SYSTEMS AND METHODS FOR INSPECTING PHOTOMASKS

A method for inspecting a photomask includes scanning the photomask with an interferometric fringe pattern generated by an interferometer, generating an interferogram associated with the photomask in response to scanning the photomask using the interferometer, and detecting one or more geometric parameters of the photomask using the generated interferogram.

Not applicable.

BACKGROUND

Photomasks are opaque patterned substrates utilized, among other things, in the production of integrated circuits via a photolithography process. A photomask may be used to project a pattern defined by the photomask onto a substrate such as a silicon wafer and the like. The initial pattern may be computer generated and formed onto an initially blank photomask (referred to as a “mask blank”) using a lithography process in which a replication of the computer-generated pattern is developed onto a resist-coated surface of the mask blank to form the photomask. Particularly, the resist image formed on the photomask acts as a mask and the pattern is transferred onto the photomask once the resist layer has been removed. Several photomasks may be used together as a mask set for producing multiple patterned layers onto the substrate.

BRIEF SUMMARY OF THE DISCLOSURE

An embodiment of a method for inspecting a photomask comprises (a) scanning the photomask with an interferometric fringe pattern generated by an interferometer, (b) generating an interferogram associated with the photomask in response to scanning the photomask using the interferometer, and (c) detecting one or more geometric parameters of the photomask using the generated interferogram. In some embodiments, (c) comprises (c1) comparing the generated interferogram with a reference interferogram. In some embodiments, the generated interferogram is associated with a fabricated pattern of the photomask, and the reference interferogram is associated with an intended pattern of the photomask. In certain embodiments, (c1) comprises performing a cross-correlation analysis between the generated interferogram and the reference interferogram. In certain embodiments, (a) comprises (a1) shaping a collimated beam using an objective lens of the interferometer to focus an incident beam on a focal point. In some embodiments, (b) comprises (b1) superpositioning a reference incident spherical wave and an edge-diffracted wave. In some embodiments, the one or more geometric parameters comprise at least one of a pattern width, an opening area width, a line-edge quality, and an opening area surface quality of the photomask. In certain embodiments, (c) comprises (c1) performing at least one of fringe analysis method and a wavelet-based feature extraction method on the interferogram.

An embodiment of a system for inspecting a photomask comprises an interferometer comprising a laser configured to generate a beam and a photodetector configured to detect the beam generated by the laser, the interferometer configured to generate an interferometric fringe pattern and to scan the photomask with the interferometric fringe pattern, and a computer system in signal communication with the interferometer, the computer system configured to generate an interferogram associated with the photomask based on data provided by the photodetector, and to detect one or more geometric parameters of the photomask using the generated interferogram. In some embodiments, the interferometer comprises an objective lens positioned between the laser and the photodetector along a beam axis of the interferometer. In some embodiments, the system comprises a motion stage coupled to the interferometer, the motion stage comprising an actuator configured to transport the photomask along a motion axis extending orthogonal to a beam axis of the interferometer. In certain embodiments, the motion axis comprises a first motion axis and the actuator is configured to transport the photomask along a second motion axis extending orthogonal to the first motion axis. In some embodiments, the computer system is configured to compare the generated interferogram with a reference interferogram. In some embodiments, the generated interferogram is associated with a fabricated pattern of the photomask, and the reference interferogram is associated with an intended pattern of the photomask. In certain embodiments, the one or more geometric parameters comprise at least one of a pattern width, an opening area width, a line-edge quality, and an opening area surface quality of the photomask.

An embodiment of a computer system for inspecting a photomask comprises a processor, and a storage device coupled to the processor and containing instructions that when executed cause the processor to scan the photomask with an interferometric fringe pattern generated by an interferometer, generate an interferogram associated with the photomask in response to scanning the photomask using the interferometer, and detect one or more geometric parameters of the photomask using the generated interferogram. In some embodiments, the instructions when executed cause the processor to compare the generated interferogram with a reference interferogram. In some embodiments, the generated interferogram is associated with a fabricated pattern of the photomask, and the reference interferogram is associated with an intended pattern of the photomask. In certain embodiments, the instructions when executed cause the processor to perform a cross-correlation analysis between the generated interferogram and a reference interferogram. In some embodiments, the one or more geometric parameters comprise at least one of a pattern width, an opening area width, a line-edge quality, and an opening area surface quality of the photomask.

