Optics: measuring and testing – Lamp beam direction or pattern
Reexamination Certificate
2002-01-02
2003-11-25
Font, Frank G. (Department: 2877)
Optics: measuring and testing
Lamp beam direction or pattern
C382S173000
Reexamination Certificate
active
06654106
ABSTRACT:
FIELD
This disclosure pertains to optical systems intended for use with a beam of light (e.g., ultraviolet light), charged particles, X-rays, and the like. More specifically, the disclosure pertains to methods and apparatus for obtaining a measurement of beam blur in such optical systems.
BACKGROUND
Beam blur is a problem that arises in various types of optical systems, especially optical systems that make use of a beam of charged particles such as electrons or ions. In a charged-particle-beam (CPB) optical system, blur is manifest whenever charged particles in the beam ideally intended to be converged at a single point on, e.g., an image plane actually exhibit a significant spread over a certain distance from the point. Such blur can arise from any of various factors. For example, blur can be caused by spherical aberration of the CPB optical system. As a result of spherical aberration, each location of a point on the image plane at which a charged particle (after having passed through the optical system) is incident is a function of the aperture angle distribution of the charged particles as they pass through the object plane.
By way of example,
FIG. 4
illustrates an exemplary “spot diagram” (or “scatter diagram”) of respective destination positions (at an image plane) of 3000 particles propagating through a CPB optical system of a CPB microlithography apparatus. In
FIG. 4
the charged particles collectively exhibit blur at the image plane due to spherical aberration. The destination position of each charged particle in the plot is determined by assigning respective computed aberration coefficients to the charged particle. The aberration coefficients of each charged particle are computed according to a probability distribution of the incident angle of the charged particle at the object plane (reticle plane). Chu and Munro,
Optik
61:121-145 (1982). In the example of
FIG. 4
, the incident angle of each charged particle incident on a reticle (at the object plane) is assigned a respective probability in the distribution of incident angles exhibited by the charged particles on the reticle.
Alternatively, for analyzing beam blur, well-known ray-tracing theory can be employed for determining the destination positions of charged particles passing through a CPB optical system. Whenever ray-tracing theory is used in this manner, the manner in which the charged particles propagate under the influence of a particular combination of electrical and magnetic fields is determined by solving an equation of motion for each particle.
A spot diagram or the like as shown in
FIG. 4
generally depicts blur as manifest in two dimensions (X and Y dimensions) at the image plane. Alternatively to a spot diagram, in the context of a CPB microlithography apparatus comprising a CPB optical system, blur can be quantified. Quantified blur commonly is defined as the “full width at half maximum” (denoted “W”) of a Gaussian distribution of beam intensity along a dimension (e.g., X or Y) in the image plane, typically at an edge of a projected pattern element. At such an edge, blur typically has a Gaussian distribution, wherein W generally is regarded as the portion of the distribution located within the range of approximately 12% to approximately 88% of maximum beam intensity. The range of W can vary (e.g., W can be from 10% to 90%) depending upon the accuracy and precision desired and upon other factors considered in determining blur of the particular system in question. Hence, “quantified blur” is distinguished from the comparatively qualitative depiction of blur such as shown in FIG.
4
.
Quantified blur is a major factor used in determining the minimum pattern linewidth resolvable by a particular CPB microlithography apparatus. Rapid and accurate quantification of blur is necessary not only when designing an actual CPB microlithography apparatus but also when evaluating a particular reticle pattern to be exposed using the apparatus. For example, quantified blur can be used to produce data concerning any local resizing or the like of the pattern as defined on the reticle, as required for correcting proximity effects.
An exemplary conventional procedure for quantifying blur is based on preparing a grouped tabulation of obtained data concerning destination positions. The grouped data thus are suitable for plotting as a histogram from which blur is quantified. The method comprises the following steps:
(a) A sequence a[i] of “i” groups (i=1, 2, 3, . . . n) is designated, wherein each group corresponds to a respective range of destination positions “x” or “y” along a respective dimension (X or Y) in the image plane. In a subsequent step, the respective numbers of individual charged particles incident in the respective range corresponding to each group are tallied. The number n of groups typically is selected based on a tradeoff of calculation accuracy and available time to perform the calculations. The total range is sufficiently large to allow accounting for all the charged particles. By way of example, whenever spherical aberration is the dominant manifestation of beam blur, it is possible to determine, at least roughly, the range of aberration data. For each charged particle, the aberration is calculated by multiplying the aberration coefficient by the third power of the particle's incident angle. E.g., if the incident angle is limited to 6 mrad and the aberration coefficient is 0.1, then the maximum destination position is (0.1)(6/1000)
3
=21.6 nm from the convergence point. In this situation, this step (a) is performed before step (b), below.
However, if no prior knowledge exists about the range of data that will be obtained in step (b), then step (b) is performed before step (a). I.e., the data obtained in step (b) is reviewed to determine a suitable number of groups and/or their respective ranges. (Alternatively, the program used to perform steps (a) and (b) can accommodate adding more groups or re-setting group ranges.)
The range of each group is determined based on the required accuracy of the calculations. Hence, if the required accuracy, the total range of the data, and the maximum destination position of the data are known, then n can be readily determined.
(b) A defined number of values of a particular beam parameter (i.e., a parameter that affects blur, such as aperture angle) is selected. The selection is performed either randomly or according to a desired distribution. For example, a randomly selected population of 100 aperture angles is selected. The values are individually substituted into an appropriate function for the particular parameter (e.g., an aberration function) or in a ray-tracing program. The corresponding destination positions of charged particles at the image plane are determined from the substitution calculations or ray traces. If a destination position determined from a single calculation or ray trace falls within a particular destination-position group as designated in step (a), then the tally for that group is incremented by one. The tally data are plotted as a histogram comprising bars corresponding to respective groups.
(c) Step (b) is repeated as required until a satisfactory discernment can be made, from the histogram, of the distribution of the destination positions of the charged particles. The histogram extends in a specific axis direction (e.g., X or Y direction), and the “components” of the distribution (each component corresponding to a respective bar of the histogram) in that axis direction are determined.
(d) For each component of the distribution determined in step (c), a convolution is performed of the distribution with a step function. For example, if the specific axis direction is the X-axis, then the convolution is performed with a step function such that the result of the convolution is 0 at x<0 and 1 at x≧0. The blur is quantified in the specific axis direction based on the result of the respective convolution. For example, the difference between respective values of x corresponding to 12% and 88% of the maximum valu
Font Frank G.
Klarquist & Sparkman, LLP
Nikon Corporation
Punnoose Roy M.
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