Illumination optimization for specific mask patterns

The present invention generally relates to methods and devices for microlithography imaging. More specifically, the present invention relates to devices and methods for optimizing the shape of an illumination according to a particular pattern being imaged.

Conventional Techniques Optical lithography is currently used in the manufacture of products of integrated circuits and other microfeatures such as programmable gate arrays. In the most general description, a lithography system connects a lighting system that supplies a projected beam of radiation, a support structure that holds patterning means, a substrate table that supports the substrate, and a patterned beam onto a target portion of the substrate. Includes a projection system (lens) for imaging.

[0003] The term patterning means is broadly interpreted as referring to an apparatus and structure that can be used to provide a patterned cross section to an incoming radiating beam, corresponding to a pattern generated on a target portion of a substrate. And. The term "optical valve" is also used in this context. In general, the pattern corresponds to a particular functional layer within the device generated in the target portion, such as an integrated circuit or other device.

An example of such a mechanism is a mask, which is usually held by a (movable) mask table. The concept of masks is well known in lithography, which includes mask types such as binary, alternating phase, decay phase shift, and various hybrid mask types. When such a mask is placed within the projected beam, the radiation incident on the mask is selectively transmitted (in the case of a transmissive mask) or reflected (in the case of a reflective mask) according to the pattern on the mask. The mask table can reliably hold the mask in a desired position within the incident projected beam, and can also reliably move the mask relative to the beam if desired.

[0005] Another example of such a mechanism is a matrix addressable surface that includes a viscoelastic control layer and a reflective surface. The basic principle behind such a device is that the addressed region of the (eg) reflective surface reflects the incident light as diffracted light, while the unaddressed region reflects the incident light as non-diffracted light. is there. An appropriate filter can be used to remove the non-diffracted light from the reflected beam, leaving only the diffracted light. In this way, the beam is patterned according to the addressing pattern of the matrix addressable surface. An alternative embodiment of the programmable mirror array uses small mirrors arranged in a matrix. Each mirror can be tilted about its axis by applying an appropriate local electric field or by using piezoelectric actuating means. Again, the mirrors are matrix addressable so that the addressed mirrors reflect the incoming radiation beam in a different direction than the unaddressed mirrors. In this way, the reflected beam is patterned according to the addressing pattern of the matrix addressable mirror. The required matrix addressing can be done using suitable electronic means. In both of the above situations, the patterning means can consist of one or more programmable mirror arrays. More detailed information about the mirror array referenced herein can be obtained, for example, from US Pat. Nos. 5,296,891 and 5,523,193, and PCT patent applications WO98 / 38597 and WO98 / 33096. These shall also be included in this application by reference. In the case of a programmable mirror array, the support structure can be embodied as a frame or table, for example fixed or movable as needed.

Another example is a programmable LCD array. In this case, the support structure can also be, for example, a frame or table. An example of such a structure is given in US Pat. No. 5,229,872. This is also included in the present application by citation.

[0007] For the sake of brevity, the rest of this document may identify and deal with examples with masks in several places. However, the general principles discussed in such examples shall be understood in the broader context of the patterning means described above.

[0008] The term projection system includes various types of projection systems. In the layman's understanding, "lens" usually means refractive optics, but here the term is used broadly to include, for example, catadioptric and catadioptric systems. Lighting systems may also include elements that operate according to any of these principles to direct, shape, or control the projected beam, which are also referred to below collectively or independently. Sometimes called a "lens".

[0009] In addition, the term "wafer table" can be used without implying that the substrate receiving the image is a silicon wafer, to support any substrate processed by the lithographic apparatus. Appropriate stage can be indicated.

[0010] The lithography projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, the patterning means can generate a circuit pattern corresponding to each layer of the IC, which pattern is an object on a substrate (silicon wafer) coated with a layer of radiation sensing material (resist). Can be imaged on a portion (consisting of one or more dies). Generally, a single wafer contains a network of adjacent target parts that are continuously irradiated one at a time by the projection system. Current equipment using mask patterning on a mask table can distinguish between two different types of machines. In one type of lithography projection apparatus, when irradiating each target portion, the entire mask pattern is exposed on the target portion at one time. Such a device is commonly referred to as a wafer stepper. The other device, commonly referred to as a step-and-scan device, gradually scans the mask pattern under the projected beam in a given reference direction (the "scanning" direction) as it illuminates each target area. Synchronously, the substrate table is scanned parallel or non-parallel to this direction. In general, a projection system has a magnification M (generally <1), so the speed V to scan the substrate table is the magnification M multiplied by the speed to scan the mask table. More detailed information about the lithographic apparatus described herein can be obtained, for example, from US Pat. No. 6,046,792. This patent is also hereby incorporated by reference.

[0011] In a manufacturing process using a lithographic projection apparatus, a pattern (eg, in a mask) is imaged on a substrate that is at least partially covered with a layer of radiation sensing material (resist). Prior to this imaging step, the substrate may be subjected to various procedures such as priming, resist coating, and soft baking. After exposure, the substrate may be subjected to other procedures such as post-exposure bake (PEB), development, hard bake, and measurement / inspection of imaged features. This sequence of procedures is used as the basis for patterning individual layers of devices, such as ICs. Such patterned layers may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, and chemical mechanical polishing. All of these are for completing the individual layers. If several layers are needed, the entire procedure or its transformation needs to be repeated for each new layer. Ultimately, there will be an array of elements on the substrate (wafer). These elements are then separated from each other by techniques such as dicing or sawing, from which individual elements can be mounted on carriers connected to pins or the like. More detailed information on such processes can be found, for example, in the book Microchip Fabrication: A Practical Guide to Semiconductor Processing, Peter van Zant, McGraw Hill Publishing Co. 1997, ISBN 0-07-067250-4. Practical Guidance for) can be obtained from the 3rd edition. This document is also included in the present application by reference.

