Litho-aware source sampling and resampling

A method includes determining a first transmission cross coefficient (TCC) operator of an optical system of a lithographic system based on an illumination source. The method includes sampling the illumination source by a first number of sampling points to produce a first discrete source and determining a second TCC operator based on the first discrete source. The method also includes determining an error between the first TCC operator and the second TCC operator. The method includes recursively adjusting the first number of sampling points to re-sample the illumination source and to re-determine the second TCC operator until the error is below a threshold level and a final discrete source and a final second TCC operator is determined.

An optical lithography process transfers a layout pattern of a photo mask to the wafer such that etching, implantation, or other steps are applied only to predefined regions of the wafer. Transferring the layout pattern of the photo mask to the resist layer on the wafer may cause resist pattern defects that are a major challenge in semiconductor manufacturing. An optical proximity correction (OPC) operation may be applied to the layout pattern of the photo mask to reduce the resist pattern defects. The OPC may modify the layout patterns of the photo mask before the lithography process to compensate for the effect of the lithography process. In addition, inverse lithographic transformation (ILT) may be performed on the layout patterns of the photo mask to further compensate for the effect of the lithography process. An efficient OPC or ILT operation on the layout patterns of the photo masks is desirable.

DETAILED DESCRIPTION

Further, spatially relative terms, such as “beneath,” “below,” “lower,” “above,” “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. In addition, the term “being made of” may mean either “comprising” or “consisting of” In the present disclosure, a phrase “one of A, B and C” means “A, B and/or C” (A, B, C, A and B, A and C, B and C, or A, B and C), and does not mean one element from A, one element from B and one element from C, unless otherwise described.

In some embodiments, one or both of the OPC operation or the ILT operation is applied to the layout pattern of the photo mask to reduce resist pattern defects. In some embodiments, both OPC and ILT operations are iteratively performed. The OPC and the ILT modify a layout pattern of the photo mask, the modified layout pattern of the photo mask is projected, by an optical system of a lithographic system, as a pattern on the resist material layer on a wafer. The projected pattern on the resist material is compared with a target layout pattern and an error between the projected pattern on the resist material and the target layout pattern in calculated. Depending on the calculated error and/or existence of some defects, e.g., a bridge or a narrowing, the layout pattern of the photo mask is further modified by the OPC and/or ILT operations. The iterative method is repeatedly applied until the defects are corrected and/or the calculated error is below a threshold level. In some embodiments, the projection of the layout pattern of the photo mask on the resist layer of a wafer is performed by a simulated projection and the projected pattern on the resist layer of the wafer is calculated. In the simulated projection, the illumination source, e.g., light source or laser source, of the optical system of the lithographic system is sampled by a sampling grid. A resolution of the sampling grid directly affects the complexity and accuracy of the simulated projection. If the illumination source sampling is performed with low resolution, the simulated projection may be fast but the simulated projection may lose accuracy. Conversely, if the illumination source sampling is performed with high resolution, the simulated projection may be slow and time consuming but the simulated projection may be more accurate. Thus, the resolution of the illumination source sampling defines the speed of the OPC and ILT operations and the accuracy of the OPC and ILT operations. Therefore, finding a suitable resolution for sampling the illumination source is desirable.

FIG. 1illustrates a schematic diagram of an exemplary integrated circuit (IC) fabrication flow100. The IC fabrication flow100begins with an IC design module102that provides layout patterns M, e.g., target layout patterns, that will be produced as a resist pattern of an IC product on the wafer. The IC design module102generates various layout shapes, e.g., geometrical patterns, based on the specification of the IC product for different steps of processing the IC product. In some embodiments, the layout patterns M are presented by one or more data files having the information of the geometrical patterns. In some embodiments, optically projecting the layout pattern of the photo mask to the wafer in the lithographic process degrades the layout pattern of the photo mask and generates pattern defects on the resist layer on the wafer. An optical proximity correction (OPC) operation may be applied to layout patterns of the photo mask to reduce the pattern defects on the wafer. The OPC may modify the layout patterns of the photo mask before the lithography process to compensate for the effect of the lithography and/or etching processes. The IC fabrication flow100also shows a mask enhancer104. As will be described in more detail below with respect toFIG. 2A, the mask enhancer104performs the OPC in some embodiments. The mask enhancer104creates an OPCed (e.g., a corrected or enhanced) layout pattern M′ on the photo mask. In some embodiments, the enhanced layout pattern M′ is presented by one or more data files having the information of the enhanced geometrical patterns.

The IC fabrication flow100further shows a mask projection system106. In some embodiments, the mask projection system106produces the enhanced layout patterns M′ on the photo mask. In some embodiments, the mask projection system106performs two functions. As a first function, the mask projection system106uses the data files of the enhanced layout pattern M′ and uses an electron beam to generate the enhanced layout pattern M′ on a mask blank (not shown) to produce the photo mask for the ICs. In addition, and as a second function, the mask projection system106optically projects the enhanced layout pattern M′ of the photo mask on the wafer108to produce the IC layouts on the wafer108.

