substrate shape data, the second warp value describing a bow of the substrate; and determining a presence of a stressor on the back surface of the substrate based on the first warp value and the second warp value. Equipped with.

[0007]

[0007] According to a second aspect of the present invention, there is provided a computer program product comprising one or more sequences of machine-readable instructions for implementing the computational steps of the method according to the first aspect of the present invention described above.

[0008] The invention further provides a processing arrangement and a lithographic apparatus comprising the computer program of the second aspect.

[0009]

[0009] These and other aspects and advantages of the apparatus and methods disclosed herein will be understood by reviewing the following description and drawings of exemplary embodiments. [Brief explanation of the drawings]

[0010]

[0010] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

[0011] [Figure 1] 1 depicts a lithographic apparatus suitable for use in one embodiment of the present invention; [Figure 2] 1 illustrates a lithographic cell or cluster in which an inspection apparatus according to the present invention may be used; [Figure 3] 2 shows a schematic representation of the measurement and exposure processes in the apparatus of FIG. 1 according to known practice; [Figure 4] 1 is a table illustrating four different scenarios of applying a stressor to a wafer. [Figure 5] FIG. 1 is a schematic diagram of parameters that can be used to describe the heterogeneity of a stressor. [Figure 6] 1 is a flowchart illustrating a method according to one embodiment. [Figure 7] 1 shows a portion of a clamped wafer and schematically illustrates how overlay correction can be determined from warp measurements according to one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0012] Before describing embodiments of the present invention in detail, it may be beneficial to present an exemplary environment in which embodiments of the present invention may be implemented.

[0013] 1 schematically depicts a lithographic apparatus LA. The apparatus includes an illumination system (illuminator) IL configured to condition a radiation beam B (e.g. UV or DUV radiation), a patterning device support or support structure (e.g. mask table) MT constructed to support a patterning device (e.g. mask) MA and coupled to a first positioner PM configured to precisely position the patterning device in accordance with certain parameters, two substrate tables WTa and WTb (e.g. substrate support or substrate / wafer tables), each comprising a plurality of burls on a support surface, and each constructed to hold a substrate (e.g. resist-coated wafer) W, and a projection system (e.g. refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W. Each substrate table may be connected to a second positioner PW configured to precisely position the substrate in accordance with certain parameters. A reference frame RF connects the various components and serves as a reference for setting and measuring the positions of the patterning device and the substrate and features thereon.

[0014]

[0013] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof, for directing, shaping, or controlling radiation. For example, devices using extreme ultraviolet (EUV) radiation will typically use reflective optical components.

[0015] The patterning device support 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 or not the patterning device is held in a vacuum environment. The patterning device support may use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The patterning device support MT may be, for example, a frame or a table, which may be fixed or movable as required. The patterning device support may ensure that the patterning device is at a desired position, for example with respect to the projection system.

[0016]

[0015] As used herein, the term "patterning device" should be interpreted broadly as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section so as to create a pattern in a target portion of a substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so-called assist features. Typically, the pattern imparted to the radiation beam corresponds to a particular functional layer of a device being created in the target portion, such as an integrated circuit.

[0017] As here depicted, the apparatus is of a transmissive type (e.g. employing a transmissive patterning device). Alternatively, the apparatus may be of a reflective type (e.g. employing a programmable mirror array of a type as referred to above, or employing a reflective mask). Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Any use of the terms "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device". The term "patterning device" may also be interpreted as referring to a device that digitally stores pattern information for use in controlling such a programmable patterning device.

[0018]

[0017] The term "projection system" as used herein should be interpreted broadly as covering any type of projection system including, for example, refractive optical systems, reflective optical systems, catadioptric optical systems, magnetic optical systems, electromagnetic optical systems and electrostatic optical systems, or any combination thereof, as appropriate depending on, for example, the exposure radiation used or other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein can be considered as synonymous with the more general term "projection system".

[0019]

[0018] 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, so as to fill a space between the projection system and the substrate. Immersion liquids may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of projection systems.

[0020]

[0019] In operation, the illuminator IL receives a radiation beam from the radiation source SO. The radiation source and the lithographic apparatus may be separate entities, for example when the radiation source is an excimer laser. In such cases, the radiation source is not considered to form part of the lithographic apparatus and the radiation beam is transmitted from the source SO to the illuminator IL with the aid of a beam delivery system BD, which may include, for example, suitable directing mirrors and / or beam expanders. In other cases, the radiation source may be an integral part of the lithographic apparatus, for example when the radiation source is a mercury lamp. The radiation source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0021] The illuminator IL may include, for example, an adjuster AD for adjusting the angular intensity distribution of the radiation beam, an integrator IN, and a condenser CO. The illuminator may be used to condition the radiation beam so that it has a desired uniformity and intensity distribution in its cross-section.

[0022]

[0021] The radiation beam B is incident on the patterning device MA, which is held on the patterning device support MT, and is patterned by the patterning device. Having traversed the patterning device (e.g. mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g. an interferometer device, a linear encoder, a 2D encoder, or a capacitive sensor), the substrate table WTa or WTb can be precisely moved, for example to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and a further position sensor (not explicitly shown in Figure 1) can be used to precisely position the patterning device (e.g. mask) MA with respect to the path of the radiation beam B, for example after a mechanical lookup in a mask library or during a scan.