[0012] For the sake of brevity, the projection system may be hereafter referred to as a "lens". However, the term is broadly interpreted as including various types of projection systems, including, for example, refraction optics, catoptrics, and catadioptric systems. The radiation system can also include components that operate according to any of these design types to direct, shape, or control the projected beam of radiation, which are referred to below. Collectively or alone, they may be referred to as "lenses." Further, the lithographic apparatus may be of a type having two or more substrate tables (and / or two or more mask tables). Such "multi-stage" equipment may use additional tables in parallel, or use one or more other tables for exposure while performing preparatory steps on one or more tables. Is also possible. Two-stage lithographic devices are described, for example, in US Pat. Nos. 5,969,441 and WO98 / 40791. These are also included in this application by reference.

[0013] As lighting systems evolve from conventional to produce annular, quadrupole, and more complex lighting shapes, the number of control parameters is now increasing. Traditional lighting patterns illuminate a circular area that includes the optical axis, and the only adjustment made to this pattern is the outer radius (σ)._r) Is to be changed. Circular lighting has an inner radius (σ) to define the ring to be illuminated._c) Must be specified. In a multi-pole pattern, the number of controllable parameters continues to increase. For example, in a quadrupole illumination shape, in addition to the two radii, the angle α of the poles defines the angle determined by each pole between the selected inner and outer radii.

At the same time, mask technology is also advancing. Binary intensity masks have been superseded by phase shift masks and other sophisticated masks. A binary mask simply sends, reflects, or blocks imaging radiation at a given point, while a phase-shifting mask sends or reflects light after some radiation is attenuated or phase-shifted. You can have them, or both. Phase shift masks are used to image features on the order of the wavelength of the imaging radiation or less. This is because the diffraction effect at these resolutions can cause inadequate contrast and line end errors, among other problems.

[0015] Various types of illumination shapes can be used to improve resolution, depth of focus, contrast, and other printed image features. However, each lighting type has some trade-offs. For example, improved contrast can be obtained at the expense of depth of focus. Each type of mask has performance that also depends on the pattern to be imaged.

[0016] Conventionally, a series of test wafers have been randomly exposed and compared in order to select the optimum illumination mode for forming a given pattern on the wafer. As mentioned above, in modern lighting systems, the number of variables that can be manipulated is increasing. As various sorts of variable settings increase, the cost of optimizing the illumination shape by trial and error becomes extremely high, and a quantitative method for selecting the illumination shape is required.

To address the previously identified needs and the like, the present invention provides a method of optimizing an illumination profile for a pattern of selected patterning means. This method: The step of defining the intertransmission coefficient function for the optical system, including the pattern of the illuminator and the selected patterning means; and the step of finding the relative relevance of the diffraction order to the imaging based on the selected pattern. It comprises the steps of calculating the optimized illumination shape from the intertransmission coefficient function and weighting the region of the illumination shape based on its relative relevance to the imaging of the diffraction order.

[0018] According to another aspect of the present invention, a device manufacturing method is provided. The method is: (a) supplying a substrate that is at least partially covered by a layer of radiation sensing material; (b) supplying a projected beam of radiation using an illumination system; (c) patterning means. The step (d) of projecting a patterned radiation beam onto the target portion of the radiation sensing material layer; and the step (d) of using the method described above to give a pattern to the cross section of the projected beam. Before, the cross-sectional intensity distribution in the projected beam generated in step (b) is adapted to the pattern used in step (c).

[0019] According to another aspect of the invention, a lithographic projection apparatus is provided. This method is: an illumination system for supplying a projected beam of radiation; a support structure for supporting the patterning means, the support structure in which the patterning means functions to pattern the projected beam according to the desired pattern. And; with a substrate table for holding the substrate; with a projection system for projecting a patterned beam onto the target portion of the substrate; this device further: the luminaire and the intertransmission coefficient function of the desired pattern. Is defined, the relative relevance of the diffraction order to the imaging is obtained based on the pattern generated by the patterning means, the optimized illumination shape is calculated from the intertransmission coefficient function, and the relative to the imaging of the diffraction order is calculated. It comprises a calculation means that weights the region of the illumination shape based on the relevance; and a selection means for selecting the cross-sectional intensity distribution in the projected beam emitted from the illumination system according to the illumination shape calculated by the calculation means.

[0020] According to yet another aspect of the present invention, there is provided a method of optimizing the selected mask design. This method is to: identify the critical features of the selected mask design; find an optimized illumination profile based on the diffraction order of the critical features; and reduce the number of pitches present in the selected mask features. To modify the selected mask design by using the selected optical proximity correction technique;

[0021] The present invention further provides a computer program for performing the methods described above.

Although it may be specifically mentioned herein that the device according to the invention is used in the manufacture of ICs, it will be expressly understood that such devices have many other possible uses. For example, it can be used in the manufacture of integrated optical systems, induction and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads and the like. In the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" in this document will be used in the more general terms "mask," "board," and "position of interest." It will be appreciated by those skilled in the art that each is considered to be replaced by.

The present invention will be further described below with reference to exemplary embodiments and accompanying drawings.

BEST MODE FOR CARRYING OUT THE INVENTION The present invention includes first mathematically modeling the imaging of a pattern onto a substrate (eg, from a mask), taking into account the details of the illumination source and the pattern. ..

[0025] There are two main methods for calculating an aerial image for a finite illumination source. These methods are Abbe's formalization and Hopkins' formalization. In Abbe's formulation, each point source in the illumination shape produces a plane wave incident on the pattern, and each of these point sources is imaged on the wafer. Since the point sources are spatially non-interfering, the total intensity in the wafer is the sum of the intensities produced by each of these point sources. Therefore, in Abbe's formulation, the integration in the illumination shape is done after the integration in the pattern.