FIGS. 2A and 2Billustrate a schematic diagram of an exemplary photo mask enhancer and an OPC enhanced layout pattern associated with a target layout pattern.FIG. 2Aillustrates a schematic diagram of the mask enhancer104that receives the target layout pattern M at an input of an OPC enhancer122and produces the enhanced layout pattern M′ at an output of the step150. The mask enhancer104performs an iterative process. In some embodiments, the mask enhancer104includes an OPC enhancer122that receives, from the IC design module102, the target layout pattern M that will be produced on the wafer108. The OPC enhancer122performs enhancements on the target layout pattern M and produces the OPCed (e.g., the corrected or enhanced) layout pattern M′. As described, OPC is a lithography technique that is used to correct or enhance the layout pattern M and to add improved imaging effects to a target layout pattern M such that the OPCed layout pattern M′ reproduces, on the wafer108, the target layout pattern M. For example, OPC is used to compensate for imaging distortions due to optical diffraction. In some embodiments, the target layout pattern M is a data file having the information of the geometrical patterns to be produced on the wafer108, and the OPC enhancer122modifies the data file and produces a corrected data file representing the enhanced layout pattern M′. In some embodiments, the target layout pattern M and the enhanced layout pattern M′ are represented by the vertices of the layout patterns in the data files. Thus, in some embodiments, the rounded corners and the bends are represented by a curvilinear shape having multiple vertices and multiple line segments connecting the vertices and the curvilinear shape is represented by the multiple vertices in the data file.

FIG. 2Afurther shows a mask projector130, e.g., a simulator for mask projection, that is applied to the enhanced layout pattern M′ to produce a projected resist pattern101on the wafer. In some embodiments, the enhanced layout pattern M′ is a data file and the mask projector130simulates the projection of the enhanced layout pattern M′ on the wafer and produces the simulated projected resist pattern101. The projected resist pattern101is inspected by an OPC verifier140for errors. In some embodiments, the OPC verifier140receives the target layout pattern M in addition to the projected resist pattern101and compares the projected resist pattern101with the target layout pattern M to find errors between target layout pattern M and the projected resist pattern101. In some embodiments, the OPC verifier140verifies the enhanced, e.g., OPCed, layout pattern M′ when the error between the target layout pattern M and the projected resist pattern101is below a threshold level and there are no defects, e.g., a bridge or narrowing shown inFIG. 3, in the projected resist pattern. In some embodiments, after verifying the enhanced layout pattern M′, the OPC verifier140generates and sends a verification signal103. In some embodiments, the OPC verifier140stores the enhanced layout pattern M′ in a database. In some embodiments, instead of a simulated result, a photo resist pattern is formed by using a photo mask fabricated with the enhanced layout pattern M′ and the shapes and dimensions of the resist patterns are measured and are fed back to the OPC enhancer. The mask projector130is described in more details with respect toFIGS. 7A and 7B.

The verification signal103is tested at step150and if the verification signal103is not successful, e.g., the error is above the threshold level or defects exist in the projected resist pattern101, iterations continue by applying further OPC enhancements by the OPC enhancer122. The iterations continue until the verification signal103is successful. When the verification signal103is successful, the enhanced layout pattern M′ is provided as the output of the mask enhancer104. In some embodiments, the error between the target layout pattern M and the projected resist pattern101is defined as a distance between the boundary of the target layout pattern M and a boundary of the projected resist pattern101.

As shown, in addition to the mask enhancer104,FIG. 2Aincludes a mask generator141and an optical system145. In some embodiments, the enhanced layout pattern M′ is sent as a data file to the mask generator141. The mask generator141produces the enhanced layout pattern M′ on a mask-blank to generate a photo mask143. In some embodiments, the photo mask143is used by the optical system145of a photo lithography system to produce a resist pattern on a resist layer of the wafer108.

FIG. 2Billustrates the target layout patterns303and the OPC enhanced, e.g., corrected, layout patterns301of a connection line. In some embodiments, the OPC enhanced layout patterns301ofFIG. 2Bis formed on a photo mask and the photo mask is projected onto a wafer, e.g., the wafer108, by the mask projection system106ofFIG. 1.

FIG. 3illustrates exemplary layout contours having two defective areas.FIG. 3shows the resist pattern300having two defective areas302and304. The resist pattern300may be produced by the mask projector130when the corrected mask layout M′, after being OPCed, is projected on the resist layer of the wafer108, disclosed herein. As shown, both of the defective areas302,304respectively include a bridging312and a bridging314(e.g., short circuits) that are connections between adjacent layout lines in the middle of the defective areas302and304. In some embodiments, the defective areas302and304are back projected to two corresponding hotspot regions in the corrected mask layout M′. In some embodiments, the ILT operation is performed on the corrected mask layout M′, e.g., on the hotspot regions in the corrected mask layout M′, to correct the corresponding defective areas302and304of the resist pattern produced in the resist layer of the wafer108.

FIG. 4illustrates a schematic diagram of an exemplary layout corrector.FIG. 4is configured to perform an ILT enhancement.FIG. 4shows the mask enhancer104that receives the target layout pattern M at an input of an ILT enhancer452and produces an enhanced mask layout462at an output of the step460. In some embodiments, the ILT enhancer452receives the corrected mask layout M′ after the OPC operation. Either the corrected mask layout M′ or the target layout pattern M includes a hotspot region corresponding to a defect on the resist layer when the corrected mask layout M′ or the target layout pattern M is projected on the resist layer of the wafer108.

The ILT enhancer452performs an enhancement, e.g., a constrained inverse filtering operation, on the hotspot region of the corrected mask layout M′ or the target layout pattern M and produces the iteration result, the enhanced mask layout462. The enhanced mask layout462is projected by the mask projector130on the resist layer of the wafer108to create a projected resist pattern458. In some embodiments, the mask projector130performs a simulated projection and is consistent with the operation performed by the configuration ofFIG. 7A. The projected resist pattern458is inspected by an ILT verifier456for defective areas. A verification outcome468is tested at step460and if the verification outcome468is not successful, e.g., defective areas exist, the iterations continue by modifying the layout enhancement at the ILT enhancer452. The iterations continue until the verification outcome468is successful and the projected resist pattern458does not have any defective areas. When the verification outcome468is successful, the enhanced mask layout462is provided at step460.

