Systems and methods for non-linear optical metrology for advanced sub-diffraction imaging

Abstract

A sensor apparatus can include a transient optical pattern, a probe beam, and a detector. The transient optical pattern can be configured to induce a material change in an alignment mark thereby forming an effective alignment mark. The probe beam can be configured to interact with the effective alignment mark. The detector can be configured to measure diffracted light from the effective alignment mark generated by the probe beam. Advantageously the sensor apparatus can induce a transient change in a refractive index of the alignment mark with visible light, detect sub-wavelength features of the alignment mark, measure asymmetry of the alignment mark, and increase a resolution of the sensor apparatus by at least a factor of 4.

Description

SYSTEMS AND METHODS FOR NON-LINEAR OPTICAL METROLOGY FOR ADVANCED SUB -DIFFRACTION IMAGINGCROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Application No. 63 / 515,749, filed July 26, 2023, and which is incorporated herein in its entirety by reference.FIELD

[0002] The present disclosure relates to optical metrology systems and methods, for example, optical metrology systems and methods for lithographic apparatuses and systems.BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern of a patterning device (e.g., a mask, a reticle) onto a layer of radiation-sensitive material (resist) provided on a substrate.

[0004] To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features that can be formed on the substrate. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus, which uses, for example, deep ultraviolet (DUV) radiation with a wavelength of 157 nm or 193 nm or 248 nm.

[0005] In order to control a lithographic process to form device features accurately on a substrate, one or more targets can be formed on the substrate and utilized for alignment and positioning. A lithographic apparatus can use one or more sensors to accurately measure a characteristic of a target (e.g., alignment mark) by shining light at the target and collecting light diffracted from the target. Current alignment systems and techniques are subject to certain drawbacks and limitations. For example, prior systems utilize linear optics that are restricted by the diffraction limit of light (e.g., 2NA), and can only detect diffracted light from a target when a pitch of the target is at least half of a detection wavelength of the measurement light.

[0006] At any smaller pitch, these prior systems cannot measure the diffracted light accurately, thereby reaching a diffraction limit of visible light. Prior systems based on linear optics cannot perform alignment on diffraction gratings far below the diffraction limit. Further, reduction of the wavelength of measurement light is limited by the photo-responsivity of the resist. The traditional diffraction limit for prior systems can be at pitches of 500 nm or greater. Additionally, an alignment mark can be deformed due to wafer processing. When such deformation is asymmetric, intensities and phases of the diffracted light can induce an apparent position offset.SUMMARY

[0007] Accordingly, there is a need to improve resolution and accuracy of measuring target positions and target asymmetry on a substrate, decrease the number of targets and the total area occupied by the targets, and decrease errors in a lithographic process. Further, it would be desirable to detect subwavelength features of a target (e.g., alignment mark), measure asymmetry of the target, and increase a resolution (e.g., by at least a factor of 4) of a sensor apparatus. To improve such lithographic processes, there is a possibility of utilizing transient change in refractive index of a target, induced by higher order non-linear effects (e.g., second-order effects) in a pump-probe scheme, to measure subwavelength structures. For example, an optical metrology system can include a sensor apparatus that uses non-linear optical effects to change the refractive index on a scale above a traditional diffraction limit, thereby allowing the sensor apparatus to obtain information on the position and asymmetry of subwavelength structures.

[0008] In some aspects, a sensor apparatus can include a transient optical pattern, a probe beam, and a detector. In some aspects, the transient optical pattern can be configured to induce a material change in an alignment mark thereby forming an effective alignment mark. In some aspects, the probe beam can be configured to interact with the effective alignment mark. In some aspects, the detector can be configured to measure diffracted light or reflected light from the effective alignment mark generated by the probe beam.

[0009] In some aspects, the material change can include a refractive index change of the alignment mark. In some aspects, the material change can be proportional to an intensity of the transient optical pattern.

[0010] In some aspects, the transient optical pattern can include an interference pattern. In some aspects, the transient optical pattern can originate from a plurality of skew beams. In some aspects, the transient optical pattern can be an arbitrary image pattern. For example, the arbitrary image pattern can be a grating pattern, a checkerboard pattern, a finite pattern, or a combination thereof.

[0011] In some aspects, the probe beam can be configured to interact with the effective alignment mark within a time frame of the material change. In some aspects, the diffracted light can include first-order diffraction beams (Li, I+i) from the effective alignment mark.

[0012] In some aspects, the diffracted light can diffract from a spatial periodic pattern of the effective alignment mark formed due to combination (e.g., a multiplication) of the transient optical pattern and the alignment mark. In some aspects, the spatial periodic pattern can include one or more spatial harmonics of the transient optical pattern. In some aspects, a relative periodicity between a period of the transient optical pattern and a period of the alignment mark increases a resolution of the sensor apparatus as the relative periodicity decreases. In some aspects, the relative periodicity can increase the resolution of the sensor apparatus by at least a factor of 4.

[0013] In some aspects, the sensor apparatus can further include a processor coupled to the detector. In some aspects, the processor can be configured to determine a position of the alignment mark based on an asymmetry of the diffracted light.

[0014] In some aspects, the alignment mark can be adjustable relative to the transient optical pattern and the probe beam. In some aspects, the transient optical pattern can be adjustable relative to the alignment mark and the probe beam. In some aspects, the probe beam can be adjustable relative to the alignment mark and the transient optical pattern.

[0015] In some aspects, the sensor apparatus can further include an interferometric device. In some aspects, the interferometric device can be configured to receive the diffracted light and interfere the diffracted light with itself to produce an alignment signal. In some aspects, the sensor apparatus can further include a processor coupled to the detector. In some aspects, the processor can be configured to determine an asymmetry of the alignment mark.

[0016] In some aspects, a method can include forming a transient optical pattern on an alignment mark thereby inducing a material change in the alignment mark and forming an effective alignment mark. In some aspects, the method can further include interacting a probe beam with the effective alignment mark. In some aspects, the method can further include measuring diffracted light from the effective alignment mark generated by the probe beam.

[0017] In some aspects, the method can further include determining a position of the alignment mark based on an asymmetry of the diffracted light. In some aspects, the method can further include determining an asymmetry of the alignment mark based on an asymmetry of the diffracted light.

[0018] In some aspects, the method can further include scanning the alignment mark relative to the transient optical pattern and the probe beam. In some aspects, the method can further include scanning the transient optical relative to the alignment mark and the probe beam. In some aspects, the method can further include scanning the probe beam relative to the alignment mark and the transient optical pattern.

[0019] Implementations of any of the techniques described above may include an EUV light source, a DUV light source, a system, a method, a process, a device, and / or an apparatus. The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.

[0020] Further features and exemplary aspects of the aspects, as well as the structure and operation of various aspects, are described in detail below with reference to the accompanying drawings. It is noted that the aspects are not limited to the specific aspects described herein. Such aspects are presented herein for illustrative purposes only. Additional aspects will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein.BRIEF DESCRIPTION OF THE DRAWINGS / FIGURES

[0021] The accompanying drawings, which are incorporated herein and form part of the specification, illustrate the aspects and, together with the description, further serve to explain the principles of the aspects and to enable a person skilled in the relevant art(s) to make and use the aspects.

[0022] FIG. 1 is a schematic illustration of a lithographic apparatus, according to an exemplary aspect.

[0023] FIG. 2 is a schematic front illustration of a sensor apparatus imparting a transient optical pattern on an alignment mark to form an effective alignment mark, according to an exemplary aspect.

[0024] FIG. 3 is a schematic front illustration of the sensor apparatus shown in FIG. 2 directing a probe beam at the effective alignment mark, according to an exemplary aspect.

[0025] FIG. 4 is a schematic graph of a combination (e.g., a multiplication) of the alignment mark with the transient optical pattern to form the effective alignment mark shown in FIG. 2, according to an exemplary aspect.

[0026] FIG. 5 is a schematic front illustration of the sensor apparatus shown in FIG. 2 directing the probe beam at a periodic pattern of the effective alignment mark, according to an exemplary aspect.

[0027] FIGS. 6A-6C are schematic plots of diffracted light from the effective alignment mark coinciding with exemplary positions of the alignment mark shown in FIG. 2, according to an exemplary aspect.

[0028] FIG. 7 is a schematic plot of spatial frequencies involving a transient optical pattern on an alignment mark, according to an exemplary aspect.

[0029] FIG. 8 is a schematic front illustration of a sensor apparatus detecting exemplary diffraction orders of a spatial periodic pattern of an effective alignment mark, according to an exemplary aspect.

[0030] FIG. 9 is a schematic illustration of a sensor apparatus external to a lithographic apparatus, according to an exemplary aspect.

[0031] FIG. 10 is a schematic graph of a material change in an asymmetric alignment mark induced by a transient optical pattern for exemplary positions of the asymmetric alignment mark, according to an exemplary aspect.

[0032] FIG. 11A is a schematic plot of a diffraction efficiency of the zeroth-order of diffracted light for a transient grating with a same period as a symmetric alignment mark, according to an exemplary aspect.