[0023]

[0022] The patterning device (e.g. mask) MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, the substrate alignment marks may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device (e.g. mask) MA, the mask alignment marks may be located between the dies. Small alignment marks may also be included within a die, between device features; in that case, they should be as small as possible and not require different imaging or process conditions than adjacent features. Alignment systems for detecting alignment markers are described further below.

[0024]

[0023] The depicted apparatus can be used in various modes. In scan mode, the patterning device support (e.g. mask table) MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the patterning device support (e.g. mask table) MT may be determined by the (de-)magnification 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-scan direction) of the target portion during a single dynamic exposure, while the length of the scanning movement determines the height (in the scan direction) of the target portion. Other types of lithographic apparatus and modes of operation are possible, as are known in the art. A step mode is known, for example. In so-called "maskless" lithography, the programmable patterning device is kept stationary while the pattern is changed and the substrate table WT is moved or scanned.

[0025] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0026] The lithographic apparatus LA is of a so-called dual-stage type and has two substrate tables WTa, WTb and two stations, an exposure station EXP and a measurement station MEA, with the substrate tables being interchangeable between the stations. While one substrate on one substrate table is being exposed in the exposure station, another substrate can be loaded onto the other substrate table in the measurement station, where various preparation steps can be performed. This allows for a substantial increase in the throughput of the apparatus. In a single-stage apparatus, preparation and exposure steps must be performed sequentially on a single stage for each substrate. The preparation steps may include mapping the surface height profile of the substrate using a level sensor LS and measuring the position of an alignment marker on the substrate using an alignment sensor AS. If the position sensor IF cannot measure the position of the substrate table when it is in the measurement station and when it is in the exposure station, a second position sensor may be provided to enable the position of the substrate table at both stations to be tracked relative to a reference frame RF. Other configurations are known and can be used in place of the dual-stage configuration shown. For example, other lithographic apparatus are known that are provided with a substrate table and a measurement table that are docked to perform preliminary measurements and then undocked while the substrate table undergoes exposure.

[0027] As shown in FIG. 2 , the lithography apparatus LA forms part of a lithography cell LC, sometimes referred to as a lithocell or cluster, which also includes apparatus for performing pre-exposure and post-exposure processes on a substrate. Conventionally, these apparatuses include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a chill plate CH, and a bake plate BK. A substrate handler, or robot RO, retrieves substrates from input / output ports I / O1 and I / O2, moves them between various processing equipment, and then delivers them to the loading bay LB of the lithography apparatus. These devices, often collectively referred to as the track, are under the control of a track control unit TCU, which is itself controlled by a supervisory control system SCS, which also controls the lithography apparatus via a lithography control unit LACU. In this way, different apparatuses can be operated to maximize throughput and processing efficiency.

[0028] To ensure that substrates exposed by a lithographic apparatus are accurately and consistently exposed, it is desirable to inspect the exposed substrates to measure properties such as overlay error between subsequent layers, linewidth, critical dimension (CD), etc. Accordingly, the manufacturing facility in which the lithocell LC is located also includes a metrology system MET that receives some or all of the substrates W processed in that lithocell. The metrology results are provided directly or indirectly to a monitoring and control system SCS. If errors are detected, adjustments may be made to the exposure of subsequent substrates.

[0029] Within the metrology system MET, an inspection device is used to determine the properties of the substrate, and in particular, how the properties of different substrates or different layers of the same substrate vary from layer to layer. The inspection device may be integrated into the lithography apparatus LA or lithocell LC, or may be a stand-alone device. To enable the fastest measurements, it would be desirable for the inspection device to measure the properties of the exposed resist layer immediately after exposure. However, not all inspection devices are sensitive enough to make useful measurements of the latent image. Therefore, measurements may be made after the post-exposure bake step (PEB), which is the first step customarily performed on exposed substrates and increases the contrast between exposed and unexposed portions of the resist. At this stage, the resist image may be referred to as semi-latent. It is also possible to make measurements of the developed resist image, at which point either the exposed or unexposed portions of the resist have been removed. Additionally, already exposed substrates may be removed and reprocessed to improve yield, or discarded, thereby avoiding further processing on substrates known to be defective. In a case where only some target portions of a substrate are defective, further exposures may be performed only on the good target portions.

[0030]

[0029] A metrology step with the metrology system MET can also be performed after the resist pattern has been etched into the product layer, which limits the possibilities for reworking defective substrates but can provide additional information about the performance of the overall manufacturing process.

[0031]

[0030] Figure 3 shows steps for exposing a target portion (e.g., a die) on a substrate W in the dual stage apparatus of Figure 1. First, a process according to conventional practice is described. The present disclosure is in no way limited to the type of dual stage apparatus shown. Those skilled in the art will recognize that similar operations are performed in other types of lithographic apparatus, for example those having a single substrate stage and a docking metrology stage.

[0032]

[0031] The dashed boxes on the left show steps that are performed in the measurement station MEA, while the ones on the right show steps that are performed in the exposure station EXP. At any given time, as described above, one of the substrate tables WTa, WTb is in the exposure station, while the other is in the measurement station. In this description, it is assumed that a substrate W is already loaded in the exposure station. In step 200, a new substrate W' is loaded into the apparatus by a mechanism not shown. These two substrates are processed in parallel to increase the throughput of the lithographic apparatus.

