Method and apparatus for compensation of time-varying optical properties of gas in interferometry

In general, in one aspect, the invention features a method, including interferometrically measuring first and second optical path lengths to a measurement object along respective first and second paths, wherein the measurement of the optical path lengths includes directing first and second measurement beams to reflect from the measurement object, measuring propagation directions of the first and second measurement beams, compensating the first measured optical path length for time-varying optical properties of gas in the first path based on the first and second measured optical path lengths and the first and second measured propagation directions.

BACKGROUND

Displacement-measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.

In many applications, the measurement and reference beams have orthogonal polarizations and different frequencies. The different frequencies can be produced, for example, by laser Zeeman splitting, by acousto-optical modulation, or internal to the laser using birefringent elements or the like. The orthogonal polarizations allow a polarizing beam splitter to direct the measurement and reference beams to the measurement and reference objects, respectively, and combine the reflected measurement and reference beams to form overlapping exit measurement and reference beams. The overlapping exit beams form an output beam that subsequently passes through a polarizer.

The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. A detector measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Because the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2 vnp/λ, where v is the relative speed of the measurement and reference objects, X is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2π phase change substantially equal to a distance change L of λ/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.

Unfortunately, this equality is not always exact. In addition, the amplitude of the measured interference signal may be variable. A variable amplitude may subsequently reduce the accuracy of measured phase changes. Many interferometers include non-linearities such as what are known as “cyclic errors.” The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnL. In particular, the first harmonic cyclic error in phase has a sinusoidal dependence on (2πpnL)/λ and the second harmonic cyclic error in phase has a sinusoidal dependence on 2 (2πpnL)/λ. Higher harmonic cyclic errors can also be present.

Another source of errors are related to environmental effects such as air turbulence and non-isotropic distributions of gases in the interferometer environment. See, for example, an article entitled “Residual Errors In Laser Interferometry From Air Turbulence And Nonlinearity,” by N. Bobroff,Appl. Opt.26(13), 2676-2682 (1987), and an article entitled “Recent Advances In Displacement Measuring Interferometry,” also by N. Bobroff,Measurement Science&Tech.4(9), 907-926 (1993). As noted in the aforementioned cited references, interferometric displacement measurements in a gas are subject to environmental uncertainties, particularly to changes in air pressure and temperature; to uncertainties in air composition such as resulting from changes in humidity and/or the presence of additional gases; and to the effects of turbulence in the gas. These time-varying optical properties of gas in a beam path alter the wavelength of the light used to measure the displacement. Under normal conditions, the refractive index of air for example is approximately 1.0003 with a variation of the order of 1×10−5to 1×10−4. In many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to less than 0.001 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and less than 1 nm, respectively, for a one meter interferometric displacement measurement.

One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on the optical path length of the measurement path. Another, more direct way to detect the effects of a fluctuating refractive index over a measurement path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by a measurement beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to determine the physical path length from the optical path length, including, in particular, the contributions of fluctuations in refractive index, provided the instrument employs at least two wavelengths. The variation of refractive index with wavelength is known in the art as dispersion and this technique is often referred to as the dispersion technique or as dispersion interferometry.

SUMMARY

In certain aspects, the invention features methods and systems for compensating interferometry measurements for time-varying optical properties of gas in the path of an interferometer measurement beam (and/or reference beam). As discussed above, time-varying optical properties of gas in an interferometer beam path give rise to uncertainty in interferometry measurements because, even if all the components are stationary, the refractive index of the gas can vary. These variations can give rise to differences in measured optical path length values, even if the physical path length remains unchanged during the measurements. In addition to affecting optical path length, time-varying optical properties of gas also affect the propagation direction of a measurement beam (and/or reference beam). However, the amount by which variations in the optical properties of the gas affects the optical path length is related to the amount the variations affect the beam propagation direction. Accordingly, when this relationship is known, a measurement of the beam propagation direction can be used to compensate for time-varying affects of the gas on the optical path length measurement.

The situation becomes more complicated when components of the interferometer are not stationary. In particular, in many interferometers (e.g., single beam plane mirror interferometers) a change in the orientation of the measurement object will cause a variation in beam propagation direction. Without additional information (e.g., the amount by which the orientation of the measurement object changes), it is not possible to decouple the change in propagation direction due to time-varying optical properties of the gas from the change in propagation direction due to an orientation change of the measurement object. This is the case in many interferometry applications, such as, for example, in photolithography systems where an interferometry system is used to monitor the position of a moving wafer stage during exposure of a wafer. Accordingly, in certain aspects, the invention features systems and methods which compensate for time-varying optical properties of a gas in a beam path while one or more components of the interferometry system may be moving.

The optical properties of a gas are determined by a number of physical parameters, each of which can vary as a function of time. These parameters include gas turbulence, gas composition, and thermodynamic properties of the gas. Accordingly, systems and methods described herein can compensate for the effect of variations of one or more of these parameters on an interferometry measurement.

The systems and methods are applicable to lithography tools.

Descriptions of various aspects of the invention follow.