[0033] FIG. 1 IB is a schematic plot of a diffraction efficiency of the zeroth-order diffracted light for a transient grating with a same period as the asymmetric alignment mark shown in FIG. 10, according to an exemplary aspect.

[0034] FIG. 12A is a schematic plot of a diffraction efficiency of first-orders of diffracted light for a transient grating with a same period as a symmetric alignment mark, according to an exemplary aspect.

[0035] FIG. 12B is a schematic plot of a diffraction efficiency of first-orders of diffracted light for a transient grating with a same period as the asymmetric alignment mark shown in FIG. 10, according to an exemplary aspect.

[0036] FIG. 13A is a schematic plot of a diffraction efficiency of second-orders of diffracted light for a transient grating with a same period as a symmetric alignment mark, according to an exemplary aspect.

[0037] FIG. 13B is a schematic plot of a diffraction efficiency of second-orders of diffracted light for a transient grating with a same period as the asymmetric alignment mark shown in FIG. 10, according to an exemplary aspect.

[0038] FIG. 14 is a schematic illustration of a sensor apparatus with an interferometric device for detecting diffracted light, according to an exemplary aspect.

[0039] The features and exemplary aspects of the aspects will become more apparent from the detailed description set forth below when taken in conjunction with the drawings. Additionally, generally, the left-most digit(s) of a reference number identifies the drawing in which the reference number first appears. Unless otherwise indicated, the drawings provided throughout the disclosure should not be interpreted as to-scale drawings.DETAILED DESCRIPTION

[0040] This specification discloses one or more aspects that incorporate the features of this present invention. The disclosed aspect(s) merely exemplify the present invention. The scope of the invention is not limited to the disclosed aspect(s). The present invention is defined by the claims appended hereto.

[0041] The aspect(s) described, and references in the specification to “one aspect,” “an aspect,” “an example aspect,” “an exemplary aspect,” etc., indicate that the aspect(s) described may include a particular feature, structure, or characteristic, but every aspect may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same aspect. Further, when a particular feature, structure, or characteristic is described in connection with an aspect, it is understood that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other aspects whether or not explicitly described.

[0042] Spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “on,” “upper” and the like, may be used herein for ease of description to describe one element or feature’s relationship to another element(s) or feature(s) as illustrated in the figures. The spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. The apparatus may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may likewise be interpreted accordingly.

[0043] The term “about” or “substantially” or “approximately” as used herein indicates the value of a given quantity that can vary based on a particular technology. Based on the particular technology, the term “about” or “substantially” or “approximately” can indicate a value of a given quantity that varies within, for example, 1-15% of the value (e.g., ±1%, ±2%, ±5%, ±10%, or ±15% of the value).

[0044] Aspects of the disclosure may be implemented in hardware, firmware, software, or any combination thereof. Aspects of the 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 (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic disk storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, and / or instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[0045] Before describing such aspects in more detail, however, it is instructive to present example environments in which aspects of the present disclosure may be implemented.

[0046] Exemplary Lithographic System

[0047] FIG. 1 shows a lithographic system comprising a radiation source SO and a lithographic apparatus LA. The radiation source SO is configured to generate an EUV and / or a DUV radiation beam B and to supply the EUV and / or DUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT (e.g., a mask table, a reticle table, a reticle stage) configured to support a patterning device MA (e.g., a mask, a reticle), a projection system PS, and a substrate table WT configured to support a substrate W.

[0048] The illumination system IL is configured to condition the EUV and / or DUV radiation beam B before the EUV and / or DUV radiation beam B is incident upon the patterning device MA. Thereto, the illumination system IL may include a faceted field mirror device 10 and a faceted pupil mirror device 11. The faceted field mirror device 10 and faceted pupil mirror device 11 together provide the EUV and / or DUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to, or instead of, the faceted field mirror device 10 and faceted pupil mirror device 11.

[0049] After being thus conditioned, the EUV and / or DUV radiation beam B interacts with the patterning device MA. This interaction may be reflective (as shown), which may be preferred for EUV radiation. This interaction may be transmissive, which may be preferred for DUV radiation. As a result of this interaction, a patterned EUV and / or DUV radiation beam B’ is generated. The projection system PS is configured to project the patterned EUV and / or DUV radiation beam B’ onto the substrate W. For that purpose, the projection system PS may comprise a plurality of mirrors 13, 14 that are configured to project the patterned EUV and / or DUV radiation beam B’ onto the substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV and / or DUV radiation beam B ’ , thus forming an image with features that are smaller than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated as having only two mirrors 13, 14 in FIG. 1, the projection system PS may include a different number of mirrors (e.g. six or eight mirrors).

[0050] The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus LA aligns the image, formed by the patterned EUV and / or DUV radiation beam B’, with a pattern previously formed on the substrate W.

[0051] Exemplary Sensor Apparatuses

[0052] As discussed above, in order to control a lithographic process to form device features accurately on a substrate, one or more diffraction targets (e.g., alignment marks, overlay marks) are provided on the substrate. A lithographic apparatus uses one or more sensors (e.g., alignment sensors, overlay sensors, and / or a combination of both) that accurately measures a characteristic (e.g., position, overlay) of the diffraction target.

[0053] Existing alignment systems and techniques are subject to certain drawbacks and limitations. For example, prior systems utilize linear optics that can only detect diffracted light when a pitch of a target is larger than half of a detection wavelength of the light. At any smaller pitch, these prior systems cannot measure the diffracted light accurately, thereby reaching a diffraction limit of visible light. Prior systems using linear optics cannot perform alignment on diffraction gratings far below the diffraction limit. The traditional diffraction limit for prior systems can be at pitches of 500 nm or greater. Additionally, an alignment mark can be deformed due to wafer processing. When such deformation is asymmetric, intensities and phases of the diffracted light can induce an apparent position offset.

[0054] Aspects of sensor apparatuses, systems, and methods as discussed below can use non-linear effects with a target pitch less than the diffraction limit of visible light, thereby bringing the pitch size closer to a product structure. This pitch can be called a sub-wavelength pitch. These imaging techniques enable such sensor apparatuses and systems to resolve objects below the tradition diffraction limit of optical resolution (e.g., diffraction limit of visible light), thus reaching super-resolution.

[0055] Aspects of sensor apparatuses, systems, and methods as discussed below can improve resolution and accuracy of measuring target positions and target asymmetry on a substrate, decrease the number of targets and the total area occupied by the targets, and decrease errors in a lithographic process.

[0056] FIGS. 2, 3, and 5 illustrate sensor apparatus 200, according to exemplary aspects. Sensor apparatus 200 can be configured to illuminate a diffraction target (e.g., alignment mark 206) and detect a characteristic (e.g., alignment position, mark asymmetry, pitch, diffraction order, depth, subsegmentation, etc.) of one or more diffraction targets, and thereby improve alignment and calibration, for example, in lithographic apparatus LA. In some aspects, sensor apparatus 200 can include a first light source 201, a second light source 212, and a detector 213. In some aspects, first light source 201 and second light source 212 can be a single light source (e.g., broadband light source, coherent light source, laser, laser diode, etc.). Although sensor apparatus 200 is shown in FIG. 2 as a stand-alone apparatus and / or system, aspects of this disclosure can be used with other apparatuses, systems, and / or methods, for example, lithographic apparatus LA, sensor apparatus 200', and / or sensor apparatus 200".

[0057] As shown in FIGS. 2, 3, and 5, sensor apparatus 200 can include probe beam 216 (e.g., from second light source 212) configured to interact with effective alignment mark 210 formed by transient optical pattern 208 inducing a material change (e.g., a transient change in refractive index) in alignment mark 206.

[0058] In some aspects, first light source 201 can be configured to use two or more light guides 202a, 202b (e.g., fiber, light pipe, mirrors, beam splitters) configured to direct two or more pump light beams 203a, 203b at a lens 205 disposed at a distance of focal length / from light guides 202a, 202b (e.g., the pupil plane). Lens 205 can be disposed at a distance of focal length / from alignment mark 206 (e.g., the object plane). A refraction of pump light beams 203a, 203b through lens 205 can redirect pump light beams 203a, 203b as skew light beams 204a, 204b at an alignment mark 206. In some aspects, light guides 202a, 202b can be configured to direct pump light beams 203a, 203b at skew angles toward alignment mark 206 without using lens 205.

[0059] In some aspects, first light source 201 can be configured to provide coherent electromagnetic broadband illumination beams (e.g. pump light beams 203a, 203b) having one or more passbands. In some aspects, the one or more passbands can be within a visible spectrum of wavelengths between about 380 nm and about 750 nm. For example, the wavelength can be in a range of about 450 nm to about 550 nm, for example, about 500 nm. In some aspects, the one or more passbands can be within an ultraviolet spectrum of wavelengths between about 100 nm and about 380 nm. For example, the wavelength can be in a range of about 350 nm to about 380 nm, for example, about 365 nm. In some aspects, the one or more passbands can be within an infrared spectrum of wavelengths between about 750 nm and about 2 microns. For example, the wavelength can be in a range of about 750 nm to about 900 nm, for example, about 850 nm.