As shown, in addition to the mask enhancer104,FIG. 4includes the mask generator141and an optical system145. A described above, the mask generator141generates the photo mask143from the enhanced mask layout462and the optical system145of the photo lithography system projects the photo mask143and produces the resist pattern on the resist layer of the wafer108. The mask projector130is described in more details with respect toFIGS. 7A and 7B.

FIG. 5illustrates a schematic diagram of an exemplary source sampler system500for optimizing a TCC operator.FIG. 5shows an input source402, e.g., an illumination source, and a TCC generator module421. In some embodiments, the input source402, e.g., the illumination source, is a parametric illumination source of an optical system, e.g., optical systems800and850ofFIGS. 8A and 8B, of a lithographic system. In some embodiments, the input source402is a laser source. In some embodiments, the input source402has a Gaussian profile with a standard deviation between about 1 cm to about 20 cm. In some embodiments, the input source402has a circular profile having a radius between 1 cm and 20 cm and having a uniform amplitude. In some embodiments, the input source402is one of a coherent or partially coherent source. In some embodiments, the input source402is a non-coherent source. In some embodiments, the input source402is a deep ultraviolet (DUV) with a wavelength of about 250 nm to about 100 nm, or an extreme ultraviolet (EUV) source with a wavelength of about 100 nm to about 10 nm. In some embodiments, the input source402has dimensions of about 1 cm by 1 cm (a diameter of about 2 cm) to about 20 cm by 20 cm (a diameter of about 40 cm).FIG. 5also shows a discretize source operator406and a TCC generator module423. The discretize source operator406performs sampling of the input source402and provides a discrete source420. As shown inFIG. 5, the TCC generator module421uses the input source402and the optical parameters411, which includes an exit pupil, consistent with the exit pupil830or831ofFIGS. 8A and 8B, and generates, e.g., calculates, a TCC operator404. The TCC generator module423uses the discrete source420and the optical parameters411and generates, e.g., calculates, a TCC operator408. In some embodiments, the TCC generator modules421and423use equation (2) below to generate the TCC operators404and408. Also, as shown inFIG. 5, the source sampler system500provides the TCC operators404and408and the discrete source420as outputs.

Thus, in some embodiments, the TCC operator404depends on the input source402, e.g., a shape and size of the input source402, and the TCC operator408depends on the discrete source420, e.g., a distribution of the sampled points of the input source402. As shown below in equation (2), the TCC operator depends on the spatial Fourier transform of the input source. Additionally, the TCC operators404and408depend on the optical parameters411of the lithographic system, e.g., the optical parameters411of the optical system of the lithographic system. Thus, the TCC operators404and408may depend on a wavelength of the illumination source of the optical system, an amount of coherency of the illumination source, a numerical aperture of the optical system, a shape and size of an exit pupil of the optical system, and an aberrations of the optical system. In some embodiments, an error calculator410determines an error between the TCC operator404and the TCC operator408. In some embodiments, the error calculator410generates an error422, which is a sum of squared differences between the TCC operator404and the TCC operator408, e.g., an L2 norm, a Frobenius-norm, which is a sum of squared differences between corresponding points of the TCC operator404and the TCC operator408.

In some embodiments, the intensity I of a projected image, e.g., the projected resist pattern101ofFIG. 2Aor the projected resist pattern458ofFIG. 4is defined with the following equations (1) and (2):
I(x)=∫∫M(α)T(α,α′)M*(α′)e2πi(α-α′)·xdαdα′Equation (1)
T(α,α′)=∫S(αs)P(α+αs)P*(α′+αs)dαsEquation (2)
Where α is the spatial frequency coordinates, M is the spatial Fourier transform of the layout pattern of the mask, P is the exit pupil function of the optical system, S is the spatial Fourier transform of the intensity distribution of the illumination source, and Tis the TCC operator. In some embodiments, the TCC operator includes the exit pupil function P and the spatial Fourier transform of the illumination source S as shown in equation (2). Additionally, the TCC operator incorporates the operation of the integral of equation (1). In some embodiments, an exit pupil of an optical system is a virtual aperture such that only the rays that pass through the exit pupil can exit the optical system. In some embodiments, an exit pupil function P(α) is a representation of the exit pupil as a function of the variable α, where α is a two-dimensional (2D) variable in a 2D coordinate system, e.g., a 2D point (α=(Fxand Fy)) in a frequency plane. In some embodiments, the TCC generator modules421and423generate the TCC operator404and the TCC operator408according to equation (2) as functions of the two variables α and α′ and the respective intensity I of equation (1) using the TCC operator404and the TCC operator408are numerically evaluated. The two variables α and α′ are sampled and the TCC operator404, the TCC operator408, and the intensity I of equation (1) are calculated at the sampled points of the variables. In some embodiments, the sampling resolution of the of two variables α and α′ in the spatial frequency coordinates is higher than the corresponding sampling resolution of the input source402and, thus, the sampling of the variables α and α′ to evaluate the TCC operators404and408and the intensity I of equation (1) causes negligible error, e.g., less than one percent, in the calculation of equation (1). In some embodiments, the exit pupil function is a real function represented by an amplitude that has a value of one inside a circle and a value of zero outside the circle. As shown above, the TCC operator depends on the exit pupil function and the illumination source distribution. In some embodiments, the exit pupil function is a complex function that is represented with an amplitude and a phase at each point of the exit pupil function, where the phase of the pupil function includes the aberrations of the optical system. The exit pupil is described with respect toFIGS. 8A and 8B. In some embodiments, the TCC operator is symmetric and positive definite and, thus, can be expanded, with non-negative expansion coefficients λn, into separable kernels φnand φ*nas shown in equation (3) below:
T(α,α′)=Σnλnφn(α)φ*n(α′),λn=1, 2, 3,  Equation (3)