In general, in one aspect, the invention features a method, including interferometrically measuring first and second optical path lengths to a measurement object along respective first and second paths, wherein the measurement of the optical path lengths includes directing first and second measurement beams to reflect from the measurement object, measuring propagation directions of the first and second measurement beams, compensating the first measured optical path length for time-varying optical properties of gas in the first path based on the first and second measured optical path lengths and the first and second measured propagation directions.

Embodiments of the method may include one or more of the following features and/or features of other aspects.

Compensating the first measured optical path length can further include compensating the first measured optical path length based on earlier measurements of the first and second optical path lengths and the first and second propagation directions. Compensating the first measured optical path length can additionally include compensating the first measured optical path length based on the velocity of gas in the first and second paths. Compensating the measured optical path length can include determining a corrected optical path length, x1,0, according to the equation:x1,0=x1-u⁢∫{θ1-[x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt]}⁢ⅆt
where x1and x2are the first and second measured optical path lengths, respectively, θ1and θ2are the first and second propagation directions, respectively, b is a distance between the first and second measurement beams, and u is a component of the gas velocity perpendicular to the beams and in the plane of the beams.

The propagation directions of the first and second measurement beams can be measured interferometrically.

The method can include deriving the first and second measurement beams from an input beam, and the input beam propagation direction can be adjusted based on variations in the propagation direction of the first or second measurement beams.

In another aspect, the invention features a method, including interferometrically measuring an optical path length to a measurement object along a first path, wherein the measurement of the optical path length includes directing a measurement beam to reflect from the measurement object. The method further includes measuring (e.g., interferometrically measuring) a propagation direction of the measurement beam, and compensating the measured optical path length for time-varying optical properties of gas in the first path based on the measured propagation direction.

Embodiments of the method may include one or more of the following features and/or features of other aspects.

Compensating the measured optical path length can include compensating the measured optical path length based on a velocity of gas in the first path.

The method can include measuring a second optical path length to the measurement object along a second path substantially parallel to the first path. In addition, the method can include measuring a propagation direction of the second measurement beam. The propagation direction of the second measurement beam can be measured interferometrically. Compensating the measured optical path length can include compensating the measured optical path length based on the measured propagation direction of the second measurement beam and the velocity of gas in the second path. The measured optical path length can also be compensated based on previous optical path length and measurement beam propagation direction measurements. In some embodiments, compensating the measured optical path length includes determining a corrected optical path length, x1,0, according to the equation:x1,0=x1-u⁢∫{θ1-[x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt]}⁢ⅆt
where x1and x2are the first and second measured optical path lengths, respectively, θ1and θ2are the first and second beam directions, respectively, b is a distance between the first and second measurement beams, and u is the component of the gas velocity perpendicular to the beams and in the plane of the beams.

The propagation direction of the measurement beam can be measured after the measurement beam reflects from the measurement object an odd number of times (e.g., once).

Measuring the optical path length can include generating a heterodyne signal from the measurement beam and determining an interference phase from the heterodyne signal.

In embodiments which include measuring a second optical path length to the measurement object along a second path substantially parallel to the first path, the first measured optical path length can be compensated for variations in the orientation of the measurement object based on the second measured optical path length and a distance between the first and second measurement beams.

The method can include deriving the measurement beam from an input beam. The input beam propagation direction can be adjusted based on variations in the propagation direction of the first measurement beam.

In a further aspect, the invention features interferometry systems configured to implement the aforementioned methods.

In one aspect, the invention features an interferometry system, including an interferometer configured to direct a measurement beam to reflect from a measurement object and interferometrically measure an optical path length to the measurement object along a first path based on the reflected measurement beam, and an angular displacement interferometer, configured to measure a propagation direction of the reflected measurement beam. The interferometry system also includes a controller in communication with the interferometer and the angular displacement interferometer, wherein during operation the controller compensates the measured optical path length for time-varying optical properties of gas in the first path based on the measured optical path length and measured propagation direction.

Embodiments of the interferometry system may include features of other aspects and/or can be configured to implement methods of other aspects.

In a further aspect, the invention features a lithography method for use in fabricating integrated circuits on a wafer, which includes supporting the wafer on a moveable stage, imaging spatially patterned radiation onto the wafer, adjusting the position of the stage, and monitoring the position of the stage using one of the aforementioned methods.

In another aspect, the invention features a lithography method for use in the fabrication of integrated circuits, which includes directing input radiation through a mask to produce spatially patterned radiation, positioning the mask relative to the input radiation, monitoring the position of the mask relative to the input radiation using one of the aforementioned methods, and imaging the spatially patterned radiation onto a wafer.

In a further aspect, the invention features a lithography method for fabricating integrated circuits on a wafer, which includes positioning a first component of a lithography system relative to a second component of a lithography system to expose the wafer to spatially patterned radiation, and monitoring the position of the first component relative to the second component using the one of the aforementioned methods.

In another aspect, the invention features a method for fabricating integrated circuits, the method including one of the aforementioned lithography methods.

In an additional aspect, the invention features a beam writing method for use in fabricating a lithography mask. The method includes directing a write beam to a substrate to pattern the substrate, positioning the substrate relative to the write beam, and monitoring the position of the substrate relative to the write beam using one of the aforementioned interferometry methods.