[0033]

[0032] Referring first to the newly loaded substrate W', this may be a substrate that has not been previously processed and that has been prepared with new photoresist for its first exposure in the apparatus. However, in general, the lithography process described is only one step in a series of exposure and processing steps, and thus the substrate W' may have already passed through this and / or other lithography apparatuses several times, and may have subsequent processes as well. In particular, with regard to the problem of improving overlay accuracy, the challenge is to ensure that a new pattern is applied in exactly the right position on a substrate that has already undergone one or more cycles of patterning and processing. Each patterning step may result in misalignment of the applied pattern, and, in turn, subsequent processing steps may gradually result in distortion of the substrate and / or the pattern applied to the substrate, which must be measured and corrected to achieve satisfactory overlay accuracy.

[0034] Previous and / or subsequent patterning steps, as described above, may be performed in other lithography tools, or even in different types of lithography tools. For example, some layers of a device fabrication process that are very demanding in parameters such as resolution and overlay may be performed in more advanced lithography tools than other layers that are less demanding. Thus, some layers may be exposed in an immersion-type lithography tool, while other layers are exposed in a "dry" tool. Some layers may be exposed in a tool operating at DUV wavelengths, while other layers are exposed using EUV wavelength radiation. Some layers may be patterned by steps that are alternatives or supplements to exposure in the illustrated lithography tool. Such alternative and supplemental techniques include, for example, imprint lithography, self-aligned multiple patterning, and directed self-assembly. Similarly, other processing steps (e.g., CMP and etching) performed for each layer may be performed in different tools for each layer.

[0035] At 202, alignment measurements using substrate marks P1 etc. and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate tables WTa / WTb. In addition, several alignment marks across the substrate W' are measured using alignment sensor AS. These measurements are used in one embodiment to establish a substrate model (sometimes referred to as a "wafer grid"), which very precisely maps the distribution of marks across the substrate, including distortions to a nominal rectangular grid.

[0036] In step 204, a map of wafer height (Z) versus XY position is measured, again using the level sensor LS. Primarily, the height map is used only to achieve precise focusing of the exposure pattern. The height map may additionally be used for other purposes.

[0037] Once the substrate W' has been loaded, recipe data 206 has been received which defines the exposures to be performed, as well as the characteristics of the wafer and the patterns that have been and will be created on the wafer. Options for the alignment marks on the substrate, if any, and for the settings of the alignment sensors, if any, are defined in an alignment recipe in the recipe data 206. The alignment recipe therefore defines how the positions of the alignment marks are to be measured and which marks are to be measured.

[0038] In 210, wafers W' and W are swapped, so that the measured substrate W' becomes the substrate W entering exposure station EXP. In the exemplary apparatus of FIG. 1, this swapping is performed by exchanging supports WTa and WTb in the apparatus, so that substrates W, W' remain precisely clamped and positioned on their supports, maintaining the relative alignment of the substrate tables with the substrates themselves. Thus, once the tables have been swapped, in order to use the measurement information 202, 204 of substrate W (formerly W') to manage the exposure step, it is only necessary to determine the relative position of projection system PS and substrate table WTb (formerly WTa). In step 212, reticle alignment is performed using mask alignment marks M1, M2. In steps 214, 216, and 218, scanning movements and radiation pulses are applied at successive target locations across substrate W to complete the exposure of several patterns.

[0039] By using the alignment data and height maps acquired at the metrology station during the exposure steps, these patterns are precisely aligned to the desired locations, and in particular to features previously placed on the same substrate. The exposed substrate, now labeled W", is unloaded from the apparatus in step 220 and subjected to an etch or other process according to the exposure pattern.

[0040] One issue with current lithography and related substrate processing techniques used in integrated circuit (IC) manufacturing is mechanical properties such as in-plane deformation. One source of in-plane distortion can be the application of stressors to the substrate, such as coating layers or thin film depositions. Thin film stress typically affects the unclamped, free-form shape of the substrate. This stressor results in a change or distortion of the substrate shape. Stressed thin films can generate local overlay errors (e.g., after resist development and / or etching); such overlay errors often have high spatial frequencies and can vary from substrate to substrate and across the substrate. Sometimes, multiple such stressors can be applied. These stressors can be referred to as front-side stressors (e.g., because they are applied to the front side of the substrate where the pattern is being applied).

[0041] It is also known to apply a rear surface coating or rear surface stressor to the rear surface of the substrate (i.e. the surface opposite to the front surface, and therefore the surface that is clamped to the substrate table). Such a rear surface stressor may comprise a compensating rear surface stressor that is applied to compensate for the aforementioned front surface stressor and thus to help return the substrate to a flatter or planar shape. That is, the compensating rear surface stressor may compensate for the (e.g. bowl) shape imposed on the substrate by the front surface stressor. Additionally or alternatively, the rear surface stressor may be applied to prevent contamination and to protect the substrate and the substrate table. Such a rear surface stressor may be applied for particularly critical layers. Applying a rear surface stressor involves a large overhead and is therefore typically performed only when necessary, and not for every (front) layer.

[0042] Manufacturers of lithography and / or metrology machines sometimes need to use data from customers (e.g., production data) where relatively little is known about the particular production step to which the data applies to the substrate to which it pertains. Such data may be used, for example, in machine, process, or software testing or development. In particular, with respect to such (customer) production data, it is not always known whether or how many front and / or back stressors have been applied. It may be desirable to ascertain the processing history of such substrates from such data, since the processing history describes the presence of such stressors. It may also be desirable (for either the manufacturer or the customer, or both) to determine or quantify the uniformity of the applied back stressor, for example, to determine which burl placements may be appropriate and / or to improve the back stressor application process. And it may also be desirable to be able to quantify the effect of (e.g., back) stressors on parameters of interest, such as on-product overlay.