In some embodiments, the kernels are numerically evaluated at sampled points of the variables α and α′. In addition, in some embodiments, the TCC operator404and the TCC operator408are approximated as a weighted sum of a finite number of the kernels. In some embodiments, the TCC operator404or TCC operator408are discretized and represented as matrices, e.g., 2D positive definite TCC matrices. In some embodiments, the TCC operator404and the TCC operator408expand in the same range of variables α and α′ and, thus, the TCC matrices corresponding the TCC operator404and the TCC operator408have the same dimensions. In addition, the integral of equation (1) is represented as a matrix multiplication of a TCC matrix and the discretized spatial Fourier transform of the layout pattern of the mask M. In some embodiments, the TCC generator modules421and423of the source sampler system500further perform a discretization and the TCC operators404and408are provided as TCC matrices at the output. In addition, the error calculator410generates the error422as a sum of squared differences between the corresponding elements of the TCC matrices.

In addition, the kernels φnand φ*nare respectively discretized and represented as horizontal or vertical vectors, e.g., one-dimensional (1D) horizontal or 1D vertical matrices. In some embodiments, the error calculator410generates the error422as a sum of squared differences between the corresponding elements of the TCC matrices. In some embodiments, when the TCC matrix is positive definite, the TCC matrix is expanded into a weighted sum, using the coefficients λnas the weights, of a plurality of matrices, where each matrix is generated as the multiplication of each vertical vector and a corresponding horizontal vector associated with one of the kernels φnand φ*n. The weighted sum is a matrix form of equation (3). In some embodiments, as shown in equation (3), the TCC operator404or TCC operator408is expanded into the weighted sum of the kernels. In some embodiments, the TCC operator404and/or the TCC operator408is approximated by selecting a subset of the kernels φnand φ*n. In addition, the projected image of the lithographic mask is approximated by the approximated TCC operators404and408. In some embodiments, the finite number of the kernels are selected by ordering the non-negative coefficients λnand then selecting the coefficients λnlarger than a threshold and the kernels associated with the coefficients larger than the threshold. The coefficients λnsmaller than the threshold and the kernels associated with the coefficients λnsmaller than the threshold are discarded.

After calculating the error422by the error calculator410, the error is compared by lower (first) and upper (second) thresholds in operation412. If the error422is within the upper threshold and the lower threshold, the discrete source420is acceptable and the discrete source420is provided as an output. In some embodiments, the discrete source420and the corresponding TCC operator408are used for calculating a projection of the mask in the mask projector130ofFIGS. 2A and 4. In some embodiments, a singular value decomposition is used for defining the kernels and selecting the kernels having the highest energy. In some embodiments, determining the TCC operator404or TCC operator408includes determining a cross section between two exit pupils P having different offsets α and α′ as shown in equation (2). In some embodiments, when the illumination source is partially coherent, determining the TCC operator404or TCC operator408includes determining a cross section between the two exit pupils and a circle having a radius equal to the coherent length of the illumination source limiting the spatial Fourier transform S of the illumination source.

In some embodiments, if the error422is more than the second threshold, the number of sampling points are increased, e.g., based on the error422, and the discrete source420is resampled. The resampling is performed by a re-discretize source414operator and the TCC operator408is re-determined based on the re-sampled discrete source. In some embodiments, by increasing the number of sampling points, the error422is decreased. In some embodiments, if the error422is less than the first threshold, the number of sampling points is reduced, e.g., based on the error422, and the discrete source420is resampled by the re-discretize source414operator and the TCC operator408is re-determined based on the re-sampled discrete source. In some embodiments, by decreasing the number of sampling points, an amount of calculation time of the mask projector130is reduced and calculating the projected image becomes faster. Either after reducing or increasing the number of sampling points, the error422is recalculated by the error calculator410to determine whether the error422is maintained between the first threshold and the second threshold. In some embodiments, the error422is defined by other norms such as the L-infinity norm (maximum value) or linear algebraic norms, e.g., the Frobenius norm or the nuclear norm, where the linear algebraic norms are used for TCC matrices.

FIGS. 6A, 6B, and 6Cillustrate schematic diagrams of exemplary systems for sampling and re-sampling an illumination source and generating a TCC operator.FIG. 6Ashows a diagram for sampling the input source402. In some embodiments, the input source402is a parametric illumination source as described above. The input source402is sampled by a sampler630that determines the number of sampling points and a distribution of the sampled points. In some embodiments, the sampler630uses the optical parameters411, described above, to determine a number of sampling points, e.g., sampling resolution, of the input source402to produce the discrete source420. In some embodiments, the sampler630uses the Nyquist rate based on a spatial frequency content of the input source402to determine the number of sampling points. In addition, a discrete source generator632receives the number of sampling points and determines how the sampling points are distributed, e.g., uniformly or non-uniformly, in the input source402. In some embodiments, a combination of the sampler630and the discrete source generator632is consistent with the discretize source operator406ofFIG. 5.