DETAILED DESCRIPTION

As described above, photomasks are opaque patterned substrates utilized in the production of semiconductor devices via a photolithography process. Additionally, certain geometric parameters of the photomask such as, for example, line edge roughness (LER), and others may be critical for the performance of the photomask in accurately and precisely producing semiconductor devices. Conventionally, completed photomasks are typically inspected using scanning electron microscopy (SEM) and other conventional advanced measurement systems. Defects in the photomask may include damaged or unwanted patterns such as the formed pattern being smaller or larger than the intended pattern. Additionally, the formed pattern may have a LER that reduces printability of the pattern due to excessive light scattering at the edges of the pattern.

Mitigating the issues identified above (e.g., damaged patterns, LER) through a robust photomask inspection metrology is essential in ensuring adequate performance of the photomask in fabricating semiconductor or other devices. Moreover, new techniques such as extreme ultraviolet (EUV) lithography has enabled high volume fabrication of photomasks, heightening the need for fast and accurate photomask inspection techniques. However, conventional techniques such as SEM-based and other microscopy-based techniques are generally inconvenient, labor and time intensive, and too expensive for wide application beyond in-process inspection.

Accordingly, embodiments of systems and associated methods for inspecting photomasks are disclosed herein in which photomasks are inspected using utilizing knife-edge interferometry. Particularly, methods of inspecting photomasks are described herein which include scanning the photomask with an interferometric fringe pattern generated by an interferometer, generating an interferogram associated with the photomask in response to scanning the photomask using the interferometer, and detecting one or more geometric parameters of the photomask using the generated interferogram. Additionally, photomask inspections systems are described herein which include an interferometer comprising a laser configured to generate a beam and a photodetector configured to detect the beam generated by the laser, the interferometer configured to generate an interferometric fringe pattern and to scan the photomask with the interferometric fringe pattern, and a computer system in signal communication with the interferometer, the computer system configured to generate an interferogram associated with the photomask based on data provided by the photodetector, and to detect one or more geometric parameters of the photomask using the generated interferogram. The disclosed systems and methods permit for the rapid and convenient inspection photomasks requiring a minimal amount of time and labor compared with conventional techniques, allowing for inspection of the photomask to occur during fabrication by the manufacturer or afterwards by the end-user.

Referring now toFIGS.1-3, an embodiment of a photomask inspection system100is shown. As will be discussed further herein, photomask inspection system100utilizes knife edge interferometry (EKEI) to identify one or more geometric parameters of a pattern (generally identified by arrow11inFIGS.1and2) of a photomask10scanned by the photomask inspection system100. Geometric parameters of the photomask include a pattern width, an opening area width, a line-edge quality, and an opening area surface quality of the photomask. In some instances, the photomask inspection system100may identify abnormalities or defects in the pattern11such as voids, scratches, residual photoresist, or dust, and other geometric parameters of the pattern11such as the LER of the pattern11. In this example, the pattern11of photomask10includes a geometric feature12having a LER defined by a period13, a depth14, and an intensity15. Not intending to be bound by any particular theory, in this example, the LER of geometric feature12may be defined in accordance with Equation (1) below, where (P) represents the period of the LER (e.g., period13shown inFIG.2), (D) represents the depth of the LER (e.g., depth14shown inFIG.2), and (I) represents the intensity of the LER (e.g., intensity15shown inFIG.2):

It may be understood that the Equation (1) only represents an exemplary technique for defining the LER of a geometric feature of a photomask pattern, and that LER may be determined differently in other embodiments. Additionally, it may be understood that photomask10and its associated pattern11are only exemplary and nonlimiting. The types of photomasks and the configuration of their respective patterns (as well as the geometric parameters associated with the patterns identifiable by system100) may vary in other embodiments.