[0043]

[0042] Substrate distortion, such as that resulting from the deposition of stressed thin films, can affect overlay accuracy in lithography processes. Freeform substrate shapes that can be measured with offline metrology tools can change as a result of this distortion. Typical shapes that can be observed in mass production are bowl (convex), umbrella (concave), and saddle shapes. Deviations from these shapes result in higher-order in-plane distortions.

[0044] In some cases, these in-plane distortions are slowly spatially varying functions and can be captured by existing alignment models, such as (for example) the High Order Wafer Alignment (HOWA) model. An important prerequisite is that the grid distortions remain global, while the polynomial-based HOWA model becomes less effective for very local distortions. Another approach is to use substrate shape or deformation measurements. Such substrate shape measurements may comprise out-of-plane deformation measurements, i.e., measurements of the shape of the substrate in the z-direction, perpendicular to the substrate surface plane. Substrate shape measurements may comprise measurements of the freeform (unclamped) substrate shape. When referring to substrate shape or wafer shape, it includes any suitable measurement of the out-of-plane deformation of the substrate by either of these or other methodologies. If the relationship between the freeform substrate shape and the post-clamped in-plane distortion (IPD) is known or can be modeled, predictions (and corrections) can be made to improve overlay accuracy.

[0045] It may be desirable to determine the substrate warp between the final burls (i.e., radially outward from the center) and the edge of the substrate, sometimes referred to as edge roll-off. Burls are (e.g., cylindrical) protrusions or bumps on the support surface of the substrate support or substrate table. The burls limit the contact surface between the clamp and the substrate, thereby reducing particle contamination of the rear surface of the substrate. Substrate flatness is provided and maintained through an extremely fine surface finish on the tops of the burls, a small burl pitch of a few millimeters, and a high (e.g., vacuum or electrostatic) clamping force.

[0046] However, the performance of known methods is unpredictable and subject to errors. The use of a stressor causes the substrate to bow, resulting in in-plane distortion after clamping the substrate on the substrate table. To compensate for the bowing of the substrate, an additional stress layer may be applied to the rear surface of the substrate, which further affects the in-plane distortion and edge roll-off and increases the overlay. As explained, clamping the substrate helps to flatten the substrate, thus reducing the overlay penalty from edge roll-off. However, this can result in the in-plane distortion being twice as large, leading to a high overlay penalty.

[0047] One solution that can reduce the effects of edge roll-off is to move the outermost burls further outward, closer to the substrate edge. However, such an approach is only feasible if the strain or warp is sufficiently uniform all the way to the proposed outermost burl location; otherwise, very high substrate-table wear is typically observed, leading to unacceptable downtime. Therefore, it is further desirable to be able to determine the deposition and / or strain uniformity of any (e.g., rear) layer and thus the feasibility of using burls closer to the substrate edge. This strain uniformity depends on the uniformity of the applied rear stressor, which may be non-uniform near the edge due to processing issues (especially if applied for contamination prevention).

[0048] It is proposed to use a combination of leveling data (substrate shape data) and alignment or overlay data (substrate position data) to determine the presence and / or uniformity / homogeneity of applied stressors. In some embodiments, the effect of these stressors on parameters of interest such as overlay may be quantified. Such a method may comprise determining the bow of a freeform substrate from both substrate shape / leveling data and substrate position / alignment data, respectively.

[0049] FIG. 4 illustrates various processing scenarios S that a substrate can undergo and the resulting free-form wafer shape FFWS and the (clamped) in-plane distortion IPD resulting from the in-plane stress. IPS and (clamped) in-plane distortion IPD resulting from edge roll-off ERO The last two columns show these distortion parameters plotted against the radial distance from the substrate center r.

[0050] The top row represents the first scenario S1, in which only a front compressive stressor is applied. This front-only stress results in an umbrella-shaped substrate. After clamping, the in-plane distortion IPD resulting from the in-plane stress IPS shows a linear relationship or scaling (symmetric expansion) with radial position r. The resulting edge roll-off IPD ERO shows the remainder of the freeform shape beyond the final burl, with positive radial strain at the substrate edge.

[0051] Scenario 2a shows the first scenario where the substrate is subjected to a homogeneous front surface deposition and a homogeneous back surface deposition. In this example, the applied front and back surface stresses are both compressive. The stress applied to the back surface of the substrate re-flattens the substrate shape FFWS and reduces the resulting edge roll-off IPD. ERO zero, but the radial scaling is twice as large as in scenario S1 (but still has a linear relationship with radial position).

[0052] Scenario 2b shows a second scenario where the substrate is subjected to a homogeneous front surface deposition and a homogeneous back surface deposition. In this case, the applied stresses are opposite on the front and back surfaces, which may be encountered when a back surface stressor is applied for contamination mitigation. Thus, the substrate is subjected to a back surface tensile stress in combination with a compressive front surface stress. In this scenario, the IPD due to edge roll-off is EROis larger than the case of frontal stress alone, but is the IPD resulting from in-plane stress, IPD IPS is zero (in each case, the front, back, and total IPDs are plotted separately).

[0053] Scenario 3 shows compressive front and rear surface deposition, but (at least) the rear surface deposition is inhomogeneous. The result is a nearly flat substrate, which has some edge roll-off and IPD due to in-plane stress. IPS is not perfectly linear and has a nonlinear component near the edges. Otherwise, the magnitude of the in-plane stress IPD is similar to that of Scenario 2a. IPS is the magnitude of the in-plane stress IPD in scenario 1 IPS In contrast to scenario 2a, the IPD due to edge roll-off is IPD ERO is now provided with additional components due to heterogeneous processing.