FIG. 6Bshows a diagram for re-sampling the discrete source420. The discrete source420is re-sampled by a re-sampler624that determines a modified number of sampling points634and a distribution of the modified sampled points. In some embodiments, the re-sampler624uses the optical parameters411, described above, and the error422to determine the modified number of sampling points634, e.g., a modified sampling resolution, of the discrete source420to produce a modified discrete source. In some embodiments, a discrete source generator626receives the modified number of sampling points634and determines how the modified sampling points are distributed. In some embodiments, a combination of the re-sampler624and the discrete source generator626is consistent with the re-discretize source414ofFIG. 5. In some embodiments, a local or a global operator is used for resampling. In some embodiments, the discrete Fourier transform operator is used for resampling such that the original sampled points of the discrete source420are Fourier transformed to the frequency domain. Then, the inverse Fourier transform is applied to the frequency domain to generate a continuous inverse Fourier transform function in the spatial domain. The inverse Fourier transform function is sampled by the modified number of sampling points at the locations defined by the discrete source generator626.

FIG. 6Cshows a diagram for distributing the modified number of sampling points and defining the locations of the modified number of sampling points. The intensity location initializer642receives the modified number of sampling points and uniformly distributes the modified number of sampling points. The discretize source operator406finds an intensity of the modified number of sampling points, e.g., by performing Fourier transform/inverse Fourier transform described above. The discretize source operator406generates a new discrete source420. The error422when using the new discrete source420to generate a new TCC operator408is calculated between TCC operator408and the TCC operator404at operation621. The location of the modified number of sampling points are recursively modified by an intensity location adjuster625until the error422is minimized. A new discrete source420is generated when the error422is minimized. In some embodiments, the error422is minimized when the error422is between the second threshold that is defined with respect toFIG. 5.

FIGS. 7A and 7Billustrate schematic diagrams of exemplary systems for calculating projection images using a TCC operator.FIGS. 7A and 7Bshow different implementations of the mask projector130ofFIGS. 2A and 4that is consistent with the mask projector130ofFIG. 5.FIG. 7Ashows a projected image calculator702that generates, consistent with equation (1), the result of performing the TCC operator404on the layout pattern of the photo mask143to produce a projected image706consistent with the projected resist pattern101ofFIG. 2Aor the projected resist pattern458ofFIG. 4.FIG. 7Bshows the projected image calculator702that generates, consistent with equation (1), the result of performing the TCC operator408on the layout pattern of the photo mask143to produce a projected image708consistent with the projected resist pattern101ofFIG. 2Aor the projected resist pattern458ofFIG. 4. As shown inFIG. 7B, the TCC operator can be factored into kernels by a kernel generator704and kernels710are used by a projected image calculator703for producing the projected image708in some embodiments.

FIGS. 8A and 8Billustrate schematic diagrams of exemplary optical systems of an optical system of a lithographic system.FIG. 8Ashows an optical system800that is used in a lithographic system in some embodiments. The optical system800shows an illumination source802at a distance808from a lens804. The lens804transmits a radiation beam of the light source through the photo mask143. The transmitted radiation beam810converges using an objective lens system806to generate the convergent beam812and to create a projected image of the photo mask143on the wafer108. As shown, blades814block any radiation that is outside an exit pupil830of the optical system800.FIG. 8Bshows an optical system850that is used in a lithographic system in some embodiments. The optical system850shows the illumination source802. The lens804transmits a radiation beam of the illumination source802. The radiation beam is reflected by a mirror820and is directed towards a mask843, e.g., a reflective mask, and produces the reflected radiation beam811that is reflected off the mask843. The reflected radiation beam811converges using the objective lens system806to generate a convergent beam812and to create a projected image of the reflected mask843on the wafer108.FIG. 8Balso shows the exit pupil831of the optical system850.

FIG. 9illustrates a flow diagram of an exemplary process for enhancing a photo mask in accordance with some embodiments of the disclosure. The process900may be performed by the system ofFIGS. 2A and 11. In some embodiments, the process900or a portion of the process900is performed and/or is controlled by the computer system1000described below with respect toFIGS. 10A and 10B. In some embodiments, the process900is performed by the system1100ofFIG. 11. The method includes an operation S902of determining a first TCC operator of an optical system of a lithographic system based on an illumination source of the optical system. In some embodiments, the TCC operator404ofFIG. 7Ais produced based on an input source402, e.g., the illumination source. In operation S904, the illumination source, e.g., the input source402, of the optical system is sampled by a first number of sampling points to produce a discrete source420. In operation S906, a second TCC operator of the optical system of the lithographic system is determined based on the discrete source. In some embodiments, the TCC operator408ofFIG. 7Bis determined based on the discrete source420.

In operation S908, an error is determined between the first TCC operator and the second TCC operator. In some embodiments, the first TCC operator and the second TCC operator are respectively discretized and a first TCC matrix and a second TCC matrix are generated. The error is determined between the first TCC matrix and the second TCC matrix. In operation S910, the first number of sampling points is recursively adjusted until the error is below a threshold level and a final discrete source and a final second TCC operator408is determined. In some embodiments, the adjusting the first number of sampling points is described with respect toFIG. 11. In some embodiments, the iterations continue until the error is less than or equal to a threshold value. In some embodiments, the error is positive and the first number of sampling points is modified such that the error is maintained in an error-range such that the error is less than a positive second threshold level but greater than a positive first threshold level smaller than the second threshold level. In some embodiments, if the error is greater than the second threshold level, the first number of sampling points is increased to increase the accuracy of determining, e.g., calculating, the projected image of the mask projectors130ofFIGS. 2A, 4, 7A, and 7B. Conversely, if the error is less than the first threshold level, the first number of sampling points is reduced to increase the speed of determining, e.g., calculating, the projected image of the mask projectors130ofFIGS. 2A, 4, 7A, and 7B.