In this exemplary embodiment, photomask inspection system100generally includes a light source or laser102, a motorized stage110, an objective lens120, a photodetector130, and a controller or controller150. The configuration of laser102may vary substantially depending on the given application, and in this exemplary embodiment is configured to generate a laser beam having a wavelength between approximately 200 nanometers (nm) and 800 nm; however, the wavelength producible by laser102may of course vary in other embodiments. The beam produced by laser102passes through an annular aperture105spaced from the laser102along a beam axis103(extending in the “Z” direction inFIG.1, thereby forming a collimated beam107that extends from aperture105along the beam axis103. In this exemplary embodiment, aperture105is approximately 1.0 millimeters (mm) in diameter; however, it may be understood that the diameter of aperture105may vary in other embodiments. Indeed, in certain embodiments, photomask inspection system100may not include aperture105.

The photomask10is positionable on the motorized stage110where stage110comprises a motor or actuator112(indicated schematically inFIG.1) for transporting photomask10relative to the stage110and beam axis103along a motion axis115. In this exemplary embodiment, motion axis115extends orthogonally to the beam axis103, extending in the “X” direction inFIG.1. It may be understood that the operation of actuator112may be controlled by the controller150of photomask inspection system100. For example, controller150may cause the photomask10to travel along motion axis115at a predefined speed whereby the photomask10passes completely across the beam axis103of system100.

Additionally, in some embodiments, actuator112may also cause photomask10to travel along a secondary motion axis117(motion axis115comprising a primary motion axis115) oriented orthogonal to both the primary motion axis115and the beam axis103and extending in the “Y” direction inFIG.1. For example, after the photomask10makes a single pass moving along the primary motion axis115, actuator112may move the photomask10along the secondary motion axis117a fixed increment that is less than the length of the photomask10(the dimension of photomask10extending along the secondary motion axis117). After moving the increment along the secondary motion axis117, the actuator112may cause the photomask10to make a second pass across the entire width of the photomask10(the dimension of photomask10extending along primary motion axis115) along the primary motion axis115. This process may be repeated until the entire pattern11of photomask10has been scanned by the photomask inspection system100. In this manner, motion stage110is configured to adjust the relative position of photomask10with respect to beam axis103to allow for the complete scanning of pattern11of photomask10by photomask inspection system100.

The objective lens120is positioned, with laser102and aperture105, along the beam axis103in a position located between the aperture105and photodetector130. The laser102, objective lens120, and photodetector130may be collectively referred to as an interferometer140of the inspection system100. In some embodiments, computer system150may also comprise a component of the interferometer. In this exemplary embodiment, objective lens120has a numerical aperture (NA) of approximately between 0.2 and 0.8 (e.g., 0.4); however, it may be understood that the NA of objective lens120may vary in other embodiments. For example, the NA of objective lens120may be selected based on the size or geometry of the given photomask inspected by the photomask inspection system100. Objective lens120shapes the collimated beam107into a spherical waveform109that incidents against or contacts the photomask10as the photomask10is transported along the primary motion axis115by the actuator112of motion stage110.

The photodetector130of photomask inspection system100is positioned along beam axis103on the opposite side of photomask10from laser102, aperture105, and objective lens120. Photodetector130receives the laser light generated by laser102and diffracted against the photomask10. In some embodiments, photodetector130comprises a single photodiode or array type photodiode such as a charge-coupled device (CCD) or a complementary metal-oxide-semiconductor (CMOS). The laser light sensed or detected by photodetector130may be recorded by controller150(in signal communication with photodetector130) a received or output intensity over time.

In this exemplary embodiment, controller150comprises a computer or computing system including a processor152, memory or storage device154, one or more input/output (I/O) devices156, and a communications device158. The communication device158of controller150may be a wireless or wired communication device that may facilitate communication between the controller150and one or more other components of photomask inspection system100including, for example, laser102, actuator112of motion stage110, photodetector130, as well as other devices The processor152of controller150may execute instructions stored on the memory154thereof to control the operation of various components of photomask inspection system100.