[0054] The proposed method involves determining a first warp value, for example the substrate warp due to in-plane stresses, IPS and a second warp value, e.g., in-plane distortion due to edge roll-off, warp ERO The first warp value can be determined from alignment data (or alternatively, overlay data or other similar position data related to positions in the substrate plane) measured via an alignment sensor, and the second warp value can be determined from leveling data (substrate shape data) measured via a leveling sensor.

[0055]

[0054] From Figure 4, it can be seen that the rear surface layer has a different effect on the IPD due to in-plane stress than on the IPD due to edge roll-off. More specifically, the total contribution to the IPD due to in-plane stress is the sum of the displacements imposed on the front surface of the substrate and the rear surface of the substrate, while the total contribution to the IPD due to edge roll-off is the difference between the IPDs imposed on the front surface of the substrate and the rear surface of the substrate. The proposed method uses this difference in the effects on IPD to determine the presence of rear surface stress, more specifically, a comparison of the warp values ​​predicted based on alignment data and leveling edge roll-off (curl up / down) data.

[0056]

[0055] With regard to the first warp value, this can be determined more specifically from the alignment magnification value (e.g., symmetric substrate scaling Mws [ppm] value). Prior to each substrate exposure, alignment marks on the substrate can be measured by an alignment sensor in a scanner in a process called fine wafer alignment (FIWA). These are used to determine the displacement of the substrate relative to its expected position and to calculate a correction. For these measurements, several marks are selected, for example, in a circular pattern. Based on the measurements, the displacement at any location on the substrate can be predicted. The simplest model used to represent alignment data is a linear four-parameter model, which describes the displacement in terms of translation, magnification, and rotation. Each displacement (dx, dy) measured for an alignment mark at a location (xc, yc) can be expressed as follows:

[0057]

number

[0058] where Tx, Ty are translations in x and y, Mws is the symmetric substrate scaling, and Rws is the symmetric rotation. The parameter values ​​can be calculated, for example, via a least-squares fit to the data for all marks. The alignment model may include additional parameters beyond these four (e.g., six-parameter models, or various higher-order models are often used), but all alignment models typically include at least these four parameters. The resulting parameters can be obtained from the scanner log file after exposure.

[0059] Assuming a homogeneous stressor, the parabolic substrate warp IPS There is a linear relationship between the in-plane strain (IPD) and linear scaling, with the slope (proportionality constant) depending on the substrate parameters (specifically the substrate height and radius, and therefore essentially constant when these parameters are normalized). Therefore, warp can be predicted from symmetric substrate scaling. The proposed equation is based on the gradient (Stoney) model of in-plane strain.

[0060]

number

[0061] (However, h w is the substrate thickness and w(r) is the substrate shape as a function of the radial coordinate r)

[0062]

number

[0063] and evaluating the IPD at the substrate edge r=R.

number

[0064] It will be appreciated that using this first warp value alone may result in an overestimation of the substrate warp, since the presence of the backside coating reduces the substrate warp, although it may cause more stress and greater expansion in the substrate.

[0065] The second warp value may comprise using the levelling data to predict an edge roll-off warp, which represents the warp of the clamped substrate between the final burl and the substrate edge. Between the centre of the substrate and the final burl, the substrate is clamped flat (as evident from the last column of Figure 4 for all scenarios). The levelling data or local levelling profile w(r) used in this embodiment may comprise the difference between the two layers (the local levelling profile difference) to compensate for the effects of the substrate table non-flatness (wear) and the burl. In the case of a uniform front (and / or) back surface coating, the local levelling profile w(r) beyond the final burl is

[0066]

number

[0067] where r is the radial coordinate, R is the substrate radius, and R b is the radial coordinate of the final bar. Therefore, the warp based on the leveling data can be calculated as follows:

[0068]

number

[0069] To estimate this warp as a single value, r>R b against

[0070]

number

[0071] The least squares method can be performed.

[0072] These warp values ​​can be used together to ascertain the processing history. For example, warp ERO =warp IPS If so, it can be assumed that there is single-sided deposition (homogeneous) and therefore no backside deposition. This is more likely to be the case for a particular calibration, matching, or setup substrate than for an actual production substrate.

[0073] For both scenarios 2a and 2b, warp ERO ≠warp IPS where there is homogeneous front and rear deposition, and thus the displacement depends only on the radius r. It can be assumed that the front and rear depositions each contribute independent warp to the total substrate warp. It can also be seen that:

[0074]

number

[0075] where the subscript FS denotes the front warp (i.e., the warp induced by only the front stressor) and the subscript BS denotes the rear warp (i.e., the warp induced by only the rear stressor). From these two equations, we can determine the two unknowns, warp FS and warp BS can be determined individually, and therefore the effect of the posterior stressor can be quantified.

[0076] Scenario 3 represents front surface deposition and non-uniform back surface deposition. The warp caused by the front surface and back surface coating can be determined from the leveling and alignment data in a similar manner as described for scenario 2. However, the warp based on the leveling data IPS Here, an additional component, warp, arising from the heterogeneous processing is δin , which can be assumed to be on the rear surface of the substrate.

[0077]

number

[0078] In this case, it can be determined whether the calculated warp matches the warp based on Stoney's equation: If the material parameters are known, the stress σ in a homogeneous layer can be calculated from Stoney's equation.