In another aspect, the invention features a lithography system for use in fabricating integrated circuits on a wafer. The system includes a stage for supporting the wafer, an illumination system for imaging spatially patterned radiation onto the wafer, a positioning system for adjusting the position of the stage relative to the imaged radiation, and the aforementioned interferometry system for monitoring the position of the wafer relative to the imaged radiation.

In a further aspect, the invention features a lithography system for use in fabricating integrated circuits on a wafer, the system includes a stage for supporting the wafer, and an illumination system including a radiation source, a mask, a positioning system, a lens assembly, and the aforementioned interferometry system. During operation of the lithography system, the source directs radiation through the mask to produce spatially patterned radiation, the positioning system adjusts the position of the mask relative to the radiation from the source, the lens assembly images the spatially patterned radiation onto the wafer, and the interferometry system monitors the position of the mask relative to the radiation from the source.

In another aspect, the invention features a beam writing system for use in fabricating a lithography mask, the system including a source providing a write beam to pattern a substrate, a stage supporting the substrate, a beam directing assembly for delivering the write beam to the substrate, a positioning system for positioning the stage and beam directing assembly relative one another, and the aforementioned interferometry system for monitoring the position of the stage relative to the beam directing assembly.

Embodiments of the invention may include any of the following advantages.

They can provide accurate interferometry measurements in the presence of time-varying optical properties of gas in the measurement and/or reference beam(s) using single wavelength interferometry techniques (i.e., non-dispersive interferometry techniques). They can compensate for optical effects of composition changes of the gas without monitoring gas composition. Similarly, they can compensate for optical effects of variations of the thermodynamic properties of the gas, such as temperature and pressure along the measurement path, without monitoring the thermodynamic properties.

They may provide a non-dispersive method and apparatus for measuring and compensation for time-varying effects of gas in a measurement path on linear and angular displacements where the refractive index may be fluctuating and/or the physical length of the measurement path may be changing. Embodiments where the physical length of the measurement path may be changing include, for example, implementations where an interferometry system is used to monitor the position of a moving wafer stage in a photolithography system.

DETAILED DESCRIPTION

Interferometry systems can provide highly accurate measurements. Such systems can be especially useful in lithography applications used in fabricating large scale integrated circuits such as computer chips and the like. Lithography is a key technology driver for the semiconductor manufacturing industry. In lithography, overlay improvement is one of the five most difficult challenges down to and below 100 nm line widths (design rules), see, for example, theSemiconductor Industry Roadmap, p.82 (1997). For a general reference on lithography, see also, for example, J. R. Sheats and B. W. Smith, inMicrolithography: Science and Technology(Marcel Dekker, Inc., New York, 1998), the contents of which is incorporated herein by reference.

Overlay depends directly on the performance, i.e., accuracy and precision, of the distance measuring interferometers used to position the wafer and reticle (or mask) stages. Since a lithography tool may produce $50-100M/year of product, the economic value from improved performance distance measuring interferometers is substantial. Each 1% increase in yield of the lithography tool results in approximately $1M/year economic benefit to the integrated circuit manufacturer and substantial competitive advantage to the lithography tool vendor.

The function of a lithography tool is to direct spatially patterned radiation onto a photoresist-coated wafer. The process involves determining which location of the wafer is to receive the radiation (alignment) and applying the radiation to the photoresist at that location (exposure).

Referring toFIG. 1, a lithography system100, also referred to as an exposure system, typically includes an illumination system110and a wafer positioning system120, and a reticle stage130. Illumination system110includes a radiation source112for providing radiation such as ultraviolet, visible, x-ray, electron, or ion radiation. Reticle stage130supports a patterned reticle132, which is also referred to as a mask. These terms are used interchangeably below. Reticle132imparts a pattern to radiation from illumination system110, thereby generating the spatially patterned radiation. For the case of reduction lithography, lithography system100also includes a reduction lens140for imaging the spatially patterned radiation onto a wafer122. Wafer positioning system120includes a wafer stage142that positions and supports wafer122during the exposure. Wafer positioning system120can also include, e.g., piezoelectric transducer elements and corresponding control electronics. The imaged radiation exposes resist coated onto the wafer. The radiation initiates photo-chemical processes in the resist that convert the radiation pattern into a latent image within the resist.

In embodiments that use proximity printing, as opposed to those implementing reduction lithography, the scattered radiation propagates a small distance (typically on the order of microns) before contacting the wafer to produce a 1:1 image of the reticle pattern.

Lithography system100also includes a wafer feeding system160and a reticle changer170. Wafer feeding system160is supplied with a batch of wafers and automatically loads wafers on the wafer stage and removes wafers once they have been exposed. Reticle changer170selects the appropriate reticle for each exposure and positions the selected reticle on reticle stage130.

To properly position the wafer, the wafer includes alignment marks on the wafer that can be measured by dedicated sensors. The measured positions of the alignment marks define the location of the wafer within the tool. This information, along with a specification of the desired patterning of the wafer surface, guides the alignment of the wafer relative to the spatially patterned radiation. Based on such information, the translatable wafer stage supporting the photoresist-coated wafer moves the wafer so that the radiation exposes the correct location of the wafer.