[0026] Hopkins' formulation changes the order of integration. That is, the integration at the source is performed first. Hopkins' formulation defines a four-dimensional intertransmission coefficient (TCC), and the inverse Fourier transform of the TCC is the intensity of the image. The derivation of TCC is described, for example, in Born and Wolf's Principles of Optics, 6th edition, pp. 528-532. This shall also be included in this application by reference.

[0027] TCC is the autocorrelation of the projected pupil multiplied by the illuminated pupil. Figure 1 shows the TCC as a set of three overlapping circles. Explaining from left to right, the first circle is Lighting Hitomi J_sIt represents (α, β), where α and β are the coordinates of the illumination shape. For later calculations, J_sThe radius of is, for example, the maximum outer radius σ possible for the lithography equipment used for imaging._rCan be set to. Also for feasibility studies, and even larger σ_rTo clarify the advantages of σ_rCan be set to 1.0 or higher.

[0028] The central circle is (-mλ / P_xNA, -nλ / P_yRepresents the projected pupil K (α, β) centered on NA). The coordinate system is normalized by a factor of λ / NA, so the radius of K is 1.0. The circle on the right also represents the projected pupil, which is (pλ / P)._xNA, qλ / P_yNA) is the center. In these last two equations, m, n, p, and q correspond to separate diffraction orders, revealing that TCC is a four-dimensional (4-D) equation as described above. The diffraction order in the x direction is represented by m and p, and the diffraction order in the y direction is represented by n and q. Although x and y coordinates are used for this explanation, it will be appreciated by those skilled in the art that the following equation can be used by appropriately modifying the coordinate system to use an alternative coordinate system.

The TCC for the 4-D distinct points (m, n, p, q) is the integral of the shaded region where all three circles overlap. Since the structure is assumed to be periodic, the Fourier transform of the pattern is discrete and the TCC is discrete. In a continuous pattern image, the pitch can be lengthened until the adjacent features do not affect the Fourier transform of the target pattern. The TCC in Figure 1 is mathematically expressed by Equation 1.<img file="JP3867904B2_D0001.tif" />[0030] The TCC can be extended to include the effect of the pattern by defining the Diffraction Order Mutual Coefficient (DOCC). DOCC is specified in Equation 2. This is obtained by multiplying the TCC by the Fourier transform factor of the pattern.<img file="JP3867904B2_D0002.tif" />Further, the radiant intensity in the wafer can be calculated by the inverse Fourier transform of DOCC as shown in Equation 3.<img file="JP3867904B2_D0003.tif" />[0032] Since the projection optical system partially acts as a low frequency filter, thereby reducing the diffraction order, only a decimal number is important in the calculated image intensity. As a result, TCC is a band-limited function. The maximum order of x and y required can be calculated according to Equations 4 and 5, respectively. In each case, both negative and positive orders are required. For example, m is negative m_maxFrom positive m_maxUp to (-m_maxm + m_max). The size of the TCC is 2m, as both negative and positive orders are required._max+1 times 2n_max+1 times 2p_max+1 times 2q_maxIt is +1. Fortunately, however, TCC has a limited band, so it is not necessary to calculate all pattern diffraction orders. As in TCC, pattern diffraction order -m in the x direction_maxm + m_maxOnly order -n in the y direction_maxn + n_maxOnly needed.<img file="JP3867904B2_D0004.tif" />Substituting Equations 1 and 2 into Equation 3 gives Equation 6 for the radiant intensity in the wafer. As shown in Equation 7, by changing the order of integration, that is, by using Abbe's formula instead of Hopkins' formula, the part of the illumination pupil that most affects the imaging can be obtained. Note that each of Equations 6 and 7 spans two lines.<img file="JP3867904B2_D0005.tif" />Since α and β represent the coordinates of the illumination pupil, a new function J_optCan be specified. New function J_optIndicates which part (α, β) of the illumination shape is used for a given diffraction order (m, n, p, q) and is expressed by Equation 8. From Equation 8, this is the inverse Fourier coefficient (e)^ikx) Is multiplied and all six variables (m, n, p, q, α, β) are summed as shown in Equation 9, and the image intensity can be calculated.<img file="JP3867904B2_D0006.tif" />[0035] As will be revealed, J_optIs a 6-dimensional function, so it is difficult to apply it to lighting geometries. It is desirable to remove some of the six variables in order to best determine which part of the illumination shape is important for image formation.

[0036] The aerial image intensity I (x, y) is obtained by taking the inverse transformation for m + p and n + q. When m + p = n + q = 0, the aerial image intensity is unmodulated. Since one of the goals of lighting optimization is to remove the part of the lighting shape that has little or no effect on the modulation, it is possible to remove the part of the lighting shape where m + p = n + q = 0. it can. In order to remove these parts and further visualize the parts of the illumination shape that are important for image formation, by transforming the variables, a 6-dimensional J_optRemove two of the variables of the function (4 diffraction order) and convert it to a 4D function (2 diffraction order). J for this 4D function_opt-2DCalled. Equation 12 can be obtained by substituting Equations 10 and 11 into Equation 9 for I (x, y).<img file="JP3867904B2_D0007.tif" />[0037] In Equation 12, J_opt-2DConverts the variables according to equations 10 and 11 and then J for m and n_optIt can be seen as the sum of. Furthermore, by substituting Equation 8 into Equation 12, J_opt-2DCan be expressed as in Equation 13, and the intensity I (x, y) can be expressed as J in Equation 14._opt-2DCan be written as a function of.<img file="JP3867904B2_D0008.tif" />[0038] Function J_opt-2DWhen the value is calculated, indicates an important part of the illumination shape for each diffraction order. J_opt-2DIs weighted by each diffraction order T (m, n), so a larger diffraction order has a greater effect on the aerial image.