[0060] In some aspects, first light source 201 can be a pulsed source. For example, first light source 201 can have a pulse width within a time frame of non-linear effects in the alignment mark 206. In some aspects, the pulse width of first light source 201 can be no greater than 1 ps.

[0061] In some aspects, alignment mark 206 can be a diffraction target. In some aspects, alignment mark 206 can include a diffraction grating. In some aspects, alignment mark 206 can be a 1-D grating, which is printed such that after development, bars are formed of solid resist lines. In some aspects, alignment mark 206 can be a 2-D array or 2-D grating, which is printed such that, after development, a grating is formed of solid resist bars, pillars, or vias in the resist. In some aspects, alignment mark 206 can include targets on a substrate to receive pump light beams 203a, 203b or skew light beams 204a, 204b. In some aspects, alignment mark 206 can be a grating having a pitch ranging from about 10 nm to about 100 nm. In some aspects, alignment mark 206 (e.g., a diffraction grating) can include lines and spaces of different materials. In some aspects, the lines of alignment mark 206 can be made from a semiconductor material. For example, the lines of alignment mark 206 can be made from silicon. In some aspects, the spaces of alignment mark 206 can be made up of a gas. For example, the spaces of alignment mark 206 can be made up of air.

[0062] In some aspects, a material of alignment mark 206 can change its refractive index when illuminated by a strong, short laser pulse (e.g., from first light source 201). Upon absorbing the laser pulse, a change in refractive index of the material (e.g., alignment mark 206) can be proportional to the electric field of the light (e.g. Pockels effect), to the square of the electric field of the light (e.g. Kerr effect, thermo-optic effect), or higher orders (e.g., nth-order non-linear effects). For example, the material change of alignment mark 206 due to the Kerr effect can be proportional to an intensity of the laser pulse (e.g., from first light source 201), generating an intensity dependent refractive index n = n0+ n2Ipumpin alignment mark 206 (e.g., an effective alignment mark 210), where n0is a linear refractive index of the material of alignment mark 206, n2is a second-order non-linear refractive index, and IpUmpis an intensity of the laser pulse (e.g., from first light source 201).

[0063] In some aspects, light guides 202a, 202b can be configured to direct first and second pump light beams 203a, 203b toward lens 205. In some aspects, light guides 202a, 202b can include any optic (e.g., mirror, lens, prism, waveguide, optical modulator, etc.). In some aspects, light guides 202a, 202b can include a beam splitter configured to split an illumination beam from first light source 201 into first pump light beam 203a and second pump light beam 203b. First light guide 202a can direct first pump light beam 203a toward lens 205. Second light guide 202b can direct second pump light beam 203b toward lens 205. In some aspects, light guides 202a, 202b can be capable of altering each angle of incidence of first and second pump light beams 203a, 203b. In some aspects, lens 205 can have a refractive index and a focal length / such that first and second pump light beams 203a, 203b can be directed toward alignment mark 206 as two or more skew light beams 204a, 204b. In some aspects, light guides 202a, 202b can be configured to direct pump light beams 203a, 203b at skew angles toward alignment mark 206 without using lens 205.

[0064] In some aspects, transient optical pattern 208 can be formed by a plurality of skew light beams (e.g., skew light beams 204a, 204b passing through lens 205 toward alignment mark 206, pump light beams 203a, 203b directed at skew angles toward alignment mark 206 without passing through lens 205, etc.). In some aspects, transient optical pattern 208 can be an interference pattern. In some aspects, transient optical pattern 208 can be an arbitrary image pattern. For example, transient optical pattern 208 can be a grating pattern, a checkerboard pattern, a finite pattern, or a combination thereof. In some aspects, transient optical pattern can have an intensity profile with a sinusoidal pattern, a triangular pattern, a rectangular pattern, or a combination thereof.

[0065] As discussed above, alignment mark 206 can include a grating (e.g., 1-D grating), and the lines and spaces of alignment mark 206 can be made of different materials, so the material change (e.g., refractive index change) in the different materials can also have different magnitudes. In some aspects, transient optical pattern 208 can create a refractive index modulation through a combination (e.g., a multiplication) of the profile of transient optical pattern 208 with alignment mark 206. For example, as shown in FIG. 4, effective alignment mark 406 can be generated due to the interaction (e.g., non-lineareffects) of alignment mark 402 with transient optical pattern 404 (e.g., combination of transient optical pattern 404 and alignment mark 402). This modulation can produce a periodic material change (e.g., refractive index change) of alignment mark 206 due to various linear and non-linear effects (e.g., second-order non-linear effects). In some aspects, a combination (e.g., a multiplication) of transient optical pattern 208 with alignment mark 206 can produce effective alignment mark 210 that is characterized by the refractive index modulation (e.g., as shown in FIG. 10).

[0066] In some aspects, transient optical pattern 208 can induce a material change in alignment mark 206, thereby forming effective alignment mark 210. In some aspects, the material change can be a refractive index change of alignment mark 206. In some aspects, first skew light beam 204a can be directed to alignment mark 206 at a first angle of incidence, and second skew light beam 204b can be directed to alignment mark 206 at a second angle of incidence. In some aspects, first and second skew light beams 204a, 204b (e.g., coherent light) can overlap spatially and temporally to form a grating-like interference pattern (e.g., transient optical pattern 208). In some aspects, a pitch of transient optical pattern 208 can be greater than a pitch of alignment mark 206. For example, transient optical pattern 208 can have a pitch of about 500 nm and alignment mark 206 can have a pitch in a range of about 10 nm to about 300 nm. In some aspects, a pitch of transient optical pattern 208 can be a similar size to a pitch of alignment mark 206. In some aspects, a pitch of transient optical pattern 208 can be smaller than a pitch of alignment mark 206. For example, transient optical pattern 208 can have a pitch of about 100 nm and alignment mark 206 can have a pitch of about 200 nm.

[0067] In some aspects, a light source (e.g., second light source 212) can be configured to direct a probe beam (e.g., probe beam 216 shown in FIG. 3) to interact with effective alignment mark 210 to produce diffracted light (e.g., diffracted light 218a, 218b shown in FIG. 3). In some aspects, first light source 201 or second light source 212 can direct the probe beam. In the exemplary aspect shown in FIG. 2, second light source 212 can direct the probe beam.

[0068] In some aspects, first light source 201 or second light source 212 can be configured to direct a probe beam (e.g., probe beam 216 shown in FIG. 3) having one or more passbands. In some aspects, the one or more passbands can be within a visible spectrum of wavelengths between about 380 nm and about 750 nm. For example, the wavelength can be in a range from about 500 nm to about 750 nm, for example, about 700 nm. In some aspects, the one or more passbands can be within an ultraviolet spectrum of wavelengths between about 100 nm and about 380 nm. For example, the wavelength can be in a range from about 350 nm to about 380 nm, for example, about 365 nm. In some aspects, the one or more passbands can be within an infrared spectrum of wavelengths between about 750 nm and about 2 microns. For example, the wavelength can be in a range from about 750 nm to about 1100 nm, for example, about 950 nm. In some aspects, a first wavelength of first light source 201 can be less than a second wavelength of second light source 212. In some aspects, the first wavelength of first light source 201 can be equal to the second wavelength of second light source 212.

[0069] In some aspects, second light source 212 can be a pulsed source. In some aspects, second light source 212 can have a pulse width in a range of millisecond accuracy, microsecond accuracy, nanosecond accuracy, picosecond accuracy, femtosecond accuracy, or attosecond accuracy. For example, the pulse width can be in a range of about 1 millisecond to about 1 nanosecond, for example, about 100 nanoseconds. For example, the pulse width can be in a range of about 1 microsecond to about 1 picosecond, for example, about 100 picoseconds. For example, the pulse width can be in a range of about 1 microsecond to about 1 femtosecond, for example, about 10 femtoseconds. For example, the pulse width can be in a range of about 1 nanosecond to about 1 attosecond, for example, about 100 attoseconds. In some aspects, second light source 212 can have a pulse width less than or equal to a time frame of a material change (e.g., refractive index change) in alignment mark 206 induced by transient optical pattern 208 (e.g., time frame of Kerr effect). For example, the pulse width of second light source 212 can be no greater (no longer) than 1 microsecond. For example, the pulse width of second light source 212 can be no greater (no longer) than 1 nanosecond. For example, the pulse width of second light source 212 can be no greater (no longer) than 1 picosecond. For example, the pulse width of second light source 212 can be no greater (no longer) than 1 femtosecond. For example, the pulse width of second light source 212 can be no greater (longer) than 1 attosecond.

[0070] In some aspects, detector 213 can be configured to measure the diffracted light (e.g., diffracted light 218a, 218b shown in FIG. 3) so that a processor, coupled to detector 213, can determine a position and / or asymmetry of alignment mark 206 based on an asymmetry (e.g., difference between first-order diffraction intensities 1 1, I+i) of the diffracted light (e.g., diffracted light 218a, 218b shown in FIG. 3) from effective alignment mark 210. In some aspects, detector 213 can be coupled to collection optics 214a, 214b (e.g., light guides, light pipes, fibers, etc.) configured to detect the diffracted light (e.g., diffracted light 218a, 218b shown in FIG. 3) at a pupil plane of sensor apparatus 200. In some aspects, the processor can be configured to measure the diffracted light (e.g., diffracted light 218a, 218b shown in FIG. 3) at an angle corresponding to a pitch of transient optical pattern 208. In some aspects, detector 213 can be configured to measure reflected light (e.g., a zeroth-order beam) from the effective alignment mark 210.