Lithography system100is enclosed in a chamber101, which allow the wafer's environment to be controlled during exposure. An access port105provides access to the exposure apparatus, wafer feeding system and reticle chamber. Chamber101also includes a gas inlet180and a gas exhaust182for introducing and removing processes gas(es) into and out of the chamber, respectively. Chamber101helps to reduce contaminants (e.g., dust or undesirable gases), which may scatter and/or absorb the exposing radiation and degrade the light pattern at the wafer. The chamber also allows control over the composition of the atmosphere adjacent the wafer. This is especially important when the exposing radiation is strongly absorbed or scattered by air. UV radiation, for example, is strongly absorbed by oxygen, making oxygen-rich atmospheres, such as air, undesirable for UV systems. Typically, an enclosed lithography system will be flushed with nitrogen, or some other gas or gas mixture more suitable for the exposing radiation wavelength.

Lithography system100also includes an interferometry system that precisely measures the position of the wafer in the lithography system. The interferometry system includes an interferometer150and a measurement object152. Interferometer150is attached to wafer positioning system120and measurement object152is attached to wafer stage142. Measurement object152includes, e.g., a plane mirror for reflecting a measurement beam155directed to the stage by interferometer150. The measurement beam reflects back to the interferometer150.

In other embodiments of the lithography system, one or more of the interferometry systems described previously can be used to measure distance along multiple axes and angles associated for example with, but not limited to, the wafer and reticle (or mask) stages. Also, rather than a UV laser beam, other beams can be used to expose the wafer including, e.g., x-ray beams, electron beams, ion beams, and visible optical beams.

In some embodiments, the lithography system can include what is known in the art as a column reference. In such embodiments, the interferometer150directs the reference beam (not shown) along an external reference path that contacts a reference mirror (not shown) mounted on some structure that directs the radiation beam, e.g., reduction lens140. The reference mirror reflects the reference beam back to the interferometry system. The interference signal produced by the interferometry system when combining measurement beam155reflected from measurement object152and the reference beam reflected from a reference mirror mounted on the reduction lens140indicates changes in the position of the stage relative to the radiation beam.

An example of a suitable interferometry system is described below. Although not included in the described embodiment, one or more interferometry systems can also be used to precisely measure the position of the reticle stage as well as other movable elements whose position must be accurately monitored in processes for fabricating lithographic structures (see supra, Sheats and Smith,Microlithography: Science and Technology).

In general, interferometry systems can be used to precisely measure the positions of each of the wafer stage and reticle stage relative to other components of the exposure system, such as the lens assembly, radiation source, or support structure. In such cases, as in the described embodiment, the interferometer is attached to a stationary structure and the measurement object attached to a movable element such as one of the mask and wafer stages. Alternatively, the situation can be reversed, with the interferometry system attached to a movable object and the measurement object attached to a stationary object.

More generally, such interferometry systems can be used to measure the position of any one component of the exposure system relative to any other component of the exposure system, in which the interferometry system is attached to, or supported by, one of the components and the measurement object is attached, or is supported by the other of the components.

An embodiment of an interferometry system200is shown schematically in FIG.2A and includes two zero-shear single-pass interferometers, indicated generally as210and220. The operation of zero-shear single-pass interferometers210and220having a dynamic beam steering element70is described in commonly-owned, provisional patent application No. 60/314,570 by Henry A. Hill and filed Aug. 23, 2001, and is summarized briefly below. The zero-shear single-pass interferometers have a common plane mirror measurement object 60. In other embodiments, other forms of single-pass interferometers, including other forms of zero-shear single-pass interferometers, may be incorporated into the interferometry system such as those described in commonly owned, provisional patent applications 60/309,608 and 60/314,345 both by Henry A. Hill and filed Aug. 2, 2001 and Aug. 23, 2001, respectively, the contents of which are incorporated herein by reference.

Interferometer210includes a pair of polarizing beam splitters,211and212, a retroreflector213, a half waveplate214, and a quarter waveplate215. Similarly, interferometer220includes polarizing beam splitters,221and222, a retroreflector223, a half-waveplate224, ad a quarter waveplate225.

During operation of the interferometry system, a source201directs an input beam towards polarizing beam splitter211, which splits the beam into a measurement beam30and a reference beam having orthogonal polarization to measurement beam30. The measurement beam is the portion of the input beam transmitted by polarizing beam splitter211. Polarizing beam splitter212transmits measurement beam30, which reflects from plane mirror object60back towards polarizing beam splitters211and212. Quarter waveplate214converts the plane polarized measurement beam exiting beam splitter212into circularly polarized light. Similarly, quarter waveplate214converts the circularly polarized measurement beam reflected from plane mirror object60back into plane polarized light. Due to measurement beam30reflecting from plane mirror object60, the plane of polarization of the reflected measurement beam is orthogonal to its original plane of polarization, so the reflected measurement beam is reflected by polarizing beam splitter212towards mirror235.

Polarizing beam splitter211reflects the component of the input beam orthogonal to the measurement beam towards retroreflector213. This component forms the reference beam. Retroreflector213directs the reference beam through half wave plate214towards polarizing beam splitter212. Half wave plate214rotates the plane of polarization of the reference beam by 90°, so that it is transmitted by polarizing beam splitter212. The reference beam exits interferometer210overlapping with the measurement beam.