[0039] A starting point for the optimum illumination shape for a particular pattern, J_totIt can be shown that J for η and ξ, as shown in Equation 15._opt-2DSum up and J_opt-2DIt is obtained by subtracting (α, β, η = 0, ξ = 0). In Equation 15, when η = 0 and ξ = 0, the aerial image is unmodulated and J_opt-2DThe (α, β, η = 0, ξ = 0) component represents zero order or DC light. The total amount of DC light is increased by points in the illumination that do not contribute to imaging. This is not very beneficial as the increased DC light does not cause modulation, and as a result the depth of focus can be shallow.

[0040] Therefore, J_totIllumination shape minimizes the amount of DC light, resulting in improved process windows. Expression J_totCan be used to indicate which parts of the luminaire are of high (or low) importance to image formation.<img file="JP3867904B2_D0009.tif" />[0041] Since the illumination shapes and patterns are combined, changing the optical proximity correction (OPC) will affect the diffraction order, and thus J._totAffects. As a result, as will be appreciated by those skilled in the art, using repeated processing by the OPC engine and the lighting engine, the initial lighting shape J_totAnd you have to make several changes to the pattern. In addition, patterns and illumination shapes need to be adjusted to optimize specific imaging criteria (depth of focus (DOF), line end (EOL), sensitivity to aberrations, etc.), which is optimization software. It can be done by wear. However, it is the pattern as a whole, not the OPC features, that has the greatest effect on the optimal lighting shape, so J._totIs the optimal initial illumination shape, which will converge fastest due to iterative optimization of the illumination shape and pattern.

[0042] Initial illumination shape J_totCan be represented by a grayscale illumination shape with continuous intensity values in the range 0 to 1. Such grayscale illumination shapes can be generated by diffractive optics (DOE) or by using dithered chrome-plated quartz plates. If grayscale illumination geometries are not possible or desirable, illuminator profiles can be forced to 0 and 1 only by applying thresholds to grayscale. In this case, values above the threshold are rounded up to 1, and values below the threshold are rounded down to 0. Any threshold can be applied, or the optimum threshold can be found by simulating the process window or by repeating the test run.

Example 1: J outlined above_totThe technique for calculating the brick wall separation pattern was applied. The 150 nm pattern was reduced to 130 nm and 110 nm design criteria and imaged by a numerical aperture (NA) 0.8 step-and-scan lithography system. Figure 2 shows the separation pattern of the 130 nm design standard.

FIG. 3 shows the magnitude of the diffraction order of this mask feature. In Figure 3, the largest order is the (0,0) order or DC background light. The order that contributed most to the imaging is the (± 2,0) order, which represents the vertical brick in the brick wall pattern. The other important order is (± 1, ± 1), which represents a clear area and defines the end of the separation pattern. Higher orders also help define the two-dimensional structure, such as the ends of each line. Since the diffraction pattern is not constant, the weighting factor in DOCC changes depending on the order, suggesting that the mask pattern affects the method of illumination.

Substituting the diffraction order coefficient T (m, n) in FIG. 3 into Equation 13, J_opt-2DCan be calculated. This is shown in Fig. 4. As you can see from Figure 4, J_opt-2DThe largest contribution to is on the order of (η = 0, ξ = 0). The (0,0) order does not contribute to imaging and makes the DOF shallow. As Equation 15 shows, this (0,0) order is the total illumination J._totCan be subtracted from. If the (0,0) order is not taken into account, the largest contribution is the (η = ± 2, ξ = 0) diffraction order, which represents the formation of separation lines along the x direction. Another component that is large and defines the end of the separation line is the (η = ± 1, ξ = ± 1) diffraction order. The (0, ± 2) diffraction order is rather small, but orders larger than this are coupled in the η = 0 and ξ = ± 2 regions of the lens. These areas also help define the end of the line. The DOCC method shows how to sample the illumination pupil to improve image formation and is an effective method for understanding the imaging of brick wall separation patterns.

[0046] Equation 15 can be used to calculate the illumination pupil of the 130 nm design standard brick wall pattern. This is shown in Fig. 5. FIG. 5 shows that the most important region for image formation is the outer part of the illumination shape along the x-axis. These outer parts form an elliptical dipole. In addition to these elliptical dipole elements, the center of the illumination pupil contributes significantly to image formation. As mentioned above, lighting pupils can be performed in grayscale or binary lighting profiles.

Grayscale illumination may be possible, depending on the device used. Grayscale illumination means controllable illumination intensity, with a choice of normalization levels from 0 to 1 for at least a given portion of the illumination shape. For example, such illumination intensity control can be performed using diffractive optics (DOE) in the illumination system. In this case, for example, the illumination shape can be implemented as shown in FIG. However, some of the theoretically calculated local spikes found in FIG. 5 are removed after filtering the illumination information with a low frequency filter as a result of the projected optical system, as described above. Therefore, when designing the illumination shape, the filtered spikes should be ignored.

[0048] When a binary illumination shape is used, that is, when only binary values (0 or 1) are possible for the intensity of the luminaire, as a basis for assigning a value of 0 or 1 to each point of the illumination shape. The threshold must be selected. For example, if a threshold of 0.8 is selected, the intensity value of the luminaire above 0.8 is rounded up to 1, and the value less than 0.8 is rounded down to 0. Other thresholds can be applied if desired.

Example 2: Using grayscale for the binary method, assuming a maximum outer radius σ of 0.88, a binary illumination shape is designed for the same brick wall separation pattern and is shown in FIG.