[0071] FIG. 3 further illustrates sensor apparatus 200, according to exemplary aspects. The above discussion of sensor apparatus 200 in FIG. 2 applies to the discussion of FIG. 3. The aspects of sensor apparatus 200 shown in FIG. 2 and the aspects of sensor apparatus 200 shown in FIG. 3 may be similar. Similar reference numbers are used to indicate features of the aspects of sensor apparatus 200 shown in FIG. 2 and the similar features of the aspects of sensor apparatus 200 shown in FIG. 3.

[0072] In some aspects, transient optical pattern 208 can interact with alignment mark 206 (e.g., light absorption), thereby resulting in a change of a refractive index of a material of alignment mark 206. For example, as shown in FIG. 3, transient optical pattern 208 can create a periodic refractive index modulation through a combination (e.g., a multiplication) of the profile of transient optical pattern 208 with alignment mark 206. In some aspects, a combination (e.g., a multiplication) of transient opticalpattern 208 with alignment mark 206 can produce effective alignment mark 210 that is characterized by the refractive index modulation.

[0073] In some aspects, a light source (e.g., second light source 212) can be configured to direct probe beam 216 to interact with effective alignment mark 210 to produce diffracted light 218a, 218b. In some aspects, probe beam 216 can interact with effective alignment mark 210 within a time frame of a material change induced by transient optical pattern 208 (e.g., time frame of Kerr effect). In some aspects, first light source 201 or second light source 212 can direct probe beam 216. In the exemplary aspect shown in FIG. 3, second light source 212 can direct probe beam 216. In some aspects, a first wavelength of first light source 201 is less than a second wavelength of second light source 212. For example, second light source 212 can have a wavelength of 700 nm and first light source can have a wavelength of 500 nm. In some aspects, the first wavelength of first light source 201 can be equal to the second wavelength of second light source 212. For example, first light source can have a wavelength of 500 nm and second light source 212 can have a wavelength of 500 nm.

[0074] In some aspects, alignment mark 206 can be adjustable relative to transient optical pattern 208 and probe beam 216. For example, alignment mark 206 can be translated along a horizontal axis (Y- axis) relative to transient optical pattern 208 and probe beam 216 that can remain fixed. In some aspects, transient optical pattern 208 can be adjustable relative to alignment mark 206 and probe beam 216. For example, transient optical pattern 208 can be translated (e.g., scanned, rastered) along a horizontal axis (Y-axis) relative to alignment mark 206 and probe beam 216 that can remain fixed. In some aspects, probe beam 216 can be adjustable relative to alignment mark 206 and transient optical pattern 208. For example, probe beam 216 can be translated (e.g., scanned, rastered) along a horizontal axis (Y-axis) relative to alignment mark 206 and transient optical pattern 208 that can remain fixed.

[0075] In some aspects, beams of diffracted light can diffract from a diffraction target such as effective alignment mark 210. For example, as shown in FIG. 3, diffracted light 218 can include first diffracted light 218a and second diffracted light 218b. In some aspects, first diffracted light 218a can be a negative diffraction order beam (e.g., -1) and second diffracted light 218b can be a positive diffraction order beam (e.g., +1). In some aspects, diffracted light 218a, 218b can be higher-order diffraction beams (e.g., a negative second-order beam and a positive second-order beam, a negative third-order beam and a positive third-order beam, etc.). As shown in FIG. 3, first and second diffracted light 218a, 218b can be transmitted toward lens 205 and can be redirected by refraction through lens 205 toward collection optics 214a, 214b that are coupled to detector 213.

[0076] In some aspects, detector 213 can be coupled to collection optics 214a, 214b. Collection optics 214a, 214b (e.g., fixed optics) can be configured to collect diffracted light 218a, 218b in a pupil plane of sensor apparatus 200 and transmit diffracted light 218a, 218b toward detector 213. Detector 213 can be configured to measure diffracted light (e.g., diffracted light 218a, 218b) or reflected light (e.g., a zeroth-order beam) and determine a position or asymmetry of alignment mark 206. In some aspects, detector 213 can be coupled to a processor configured to determine a position or asymmetry ofalignment mark 206. In some aspects, detector 213 can be configured to measure a characteristic of a diffraction target such as alignment mark 206 based on diffracted light 218a, 218b. In some aspects, the characteristic of a diffraction target such as alignment mark 206 measured by detector 213 is an alignment position. In some aspects, the characteristic of a diffraction target such as alignment mark 206 measured by detector 213 is an asymmetry of alignment mark 206. In some aspects, the characteristic of a diffraction target such as alignment mark 206 measured by detector 213 is an overlay. In some aspects, detector 213 can measure diffracted light 218a, 218b at an angle corresponding to a pitch of transient optical pattern 208. In some aspects, detector 213 can be a photodetector, photodiode, charge-coupled device (CCD), avalanche photodiode (APD), camera, PIN detector, multi-mode fiber, single-mode fiber, or any other suitable optical detector.

[0077] FIG. 4 illustrates graph 400 of a combination (e.g., a multiplication) of a unit cell of alignment mark 402 with a single period of transient optical pattern 404 to form a unit cell of effective alignment mark 406, according to some aspects. FIG. 4 shows graph 400 with an amplitude 408 on a Y-axis and a position 410 on an X-axis.

[0078] In some aspects, alignment mark 402 can be depicted as a unit cell on a graph illustration with an amplitude 408 on a Y-axis and a position 410 on an X-axis. Alignment mark 402 can include multiple alignment mark peaks 412 that correspond to lines of material of alignment mark 402. In some aspects, a unit cell of alignment mark 402 can include a first, second, third, fourth, and fifth alignment mark peaks 412a-412e. Alignment mark 402 can include gaps between alignment mark peaks 412 that correspond to spaces of material of alignment mark 402. Amplitude 408 of gaps between alignment mark peaks 412 can be a value of zero.

[0079] In some aspects, transient optical pattern 404 can be depicted as a single period on a graph illustration with an amplitude 408 on a Y-axis and a position 410 on an X-axis. Transient optical pattern 404 can include a transient optical pattern curve 414 that spans the length of the period of transient optical pattern 404. In some aspects, transient optical pattern 404 can be an arbitrary image pattern. For example, transient optical pattern 404 can be a grating pattern, a checkerboard pattern, a finite pattern, or a combination thereof. In some aspects, transient optical pattern can have an intensity profile with a sinusoidal pattern, a triangular pattern, a rectangular pattern, or a combination thereof. In the exemplary aspect shown in FIG. 4, transient optical pattern curve 414 can be a sinusoidal pattern.

[0080] In some aspects, effective alignment mark 406 can be depicted as a unit cell on a graph illustration with an amplitude 408 on a Y-axis and a position 410 on an X-axis. Effective alignment mark 406 can be a combination (e.g., a multiplication) of alignment mark 402 and transient optical pattern 404, thereby adopting a shape that shares characteristics of alignment mark peaks 412 and transient optical pattern curve 414. For example, effective alignment mark 406 can include multiple effective alignment mark peaks 416 that correspond to lines of material of alignment mark 402. Effective alignment mark peaks 416 acquire a curvature that matches a curvature of transient optical pattern curve 414. In some aspects, a unit cell of effective alignment mark 406 can include a first,second, third, fourth, and fifth effective alignment mark peaks 416a-416e. Effective alignment mark 406 can include gaps between effective alignment mark peaks 416 that correspond to spaces of material of alignment mark 402. Amplitude 408 of gaps between effective alignment mark peaks 416 can be a value of zero, thereby reducing amplitude 408 of transient optical pattern curve 414 to zero at those corresponding positions by way of a combination (e.g., a multiplication) of values.

[0081] FIG. 5 further illustrates sensor apparatus 200, according to some aspects. The above discussion of sensor apparatus 200 in FIGS. 2 and 3 applies to the discussion of FIG. 5. The aspects of sensor apparatus 200 shown in FIGS. 2 and 3 and the aspects of sensor apparatus 200 shown in FIG. 5 may be similar. Similar reference numbers are used to indicate features of the aspects of sensor apparatus 200 shown in FIGS. 2 and 3 and the similar features of the aspects of sensor apparatus 200 shown in FIG. 5. FIG. 5 illustrates a visualization of a repeating pattern for effective alignment mark 210, similar to the graph illustration of effective alignment mark 406 shown in FIG. 4.