FIGS. 10A and 10Billustrate an apparatus for enhancing a photo mask in accordance with some embodiments of the disclosure. In some embodiments, the computer system1000is used for enhancing a photo mask. Thus, in some embodiments, the computer system1000performs the functions of the OPC enhancer122, the mask projector130, and the OPC verifier140ofFIG. 2A. In some embodiments, as will be described inFIG. 11, the computer system1000performs the functions of the analyzer module1130, main controller1140, the mask enhancer1104, and the mask verifier1108. In some embodiments, the computer system1000performs a simulation of the mask projector1106and the optical system1105.FIG. 10Ais a schematic view of a computer system that performs the enhancing of a photo mask. All of or a part of the processes, method and/or operations of the foregoing embodiments can be realized using computer hardware and computer programs executed thereon. InFIG. 10A, a computer system1000is provided with a computer1001including an optical disk read only memory (e.g., CD-ROM or DVD-ROM) drive1005and a magnetic disk drive1006, a keyboard1002, a mouse1003, and a monitor1004.

FIG. 10Bis a diagram showing an internal configuration of the computer system1000. InFIG. 10B, the computer1001is provided with, in addition to the optical disk drive1005and the magnetic disk drive1006, one or more processors, such as a micro processing unit (MPU)1011, a ROM1012in which a program such as a boot up program is stored, a random access memory (RAM)1013that is connected to the MPU1011and in which a command of an application program is temporarily stored and a temporary storage area is provided, a hard disk1014in which an application program, a system program, and data are stored, and a bus1015that connects the MPU1011, the ROM1012, and the like. Note that the computer1001may include a network card (not shown) for providing a connection to a LAN.

The program for causing the computer system1000to execute the functions of an apparatus for performing the enhancement of a photo mask in the foregoing embodiments may be stored in an optical disk1021or a magnetic disk1022, which are inserted into the optical disk drive1005or the magnetic disk drive1006, and transmitted to the hard disk1014. Alternatively, the program may be transmitted via a network (not shown) to the computer1001and stored in the hard disk1014. At the time of execution, the program is loaded into the RAM1013. The program may be loaded from the optical disk1021or the magnetic disk1022, or directly from a network. The program does not necessarily have to include, for example, an operating system (OS) or a third party program to cause the computer1001to execute the functions for enhancing a photo mask in the foregoing embodiments. The program may only include a command portion to call an appropriate function (module) in a controlled mode and obtain desired results.

FIG. 11illustrates an exemplary system1100of enhancing a photo mask in accordance with some embodiments of the disclosure. The system1100includes an analyzer module1130and a main controller1140coupled to each other. The analyzer module1130receives the layout pattern1110, which is consistent with the target layout pattern M ofFIGS. 1 and 2A. The analyzer module1130may send the layout pattern1110to a mask enhancer1104that is coupled to the main controller1140. In some embodiments, the analyzer module1130, which is consistent with the discretize source operator406and the re-discretize source414ofFIG. 5, determines the initial number of sampling points and the initial location of the sampling points. The initial location of the sampling points may be uniformly distributed in an intensity or amplitude profile of the illumination source1107, which is consistent with the illumination source802ofFIGS. 8A and 8B. The main controller1140is also coupled to a mask projector1106, consistent with mask projector130ofFIGS. 1 and 2A, an optical system1105, and a mask verifier1108. The optical system1105is consistent with the optical systems800and850ofFIGS. 8A and 8Band the mask verifier1108is consistent with the OPC verifier140ofFIG. 2Aand the ILT verifier456ofFIG. 4.

In some embodiments, the mask enhancer1104performs the OPC or ILT operations on the layout pattern1110and the mask enhancer1104is consistent with the ILT enhancer452ofFIG. 4or the OPC enhancer122ofFIG. 2A. In some embodiments, instead of the mask enhancer1104, the analyzer module1130performs the OPC or ILT operations on the layout pattern1110and, thus, the analyzer module1130is further consistent with the ILT enhancer452ofFIG. 4or the OPC enhancer122ofFIG. 2A. In some embodiments, the mask enhancer1104or the analyzer module1130determines the TCC operator, e.g., the TCC operator404or the TCC operator408, of an optical system1105of a lithographic system and, thus, the mask enhancer1104or the analyzer module1130and the main controller1140together are further consistent with the source sampler system500. In some embodiments, the optical system1105is consistent with the optical systems800and850ofFIGS. 8A and 8B. In some embodiments, the mask enhancer1104or the analyzer module1130determines the TCC operator, e.g., the TCC operator404, of the optical system1105of the lithographic system based on an illumination source, e.g., illumination source802ofFIG. 8A or 8Bor illumination source1107ofFIG. 11. In addition, the mask enhancer1104or the analyzer module1130determines the TCC operator of the optical system1105of the lithographic system based on an exit pupil of an optical system, e.g., the exit pupils830and831ofFIGS. 8A and 8Bas shown in equation (2). The mask enhancer1104or the analyzer module1130also determines another TCC operator, e.g., TCC operator408, of the optical system1105or of the optical systems800and850ofFIGS. 8A and 8Bbased on a discrete source, e.g., the sampled source, and the exit pupils830or831.

As shown in the system1100, the mask enhancer1104is coupled to the analyzer module1130through the main controller1140. In some embodiments, the mask enhancer1104is consistent with the OPC enhancer122ofFIG. 2A. The system1100includes a mask projector1106that is coupled to the analyzer module1130through the main controller1140. In some embodiments, the mask projector1106is consistent with the mask projector130ofFIG. 2A. The system1100further includes a mask verifier1108that is coupled to the analyzer module1130through the main controller1140. In some embodiments, as noted, the mask verifier1108is consistent with the OPC verifier140ofFIG. 2A. In some embodiments, the mask enhancer1104, the mask projector1106, and the mask verifier1108are included in the main controller1140. In some embodiments, adjusting the first number of sampling points is performed by either of the analyzer module1130or the mask enhancer1104. In some embodiments, the mask projector1106is consistent with the combination of the operations performed inFIGS. 7A and 7B.