The optimized illumination geometry performance of FIG. 6 was then simulated for binary masks on NA = 0.8 and λ = 248 nm step-and-scan lithography equipment to simulate annular illumination. Compared with performance. In this simulation, the numerical aperture exceeded 0.7, so a vector (thin film) imaging resist model was used. In this model, the resist is a type with a refractive index of n = 1.76-j0.0116) and a thickness of 400 nm, n = 1.45-j0.3 on a polysilicon material with n = 1.577-j3.588. It is on top of another type of 66nm that has. Figures 7 and 8 show the annular illumination (σ)._in= 0.58 and σ_{out out}= 0.88) and optimized lighting equipment (σ)_{out out}The results of = 0.88) are shown respectively. Both Figures 7 and 8 show the results of the cross section in the center of the separation region and the top-down simulation results. In these figures, the Bossung plot B is calculated from the aerial image threshold by averaging the intensities through the resist, and the resulting line width lw is graphed for the intensity of the threshold with respect to the focal point f. To do. This technique tends to overpredict DOF as a loss of thickness and does not take into account the slope of the resist profile. Perhaps we need a resist model that at least calculates the thickness loss. In each of the figures, the top-down results are drawn as a solid curve at the optimal threshold (optimal dose) as calculated by the Bossung plot. Compare these simulated threshold images with the actual mask data shown by the dotted straight lines.

FIG. 7 shows an annular illumination (σ)._in= 0.58 and σ_{out out}The simulation result of the brick wall separation pattern of the 130 nm design standard is shown for the binary mask feature at 0.8 NA using = 0.88). This annular setting has a DOF of approximately 0.4 μm from -0.4 μm to 0.0 μm focal point. The contrast of the resist is low throughout all focal points and can be imaged with a low contrast resist. However, at this low intensity contrast, the mask error increasing factor (MEEF) is large and the exposure latitude (EL) is small. Also, the top-down image in Figure 7 shows that the line end (EOL) shortening is about 20 nm, which allows the line to be slightly extended and fixed for the 130 nm design criteria. .. However, as design criteria continue to shrink, line extensions are no longer feasible, as extended lines can collide with other features. Therefore, it is desirable to fix the EOL by lighting.

FIG. 8 illustrates the simulation results for the 130 nm design criteria brick wall separation pattern for binary mask features with a NA of 0.8 and the optimized binary illumination shape of FIG. Optimal illumination shapes have a DOF of approximately 0.6 μm, from -0.45 μm to +0.15 μm focal point. Comparing the cross-sectional image of FIG. 8 with that of FIG. 7, the optimized illumination shape has higher contrast throughout all focal points than the annular illumination. This large contrast suggests that the MEEF for the optimized illumination shape is small compared to the annular illumination and the exposure latitude for the optimized illumination shape is large. Another advantage of this optimized illumination shape is that the performance at the end of the line is improved compared to annular illumination. The top-down image in Figure 8 shows that this optimized illumination shape can maintain EOL without extending the lines on the pattern, which is advantageous for bolder reductions in design criteria. ..

Example 3: The results for the binary mask (BIM) in Figures 7 and 8 were compared with the simulation results for the chromeless mask (CLM). A chromeless brick wall separation pattern was designed from the experimental results of software simulation by a method known to those skilled in the art. Chromeless technology requires light on the order of (0,0) to fully benefit from the improved DOF gained by off-axis lighting. Experimental results from the simulation support the need for light on the order of (0,0). For this, the dithering layer must be dithered or halftone. The pitch of the halftone may be selected so that the first order in the dithering direction does not enter the projection pupil. In this example, λ / [NA (1 + σ)_{out out})] Dithered the line vertically with a pitch of less than. However, the duty cycle of dithering must be adjusted to optimize the amount of light on the order of (0,0) for optimal DOF and pattern fidelity. Simulation results for CLM showed a halftone pitch of 155 nm with a 50% duty cycle (77.5 nm chromium island). At this pitch, the (0, ± 1) order is largely prevented from entering the projection pupil. However, this duty cycle must be adjusted to maximize DOF by computer-aided design tools.

Example 4: Simulation results for a 130 nm design reference layer are illustrated for a CLM with a 155 nm halftone pitch and a 50% duty cycle. 0.8 NA and annular lighting (σ_in= 0.58 and σ_{out out}The CLM was exposed with a device of λ = 248 nm according to = 0.88). The CLM in this annular setting had a DOF of 0.5 μm (from -0.4 μm focus to +0.1 μm focus). The ring-shaped CLM had a larger DOF and better contrast throughout all focal points than the ring-shaped BIM. This indicates that CLM performance was superior to BIM masks. The results of the top-down simulation show that the EOL performance by CLM is theoretically superior to the EOL performance by BIM, and that CLM more well defines the landing area of the contact hole than BIM. I showed that I was able to do it.

Example 5: The simulation results for the 130 nm brick wall separation pattern separation layer are illustrated for a device with a NA of 0.8 and an optimized elliptical dipole shown in FIG. 6 at λ = 248 nm. These results were simulated using the same reticle as the CLM reticle used in the previous example with a 155 nm halftone pitch and a 50% duty cycle. The CLM exposed with this optimized illumination shape had a DOF of 0.7 μm (-0.5 μm to +0.2 μm), an improvement of 40%. The Bossung plot showed that the equifocal intensity was about 0.21. In addition, model-based OPC techniques could be applied to adjust the reticle for accurate line width magnitude and further improve performance. To correct the line width, for example, biasing and changing the halftone duty cycle may be performed. Top-down simulation results show that CLM can define the landing area of the contact and maintain CD uniformity. This elliptical illumination shape reduced constrictions and other line width discrepancies. In addition, the CLM reticle can be biased to improve DOF, which should improve EOL performance. In addition, model-based OPCs should be able to further correct EOL.