[0082] In some aspects, effective alignment mark 210 can be visualized as a repeating periodic pattern 209 of effective alignment mark peaks 416a-416n of a unit cell of effective alignment mark 406 as shown in FIG. 4. Effective alignment mark 210 can include first through nth effective alignment mark peaks 416a-416n, where n is an integer greater than 1. Effective alignment mark peaks 416a-416n can correspond to lines of material of alignment mark 206 shown in FIGS. 2 and 3. Gaps between effective alignment mark peaks 416a-416n can correspond to spaces of material of alignment mark 206 shown in FIGS. 2 and 3. In some aspects, each of effective alignment mark peaks 416a-416n can have a pitch ranging from about 10 nm to about 100 nm. In some aspects, effective alignment mark 210 can include first through nth periodic patterns 209a-209n, where n is an integer greater than 1. Periodic patterns 209a-209n can be visualized as a repeating pattern of a unit cell of effective alignment mark 406 as shown in FIG. 4. In some aspects, a periodic pattern 209 (e.g., periodic pattern 209a) can include a plurality of effective alignment mark peaks 416a-416n (e.g., effective alignment mark peaks 416a- 416d). In some aspects, each periodic pattern 209a-209n can have a pitch of about 500 nm.

[0083] FIGS. 6A-6C illustrate plots 600a, 600b, 600c of diffracted light (e.g., first-order diffraction intensities 614a-614c, 616a-616c) from effective alignment mark 606 due to a combination (e.g., a multiplication) of a unit cell of alignment mark 602 with a single period of transient optical pattern 604 to form a unit cell of effective alignment mark 606, according to exemplary aspects. FIGS. 6A-6C show plots 600a, 600b, 600c, with an amplitude 608 on a Y-axis and a position 610 on an X-axis, of diffracted light from effective alignment mark 606 coinciding with exemplary positions 610 of alignment mark 602 (e.g., 0, p / ^, p / 2). Pitch p represents a period of alignment mark 602 and can be a distance between peaks of alignment mark 602.

[0084] In some aspects, probe beam 612 can be directed toward effective alignment marks 606a-606c, respectively, to produce negative first-order diffraction intensities 614a-614c and positive first-order diffraction intensities 616a-616c, respectively. A detector (e.g., detector 213 shown in FIG. 5) can measure an asymmetry in an intensity of negative first-order diffracted light 614a-614c and an intensityof positive first-order diffracted light 616a-616c, respectively. For example, the detector (e.g., detector 213 shown in FIG. 5) can measure an asymmetry between the intensity of negative first-order diffracted light 614a and the intensity of positive first-order diffracted light 616a. The asymmetry between the intensities of negative first-order diffracted light 614a-614c and the intensities of positive first-order diffracted light 616a-616c, respectively, can be based on a reactive index change in lines or spaces of material of alignment mark 602. In some aspects, mark position information and / or mark asymmetry information can be extracted from the diffraction efficiency alone, for example, if the lines and spaces of the material of alignment mark 602 have different linear or non-linear refractive indexes. The asymmetry between the intensities of negative first-order diffracted light 614a-614c and positive first- order diffracted light 616a-616c, respectively, can oscillate with a period corresponding to a period of pitch p of alignment mark 602. As a result, a sensor apparatus (e.g., sensor apparatus 200) can detect a position and / or asymmetry of alignment mark 602 for alignment purposes.

[0085] In some aspects, a position of alignment mark 602 can vary with respect to transient optical pattern 604 ranging over a period of 0 to p, where p is a pitch of alignment mark 602. As seen in three exemplary aspects in FIGS. 6A-6C, a position of alignment mark 602 can vary with respect to transient optical pattern 604 ranging over a period of 0 to p / 2. For example, as shown in FIG. 6A, plot 600a of a unit cell of alignment mark 602a, at a position of X = 0, with a single period of transient optical pattern 604a can form a unit cell of effective alignment mark 606a. For example, as shown in FIG. 6B, plot 600b of a unit cell of alignment mark 602b, at a position of X = p!^. with a single period of transient optical pattern 604b can form a unit cell of effective alignment mark 606b. For example, as shown in FIG. 6C, plot 600c of a unit cell of alignment mark 602c, at a position of X = p / 2, with a single period of transient optical pattern 604c can form a unit cell of effective alignment mark 606c.

[0086] In some aspects, plot 600a can represent a position of X = 0, which begins a period of pitch p of alignment mark 602a. A beginning of a space of material of alignment mark 602a can be located at a position of X = 0. This space of material of alignment mark 602a can coincide with a peak of transient optical pattern 604a to form effective alignment mark 606a. Probe beam 612 can be directed toward effective alignment mark 606a to produce a negative first-order diffracted light 614a and a positive first- order diffracted light 616a. At a position of X = 0, an intensity of negative first-order diffracted light 614a can be greater than an intensity of positive first-order diffracted light 616a due to refractive index modulation in alignment mark 602a, thereby producing an asymmetry between negative first-order diffracted light 614a and positive first-order diffracted light 616a. A sensor apparatus (e.g., sensor apparatus 200) can detect this asymmetry and therefore the position of X = 0 of alignment mark 602a for this position 610.

[0087] In some aspects, plot 600b can represent a position of X = p!^. which is a first quarter of a period of pitch p of alignment mark 602b. A middle of a space of material of alignment mark 602b can be located at a position of X = / 4. This space of material of alignment mark 602b can coincide with a peak of transient optical pattern 604b to form effective alignment mark 606b. Probe beam 612 can bedirected toward effective alignment mark 606b to produce a negative first-order diffracted light 614b and a positive first-order diffracted light 616b. At a position of X = p / ^, an intensity of negative first- order diffracted light 614b can be equal to an intensity of positive first-order diffracted light 616b due to refractive index modulation in alignment mark 602b, thereby producing a symmetry between negative first-order diffracted light 614b and positive first-order diffracted light 616b. A sensor apparatus (e.g., sensor apparatus 200) can detect this symmetry and therefore the position of X = / 4 of alignment mark 602b for this position 610.

[0088] In some aspects, plot 600c can represent a position of X = p / 2, which is a first half of a period of pitch p of alignment mark 602c. A beginning of a line of material of alignment mark 602c can be located at a position of X = p / 2. This line of material of alignment mark 602c can coincide with a peak of transient optical pattern 604c to form effective alignment mark 606c. Probe beam 612 can be directed toward effective alignment mark 606c to produce a negative first-order diffracted light 614c and a positive first-order diffracted light 616c. At a position of X = p / 2, an intensity of negative first-order diffracted light 614c can be less than an intensity of positive first-order diffracted light 616c due to refractive index modulation in alignment mark 602c, thereby producing an asymmetry between negative first-order diffracted light 614c and positive first-order diffracted light 616c. A sensor apparatus (e.g., sensor apparatus 200) can detect this asymmetry and therefore the position of X = p / 2 of alignment mark 602c for this position 610.

[0089] FIG. 7 illustrates plot 700 (e.g., Fourier transform) showing spatial frequencies of a sensor apparatus, according to some aspects. FIG. 7 shows plot 700 with an amplitude 702 on a Y-axis and spatial frequency 704 on an X-axis. In some aspects, a diffraction limit of visible light 706 can separate spatial frequencies that are visible (e.g., a region left of diffraction limit of visible light 706) and non- visible (e.g., a region right of diffraction limit of visible light 706) to optical detection. An alignment mark frequency 708 (e.g., alignment mark 206) can be located in the non-visible region right of diffraction limit of visible light 706. A sub-wavelength alignment mark (e.g., alignment mark 206) can be optically excited by a transient optical pattern (e.g., transient optical pattern 208) to produce an interference within the optically detectable visible region left of diffraction limit of visible light 706. For example, a transient optical pattern frequency 710 can be located in the visible region left of diffraction limit of visible light 706. In some aspects, a first pitch of the transient optical pattern (e.g., transient optical pattern 208) is greater than a second pitch of the sub-wavelength alignment mark (e.g., alignment mark 206).

[0090] In some aspects, a combination (e.g., a multiplication) of a sub-wavelength alignment mark (e.g., alignment mark 206) and a transient optical pattern (e.g., transient optical pattern 208) can generate new spatial frequencies due to higher order non-linear effects. In some aspects, one or more of the new spatial frequencies can be detected by visible light. In some aspects, an interaction between transient optical pattern frequency 710 and alignment mark frequency 708 can generate additional spatial frequencies such as a first-order difference spatial frequency 714 and a first-order sum spatialfrequency 716. First-order difference spatial frequency 714 and first-order sum spatial frequency 716 can be located in the non-visible region right of diffraction limit of visible light 706. In some aspects, transient optical pattern frequency 710 can produce a harmonic spatial frequency 712. Harmonic spatial frequency 712 can be located in the non-visible region right of diffraction limit of visible light 706. In some aspects, an interaction between harmonic spatial frequency 712 and alignment mark frequency 708 can generate additional spatial frequencies such as a second-order difference spatial frequency 718 and a second-order sum spatial frequency 720. Second-order difference spatial frequency 718 can be located in the visible region left of diffraction limit of visible light 706. Second-order sum spatial frequency 720 can be located in the non-visible region right of diffraction limit of visible light 706.