[0079]

number

[0080] where σ is the stress in the layer and E s is the Young's modulus of the substrate, and h w is the thickness of the substrate,

[0081]

number

[0082] is the curvature of the substrate and layer, and h f is the film thickness, and ν s is the Poisson's ratio of the substrate. In this case, the stress and curvature are constant, which means that the shape is a perfect parabola.

[0083]

[0063] If this is not the case, a training mechanism may be used to train the model. For this purpose, a look-up table may be constructed from FEM simulations. Since the standard Stoney model is no longer valid for non-uniform stresses, for these simulations the following modified physical model may be used:

[0084]

number

[0085] where:

[0086]

number

[0087] is the mean curvature of the substrate. For this case, the stress and curvature are no longer constant but depend on the location (x, y) on the substrate. This equation is valid for axisymmetric stress distributions, i.e. it depends only on the radial coordinate r. For the general case, there is an additional term between the brackets that depends on the radial coordinate and the polar coordinate (angle) phi.

[0088] The proposed method for constructing the lookup table will now be described in conjunction with FIG. 5. FIG. 5 shows a detail of the substrate W at the edge (e.g., within the box shown in column 1 of FIG. 4, scenario 3). The figure shows a portion of the substrate W and the inhomogeneous back surface stressor BSS. Finite element simulations can be used to determine the impact on in-plane strain for various back surface layer inhomogeneities. Each back surface layer inhomogeneity at the substrate edge layer can be characterized by the following inhomogeneity parameters: Layer thickness h before the onset of thickness reduction (inhomogeneity) layer , The radial position r at which the thickness reduction begins start , and The slope of the decrease is characterized by the angle α.

[0089]

[0065] A look-up table can be created by running a simulation for various values ​​of these parameters. Thus, the input to the simulation can comprise these three parameters describing the profile, or a function describing the profile. The output of the simulation can be in-plane distortion and out-of-plane distortion. The out-of-plane distortion can be converted to a leveling profile, and the in-plane distortion can be converted to overlay / alignment. For each coordinate, the extended Stoney equation can be used to determine the warp for different wafers.

[0090] 6 is a flow chart illustrating a method according to one embodiment. The method comprises determining from alignment and leveling data which of the above scenarios the substrate is following. This may be used to determine whether the outermost burls can be moved closer to the edge, which is acceptable for scenarios 1, 2a, and 2b where the distortion is homogeneous, but not for scenario 3 where the distortion is heterogeneous.

[0091] Substrate position or alignment data (more specifically symmetric expansion data) and substrate shape or leveling data 600 are obtained from measurements of the substrate, for example using alignment and leveling sensors, respectively. Typically, such data will be routinely measured for each substrate as part of a known alignment and leveling metrology. In a calculation step 605, a first warp value warp is calculated using the methods and relationships described. IPS is determined from the alignment data, and a second warp value warp ERO is determined from the leveling data. In step 610, a first warp value warp IPS and the second warp value warp EROIt is determined whether warp and are equal (or at least substantially equal within a threshold margin). If yes, then scenario 1 (substrate has stressor on only one side) can be concluded (615). If there is deposition on only one side (homogeneous), then the first warp value warp IPS is the second warp value warp ERO Therefore, it can be concluded (620) that the outermost burls may be located further towards the edge (e.g., further than 145 mm, further than 146 mm, further than 147 mm, or at or further than 148 mm from the substrate table centre). This step further involves calculating a second warp value, warp ERO determining an overlay correction for edge roll-off based on

[0092] Step 620 also includes:

[0093]

number

[0094] the in-plane (xy) stress contribution from the alignment data via, and

[0095]

number

[0096] It may also comprise determining the out-of-plane (z) contribution from the leveling data via: This is possible for scenarios 1 and 2, but not for scenario 3.

[0097] If the determination at step 610 is no, then at step 625 it may be determined whether the designed and actual layer thicknesses are known. If yes, then the equations for scenario 2 (scenarios 2a and 2b) may be applied (630), after which a determination may be made as to whether the actual layer thickness is the same as the designed thickness (635). If yes, then the posterior layer may be assumed to be homogenous (640) (scenario 2a or 2b), and the method proceeds to step 620 as previously described (e.g., the outermost burls may be moved and / or the in-plane and / or out-of-plane distortion may be determined).

[0098] If either decision 625, 635 is no, then the equation for scenario 3 is applied (645) based on the lookup table to calculate the additional warp component warp resulting from the non-uniform processing. δin is determined.

[0099] In step 650, an additional warp component warp δin is less than a threshold tolerance indicative of non-uniformity. If no, then scenario 3 is assumed (655), and a decision may be made to place the final bur away from the edge (e.g., less than 145 mm, or less than 144.5 mm, e.g., 144 mm, from the center). Such a determination may also be used to prompt an investigation into why the backside deposition is non-uniform and / or to modify the backside deposition process to improve uniformity (or even to decide not to apply a backside stressor for one or more problematic layers).

[0100]

[0072] If the determination at step 650 is yes Y, the posterior layer can be assumed to be homogeneous (640) (scenario 2a or 2b) and the method proceeds to step 620 already described (e.g., the outermost burls can be moved and / or in-plane and / or out-of-plane distortion can be determined).