The processor152of controller150may be any type of computer processor or microprocessor capable of executing computer-executable code. The processor152may also include multiple processors that may perform the operations described below. The memory154of controller150may be any suitable articles of manufacture that can serve as media to store processor-executable code, data, or the like. These articles of manufacture may represent computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor152to perform the presently disclosed processes. Generally, the processor152of controller150may execute software applications that include programs that automate the operation of photomask inspection system100.

The memory154of controller150may also be used to store the data, analysis of the data, the software applications, and the like. The memory154of controller150may represent non-transitory computer-readable media (e.g., any suitable form of memory or storage) that may store the processor-executable code used by the processor152of controller150to perform various techniques described herein. It should be noted that non-transitory merely indicates that the media is tangible and not a signal. Additionally, the I/O devices156of controller150may be interfaces that may couple to other peripheral components such as input devices (e.g., keyboard, mouse), sensors, displays, input/output (I/O) modules, and the like. I/O devices156of controller150may enable controller150to communicate with the other computing devices of the photomask inspection system100.

With the foregoing in mind, the present techniques described herein may also be performed using a controller150that employs multiple computer systems, a cloud-based computer system, or the like to distribute processes to be performed across multiple computer systems. In this case, each computer system operating as part of a supercomputer may not include each component listed as part of the controller150.

The spherical waveform109formed by objective lens120may form a Fresnel zone on an obstruction (e.g., photomask) that is positioned to at least partially intersect the spherical waveform109. Resulting from the superposition of the reference incident spherical waveform109and an edge-diffracted wave as the photomask10is scanned, the Fresnel zone defines an interferometric fringe pattern including one or more half-period zones depending on the Fresnel number (F) of the given Fresnel zone. In this exemplary embodiment, the Fresnel zone defines an interferometric fringe pattern121(shown specifically inFIG.3) having a central high intensity region122surrounded by alternating annular or ring-shaped low intensity regions123,125, and127and annular or ring-shaped high intensity regions124,126, and128, respectively. The high intensity regions122,124,126, and128of interferometric fringe pattern121correspond to the odd term of the Fresnel zone having a constructive contribution to the interference with the obstruction while low intensity regions123,125, and127correspond to the even term of the Fresnel zone having a destructive contribution to the interference with the obstruction.

It may be understood that the interferometric fringe pattern121formed by spherical waveform109may be modeled or simulated by the controller150of photomask inspection system100. Particularly, the interferometric fringe pattern121formed from the spherical waveform109intersecting an obstruction having an edge with varying degrees of LER, including zero roughness (LER=0), may be simulated by controller150. In some embodiments, controller150may simulate the interferometric fringe pattern121using a Fresnel number-based computation model. Not intending to be bound by any particular theory, the Fresnel number-based computation model may be based on Equation (2) as follows, where (F) represents the Fresnel number, (NA) represents the numerical aperture of the objective lens (e.g., the NA of objective lens120), (λ) represents the light wavelength (e.g., the wavelength of the light comprising waveform109), (Zsrc) represents the distance between the objective lens focal point and the photomask pattern along the beam axis (e.g., along beam axis103)

As an example, the distance between the objective lens focal point and the pattern11of photomask10is indicated by numeral131inFIG.2. Referring still toFIGS.3-5,FIG.4illustrates a interferogram160of output intensity161of a simulated interferometric fringe pattern121as a function of the position of an edge52of an obstruction50(e.g., a photomask), where an ideal sharp edge52has a LER equal to zero (perfectly smooth). Particularly, in this example, the obstruction50(shown inFIG.5) is slid across the simulated interferometric fringe pattern121to produce the output intensity161shown in interferogram160. Output intensity161includes a plurality of peaks and corresponding troughs associated with the sharp edge52of obstruction50passing across the different high intensity regions122,124,126, and128, and low intensity regions123,125, and127of the simulated interferometric fringe pattern121used to produce interferogram160. For example, a first trough162of output intensity161corresponds to a first position53of the obstruction50shown inFIG.5, while a peak163of output intensity161corresponds to a second position54of the obstruction50that is spaced from the first position53along the primary motion axis115. It may be noted that the trough162of output intensity161corresponds to the sharp edge52of obstruction50aligning with a radially outer edge of low intensity region123while peak163corresponds to the sharp edge52of obstruction50aligning with a radially outer edge of high intensity region122.