[0091] In some aspects, diffracted light can be a spatial periodic pattern of an effective alignment mark (e.g., effective alignment mark 210) formed due to a combination (e.g., a multiplication) of the transient optical pattern (e.g., transient optical pattern 208) and the alignment mark (e.g., alignment mark 206). The spatial periodic pattern can include one or more spatial harmonics of the transient optical pattern (e.g., transient optical pattern 208). In some aspects, a processor can measure a diffraction signal from a spatial periodic pattern. As a result, diffraction signals from new spatial frequencies, for example, harmonic spatial frequency 712 and second-order difference spatial frequency 718, can indicate a point in the spatial periodic pattern and therefore position and / or asymmetry of the alignment mark (e.g., alignment mark 206).

[0092] In some aspects, a relative periodicity between a period of the transient optical pattern and a period of the alignment mark increases resolution as the relative periodicity decreases. An increase in resolution can allow for a reduction in a minimum pitch of the sub-wavelength alignment mark (e.g., alignment mark 206). In some aspects, in linear pump and probe processes involving a one-photon transition, a resolution improvement of ^2 can be expected compared to the resolution achieved by linear optical microscopy at the same wavelengths. For example, a measurement based on harmonic spatial frequency 712 can allow for a reduction in a minimum pitch of the sub-wavelength alignment mark (e.g., alignment mark 206) by at least a factor of 2. In some aspects, when nth-order non-linearity is used for imaging, the resolution can improve by ^n. For example, imaging with second-order nonlinear effects can improve resolution by A / 2. A measurement based on second-order difference spatial frequency 718 can allow for a reduction in a minimum pitch of the sub-wavelength alignment mark (e.g., alignment mark 206) by at least a factor of 2, thereby resulting in a total resolution improvement of at least a factor of 4 in a pump-probe scheme that uses imaging with second-order non-linear effects.

[0093] FIG. 8 illustrates a sensor apparatus 200', according to some aspects. The above discussion of sensor apparatus 200 shown in FIGS. 2 and 3 applies to sensor apparatus 200' shown in FIG. 8. The aspects of sensor apparatus 200 shown in FIGS. 2, 3, and 5, for example, and the aspects of sensor apparatus 200' shown in FIG. 8 may be similar. Similar reference numbers are used to indicate features of the aspects of sensor apparatus 200 shown in FIGS. 2, 3, and 5 and the similar features of the aspects of sensor apparatus 200' shown in FIG. 8. As shown in FIG. 8, sensor apparatus 200' can detect spatiallydiffracted light 220a, 220b from a spatial periodic pattern of effective alignment mark 210 (e.g., different diffraction angle), rather than detecting diffracted light 218a, 218b (e.g., first-order diffraction at angle corresponding to pitch of transient optical pattern 208) from effective alignment mark 210 of sensor apparatus 200 shown in FIGS. 2, 3, and 5. Sensor apparatus 200' can be an alternative aspect of sensor apparatus 200, in which sensor apparatus 200' can include higher-order collection optics 215a, 215b (e.g., corresponding to diffraction angles of spatial periodic pattern).

[0094] In some aspects, a light source can be configured to direct a probe beam 216 at effective alignment mark 210 to produce spatially diffracted light 220a, 220b (as discussed above in regard to FIG. 7). In some aspects, first light source 201 or second light source 212 can direct probe beam 216. In the exemplary aspect shown in FIG. 8, second light source 212 can direct probe beam 216. In some aspects, a detector 213 can be configured to receive the spatially diffracted light 220a, 220b by way of higher order collection optics 215a, 215b, instead of collection optics 214a, 214b, so that sensor apparatus 200' can measure a position and / or asymmetry of alignment mark 206 based on an asymmetry of the spatially diffracted light 220a, 220b from a spatial periodic pattern of effective alignment mark 210.

[0095] In some aspects, spatially diffracted light 220a, 220b can be a spatial periodic pattern of effective alignment mark 210. In some aspects, the spatial periodic pattern can include nth harmonic spatial frequencies of a frequency of transient optical pattern 208, where n is an integer greater than 1. For example, a component of spatially diffracted light 220a, 220b can be a second harmonic spatial frequency of transient optical pattern 208. In some aspects, an interaction between nth harmonic spatial frequencies of a frequency of transient optical pattern 208 (e.g., harmonic spatial frequency 712) and a frequency of alignment mark 206 (e.g., alignment mark frequency 708) can generate additional spatial frequencies such as a sum spatial frequency (e.g., second-order sum spatial frequency 720) and a difference spatial frequency (e.g., second-order difference spatial frequency 718). In some aspects, the additional spatial frequencies can be either visible or non-visible. For example, a difference spatial frequency (e.g., second-order difference spatial frequency 718) can be in the visible spectrum.

[0096] In some aspects, a relative periodicity between a period of transient optical pattern 208 and a period of alignment mark 206 increases resolution as the relative periodicity decreases. An increase in resolution can allow for a reduction in a minimum pitch of alignment mark 206. In some aspects, in linear pump and probe processes involving a one-photon transition, a resolution improvement of ^2 can be expected compared to the resolution achieved by linear optical microscopy at the same wavelengths. For example, a measurement based on the second harmonic spatial frequency of the frequency of transient optical pattern 208 (e.g., harmonic spatial frequency 712) can allow for a reduction in a minimum pitch of alignment mark 206 by at least a factor of 2.

[0097] In some aspects, when nth-order non-linearity is used for imaging, the resolution can improve by ^n. For example, imaging with second-order non-linear effects can improve resolution by A / 2. A measurement based on a difference spatial frequency (e.g., second-order difference spatial frequency718) can allow for a reduction in a minimum pitch of alignment mark 206 by at least a factor of 2, thereby resulting in a total resolution improvement of at least a factor of 4 in a pump-probe scheme that uses imaging with second-order non-linear effects.

[0098] FIG. 9 is a schematic illustration of a sensor apparatus 200" connected to a lithographic apparatus LA, according to some aspects. In some aspects, a sensor apparatus 200" can be external to lithographic apparatus LA and coupled to lithographic apparatus LA. In some aspects, sensor apparatus 200" can be sensor apparatus 200 or 200'. In some aspects, sensor apparatus 200" can serve as a reference and / or calibration tool for alignment processes conducted by lithographic apparatus LA. For example, a slow but accurate measurement can be performed with sensor apparatus 200" using the disclosed non-linear techniques and fast alignment can then be performed by lithographic apparatus LA. Non-linear optical sensor data from sensor apparatus 200" can be used to calibrate and provide reference for lithographic apparatus LA because non-linear techniques used by sensor apparatus 200" can be sensitive to mark asymmetry and smaller imperfections of alignment marks.

[0099] FIG. 10 illustrates a material change in an alignment mark occurring within sensor apparatus 200, according to some aspects. In some aspects, the material change in the alignment mark can be induced by a transient optical pattern. In some aspects, a material of the alignment mark can have a linear refractive index n0. In some aspects, the alignment mark can be alignment mark 206 (as discussed above) or an asymmetric alignment mark 207. In some aspects, asymmetric alignment mark 207 can be a “rooftop” shape having a variable steepness of a surface slant. In the exemplary aspect in FIG. 10, asymmetric alignment mark 207 with a “rooftop” shape can have a total height of 120 nm and a slant height of 10 nm.

[0100] In the exemplary aspect in FIG. 10, the material of asymmetric alignment mark 207 can change its refractive index when illuminated with a transient optical pattern 208 from a light source (e.g., first light source 201). Upon absorbing the transient optical pattern 208, the change in refractive index can be proportional to the electric field (e.g. Pockels effect), to the square of the electric field (e.g. Kerr effect, thermo-optic effect), or higher orders (e.g., nth-order non-linear effects). For example, the Kerr effect changes the refractive index of the material of asymmetric alignment mark 207 proportional to the intensity of an incident laser pulse from the light source, such that an intensity dependent refractive index n = n0+ n2Ipump, where n0is a linear refractive index of the material of asymmetric alignment mark 207, n2is a second-order nonlinear refractive index, and Ipumpis an intensity of the laser pulse from the light source.

[0101] In some aspects, a processor can detect position and / or asymmetry information about asymmetric alignment mark 207 based on a location of the material change (e.g., refractive index change). As discussed above, pitch p can be a distance between peaks of an alignment mark such as asymmetric alignment mark 207. At position X = -p / 2, transient optical pattern 208 can occupy the space between asymmetric alignment marks 207, thereby causing no change in refractive index ofasymmetric alignment mark 207. At position X = -p / A. transient optical pattern 208 can illuminate a portion of asymmetric alignment mark 207, thereby inducing an intensity dependent refractive index n only in the illuminated portion of asymmetric alignment mark 207 and forming an effective alignment mark 210 in that portion of asymmetric alignment mark 207. At position X = 0, transient optical pattern 208 can illuminate an entire asymmetric alignment mark 207, thereby inducing an intensity dependent refractive index n in the entire portion of asymmetric alignment mark 207 and forming an effective alignment mark 210 in the entire portion of asymmetric alignment mark 207. At position X = pl A, transient optical pattern 208 can illuminate a portion of asymmetric alignment mark 207, thereby inducing an intensity dependent refractive index n only in the illuminated portion of asymmetric alignment mark 207 and forming an effective alignment mark 210 in that portion of asymmetric alignment mark 207. At position X = p / 2, transient optical pattern 208 can occupy the space between asymmetric alignment marks 207, thereby causing no change in refractive index of asymmetric alignment mark 207.