Example 6: Optimized illumination shapes were generated by equations 13 and 15 for the 110 nm design criteria separation layer using the mask pattern of FIG. To visualize the sampling of the lighting pupil, J_opt-2DIs shown in FIG. 9, with the x-order (η = m + p) shown in the horizontal direction and the y-order (ξ = n + q) shown in the vertical direction. Similar to FIG. 4 for the 130 nm design criterion, the largest contribution to the 110 nm design criterion in FIG. 11 is on the order of (η = 0, ξ = 0). This light on the order of (0,0) is harmful to DOF, and as shown in Equation 15, J_totIs removed at. Also, FIG. 9 shows that the (± 1, ± 1) order, not the (± 2, 0) order, makes the greatest contribution to the optimization of the illumination shape. This is due to the fact that the 110 nm design criteria are too aggressive for a 248 nm device with NA = 0.8, and a slightly higher NA is preferred to achieve this resolution. The order that contributes most to defining the separation line width is the (± 2, 0) order. However, the (± 2, 0) order is at the far edge of the illumination shape (0.8 &lt;σ &lt;1.0), which can improve the implementation of 110 nm design criteria at this wavelength when σ is 1. It is shown that.

Using the results of Equation 15 and FIG. 9, FIG. 10 shows the optimized illumination shape for the 110 nm brick wall separation layer. FIG. 10 shows that the illumination shape regions that contribute most to image formation are the central small portion and the distant edge of the illumination shape. FIG. 11a illustrates one possible embodiment of this illumination shape. To print more aggressive design criteria using the 248 nm device and impose a limit on the projected numerical aperture, σ is 1.0 and has a small sector (σ ring width is 0.2), as shown in Figure 11b. Use the illumination shape.

[0058] Embodiments of the present invention include the selection of critical cells or specific gates. These critical features are then processed to J as described above._totTo ask. Section 1 showed that the lighting shape depends on the pattern. Therefore, for all critical features, a single illumination shape that optimizes the process window can be generated if there is no significant difference in pitch for the critical features. Figure 12 shows the critical gate g₁, G₂, G₃And an example of a circuit with a critical cell cc is shown. The diffraction order of these tagged critical features can be calculated, and by using the theory already described, the optimized illumination shape can be calculated. After calculating the optimized illumination shape, the process window can be calculated and compared with process windows with other illumination shapes.

Another way to optimize the illumination / pattern interaction is to modify the pattern design with scatter bars. The scatter bar truncates the pitch from a semi-continuous function for ASICs or logical designs. After arranging the scattering bars, the pitch is reduced. This can be demonstrated in the simulation software by arranging the scattering bars with an edge-to-edge separation of 0.61λ / NA. In FIG. 13, the design of FIG. 12 is modified by adding a plurality of scattering bars. The illumination shape can then be optimized for this modified design. The lighting shape process window performance optimized for designs with scattering bars can then be compared to the lighting shape process window optimized without having scattering bars. Since designs with scatter bars cut off the pitch, the combination of scatter bars and optimized off-axis illumination (OAI) has the maximum possible DOF process window.

Another concept for performing illumination geometry optimization is by arranging scattering bars based on spatial width (SW) considerations. Scatter bars are placed by rule-based OPC. This rule can be specified by the spatial width. Simulation software should be able to calculate the probability density function (pdf) of the spatial width with and without scatter bars. Then J as shown in Equation 16_opt-2DLighting can be optimized in consideration of pdf by changing. Assuming that the vertical and horizontal lines are infinite, it is also possible to calculate the diffraction order T (m, n). In Equation 17, the diffraction order is calculated as a function of m and n. Where w is the line width, τ is the intensity transmittance of the reticle, and P_x= SW_x+ w and P_y= SW_y+ w is the pitch in the x and y directions, respectively.<img file="JP3867904B2_D0010.tif" />Equation 17 is a matrix of four equations, with m = n = 0, m = 0, n 0, m 0, n = 0, and m 0, n 0 in the order of presentation. is there.<img file="JP3867904B2_D0011.tif" />[0062] Since it is suggested that some pitches are not as important as others, calculating the optimal illumination shape by pdf raises some problems. If all gates in the pdf are considered critical, then the pdf must be modified by a weighting factor. This weighting factor is a function of pitch called wf (Px). With this weighting factor, all critical pitches must be treated the same so that wf (Px) · pdf (Px) = 1. This weighting coefficient shall be added to Equation 16 by replacing pdf (Px) in Equation 16 with wf (Px) · pdf (Px). If all of the pitches are critical, the weighting factors do not help determine the optimization and it is difficult to generate an optimized illumination shape without changing the design (of the pattern).

[0063] One solution to this problem is to modify the design by adding the scatter bar described above. Scatter bars help reduce the pitch for separated features. Once a scatter bar is added to the design, previously separated features tend to act as dense features. For this reason, the scattering bar truncates the pitch from continuous pdf to more discrete pdf. FIG. 14 is an example pdf of a logical pattern with features oriented in the y direction (ie, the "vertical" direction) with and without the scatter bar. FIG. 14 shows the vertical gate space width (μm) on the x (horizontal) axis. In the unchanged design D without scatter bars, there are three separate bumps in the pdf at space widths of 0.2, 0.6, and 1.5 μm. After arranging the scattering bars, in D + SB, the number of pitches is reduced so that most of the space width is at a dense pitch of 0.2 μm. By changing this pdf, the probability that the lighting shape can be optimized increases.

[0064] The overall lighting shape for a design that has both horizontal (x-axis) and vertical features is the sum of the horizontal and vertical lighting shapes. Illumination shape for vertical features σ_cxFocus on the horizontal features σ_cyIf you want to focus on<img file="JP3867904B2_D0012.tif" />If so, the optimal illumination shape is the "conventional" quadrupole illumination shape. In other cases, this type of analysis results in a quadrupole illumination shape rotated 45 degrees.