In some embodiments, the illumination source, e.g., input source402ofFIGS. 5, and 6A, is a polarized illumination source. Thus, each one of the electrical or magnetic fields at each point of the input source402may be represented by a vector in a plane perpendicular to the direction of travel of the light. In some embodiments, the light at each point of the input source402travels in the Z-direction and, thus, the electrical or magnetic fields of the light are in the XY-plane and may be represented by components in the X-direction and Y-direction. In some embodiments, the spatial Fourier transform S of the intensity distribution of the input source402, at each spatial frequency αs, is represented as a 2 by 2 matrix S2×2in equation (4) below where Sxy=S*yx.

In some embodiments, the polarization of the input source402continuously change with time and, thus, instead of the temporal values of the input source402, a time-averaged variance of the electrical or magnetic fields in the two X-direction (sxx) and Y-direction (syy) and a time-averaged covariance between the electrical or magnetic fields in the two directions (sxyor syx) are used. In some embodiments, the matrix elements of equation (4) are the spatial Fourier transform of the variance functions and the covariance function at a spatial frequency αs.

FIG. 12illustrates a schematic diagram of an exemplary source sampler system for optimizing a TCC operator for vector optics.FIG. 12shows a vector source, e.g., a polarized illumination source1202. As described above the variance and covariance of the polarized illumination source1202are determined, e.g., calculated. As shown, a first source component1204is the variance sxxof the polarized illumination source1202, a second source component1206is the variance syyof the polarized illumination source1202, and a third source component1208is the covariance sxyof the polarized illumination source1202. Because of the covariance symmetry, one of the sxyor syxis used. The first, second, and third source components1204,1206, and1208are used as independent illumination sources for the three source sampler systems500ofFIG. 12. As shown inFIG. 5, each one of the source sampler systems500provide a sampled/re-sampled discrete source420at the output. The sampled/re-sampled discrete sources420are added component-wise, at operation430, and the polarized sampled/re-sampled illumination source1210is generated. In some embodiments, the polarized illumination source1202is not yet sampled and each source sampler system500provides a sampled source. In some embodiments, the polarized illumination source1202is already sampled and each source sampler system500provides a resampled source. In some embodiments, a single sampling resolution is selected for the first, second, and third source components1204,1206, and1208. In some embodiments, a highest sampling resolution provided by the three source sampler systems500is selected for all three of the source sampler systems500. The source components having sampling resolutions lower than the highest sampling resolution are resampled such that the first, second, and third source components1204,1206, and1208have the same highest sampling resolution. The first, second, and third source components1204,1206, and1208are combined to produce a single polarized sampled illumination source1210. Then a TCC operator or a TCC matrix corresponding to the single polarized sampled illumination source1210is computed using a generalization of equation (2) using the components of the single polarized sampled illumination source1210to determine a TCC operator or a TCC matrix and the TCC operator or the TCC matrix is used to determine the intensity I of the projected image using a generalization of equation (1).

According to some embodiments of the present disclosure, a method of enhancing a layout pattern includes determining a first transmission cross coefficient (TCC) operator of an optical system of a lithographic system based on an illumination source of the optical system of the lithographic system. The method includes sampling the illumination source of the optical system by a first number of sampling points to produce a first discrete source and determining a second TCC operator of the optical system of the lithographic system based on the first discrete source. The method also includes determining an error between the first TCC operator and the second TCC operator. The method further includes recursively adjusting the first number of sampling points to re-sample the illumination source and to re-determine the second TCC operator based on the re-sampled illumination source until the error is below a threshold level and a final discrete source and a final second TCC operator is determined. The method includes performing an optical proximity correction (OPC) operation of a first layout pattern of a photo mask, the OPC operation uses the final discrete source and the final second TCC operator to determine a projected image of the first layout pattern of the photo mask on a wafer. In an embodiment, the first layout pattern of the photo mask includes one or more of specific features, and using the final discrete source and the final second TCC operator to determine the projected image of the first layout pattern generates the one or more specific features on a resist layer on the wafer. In an embodiment, the specific features include one or more of a curvature, a vertical line, or a horizontal line. In an embodiment, the method further includes receiving an illumination profile of the illumination source and sampling the illumination profile of the illumination source at a number of locations equal to the first number of sampling points. In an embodiment, the sampling the illumination source is a non-uniform sampling and the re-sampling the illumination source is a uniform sampling. In an embodiment, the illumination profile is one of an amplitude profile or an intensity profile of the illumination source. In an embodiment, the method further includes producing the OPC corrected first layout pattern on a mask-blank to create a photo mask.