The overlapping measurement and reference beam form an output beam, which is directed by mirror235to angular displacement interferometer50and a detector42. Angular displacement interferometer50measure changes in the direction of propagation of measurement beam30. An embodiment of a suitable angular displacement interferometer is described below. In addition, a beam splitter240directs a portion of the output beam to a detector40, which measures a linear displacement, which corresponds to an optical path length between interferometer210and plane mirror object60.

Interferometer220operates similarly to interferometer210. A beam splitter205and a mirror208direct a portion of the input beam towards interferometer220. Interferometer220splits the input beam into a reference beam and a measurement beam230, and, after reflecting measurement beam230from plane mirror object60, overlaps the beams as an output beam. Mirror245and beam splitter250direct a portion of the output beam to angle displacement interferometer250and a detector242, and another portion to detector240, which respectively measure changes in the direction of propagation of measurement beams230and a linear displacement corresponding to an optical path length between interferometer220and plane mirror object60.

In addition, interferometry system200includes a common, dynamic beam steering element70. Beam steering element70is servo-ed to the orientation of plane mirror object60to maintain measurement beams30and230normal to the surface of the measurement object over the range of angular orientations of the stage on which the measurement object is mounted relative to the structure supporting the interferometers. In the present embodiment, the dynamic beam steering element is responsive to a servo signal derived from detector42, which detects an output beam from angular displacement interferometer50. Dynamic element70and its general use in interferometry systems are disclosed in commonly owned U.S. Pat. Nos. 6,271,923 and 6,313,876 issued Aug. 7, 2001 and Nov. 6, 2001, respectively, the contents of which are incorporated herein by reference. Dynamic beam steering element70can reduce errors associated with beam shear in the system. In other embodiments, alternative or additional components/methods can be used to reduce these errors. Examples include using high-stability plane mirror interferometers (HSPMI's) instead of single-pass interferometers. An embodiment of an HSPMI is described below.

Interferometry system200also includes an electronic processor299, which is connected to detectors40,42,240, and242. Electronic processor299receives electrical signals from these detectors, and processes them according to one or more algorithms to determine the position and orientation of plane mirror object60. The electronic processor also compensates the measured position and orientation for time-varying effects of gas in the measurement beam paths based on the relationship derived below.

Interferometer210, with measurement beam30, measures a linear displacement x1and an angular displacement θ1at a first position on plane mirror object60and interferometer220, with measurement beam230, measures a linear displacement x2and an angular displacement θ2at a second position on plane mirror object60(see FIG.2A). The linear displacements x1and x2correspond to an optical path lengths between the interferometers210and220and the first and second positions on plane mirror object60, respectively. The linear displacements can each be written as the sum of two terms wherein one of the two terms includes the time-varying optical properties of gas in the respective measurement paths. Accordingly,
x1=x1,0+x1,T,  (1)
x2=x2,0+x2,T,  (2)wherex1,T=∫p1⁢(n-1)⁢ⅆs;(3)x2,T=∫p2⁢(n-1)⁢ⅆs;(4)
x1,0and x2,0are the physical displacements of plane mirror object60at the first and second positions, respectively; x1,Tand x2,Tare the respective contributions of the gas to the linear displacements x1and x2of plane mirror object60; n is the refractive index of the gas at wavelength λ; λ is the wavelength of the input beam to the interferometer assembly; and ds is an infinitesimal path length along a respective optical paths p1and p2of measurement beams30and230, respectively. Optical paths p1 and p2 are indicated on FIG.2A.

Each of the angular displacements θ1and θ2can also be written as the sum of two terms wherein one of the two terms comprises the time-varying effects of the gas in the respective measurement paths. Accordingly
θ1=α+θ1,T,  (5)
θ2=α+θ2,T,  (6)
whereθ1,T=⁢∫p1⁢(∂n∂r)⁢ⅆs=⁢∫p1⁢[∂(n-1)∂r]⁢ⅆs;(7)θ2,T=⁢∫p2⁢(∂n∂r)⁢ⅆs=⁢∫p2⁢[∂(n-1)∂r]⁢ⅆs;(8)
α is the angular displacement of plane mirror object60(see FIG.2A); (∂n/∂r) is the partial derivative of the refractive index n with respect to r; and r is a coordinate locally orthogonal to a curvilinear optical path s in the plane of FIG.2A. The effects of gradients in the refractive index on the direction of propagation of a beam are described for example in an article entitled “Compensation for the Lateral Color Aberration Produced by the Atmosphere” by H. A. Hill and C. A. Zanoni,JOSA56, 1655-1659 (1966).

An independent value for angular displacement α is obtained from the difference of measured linear displacements x1and x2. Using Equations (1) and (2), the independent value for α can be written asα=x2-x1b-(1b)⁡[∫p2⁢(n-1)⁢ⅆs-∫p1⁢(n-1)⁢ⅆs](9)
where b is the separation of beams30and230at plane mirror object60(see FIG.2A). The difference of the measured angular displacements of θ1and θ2can be written using Equations (5)-(8) asθ2-θ1=∫p2⁢[∂(n-1)∂r]⁢ⅆs-∫p1⁢[∂(n-1)∂r]⁢ⅆs.(10)

The second term on the right hand side of Equation (9) is related to the right hand side of Equation (10) by a spatial integration. Consequently, the difference θ2−θ1can be used to correct for the effect of the second term to yield a measured value of α compensated for the effects of time-varying effects of the gas.