The 5 lighting techniques presented herein can be extended to account for aberrations. The inclusion of aberrations allows the operator to determine which portion of the illumination shape is coupled to the aberrations. The amount of coupling is directly related to the sensitivity of the image intensity to aberrations. Understanding this coupling may allow the illumination geometry to be modified to minimize design aberration sensitivity.

The projected pupil K (α, β) for scalar imaging includes an exponential function of the wave plane represented by the tilt factor, out-of-focus, and Zernike polynomials. This scalar imaging pupil is shown in Equation 18. This pupil can be further divided into two parts. That is, non-deviation Hitomi K₀(α, β) and deviant pupil (exponential function of wave surface), these two parts are multiplied together as shown in Equation 19.<img file="JP3867904B2_D0013.tif" />From Equation 22, the wave plane can be written as a linear approximation. This is shown in Equation 23. By substituting Equation 23 into Equation 22, the linear approximation for the projected pupil K (α, β) can be calculated by Equation 24.<img file="JP3867904B2_D0014.tif" />Since TCC is a function of the projected pupil K (α, β), the linear approximation to the pupil in Equation 24 shows that the TCC can be represented by a linear approximation. This is achieved by substituting Equation 24 into Equation 1. This gives Equation 25. Again, the TCC of Equation 25 can be simplified as shown in Equation 26 by ignoring the two or more power terms.

[0069] The wave surface W (α, β) is most often expressed by the sum of Zernike fringe polynomials, as shown in Equation 21. Using the linear theory of aberration, the exponent e^xCan be expressed by the expansion of the Taylor series. The Taylor series expansion is valid for small x, and according to previous studies, Z_vIf is less than 0.04λ, good agreement is shown for the aerial image. In equation 22, e^xShows the Taylor series expansion of. Equation 22 truncates two or more power terms, which is Z_vValid when is less than 0.04 (0.04²= 0.0016, which can be ignored).<img file="JP3867904B2_D0015.tif" />[0070] Non-deviation TCC, TCC of equations 27 and 28₀(m, n, p, q), and deviant TCC, TCC_vBy specifying (m, n, p, q) respectively, TCC as shown in Equation 29₀And TCC_vTCC can be represented by a linear function of.<img file="JP3867904B2_D0016.tif" />Since TCC can be constructed as a linear approximation as shown in Equation 29, J_optCan also be written as a linear approximation. J_optA linear approximation to J_optEq. 8 is used, and Eq. 30 is obtained by following the methodology for linear approximation of TCC as outlined in Eqs. 18 and 29.<img file="JP3867904B2_D0017.tif" />Next, J_optEquation 30 for, as shown in Equation 33, non-deviation J_opt0And deviation J_optvCan be divided into the sum of. In equations 31 and 32, J_opt0And J_optvThe definitions of are shown below.<img file="JP3867904B2_D0018.tif" />Equation 32 describes a portion of the illumination shape that is coupled to a particular aberration. The amount of coupling affects the image intensity and helps to understand the sensitivity of aberrations to illumination. By combining equations 31 and 32, J_optCan be written as a linear approximation.<img file="JP3867904B2_D0019.tif" />[0074] In another aspect of the invention, a weighting factor is introduced to respond to a particular metric, including, for example, depth of focus (DOF), image log tilt (ILS), image tilt (IS), or aberration sensitivity. Can be maximized or minimized. Optimal J in Equation 15 to include these weighting factors, as shown in Equation 34._totCan be changed.<img file="JP3867904B2_D0020.tif" />[0075] In general, a photoresist reacts in proportion to the logarithm of the intensity of the light incident on it. As the intensity, and thus the logarithm of intensity, increases, the features are printed in the resist with higher fidelity (ie, the resist profile improves and the process window improves). Therefore, it is desirable to maximize the logarithmic change in intensity (ILS). ILS is defined in Equation 35.<img file="JP3867904B2_D0021.tif" />[0076] Since the derivative of intensity changes faster than the reciprocal of intensity, Eq. 35 is further increased by increasing the derivative of intensity. The intensity can be calculated from Equation 3, and the derivative of the intensity with respect to x is defined in Equation 36. By the derivative of x, the weighting function w, as shown in Equation 37._xIs obtained. Similarly, as shown in Equation 38, the weighting function w for y_yCan be defined.<img file="JP3867904B2_D0022.tif" />Since the pattern and intensity features are two-dimensional, the norm of inclination can be used to indicate the change in intensity with respect to position. Equation 39 defines the norm of intensity gradient. This allows us to J in Equation 34._totA weighting function can be defined to calculate. Equation 40 defines a weighting function for maximizing the image log tilt.<img file="JP3867904B2_D0023.tif" />Equation 40 shows that the weighting function is 0 when m + p = 0 and n + q = 0. When m + p = 0 and n + q = 0, these orders make no contribution to image modulation and reflect the DC contribution to the image. Furthermore, as m + p and n + q increase, w_ILSIncreases. This indicates that higher order diffraction order terms are weighted more and contribute more to ILS.