According to some embodiments of the present disclosure, a method of enhancing a layout pattern includes determining a first transmission cross coefficient (TCC) operator of an optical system of a lithographic system based on an illumination source of the optical system and an exit pupil of the optical system of the lithographic system. The method includes sampling the illumination source of the optical system by a first number of sampling points at a first number of sampling locations to make a first discrete source and determining a second TCC operator of the optical system of the lithographic system based on the first discrete source and the exit pupil of the optical system. The method also includes determining an error between the first TCC operator and the second TCC operator. The method further includes recursively adjusting the first number of sampling points and the first number of sampling locations to re-sample the illumination source and to re-determine the second TCC operator based on the re-sampled illumination source until the error is within a threshold error range and a final discrete source and a final second TCC operator is determined, the threshold error range has an upper limit and a lower limit. The method includes performing an inverse lithographic transformation (ILT) operation of the first layout pattern of a photo mask, the ILT operation uses the final discrete source and the final second TCC operator to determine a projected image of the first layout pattern of the photo mask on a wafer for determining an ILT enhancement of the first layout pattern and producing the ILT enhanced first layout pattern on a mask-blank to create the photo mask. In an embodiment, the error is above the upper limit of the threshold error range and the re-sampling the illumination source includes increasing the first number of sampling points to a second number of sampling points, uniformly sampling the illumination source with the second number of sampling points, and recursively adjusting sampling locations of the second number of sampling points to re-sample the illumination source and to re-determine the second TCC operator based on the re-sampled illumination source until the error is minimized. In an embodiment, the error is below the lower limit of the threshold error range and the re-sampling the illumination source includes decreasing the first number of sampling points to a second number of sampling points, uniformly sampling the illumination source with the second number of sampling points, and recursively adjusting sampling locations of the second number of sampling points to re-sample the illumination source and to re-determine the second TCC operator based on the re-sampled illumination source until the error is minimized. In an embodiment, the method further includes representing the final second TCC operator by a weighted sum of a plurality of kernels in a kernel space, approximating the final second TCC operator by a weighted sum of two or more kernels of the plurality of kernels, and using the approximated final second TCC operator and the first discrete source to determine the projected image of the first layout pattern of the photo mask on the wafer. In an embodiment, the first TCC operator and the second TCC operator are respectively discretized to generate a first TCC matrix and a second TCC matrix, and the method further includes determining the error by determining a Frobenius-norm error between the first TCC matrix and the second TCC matrix. In an embodiment, the method further includes that prior to the performing the ILT operation of the first layout pattern: performing an optical proximity correction (OPC) operation of the first layout pattern, the ILT operation uses the final discrete source and the final second TCC operator to determine a projected image of the first layout pattern of the photo mask on the wafer, and performing the ILT operation of the OPC corrected first layout pattern using the final discrete source and the final second TCC operator to determine the projected image of the OPC corrected first layout pattern of the photo mask on the wafer. In an embodiment, the method further includes receiving a second layout pattern, different from the first layout pattern, of the photo mask of the lithographic system, and performing the ILT of the second layout pattern using the final discrete source and the final second TCC operator to determine a projected image of the second layout pattern of the photo mask on the wafer.

According to some embodiments of the present disclosure, a lithographic system includes a main controller, a photo mask, a mask enhancer coupled to the main controller, an optical system including an illumination source and coupled to the main controller, and a mask projector coupled to the main controller and the mask enhancer and to produce a projection of the photo mask on a wafer. The system also includes an analyzer module coupled to the main controller, the analyzer module receives a first layout pattern of the photo mask to be produced on the wafer. The mask enhancer is coupled to the analyzer module through the main controller and receives the first layout pattern from the analyzer module and to perform one of an optical proximity correction (OPC) operation or an inverse lithographic transformation (ILT) operation of the first layout pattern. The mask enhancer also determines a final discrete source and a final second TCC operator by receiving a first number of sampling points from the analyzer module, determining a first transmission cross coefficient (TCC) operator of an optical system of the lithographic system based on the illumination source of the optical system and an exit pupil of the optical system, sampling the illumination source of the optical system by the first number of sampling points to make a first discrete source, determining a second TCC operator of the optical system of the lithographic system based on the first discrete source and the exit pupil of the optical system, determining an error between the first TCC operator and the second TCC operator, and recursively adjusting the first number of sampling points to re-sample the illumination source and to re-determining the second TCC operator based on the re-sampled illumination source until the error is below a threshold level and the final discrete source and the final second TCC operator is determined. The mask projector performs the projection of the photo mask on the wafer for the OPC operation or the ILT operation using the final discrete source and the final second TCC operator to determine a projected image of the first layout pattern of the photo mask on the wafer. In an embodiment, the illumination source is a laser source. In an embodiment, the illumination source is one of a coherent source or a partially coherent source. In an embodiment, the profile of the illumination source is either a circular profile having a radius between 1 cm and 20 cm and having a constant amplitude, Or a Gaussian profile with a standard deviation between 1 cm and 20 cm. In an embodiment, the illumination source of the optical system is a polarized illumination source with two time varying electric or magnetic components in a first direction and in a second directions perpendicular to the first direction. The first and second directions are perpendicular to a direction of travel of a beam of the polarized illumination source. The analyzer module further determines a first variance profile of the component in the first direction, a second variance profile of the component is the second direction, and a covariance profile between the components of the first and second directions of the polarized illumination source. The mask enhancer also assigns one of the first variance profile, the second variance profile, or the covariance profile to the profile of the illumination source, determines a final discrete profile of the assigned first variance profile, second variance profile, or the covariance profile, and determines a final second TCC operator of the assigned first variance profile, second variance profile, or the covariance profile. The mask projector also performs a projection of the first layout pattern of the photo mask by the assigned profile of the polarized illumination source on the wafer for the OPC operation or the ILT operation using the determined final discrete profile and the final second TCC operator. In an embodiment, the illumination source is one of a deep ultraviolet or an extreme ultraviolet illumination source.

In some embodiments, implementing the processes and methods mentioned above, adapts the target layout pattern to a modified target layout pattern by using projection simulation. The illumination source of the simulated projection is the illumination source of the optical system of the lithographic system that is sampled. The number of sampling points is adjusted such that the number of sampling points is not too many to create a calculation burden and so that the number of sampling points is not too few to generate a discrepancy between the simulated projection and the physical projection. Therefore, the described methods above provide an efficient number of sampling points to maintain the error between the simulated projection and the physical projection within a desired range without creating unnecessary calculations.