The order of integration with respect to t and s may be inverted to a good approximation in Equation (11) to obtain∫(θ2-θ1)⁢ⅆt=∫ⅆs⁢∫p2⁢[∂(n-1)∂r]⁢ⅆt-∫ⅆs⁢∫p1⁢[∂(n-1)∂r]⁢ⅆt.(12)

The rate at which gas refractivity in the measurement beam paths change is proportional to the component of the gas velocity perpendicular to the measurement beam paths in the plane of FIG.2A. Therefore, for a non-zero gas flow with a velocity component u in the plane of FIG.2A and perpendicular to the measurement beam paths, the temporal integration Equation (12) can be transformed into a spatial integration with the result∫(θ2-θ1)⁢ⅆt=(1u)⁢{∫ⅆs⁢∫p2⁢[∂(n-1)∂r]⁢ⅆr-∫⁢⁢ⅆs⁢∫p1⁢[∂(n-1)∂r]⁢ⅆr}⁢=(1u)⁡[∫p2⁢(n-1)⁢ⅆs-∫p1⁢(n-1)⁢ⅆs].(13)

The velocity component u can be determined in a number of ways. For example, gas velocity can be monitored empirically using one or more gas flow meters. Information from the gas flow meter(s) can be input to the electronic processor and used to compensate the optical path length measurement in real time. Where the interferometry system is used in environments which repeat gas flow patterns cyclically, such as in lithography systems, empirical gas velocity data for, e.g., a single exposure cycle can be used for subsequent cycles, removing the need for constant gas monitoring.

Alternatively, or additionally, gas velocity data can be determined using computational methods. An example of a computational method is to determine the gas velocity using commercial computational fluid dynamics programs. One example of such a program is Star CD, available from the CD adapco Group (Melville, N.Y.). In general, computational fluid dynamics solve fluid dynamics problems in complex systems by solving one or more sets of differential equations relating parameters of the fluid (e.g., density, temperature) at a set of discrete locations and times within the system. For example, for an incompressible fluid, one might use the Navier-Stokes equation, which is the fundamental partial differential equation that describes the flow of such fluids. The set of discrete locations, often referred to as a mesh, is usually defined according to the physical structure of the system. The differential equation(s) usually requires a set of user-defined boundary values describing, e.g., initial system conditions to be entered prior to solving. These can include boundary conditions for any parameter, such as an initial temperature profile, or the temperature of certain portions of the mesh at particular times during a cycle. Accordingly, by determining an appropriate mesh and entering conditions for the exposure cycle, one can computationally determine values of the gas velocity and/or other parameters at different locations in the chamber during the cycle.

Gas velocity data can also be determined based on the interferometry measurements themselves. Measured values x1, θ1, x2, and θ2, for example, each have a component that depends on time-varying effects of the gas. Accordingly, the rate of change of(x2−x1) and the time integral Of (θ2−θ1) will have a component that depends on the changes of gas refi-activity due to, for example, the gas turbulence. Thus, the component of (x2−x1) and the time integral of (θ2−θ1) related to changes in the gas will be correlated. Therefore, a velocity component u can be selected as the value that provides the best correlation coefficient between (x2−x1) and the time integral Of (θ2−θ1).

Because Equation (13) includes a (1/u) term, the velocity component u should be non-zero for the described compensation technique to provide accurate results. Accordingly, the interferometry system should be positioned in the lithography system with the measurement beam path non-parallel to the gas flow direction.

The following equation for α compensated of time-varying effects of the gas is obtained by combining Equations (9) and (13):α=x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt.(14)

The angular displacement α compensated of time-varying effects of the gas is used as a signal by servo controller72to control the orientation of dynamic beam steering element70in the plane of FIG.2A.

Next, the measured value of α given by Equation (14) is used in Equation (5) to obtain the time-varying effects θ1,Tof the gas on the direction of propagation of beam30, i.e.θ1,T=θ1-[x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt].(15)

A subsequent integration of Equation (15) with respect to t, a change in order of integration, and changing the integration with respect to t to an integration with respect to r gives to a good approximation the time-varying effects of the gas on the measured optical path length of beam30, i.e.x1,T=u⁢∫{θ1-[x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt]}⁢ⅆt.(16)

The following equation for x1,0compensated of time-varying effects of the gas is obtained by combining Equations (1) and (16),x1,0=x1-u⁢∫{θ1-[x2-x1b-(ub)⁢∫(θ2-θ1)⁢ⅆt]}⁢ⅆt.(17)

It will be evident to those skilled in the art that a measurement of x2,0compensated of time-varying effects of the gas can be obtained by a data processing analogous to that for the determination of x1,0.

Note that the measured values for x1,0and α are compensated for the time-varying effects of gas turbulence, time-varying changes in a uniform or non-uniform gas composition, and time-varying changes in thermodynamic properties of the gas along the optical paths of beams 30 and 230.