Continuing with this example, as the obstruction50gradually occludes high intensity region122as the obstruction50passes from the second position54to a third position55, the output intensity161gradually declines from the peak163towards zero, generating a final peak165as the sharp edge52of obstruction50enters into alignment with a radially inner edge of high intensity region128when obstruction50enters a fourth position56. Interferogram160illustrates the plurality of peaks and corresponding troughs in output intensity161which may be obtained from the interferometric fringe pattern121in response to the movement of an obstruction50having the ideal sharp edge52across the interferometric fringe pattern121. The plurality of peaks and corresponding valleys of the output intensity161shown in interferogram160may conveniently act as points of comparison with respect to the output intensity obtained when an obstruction (e.g., a patterned photomask) having one or more edges with some degree of roughness (e.g., LER>0) is transported across the interferometric fringe pattern121. To state in other words, the output intensity161shown in interferogram160may, in some embodiments, used as a baseline for comparison with other obtained output intensities produced from patterned photomasks in order to determine one or more geometric parameters of the patterned photomasks, with the peaks and valleys of output intensity providing convenient data points for the comparison.

Referring now toFIGS.6and7, another interferogram170is shown inFIG.6, and a graph180is shown inFIG.7. Particularly, interferogram170includes a first or ideal output intensity171produced by transporting a first obstruction having an ideal sharp edge across the interferometric fringe pattern121producible by photomask inspection system100. Additionally, interferogram170includes a second output intensity172produced by transporting a second obstruction across interferometric fringe pattern121having an edge with a non-zero first LER, and a third output intensity173produced by transporting a third obstruction across interferometric fringe pattern121having an edge with a non-zero second LER that is greater (rougher or less sharp) than the first LER. In this example, the first LER is equal to approximately 2.4 micrometers (μm) while the second LER is equal to approximately 5.9 μm.

It may be noted from interferogram170that output intensities172and173follow a similar pattern as first output intensity171in response to the edges of the different obstructions travelling across the different high intensity regions122,124,126, and128and low intensity regions123,125, and127of interferometric fringe pattern121. However, output intensities172and173demonstrate a greater degree of attenuation than first output intensity171, with second output intensity173having even greater attenuation than second output intensity172. To state in other words, first output intensity171has relatively more pronounced peaks and corresponding troughs compared with second output intensity172, while second output intensity172has relatively more pronounced peaks and corresponding troughs compared with third output intensity173. Given that the roughness of the edge of the obstruction used to produce the given output intensity171,172, and173is positively correlated with the relative attenuation of the given output intensity, the degree of roughness (as well as other geometric parameters) of the edge of a given obstruction may be estimated based on the difference between the output intensity produced from transporting the given obstruction across interferometric fringe pattern121with the output intensity produced by an obstruction having an ideal sharp edge.

As an example, graph180ofFIG.7plots the LER181of ten different sample obstructions transportable across interferometric fringe pattern121, where the tenth sample obstruction (identified as sample “10” along the X-axis of graph180) has an ideal sharp edge with an LER equal to zero. Additionally, graph180plots a plurality of similarity scores182relating the similarity from the output intensity obtained from transporting each sample obstruction across the interferometric fringe pattern121to the output intensity obtained from the ideal sharp sample (sample10in this example). In this example, similarity scores182are obtained by cross-correlating the output intensity obtained from the ideal sharp sample (the reference sample in this comparison) with the output intensities obtained from the other sample obstructions; however, it may be understood that in other embodiments other methodologies may be utilizes to compare the different output intensities. In this manner, the LER plot181and similarity score plot182can be used to estimate the LER of other sample obstructions (e.g., patterned photomasks having rough edges) to estimate their respective LER. It may be further understood that similar techniques (e.g., cross-correlation analysis) may be used to identify geometric parameters other than LER, such as the presence and magnitude of defects in a patterned photomask.