[0102] FIGS. 11A-13B illustrate schematic graphs that indicate how sub-diffraction imaging can enable detection of alignment mark asymmetry and can help distinguish asymmetry-induced offsets from real alignment mark position offsets. FIGS. 11A-13B use shallow grating approximation for calculating signal strength of diffracted light. Shallow grating approximation means that a reflected wavefront from an alignment mark is approximated by a profile of a grating scaled with an optical path difference. Shallow grating approximation can model a diffraction efficiency by using two phase gratings with refractive index n0and n and profilesA reflection coefficient is defined by R(x) = RQel2AnokopnoM+l2AnkoPnMwhereAn0= n0— 1 and An = An0+ n2I are refractive index differences of nominal and illuminated regions with respect to the grating space. Diffraction orders can be calculated by Rm= f^2R(x)e~lkmXdx where km= m- This integral can be evaluated by using +1 (for the case 0 < xTG< and similarly forel22*nkoPnother cases.

[0103] FIGS. 11A and 11B illustrate zeroth-order diffraction efficiency 1100, according to some aspects. Zeroth-order diffraction efficiency 1100 is plotted on a graph, showing a diffraction intensity1102 on the Y-axis as a function of a transient optical pattern position 1104 on the X-axis. Units of transient optical pattern position 1104 can be depicted in microns. A constant diffraction intensity 1106 can illustrate the absence of the Kerr effect on a refractive index of an alignment grating. A diffraction intensity curve 1108 can illustrate how diffraction intensity 1102 varies with transient optical pattern position 1104 under conditions where the Kerr effect changes a refractive index of the alignment grating.

[0104] FIG. 11 A illustrates a zeroth-order diffraction efficiency 1100a of diffracted light from a binary grating (e.g., alignment mark 206), according to some aspects. In some aspects, the binary grating (e.g., alignment mark 206) can have a height of 120 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633 nm. With this configuration, the binary grating, as a symmetric grating shape, can form a symmetric signal along diffraction intensity curve 1108a with respect to an aligned transient optical pattern position 1104 of 0. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted zeroth-order diffraction efficiency 1100a.

[0105] FIG. 11B illustrates a zeroth-order diffraction efficiency 1100b of diffracted light from a rooftop grating (e.g., asymmetric alignment mark 207), according to some aspects. In some aspects, the rooftop grating (e.g., asymmetric alignment mark 207) can have a total height of 120 nm and a slant height of 10 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633 nm. With this configuration, the rooftop grating, as an asymmetric grating shape, can form asymmetric signals along diffraction intensity curve 1108b with respect to an aligned transient optical pattern position 1104 of 0. As seen in FIG. 1 IB, a kink appears at this aligned position. As a result, the zeroth- order diffraction efficiency 1100b can become position-dependent with an asymmetric grating. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted zeroth-order diffraction efficiency 1100b.

[0106] FIGS. 12A and 12B illustrate first-order diffraction efficiency 1200, according to some aspects. First-order diffraction efficiency 1200 is plotted on a graph, showing a diffraction intensity 1202 on the Y-axis as a function of a transient optical pattern position 1204 on the X-axis. Units of transient optical pattern position 1204 can be depicted in microns. A constant diffraction intensity 1206 can illustrate the absence of the Kerr effect on a refractive index of an alignment grating. A positive first-order diffraction intensity curve 1208 and a negative first-order diffraction intensity curve 1210 can illustrate how diffraction intensity 1202 varies with transient optical pattern position 1204 under conditions where the Kerr effect changes a refractive index of the alignment grating.

[0107] FIG. 12A illustrates a first-order diffraction efficiency 1200a of diffracted light from a binary grating (e.g., alignment mark 206), according to some aspects. In some aspects, the binary grating (e.g., alignment mark 206) can have a height of 120 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633 nm. With this configuration, the binary grating, as a symmetric grating shape, can form anti-symmetric signals between positive first-order diffraction intensity curve 1208aand negative first-order diffraction intensity curve 1210a with respect to an aligned transient optical pattern position 1204 of 0. As seen in FIG. 12A, positive first-order diffraction intensity curve 1208a and negative first-order diffraction intensity curve 1210a intersect at this aligned position. As a result, the first-order diffraction efficiency 1200a can become position-dependent with a symmetric grating. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted first-order diffraction efficiency 1200a.

[0108] FIG. 12B illustrates a first-order diffraction efficiency 1200b of diffracted light from a rooftop grating (e.g., asymmetric alignment mark 207), according to some aspects. In some aspects, the rooftop grating (e.g., asymmetric alignment mark 207) can have a total height of 120 nm and a slant height of 10 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633 nm. With this configuration, the rooftop grating, as an asymmetric grating shape, can form asymmetric signals between positive first-order diffraction intensity curve 1208b and negative first-order diffraction intensity curve 1210b with respect to an aligned transient optical pattern position 1204 of 0. As seen in FIG. 12B, a kink appears at this aligned position. As a result, the first-order diffraction efficiency 1200b can become position-dependent with an asymmetric grating. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted first-order diffraction efficiency 1200b.

[0109] FIGS. 13A and 13B illustrate second-order diffraction efficiency 1300, according to some aspects. Second-order diffraction efficiency 1300 is plotted on a graph, showing a diffraction intensity 1302 on the Y-axis as a function of a transient optical pattern position 1304 on the X-axis. Units of transient optical pattern position 1304 can be depicted in microns. A constant diffraction intensity 1306 can illustrate the absence of the Kerr effect on a refractive index of an alignment grating. A positive second-order diffraction intensity curve 1308 and a negative second-order diffraction intensity curve 1310 can illustrate how diffraction intensity 1302 varies with transient optical pattern position 1304 under conditions where the Kerr effect changes a refractive index of the alignment grating.

[0110] FIG. 13A illustrates a second-order diffraction efficiency 1300a of diffracted light from a binary grating (e.g., alignment mark 206), according to some aspects. In some aspects, the binary grating (e.g., alignment mark 206) can have a height of 120 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633 nm. With this configuration, the binary grating, as a symmetric grating shape, can form a symmetric signal between positive second-order diffraction intensity curve 1308a and a negative second-order diffraction intensity curve 1310a with respect to an aligned transient optical pattern position 1304 of 0. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted second-order diffraction efficiency 1300a.

[0111] FIG. 13B illustrates a second-order diffraction efficiency 1300b of diffracted light from a rooftop grating (e.g., asymmetric alignment mark 207), according to some aspects. In some aspects, the rooftop grating (e.g., asymmetric alignment mark 207) can have a total height of 120 nm and a slant height of 10 nm. In some aspects, a probe beam (e.g. probe beam 216) can have a wavelength of 633nm. With this configuration, the rooftop grating, as an asymmetric grating shape, can form asymmetric signals between positive second-order diffraction intensity curve 1308b and a negative second-order diffraction intensity curve 1310b with respect to an aligned transient optical pattern position 1304 of 0. As seen in FIG. 13B, a kink appears at this aligned position. As a result, the second-order diffraction efficiency 1300b can become position-dependent with an asymmetric grating. A processor can therefore determine the asymmetry of an alignment mark if the alignment mark deviates from the plotted second- order diffraction efficiency 1300b.

[0112] FIG. 14 illustrates a sensor apparatus 200"', according to some aspects. The above discussion of sensor apparatus 200 shown in FIGS. 2, 3, and 5 and sensor apparatus 200' in FIG. 8 applies to sensor apparatus 200'" in FIG. 14. The aspects of sensor apparatus 200 shown in FIGS. 2, 3, and 5, for example, and the aspects of sensor apparatus 200' shown in FIG. 8 may be similar to the aspects of sensor apparatus 200'" shown in FIG. 14. Similar reference numbers are used to indicate features of the aspects of sensor apparatus 200 shown in FIGS. 2, 3, and 5 and of the aspects of sensor apparatus 200' shown in FIG. 8 that are similar to features of the aspects of sensor apparatus 200'" shown in FIG. 14. Sensor apparatus 200'" can be an alternative aspect of sensor apparatus 200 and / or 200', in which sensor apparatus 200'" can include an interferometric device (e.g., interferometric device 222) that can receive diffracted light and interfere the diffracted light with itself to produce an alignment signal.

[0113] In some aspects, first light source 201 (shown in FIGS. 2, 3, 5, and 8) can be configured to use two or more light guides 202a, 202b (shown in FIGS. 2, 3, 5, and 8) configured to direct a plurality of skew light beams toward alignment mark 206 (e.g., skew light beams 204a, 204b passing through lens 205 toward alignment mark 206, pump light beams 203a, 203b directed at skew angles toward alignment mark 206 without passing through lens 205, etc.). In some aspects, second light source 212 directs probe beam 216 at optic 217 (e.g., mirror, lens, prism, waveguide, optical modulator, etc.) to redirect probe beam 216 toward alignment mark 206. In some aspects, probe beam 216 can interact with effective alignment mark 210 to produce diffracted light 221a, 221b. In some aspects, diffracted light 221a, 221b can be diffracted light 218a, 218b shown in FIGS. 3 and 5 or spatially diffracted light 220a, 220b shown in FIG. 8.