In embodiments, the integrand in Eq. (17) can include a weighting function to prevent the integral from diverging, e.g., due to noise. The form of the weighting function can vary. One example of a weighting function is a step function (e.g., equal to one for measurements made within a cutoff time from the present time, and equal to zero for measurements made prior to the cutoff time.) Other examples include exponential or geometrically decaying functions that weight the most recent measurements more heavily than measurements made longer ago.

The time increment between measurements should be less than about (u/b), which is the amount of time taken for a parcel of gas to traverse the space between the measurement beams.

The compensation procedure of the described embodiment can be adapted to compensate for the time-varying effects of a gas that has a non-isotropic gas flow pattern. Non-isotropic flow patterns include those in which the gas velocity differs along different portions of the measurement beam paths. For the adapted compensation procedure, the measured values of respective quantities are first Fourier transformed to frequency space and portions of the frequency spectra associated with a flow velocity component uifor i=1,2, . . . . The portions are then inverse Fourier transformed and subsequently processed according to Equations (15) and (17)with associated uifor compensation for the time-varying effects of a gas that has a non-isotropic gas flow pattern.

For applications that include measurement of changes of orientation of plane mirror object60in a plane orthogonal to the plane ofFIG. 2Athat are compensated for time-varying effects of the gas, a third zero-shear single-pass interferometer and additional angular displacement interferometers are added to the interferometer assembly of the first embodiment to form a modified interferometer assembly. The third zero-shear single-pass interferometer and additional angular displacement interferometers are added to the interferometer assembly to measure angular displacements of plane mirror object 60 in a plane orthogonal to the plane of FIG.2A. The description of the processing of information obtained by the modified interferometer assembly is the same as corresponding portions of the description given for the first embodiment for measurement of changes in orientation of plane mirror object60orthogonal to the plane ofFIG. 2Athat are compensated for time-varying effects of the gas.

Although system200includes single-pass interferometers, other embodiments can include interferometers in which the measurement beam contacts the measurement object more than once. For example, in some embodiments, the interferometry system can includes a high-stability plane mirror interferometer (HSPMI). An example of an HSPMI300is shown in FIG.2B. HSPMI300includes a polarizing beam splitter (PBS)310, a reference mirror320, a plane mirror measurement object330, and a retroreflector340. PBS310splits an input beam301into a reference beam and a measurement beam, the reference beam polarization being orthogonal to the measurement beam polarization. Reference mirror320reflects the measurement beam. A quarter waveplate325positioned between PBS310and reference mirror320causes the once reflected reference beam to have orthogonal polarization to the beam's initial polarization state. Accordingly, the once reflected reference beam is transmitted by PBS310. Retroreflector340directs the reference beam back towards reference mirror320. The second reflection and double pass through quarter wave plate325restores the reference beam polarization to its original state. Subsequently, PBS310reflects the reference beam, which exits the interferometer as a component of output beam302.

The path of the measurement beam is analogous to that of the reference beam. PBS initially transmits the measurement beam through to plane mirror measurement object330. Retardation due to a quarter wave plate335and reflection from measurement object330transform the measurement beams polarization state to a state orthogonal to its original polarization state. Thus, the reflected measurement beam is now reflected by PBS310to retroreflector340. Subsequently, PBS310directs the measurement beam back towards measurement object330, before the measurement beam, now twice-reflected by the measurement object, exits the interferometer as a component of output beam302.

Due to the double pass to the measurement object, the output beam is parallel to the input beam, even in the absence of a dynamic beam steering element to compensate for variations in the orientation of the measurement object. Due to the insensitivity of the propagation direction of output beam302to variations in the orientation of measurement object330, information about these variations is not carried by output beam302. Accordingly, interferometer300includes a non-polarizing beam splitter350that directs a second output beam303to an angular displacement interferometer. Second output beam303includes a measurement beam component that has only contacted measurement object330once and therefore still contains information about the orientation of the measurement object. However, the path of the reference beam component of the output beam is unaffected by variations in the orientation of measurement object330. Therefore, in the present embodiment, the reference beam component of second output beam303is removed by a polarizer360(e.g., an absorptive sheet polarizer or a polarizing beam splitter), prior to the angular displacement interferometer. Accordingly, the beam propagation direction measurement is made using only the measurement beam component. Alternatively, the angular displacement interferometer could be replaced with a differential angular displacement interferometer, which measures variations in a difference between the propagation directions of a measurement and reference beam components in an output beam. In such embodiments, the beam propagation direction measurement can be made using both the measurement and reference beam components of second output beam303. Examples of differential angular displacement interferometers are described in U.S. patent application Ser. No. 10/272,034 by Henry A. Hill, filed Oct. 15, 2002 and entitled “INTERFEROMETER FOR MEASURING CHANGES IN OPTICAL BEAM DIRECTIONS”.

In other embodiments, the system can include interferometers that direct the measurement beam to contact the measurement object more than twice.