Referring again toFIGS.1-3, it may be understood that the controller150of photomask inspection system100may generate one or more interferograms in response to transporting one or more corresponding obstructions (e.g., photomask10) across the interferometric fringe pattern121generated by system100. Additionally, controller150may compare the output intensity produced by transporting a given obstruction across the interferometric fringe pattern121with a simulated output intensity (e.g., determined from a Fresnel number-based computation model) from an ideal sample or pattern. For example, controller150may simulate the output intensity produced from the ideal or intended pattern11of photomask10, and compare the simulated output intensity with the actual output intensity obtained from transporting the photomask10across the interferometric fringe pattern121. In some embodiments, controller150may perform a cross-correlation analysis of the different output intensities or interferograms produced by system100to determine or detect one or more geometric parameters of the pattern11of photomask10such as the LER of one or more edges of the pattern11. However, in other embodiments, controller150may employ other comparison techniques for determining the one or more geometric parameters of the pattern11of photomask10.

Referring now toFIG.8, an embodiment of a method200for inspecting photomasks is shown. In this exemplary embodiment, method200begins at block202by scanning the photomask with an interferometric fringe pattern generated by an interferometer. In some embodiments, block202includes shaping a collimated beam using an objective lens of the interferometer to focus an incident beam on a focal point. In certain embodiments, block202comprises scanning the photomask10(shown inFIGS.1and2) with the interferometric fringe pattern121(shown inFIG.3) generated by the interferometer140(shown inFIGS.1and2) of the photomask inspection system100(shown inFIG.1).

At block204, method200includes generating an interferogram associated with the photomask in response to scanning the photomask using the interferometer. In this context, “in response to” does not necessarily mean automatically following the scanning of the photomask using the interferometer. In some embodiments, block204includes superpositioning a reference incident spherical wave (e.g. spherical waveform109and an edge-diffracted wave as the photomask is scanned whereby interference between the spherical wave and the edge-diffracted wave produces an interferometric fringe pattern. In certain embodiments, block204comprises generating an interferogram associated with the photomask10(shown inFIGS.1and2) in response to scanning the photomask using the interferometer (shown inFIGS.1and2).

At block206, method200includes detecting one or more geometric parameters of the photomask using the generated interferogram. In some embodiments, block206includes comparing the generated interferogram with a reference interferogram. In some embodiments, the generated interferogram is associated with a fabricated pattern of the photomask, and the reference interferogram is associated with an intended pattern of the photomask. In some embodiments, block206includes performing at least one of a fringe analysis method and a wavelet-based feature extraction method on the interferogram. In certain embodiments, block206includes performing one or more of a cross-correlation analysis, a logarithm decrement analysis, a wavelet transform analysis, and computer vision or image training analysis using a machine learning algorithm. Experiments were conducted for estimating one or more geometric parameters of photomasks utilizing EKEI. It may be understood that the following experiments described herein are not intended to limit the scope of this disclosure and the embodiments described above and shown inFIGS.1-8. Particularly, in an experimental study, a collimated laser (wavelength of approximately 532 nanometers (nm)) passed through an aperture (ϕ1.0 millimeters (mm)) and was beam-shaped by an objective lens (NA of 0.4). The beam-shaped laser passed through a sample photomask and the diffraction interferometric fringe pattern was recorded by the photodetector (PD) sensor. In this study, the beam diameter on the photomask surface was approximately 100 μm.

Additionally, a photomask with nine groups of line patterns containing different characterized LER was tested during this study. The photomask was securely fixed on an XY motorized scanning stage, and the scanning speed was set to approximately 1 millimeter per second (mm/s). By scanning different areas on the photomask, the interferometric fringe patterns created from different LER decorated lines were recorded. Particularly, in this study, the signal was recorded by an optical fiber-pigtailed photodiode and a lock-in amplifier was used for signal processing. While all datasets from the photomask were recorded, the photomask was used for lithography to make a lift-off replica wafer with the chromium (Cr) coating layer.