[0101]

[0073] Figure 7 is a diagram illustrating the effect of edge roll-off, showing part of a substrate WA on a substrate table WT with burls BL, one of the burls being provided with the final burl BLF as described. F The radial position of defines the boundary between the clamped portion of the substrate CLP and the unclamped portion of the substrate WA.

[0102] As already mentioned, in one embodiment, the overlay correction is performed by adjusting the measured warp (e.g., the first warp value warp IPS ,for example

[0103]

number

[0104] The final bar BL of the substrate table WT can be calculated from F Beyond, the leveling map shows the remainder of the warp on the substrate. The substrate is clamped to the last burl, with local bending maintained in the unclamped areas. Edge distortion is determined by the substrate shape only. Distortion should be similar for different warp levels and on different substrate tables (e.g., assuming similar burl layouts). The local angle θ from the out-of-plane deflection is

[0105]

number

[0106] According to the out-of-plane displacement IPD Z is converted to

[0107] Furthermore, the in-plane (xy) stress contribution is

[0108]

number

[0109] can be determined from the alignment data via

[0110]

[0076] The in-plane and out-of-plane displacements can be used to determine the overlay and therefore the overlay corrections that compensate for these displacements.

[0111]

[0077] IPD Z and IPD xy The above calculation for is only applicable to scenarios 1 and 2 (2a or 2b). For scenario 3, overlay correction may use a different approach, for example using an extended Stoney equation and / or via a look-up table.

[0112]

[0078] Thus, disclosed herein is a method that enables quantification of backside deposition uniformity without the need for additional metrology, for example using a scanner as an inspection tool. Thus, the disclosed method allows for the replacement of frequent offline measurements such as substrate shape measurements. For example, the proposed method allows for substrate shape feedforward of the substrate edge with only scanner input. In addition to leveling information, the proposed method also allows for the determination of the impact of in-plane distortion at the substrate edge. This method allows for a priori determination of whether the outermost burls can be moved closer to the edge.

[0113] In relation to the lithographic apparatus hardware and the lithocell LC, an embodiment may include a computer program comprising one or more sequences of machine-readable instructions for causing a processor of a lithographic manufacturing system to implement the above-described model mapping and control method. This computer program may, for example, be executed in a separate computer system used for the image calculation / control process. Alternatively, the calculation steps may be performed in whole or in part within the processor, metrology tool, and / or control unit LACU and / or supervisory control system SCS of Figures 1 and 2. A data storage medium (e.g., a semiconductor memory, a magnetic disk, or an optical disk) having such a computer program stored thereon in non-transitory form may also be provided.

[0114]

[0080] While specific reference may have been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other patterning applications, for example imprint lithography. In imprint lithography, a topography of a patterning device defines the pattern to be created on a substrate. The topography of the patterning device is imprinted into a layer of resist supplied to the substrate, and the resist is then cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. The patterning device is then removed from the resist, leaving behind a pattern when the resist has hardened.

[0115]

[0081] Further embodiments are disclosed in the following list of numbered clauses: 1. A method for determining the presence of a stressor on a substrate, comprising: obtaining substrate position data describing position information of structures on the substrate within a plane of the substrate; obtaining substrate shape data describing a shape of the substrate; determining a first warp value from the substrate position data, the first warp value describing a bow of the substrate; determining a second warp value from the substrate shape data, the second warp value describing a bow of the substrate; determining a presence of a stressor on the back surface of the substrate based on the first warp value and the second warp value; A method for providing the above. 2. The method of clause 1, comprising determining the presence of a stressor on the rear surface of the substrate based on a comparison of the first warp value and the second warp value. 3. The method of clause 1 or 2, comprising determining that the substrate does not have a rear surface stressor on the rear surface of the substrate when the first warp value and the second warp value are substantially equal. 4. The method of any of clauses 1 to 3, comprising determining that the substrate comprises at least one backside stressor when the first warp value and the second warp value are not substantially equal. 5. Determining the value of the warp component resulting from the non-uniform processing; determining whether the at least one posterior stressor is homogeneous or heterogeneous based on the magnitude of the warp component; 5. The method of clause 4, further comprising: 6. Comparing the value of the warp component to a threshold; determining that the at least one posterior stressor is homogeneous if the value of the warp component is less than a threshold, and determining that the at least one posterior stressor is heterogeneous if the value of the warp component is greater than or equal to the threshold; 6. The method of claim 5, comprising: 7. The method of clause 5 or 6, comprising determining the outermost crowbar position based on the presence or absence of a heterogeneous posterior stressor. 8. The method of clause 7, wherein the outermost burl location is determined to be 145 mm or more from the center of the substrate when it is determined that there is no inhomogeneous rear stressor. 9. The method of clause 7, wherein when the substrate is determined to have no inhomogeneous rear surface stressors, the outermost burl location is determined to be 147 mm or greater from the center of the substrate. 10. The method of clause 7, 8, or 9, wherein when the substrate is determined to have at least one non-homogeneous backside stressor, the outermost burl location is determined to be less than 145 mm from the center of the substrate. 11. A method according to any of clauses 5 to 10, comprising determining values ​​for a front warp contribution and a back warp contribution from the first warp value, the second warp value, the substrate position data, and the substrate shape data. 12. The method of clause 11, wherein the values ​​of the front warp contribution and the rear warp contribution are determined by solving, for the front warp contribution and the rear warp contribution, a first equation that sets a first warp value equal to at least the sum of the front warp contribution and the rear warp contribution, and a second equation that sets a second warp value equal to the difference between the front warp contribution and the rear warp contribution. 13. The method of clause 12, wherein the first equation comprises an additional term comprising a warp component resulting from non-homogeneous processing when the warp component exceeds a threshold. 14. The method of clause 13, wherein the solving step is performed with reference to a look-up table describing the effect of one or more inhomogeneity parameters on stress in and / or strain of the substrate. 15. The heterogeneity parameter is the layer thickness before the onset of inhomogeneity, the radial position where the inhomogeneity begins, and The slope of the decrease in layer thickness characterizes the inhomogeneity 15. The method of claim 14, comprising one or more of: 16. The method of any of clauses 1 to 15, wherein the substrate position data comprises alignment data. 17. The method of clause 16, wherein the alignment data comprises symmetric substrate scaling data. 18. The method of clause 17, wherein the step of determining the first warp value assumes a substantially linear relationship between the symmetric substrate scaling data and the first warp value. 19. The method of any of clauses 1 to 18, wherein the substrate shape data comprises leveling data. 20. The method of clause 19, wherein the leveling data comprises a local leveling profile between the radial position of the final burl and the edge of the substrate. 21. The method of any of clauses 1 to 20, further comprising determining an overlay correction from the first warp value. 22. The method of any of clauses 1 to 21, wherein the stressor comprises an applied stressor layer that applies stress to the substrate, causing it to deform. 23. A method according to any of clauses 1 to 22, comprising measuring a substrate to obtain substrate position data and substrate shape data. 24. A computer program comprising program instructions operable to perform any of the methods of clauses 1 to 23 when run on a suitable device. 25. Non-transitory computer program carriers comprising computer programs according to clause 24. 26. A computer program carrier comprising a computer program according to clause 24; a processor operable to execute a computer program; A processing configuration comprising: 27. A lithographic apparatus comprising the processing arrangement of clause 26. 28. An alignment sensor operable to measure the substrate to obtain substrate position data; a leveling sensor operable to measure the substrate to obtain substrate shape data; 28. The lithographic apparatus of clause 27, further comprising: 29. A substrate support for supporting a substrate, the substrate support comprising a plurality of burls on a support surface. 29. The lithographic apparatus of clause 27 or 28, further comprising:

