1.  Field of the Invention
The present invention relates to incorporating lens aberration information into various process flows and particularly to allowing stepper users to perform stepper and field aberration dependent simulations without direct access to the lens aberration information. 
2.  Description of the Related Art
To fabricate an integrated circuit (IC), a physical representation of the features of the IC, e.g. a layout, is transferred onto a plurality of masks.  The features make up the individual components of the circuit, such as gate electrodes, field oxidation regions, diffusion regions, metal interconnections, and so on.  A mask is generally created for each layer of the IC.  A mask includes clear regions and opaque regions, wherein the pattern of these two regions defines the features of a particular semiconductor layer. 
Typically, a mask includes patterns that can be transferred to the entire semiconductor substrate (for example, a wafer) in a single exposure.  In contrast, a reticle must be stepped and repeated to expose the entire wafer.  However, for ease of reference herein, the term “mask” refers to either a reticle or a mask. 
To create a mask, the data representing the layout for a corresponding IC layer can be input, after fracturing, into an electron beam or optical exposure system, which writes a pattern for creating IC features using the data onto a mask (e.g. quartz substrate).  Once a mask has been created, the pattern on the mask can be transferred onto the wafer surface using a lithographic process. 
In one exemplary lithographic system, refractive optics can be used to transfer a pattern from a mask onto a portion of the total area of a wafer. ( Note that in the case of certain next generation lithographic (NGL) systems, the optics may be reflective, e.g. extreme ultraviolet (EUV), 157 nm, etc.)  In one embodiment, this smaller field size is approximately {fraction (1/50)} the area of a 100 mm wafer.  Because only a portion of the wafer can be written at one time, certain components of this lithographic system must be physically “stepped”, or “scanned”, across the wafer to expose other portions of the wafer.  Lithographic systems that perform a stepping operation are called “steppers” and those that perform a combination stepping and scanning operation are called “scanners”.  The techniques described herein are equally applicable to steppers and scanners.  The term “stepper” as used hereafter refers to both steppers and scanners. 
FIG.  1 illustrates a stepper 100 including illumination optics 102 that direct radiation from an illumination source 101, such as a mercury lamp, to a mask 103.  A projection lens 104 focuses the radiation emitted by mask 103 onto a portion of wafer 105, thereby transferring the mask feature (in this case, an “X”) onto that portion.  Although projection lens 104 is shown as a single component, multiple (e.g. 20-40) simple lens elements are actually mounted within a casing in an attempt to correct for optical aberrations. 
In an ideal system, all rays emanating from a point in the object plane (i.e. mask 103) converge to one point in the image plane (i.e. wafer 105), thereby providing a clear image.  FIG.  2A illustrates a simplified optical system 200 including two thin lens 201 and 202, positioned along an optical axis 207, that provide imaging of an on-axis object point P(object).  Note that P(image) is the corresponding Gaussian image point for P(object).  An aperture stop 203 limits the solid angle of the rays from P(object).  An entrance pupil 205 is defined as the image of the aperture stop by surfaces between aperture stop 203 and P(object), whereas an exit pupil 204 is defined as the image of the aperture stop by surfaces between aperture stop 203 and P(image).  A ray passing through the center of aperture stop 203, entrance pupil 205, and exit pupil 204 is called the chief ray.  Rays other than the chief ray are called marginal rays. 
If the rays from P(object) are followed through system 100 to exit pupil 204 such that each ray travels an optical distance equal to the chief ray, the surface passing through the rays' end points is called the system wavefront for P(object).  If the wavefront is spherical, see wavefront 208 shown in FIG.  2B, then the Gaussian image is considered “perfect”.  On the other hand, if the wavefront includes deviations from the spherical form, see wavefront 209 shown in FIG.  2C, then the Gaussian image is considered to be aberrated.  Note that the rays of aberrated wavefront 209 fail to converge and instead create two object points P(object1) and P(object2).  An optical aberration can be any influence that causes rays from an image point to not converge as an object point in the image plane. 
To account for aberrations in a system, an assumption can be made that the exit pupil is illuminated by a spherical wave, but that an imaginary phase-shifting plate exists within the aperture, thereby deforming the wavefront that leaves the aperture.  If the phase error at a point (x,y) in the exit pupil is represented by kW(x,y), wherein k=2Π/λ and W is an effective path length error, then the complex transmittance P of the imaginary phase-shifting plate is equal to:P(x,y)=P(x,y)exp[jkW(x,y)]  Equation 1
W(x,y) can be reduced to a set of Zernike polynomials [Zi(ν, Φ)] that describe the types of aberrations.  For example, Zernike polynomials exist to describe defocus, x-astigmatism, y-astigmatism, x-coma, y-coma, three-leaf clover, and spherical aberrations. 
This lens aberration information can be used as input data to various tools, thereby improving the accuracy of the tools' output data.  Currently, to obtain this lens aberration information, the users must contact the stepper companies directly.  However, stepper companies closely guard this information because it can disclose how the lenses of their steppers were optimized, i.e. balancing the various aberrations, which is considered a trade secret to the lens manufacturers (which are sometimes part of the stepper companies) and/or the stepper companies.  Therefore, such information is rarely given, and even then typically only to users that have strategic relationships with the stepper companies. 
Moreover, users now purchase a stepper based only on user-specified feature sizes.  Users who understand that a particular type of aberration significantly impacts their specific patterns could use the lens aberration information as another criterion for stepper purchase.  In other words, the lens aberration information could be a reason not to accept a particular stepper, e.g. tendered for delivery by the manufacturer.  Thus, it is in the best interests of the stepper companies to provide the information to the stepper users in a controlled fashion. 
Finally, this lens aberration information, even if provided by the stepper companies, is highly complex.  For example, this aberration information can vary, not only from one type of stepper to another type of stepper, but even from one lens to another of the same model.  Therefore, many users could have difficulty fully leveraging this information to their advantage. 
Based on all of the above reasons, stepper companies would prefer to prevent all disclosure of lens aberration information.  However, lens aberration can significantly affect the printing quality of sub-partial coherence features, particularly when trying to print features that are small compared to the wavelength of the exposure radiation λ.  Specifically, lithography must be aggressive, e.g. indicated by a process-related parameter k1 below 0.75, to print these small features.  Note that the minimum resolution, or critical dimension, is given by the formula CD=k1 (λ/NA).  Conventionally, for lithography using k1 above 0.75, the effects from the aberration of the imaging system can either be ignored or represented as one set of polynomial coefficients across the entire field.  In contrast, as feature sizes decrease, the variation of aberrations across the field may become too significant to ignore.  If that occurs, then sub-fields indicating variations of the aberrations can be provided, wherein each sub-field can be defined by a different set of aberration coefficients. 
Therefore, users are increasingly concerned regarding lens aberration and are requesting disclosure of this previously confidential information.  Therefore, a need arises for a method of allowing users to perform stepper and field aberration dependent simulations without directly disclosing the lens aberration information, thereby fulfilling the needs of both the users and the stepper companies.