After the lithography process, both the photomask and the replica wafer patterns were measured by optical microscopy. Referring toFIGS.9and10, a graph220is shown inFIG.9indicating the LER values for intended or designed patterns (indicated by221in graph220), fabricated photomasks (indicated by222in graph220), and of the replica wave (indicated by223in graph220) of ten different samples from this study. It may be understood that the LER values221for the designed patterns were simulated using a model. Additionally,FIG.10illustrates images of the patterns for samples1,9, and10shown in graph220ofFIG.9. Particularly,FIG.10illustrates images of the intended or designed patterns for samples1(image230),9(image231) and10(image232), images of the fabricated photomasks for samples1(image240),9(image241), and10(image242), and images of the respective replica wafers for samples1(image250),9(image251), and10(image252).

The LER values for the photomask (LER values222) and wafer (LER values223) in graph220were calculated by analyzing images from a microscope. From graph220, generally, the LER values221-223decrease as the group or sample number increases for both photomask and replica wafers. However, there were still some differences between the designed and fabricated photomasks. First, although the fabricated photomask maintained the designed LER pattern fromFIG.10, there was still approximately a 1 μm LER deviation compared with the designed and fabricated photomask LER values221and222, respectively, which may have been caused by the resolution of the images (e.g., images230-232and images240-242). Particularly, in those respective images, 10 μm implied 34-pixel points. In that circumstance, it was difficult to define the position of the edge precisely due to the diffraction when obtaining the images. A 1 um of LER deviation indicated an approximately 0.33 μm difference in standard deviation, which was just a 1-pixel variance, which might be the reason for the LER deviation between the designed and fabricated photomasks.

Additionally, there was also deviations between the fabricated photomask LER values222and the wafer LER values223. For that issue, one of the reasons may have been the resolution of the images (e.g., images240-242for the fabricated photomask and images250-252for the wafers), and the other may have been the result of the lithography process. In this study, the replica wafer was fabricated by lift-off processing. During the manufacturing process, there were many uncertainties that might have caused imperfection in duplication due to, for example, diffraction, scattering, photoresist, or catalyst during the lithography. Last, the replica wafer was scanned by an experimental EKEI system (e.g., a system similar in configuration in at least some respects to inspection system100shown inFIGS.1and2) to record the interferometric fringe patterns in comparison with those of the photomask patterns.

Specifically, the experimental EKEI system scanned the photomask and its replica wafer. As mentioned above, on the fabricated photomask, there were 9-line patterns with different LER values, and the LER was defined by the intensity and duty cycle for the rectangular function on the edge. From sample1to sample9, the LER value decreased from approximately 5.88 μm to approximately 2.40 μm. Additionally, sample10was designed as a control or reference group with no LER (ideal sharp edge) for comparison. Referring toFIGS.11and12, interferograms260and270are shown, respectively. Particularly, interferogram260illustrates normalized output intensity261,262, and263for three selected fabricated photomasks while interferogram270illustrates normalized output intensity271,272, and273for three selected photomasks. In this example, output intensity261and output intensity271correspond to the reference sample having zero LER, output intensity262and output intensity272correspond to a pattern having an LER equal to approximately 2.40 μm, and output intensity263and output intensity273correspond to a pattern having an LER equal to approximately 5.88 μm. The 2.40 μm LER and 5.88 ∞m LER implies the lowest and the highest LER value in this study.

Based on the output intensities261-263of interferogram260, the fringes generally were attenuated when the LER value increases. When the LER changes from smooth (LER=0) to LER=5.88 μm, the intensity of the first order fringe decreased from 1.147 to 1.028. Not only does the amplitude of the first-order fringe decrease, but the higher-order fringes were also attenuated or vanished when the LER value increased. In interferogram260, compared with the 5 orders of fringes from the smooth case, when the LER increased to 5.88 μm, only the first and the second order of fringes can be distinguished, and all higher order fringes vanished.

Interferogram270shows the scanning result from the replica wafer. Comparing interferograms260and270, the fringes generated by the replica wafer maintained the same trend of attenuation as the fringes from the photomask. Additionally, the trend of the interferometric fringe pattern agreed with the simulation results indicated in graph220ofFIG.9. Overall, the experimental approaches indicated the following results: (1) the LER can be printed on the photomask and can be replicated to the wafer by photolithography; and (2) the fringes from edge diffraction attenuate when the LER value of the edge increases. In this study, the similarity decreased by approximately 0.017 when the LER value increased from 2.40 μm to 5.88 μm. Generally, because of the attenuation, the intensity for the first-order fringe decreased and some higher-order fringes vanished.