[0116]

[0083] The foregoing description of specific embodiments sufficiently reveals the general nature of the present invention so that others, by applying knowledge of the art, can easily modify and / or adapt such specific embodiments to various uses without undue experimentation and without departing from the general concept of the present invention. Such adaptations and modifications are therefore intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It should be understood that the terminology or phraseology used herein is for purposes of illustration by way of example and not of limitation, and should therefore be interpreted by those skilled in the art in light of the teaching and guidance.

[0117]

[0084] The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

1. 1. A method for determining the presence of a stressor on a substrate, comprising: obtaining substrate position data describing position information of structures on the substrate within a plane of the substrate; obtaining substrate shape data describing a shape of the substrate; determining a first warp value from the substrate position data, the first warp value describing a bow of the substrate; determining a second warp value from the substrate shape data, the second warp value describing the bow of the substrate; determining the presence of the stressor on the back surface of the substrate based on the first warp value and the second warp value; A method for providing

2. The method of claim 1 , comprising determining the presence of the stressor on the back surface of the substrate based on a comparison of the first warp value and the second warp value.

3. The method of claim 1 or 2, comprising determining that the substrate does not comprise a back surface stressor on the back surface of the substrate when the first warp value and the second warp value are substantially equal.

4. The method of claim 1 , further comprising determining that the substrate comprises at least one backside stressor when the first warp value and the second warp value are not substantially equal.

5. determining a value of a warp component resulting from the non-uniform processing; determining whether the at least one posterior stressor is homogeneous or heterogeneous based on the magnitude of the warp component; The method of claim 4 further comprising:

6. comparing the value of the warp component to a threshold; determining that the at least one posterior stressor is homogeneous if the value of the warp component is less than the threshold, and determining that the at least one posterior stressor is heterogeneous if the value of the warp component is greater than or equal to the threshold; The method of claim 5 , comprising:

7. 7. The method of claim 5 or 6, comprising determining an outermost burl position based on the presence or absence of a non-homogeneous posterior stressor.

8. 8. A method according to any one of claims 5 to 7, comprising determining front and back warp contribution values ​​from the first warp value, the second warp value, the substrate position data and the substrate shape data.

9. 9. The method of claim 8, wherein the values ​​of the front warp contribution and the back warp contribution are determined by solving, for the front warp contribution and the back warp contribution, a first equation that sets the first warp value equal to at least the sum of the front warp contribution and the back warp contribution, and a second equation that sets the second warp value equal to the difference between the front warp contribution and the back warp contribution.

10. The method of claim 9 , wherein the first equation comprises an additional term comprising the warp component resulting from the non-uniform processing when the warp component exceeds the threshold.

11. The method of claim 10 , wherein the solving step is performed with reference to a look-up table describing the effect of one or more inhomogeneity parameters on stress in and / or strain of the substrate.

12. The heterogeneity parameter is the layer thickness before the onset of inhomogeneity, the radial location at which the inhomogeneity begins, and the slope of the decrease in the layer thickness characterizing the inhomogeneity The method of claim 11 , comprising one or more of:

13. The method of any preceding claim, wherein the substrate position data comprises alignment data.

14. The method of any preceding claim, wherein the substrate shape data comprises leveling data.

15. A computer program comprising program instructions operable to perform the method of any of claims 1 to 14 when run on a suitable device.

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