[0079] In addition to maximizing the ILS, the improved ILS to minimize the intensity response to the focus increases the depth of focus of the process. Focus is explained by Hitomi K (α, β). Hitomi K (α, β) is shown in Equation 41, where the focus is shown as z. Equation 41 can be divided into two terms. That is, as shown in Equation 42, there are z-dependent terms (out-of-focus terms) and z-independent terms (out-of-focus terms).<img file="JP3867904B2_D0024.tif" />[0080] By setting the derivative of the intensity with respect to z to zero, the fluctuation of the intensity due to the focal point z can be minimized. By substituting Equation 42 into Equations 1 to 3, the cost function f (α, β, z) can be defined as shown in Equation 43. This is a cost function of the intensity imaging term that depends on z.<img file="JP3867904B2_D0025.tif" />On the other hand, the cost function f (α, β, z) is minimized when g (α, β, m, n, p, q) is equal to zero (see Equation 44 below). .. In Equation 44, the phase term is removed because the derivative for z is equal to zero only if the magnitude term is equal to zero. When g (α, β, m, n, p, q) is zero, the pupil region (α, β) for a given order (m, n, p, q) has the least sensitivity to focus. Is. These are the most desirable areas of the pupil for constructing lighting geometries. In equation 45, the weighting function w_focusDefine (α, β, m, n, p, q). This weighting function is equal to 1 in the region with the lowest sensitivity to focus and equal to 0 in the region with the highest sensitivity to focus. Equation 46 then defines a new weighting function that maximizes the ILS across all focal points, which can be used to change the illumination shape.<img file="JP3867904B2_D0026.tif" />[0082] By the above methodology, the sensitivity of intensity to the influence of focal point and aberration can be minimized. Since the effect of focus on intensity is minimized, the effect of intensity on specific aberrations is minimized. This is desirable for any pattern that has been demonstrated to be highly sensitive to certain aberrations. The projected pupil in Equation 19 has the deviation term K, as shown in Equation 47._aNon-deviation term K multiplied by (α, β)₀It can be written as (α, β).<img file="JP3867904B2_D0027.tif" />Specific Aberration Z_iIntensity sensitivity to Z_iIt can be minimized by setting the derivative of the intensity to zero. By substituting Equation 47 into Equations 1 to 3 and taking the derivative of the intensity, aberration sensitivity is minimized when h (α, β, m, n, p, q) in Equation 48 is equal to zero. ..<img file="JP3867904B2_D0028.tif" />[0084] Equation 48 can also be written in a simplified manner as in Equation 49. Weighting function w in Equation 50_abDefine (α, β, m, n, p, q), which is Z_iIn the pupil region (α, β) where the sensitivity is the lowest, it is equal to 1 and Z_iIs equal to 0 in the region of highest sensitivity.<img file="JP3867904B2_D0029.tif" />[0085] Next, in Equation 51, the specific aberration Z_iYou can define a weighting function that minimizes the ILS sensitivity to. Furthermore, in Equation 52, the specific aberration Z_iA weighting function can also be defined that minimizes the ILS sensitivity to and maximizes the ILS across all focal points. Any of these equations can be substituted into Equation 34 to calculate the luminaire with the optimum response to a given metric.<img file="JP3867904B2_D0030.tif" />[0086] FIG. 15 is a schematic view of an example of a lithography apparatus used according to the present invention. This device includes a radiation system. The radiation system consists of a lamp LA (which could be an excimer laser, for example) and a lighting system. The illumination system can include, for example, beam shaping optics EX, integrator IN, and condenser lens CO. The radiation system supplies a projected beam PB of radiation. For example, the radiation system can supply ultraviolet, deep or ultra-ultraviolet radiation. Also, in general, radiation systems can also supply soft X-rays or other forms of radiation.

The first object table or mask table MT holds the mask MA. The mask MA includes a pattern region C containing a mask pattern to be imaged. Since the mask table MT can move with respect to the projected beam PB, it is possible to illuminate different parts of the mask. Alignment Mask M to determine if the mask is properly aligned with the substrate or wafer W₁And M₂Is used.

The projection system PL projects the projection beam PB onto the wafer W. Wafer W has two alignment masks P₁And P₂These include masks M before starting imaging.₁And M₂Is aligned with. The wafer W is supported by a substrate table WT, which can be moved relative to the projected beam to expose different parts of the wafer W. In this way, the mask pattern C can be imaged on different target portions c of the wafer W. An interference position monitor IF is used to ensure that the wafer table WT is in the correct position with respect to the position of the mask table MT.

Although the present invention has been described in connection with specific embodiments, the present invention is not limited to the disclosed embodiments, and conversely, various modifications and equalities included in the claims. It will be understood that it is intended to include the composition of.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram of an intertransmission coefficient function for a generalized image forming system.

FIG. 2 is an example of a mask feature by microlithography of a brick wall separation pattern.

FIG. 3 is a diagram of the diffraction order of the mask features of FIG.

FIG. 4 is a map of the calculated optimized 4D illumination shape for the mask features of FIG.

FIG. 5: Calculated initial grayscale illumination geometry (J) for the mask feature of FIG._tot).

FIG. 6 is a binary representation of the illumination shape of FIG.

FIG. 7 shows an analysis of the printed matter of the mask features of FIG. 2 printed by the annular illumination shape.

FIG. 8 shows an analysis of the printed matter of the mask features of FIG. 2 printed with an optimized elliptical illumination shape.

FIG. 9 is a map of the calculated optimized 4D illumination shape for the mask features of FIG. 2 reduced to 110 nm design criteria.

FIG. 10 is a calculated initial grayscale illumination shape for the mask features of FIG. 2 reduced to 110 nm design criteria.

FIG. 11a is a binary representation of the illumination shape of FIG. 10 with different σ values.

FIG. 11b is a binary representation of the illumination shape of FIG. 10 with different σ values.

FIG. 12 is an example of a mask pattern showing critical gates and cells.

FIG. 13 is a mask pattern of FIG. 12 with auxiliary features added to reduce the number of pitches in the pattern.

FIG. 14 compares the probability density functions of the spatial widths of the mask patterns of FIGS. 12 and 13.

FIG. 15 is a schematic view of an apparatus for microphotolithography.