As part of this study, after collecting the interferometric fringe patterns from the photomask edge patterns under different LER conditions, the cross-correlation-based similarity values were obtained to numerically express the features that represent a change in the fringes. Referring toFIGS.13and14, the analysis results from the cross-correlation method are presented in a graph280shown inFIG.13. Particularly, graph indicates LER values281along with similarity scores282,283, and284for the intended (simulated) pattern, the fabricated photomask, and the wafer, respectively. This result indicated that the similarity score increased while the LER decreased. Based on the similarity results from photomask interferometric fringe patterns, the similarity decreased by 0.0183 when the LER value changed from 2.40 μm to 5.88 μm. Although the basic dimension of the characterized rectangular function followed the LER pattern design (intensity and duty cycle), there were still some deviations from the intended pattern and the pattern of the fabricated photomask, which caused the difference in the variation of similarities. Additionally, the diffraction and the imperfection of the lift-off replica wafer induced the error between the replica wafer and the fabricated photomask, which caused the deviation of the similarity values as well. Overall, these results indicate the experimental EKEI system can track and characterize the LER based on the changes in similarity values, where the similarity has a negative correlation with the LER value.

FIG.14includes an interferogram290illustrating normalized output intensities291and292for both a normal edge and an abnormal edge, respectively. Particularly, interferogram290shows the interferometric fringe pattern changes in case there is a residue on the photomask after the lithography process. Compared with the fringes from the smooth edge, the fringe from an abnormal (residue-contaminated) edge shows different features. First, the boundary of the abnormal edge becomes fuzzy. In a conventional coated pattern, the light intensity increases dramatically when the incident light is not blocked by the opaque pattern, which follows the trend inFIG.14, normal edge (output intensity291), from 100 μm to 200 μm. However, the boundary for a residue-contaminated edge did not follow that feature. InFIG.14, the abnormal edge (output intensity292), from 100 μm to 250 μm, shows that the normalized intensity increased gradually. The abnormal edge did not block the light 100 percent, where the light was permitted to partially pass through the edge and its contaminated area. Second, the interferometric fringe pattern vanished in fringes from the abnormal edge, which may have been due to the difference in the light interference. Based on the Huygens-wavelet theory, the incoming light source and the Huygens wavelets emitted on the edge generated the edge diffraction pattern. However, when the edge changes to an abnormal edge, not only is there present the incoming light source and Huygens wavelets from the edge, but also the light that is modulated by that residue-contaminated area. This third wave source can change the interferometric fringe pattern from the conventional edge diffraction. Based on the results fromFIG.14, the experimental EKEI system could also track the variance of the fringes when the residue photoresist damaged or contaminated the photomask. In that case, the experimental EKEI system may be effective for an in-situ photomask monitoring system to track the status of the photomask in industries. Specifically, the EKEI system could track and report those residues directly in the semiconductor manufacturing process.

This study indicated the experimental EKEI system for LER characterization. Particularly, the Fresnel number-based geometrical EKEI model with LER characterization was developed. The EKEI model simulated interferometric fringe patterns concerning different LER conditions. The LER of the pattern was characterized by using rectangular functions in different duty cycles and intensities. The simulation results indicated that the increase in the LER value result in attenuation of the interferometric fringe pattern. In addition, the cross-correlation method analyzed the generated interferometric fringe patterns. As a result, the similarity value decreased as the LER increased. The cross-correlation method also implemented this analytical method in experimental data analysis. From the study, LER-characterized photomask patterns and lithography-printed patterns recorded the fringes. The computation model indicated agreement with the experimental results obtained from the cross-correlation analysis method. As a result, the experimental EKEI system successfully characterized the LER on both the photomask patterns and the printed patterns. Successful integration of the proposed inspection system sheds light not only on the LER characterization but also on photomask defectivity metrology and inspection, improving the lithography processes and increasing yield.