[0114] In some aspects, interferometric device 222 can be configured to receive diffracted light 221a, 221b. In some aspects, interferometric device 222 can output modified light beams of the received diffracted light 221a, 221b with a relative rotation and overlap, thereby interfering beams of diffracted light 221a, 221b to form transformed diffracted light 224a, 224b. In some aspects, interferometric device 222 can direct transformed diffracted light 224a, 224b toward optic 223 (e.g., mirror, lens, prism, waveguide, optical modulator, etc.) to redirect transformed diffracted light 224a, 224b toward lens 226. In some aspects, lens 226 can be disposed at a distance of focal length / from detector 213 (e.g., the image plane). In some aspects, lens 226 can direct transformed diffracted light 224a, 224b toward detector 213.

[0115] The embodiments may further be described using the following clauses:1. A sensor apparatus comprising: a transient optical pattern configured to induce a material change in an alignment mark thereby forming an effective alignment mark; a probe beam configured to interact with the effective alignment mark; and a detector configured to measure diffracted light or reflected light from the effective alignment mark generated by the probe beam.2. The sensor apparatus of clause 1 , wherein the material change comprises a refractive index change of the alignment mark.3. The sensor apparatus of clause 1, wherein the material change is proportional to an intensity of the transient optical pattern.4. The sensor apparatus of clause 1 , wherein the transient optical pattern comprises an interference pattern.5. The sensor apparatus of clause 1, wherein the transient optical pattern originates from a plurality of skew beams.6. The sensor apparatus of clause 1 , wherein the transient optical pattern comprises an arbitrary image pattern, a grating pattern, a checkerboard pattern, a finite pattern, or a combination thereof.7. The sensor apparatus of clause 1, wherein the probe beam is configured to interact with the effective alignment mark within a time frame of the material change.8. The sensor apparatus of clause 1, wherein the diffracted light comprises first-order diffraction beams (Li, I+i) from the effective alignment mark.9. The sensor apparatus of clause 1, wherein the diffracted light diffracts from a spatial periodic pattern of the effective alignment mark formed due to a combination of the transient optical pattern and the alignment mark.10. The sensor apparatus of clause 9, wherein the spatial periodic pattern comprises one or more spatial harmonics of the transient optical pattern.11. The sensor apparatus of clause 10, wherein a relative periodicity between a period of the transient optical pattern and a period of the alignment mark increases a resolution of the sensor apparatus as the relative periodicity decreases.12. The sensor apparatus of clause 11, wherein the relative periodicity increases the resolution of the sensor apparatus by at least a factor of 4.13. The sensor apparatus of clause 1, further comprising a processor coupled to the detector and configured to determine a position of the alignment mark based on an asymmetry of the diffracted light.14. The sensor apparatus of clause 1, wherein: the alignment mark is adjustable relative to the transient optical pattern and the probe beam,the transient optical pattern is adjustable relative to the alignment mark and the probe beam, or the probe beam is adjustable relative to the alignment mark and the transient optical pattern.15. The sensor apparatus of clause 1, further comprising an interferometric device configured to receive the diffracted light and interfere the diffracted light with itself to produce an alignment signal.16. The sensor apparatus of clause 1, further comprising a processor coupled to the detector and configured to determine an asymmetry of the alignment mark.17. A method comprising: forming a transient optical pattern on an alignment mark thereby inducing a material change in the alignment mark and forming an effective alignment mark; interacting a probe beam with the effective alignment mark; and measuring diffracted light from the effective alignment mark generated by the probe beam.18. The method of clause 17, further comprising determining a position of the alignment mark based on an asymmetry of the diffracted light.19. The method of clause 17, further comprising determining an asymmetry of the alignment mark based on an asymmetry of the diffracted light.20. The method of clause 17, further comprising scanning: the alignment mark relative to the transient optical pattern and the probe beam, the transient optical relative to the alignment mark and the probe beam, or the probe beam relative to the alignment mark and the transient optical pattern.

[0116] Although specific reference can be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, LCDs, thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “wafer” or “die” herein may be considered as synonymous with the more general terms “substrate” or “target portion”, respectively. The substrate referred to herein may be processed, before or after exposure, in for example a track unit (a tool that typically applies a layer of resist to a substrate and develops the exposed resist), a metrology unit and / or an inspection unit. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. Further, the substrate may be processed more than once, for example in order to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0117] Although specific reference may have been made above to the use of aspects in the context of optical lithography, it will be appreciated that aspects may be used in other applications, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography, a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substratewhereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

[0118] It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by those skilled in relevant art(s) in light of the teachings herein.

[0119] The term “substrate” as used herein describes a material onto which material layers are added. In some aspects, the substrate itself may be patterned and materials added on top of it may also be patterned, or may remain without patterning.

[0120] The following examples are illustrative, but not limiting, of the aspects of this disclosure. Other suitable modifications and adaptations of the variety of conditions and parameters normally encountered in the field, and which would be apparent to those skilled in the relevant art(s), are within the spirit and scope of the disclosure.

[0121] Although specific reference may be made in this text to the use of the apparatus and / or system in the manufacture of ICs, it should be explicitly understood that such an apparatus and / or system has many other possible applications. For example, it can be employed in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, LCD panels, thin-film magnetic heads, etc. The skilled artisan will appreciate that, in the context of such alternative applications, any use of the terms “reticle,” “wafer,” or “die” in this text should be considered as being replaced by the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0122] While specific aspects have been described above, it will be appreciated that the aspects may be practiced otherwise than as described. The description is not intended to limit the scope of the claims.

[0123] It is to be appreciated that the Detailed Description section, and not the Summary and Abstract sections, is intended to be used to interpret the claims. The Summary and Abstract sections may set forth one or more but not all exemplary aspects as contemplated by the inventor(s), and thus, are not intended to limit the aspects and the appended claims in any way.

[0124] The aspects have been described above with the aid of functional building blocks illustrating the implementation of specified functions and relationships thereof. The boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed.

[0125] The foregoing description of the specific aspects will so fully reveal the general nature of the aspects that others can, by applying knowledge within the skill of the art, readily modify and / or adapt for various applications such specific aspects, without undue experimentation, without departing from the general concept of the aspects. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed aspects, based on the teaching and guidance presented herein.

[0126] The breadth and scope of the aspects should not be limited by any of the above-described exemplary aspects, but should be defined only in accordance with the following claims and their equivalents.

Claims

CLAIMS1. A sensor apparatus comprising: a transient optical pattern configured to induce a material change in an alignment mark thereby forming an effective alignment mark; a probe beam configured to interact with the effective alignment mark; and a detector configured to measure diffracted light or reflected light from the effective alignment mark generated by the probe beam.

2. The sensor apparatus of claim 1 , wherein the material change comprises a refractive index change of the alignment mark.

3. The sensor apparatus of claim 1, wherein the material change is proportional to an intensity of the transient optical pattern.

4. The sensor apparatus of claim 1 , wherein the transient optical pattern comprises an interference pattern.

5. The sensor apparatus of claim 1, wherein the transient optical pattern originates from a plurality of skew beams.

6. The sensor apparatus of claim 1 , wherein the transient optical pattern comprises an arbitrary image pattern, a grating pattern, a checkerboard pattern, a finite pattern, or a combination thereof.

7. The sensor apparatus of claim 1, wherein the probe beam is configured to interact with the effective alignment mark within a time frame of the material change.

8. The sensor apparatus of claim 1, wherein the diffracted light comprises first-order diffraction beams (Li, I+i) from the effective alignment mark.

9. The sensor apparatus of claim 1, wherein the diffracted light diffracts from a spatial periodic pattern of the effective alignment mark formed due to a combination of the transient optical pattern and the alignment mark.

10. The sensor apparatus of claim 9, wherein the spatial periodic pattern comprises one or more spatial harmonics of the transient optical pattern.

11. The sensor apparatus of claim 10, wherein a relative periodicity between a period of the transient optical pattern and a period of the alignment mark increases a resolution of the sensor apparatus as the relative periodicity decreases.

12. The sensor apparatus of claim 11, wherein the relative periodicity increases the resolution of the sensor apparatus by at least a factor of 4.

13. The sensor apparatus of claim 1, further comprising a processor coupled to the detector and configured to determine a position of the alignment mark based on an asymmetry of the diffracted light.

14. The sensor apparatus of claim 1, wherein: the alignment mark is adjustable relative to the transient optical pattern and the probe beam, the transient optical pattern is adjustable relative to the alignment mark and the probe beam, or the probe beam is adjustable relative to the alignment mark and the transient optical pattern.

15. The sensor apparatus of claim 1, further comprising an interferometric device configured to receive the diffracted light and interfere the diffracted light with itself to produce an alignment signal.

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