Referring now toFIG. 3, an embodiment of an angle interferometer is shown schematically and makes angle measurements in one plane of the average direction of propagation of beam712relative to a predefined optical axis. The first embodiment comprises beam-shearing assembly generally shown at element numeral830, analyzer840, lens846, detector860, and electronic processor870. For heterodyne interferometry, input beam712comprises two orthogonally polarized optical beam components having a difference in frequencies of f1. The planes of polarization of the two orthogonally polarized components are parallel and orthogonal to the plane ofFIG. 3, respectively.

Beam-shearing assembly830introduces a lateral shear Sa1between the two orthogonally polarized beams850and852, respectively (see FIG.3). A portion of each of the spatially sheared output beams850and852are transmitted by analyzer840as components854and856, respectively. Analyzer840is orientated so that beam components854and856are both polarized in a common plane orientated at 45 degrees to the plane of FIG.3.

Next, beam components854and856are incident on lens846wherein lens846focuses beam components854and856to spots on detector860to be detected preferably by a quantum photon detector to generate electrical interference signal862or heterodyne signal s1. The spots substantially overlap. Heterodyne signal s1is transmitted to electronic processor870for determination of the heterodyne phase of signal s1and a corresponding average direction of propagation of beam712in the plane of FIG.3.

Beam-shearing assembly830comprises polarizing beam-splitters832and838, right angle prisms833and837, and truncated Porro prisms835and836. The component of beam712polarized in the plane ofFIG. 3is transmitted by polarizing beam-splitter832, reflected by right angle prism833, redirected by truncated Porro prism836, and reflected by polarizing beam-splitter838as beam850. The component of beam712polarized orthogonal to the plane ofFIG. 3is reflected by polarizing beam-splitter832, redirected by truncated Porro prism835, reflected by right angle prism837, and transmitted by polarizing beam-splitter838as beam852.

Note that the optical path in glass for each of beams854and856through beam-shearing assembly830and analyzer840are preferably the same. This feature of the apparatus design of the first embodiment produces a high stability interferometer system with respect to changes in temperature.

Heterodyne signal s1may be written as
s1=A1cos(ω1t+φ1+ζ1)  (18)
where
φ1=2k1n[d1cos θ′1+d2cos θ′2−d3cos θ′3−d4cos θ′4],  (19)
ω1=2πf1, ζ1is an offset phase not associated with phase φ1, k1=2π/λ1, λ1is the wave length of input beam712, θ′1and θ′2are angles of incidence of beam850at right angle prism833and at the polarizing beam-splitter838, respectively, (see FIG.4), θ′3and θ′4are angles of incidence of beam852at polarizing beam-splitter832and at right angle prism837, respectively, and d1, d2, d3, and d4are defined in FIG.4. It has been assumed in Eq. (19) for the purposes of demonstrating the features of the present invention in a simple fashion without departing from the scope and spirit of the present invention that all of the optical paths in beam-shearing assembly30have the same index of refraction. For a non-limiting example of d1=d3, d2=d4, θ′1+θ′2=π/2, and θ′3+θ′4=π/2, Eq. (19) reduces to the simpler expression for φ1,φ1=21/2⁢k1⁢n⁡[(d1-d2)⁡[cos⁡(θ1′+π/4)+cos⁡(θ4′+π/4)]+(d1+d2)⁡[sin⁡(θ1′+π/4)-sin⁡(θ4′+π/4)]].(20)
Lateral shear Sa1is related to properties of beam-shearing assembly830according to the equationSa1=2⁡[(d1⁢sin⁢⁢θ1′-d2⁢sin⁢⁢θ2′)⁢sec⁢⁢ϕ1′⁢cos⁢⁢ϕ1+(d3⁢sin⁢⁢θ3′-d4⁢sin⁢⁢θ4′)⁢sec⁢⁢ϕ3′⁢cos⁢⁢ϕ3](21)
where φ1and φ′1are the angles of incidence and refraction of beam850at entrance facet of polarizing beam-splitter832and φ3and φ′3are the angles of incidence and refraction of beam852at entrance facet of polarizing beam-splitter832(see FIG.4). For the non-limiting example,Sa1=21/2⁢{(d1-d2)⁡[sin⁡(θ1′+π/2)⁢sec⁢⁢ϕ1′⁢cos⁢⁢ϕ1+sin⁡(θ4′+π/2)⁢sec⁢⁢ϕ3′⁢cos⁢⁢ϕ3]+(d1+d2)⁡[sin⁡(θ1′-π/2)⁢sec⁢⁢ϕ1′⁢cos⁢⁢ϕ1-sin⁡(θ4′-π/2)⁢sec⁢⁢ϕ3′⁢cos⁢⁢ϕ3]}.(22)

The expression given for Sa1by Eqs. (21) and (22) represent the primary mechanism used for generation of the beam shear. However, there are other mechanisms for introducing a beam shear such as associated with angle of incidence dependent phase shifts (e.g., Goos-Hänchen effect).

Amplitude A1is proportional to a good approximation to a Fourier component of the Fourier transform of |h(p1)|2, i.e.,A1∝∫|h⁡(p1)⁢|2⁢cos⁡[4⁢k1⁢p1⁢S1]⁢ⅆp1(23)
where h(p1) is the Fourier transform of the amplitude of one of the beams854or856at lens846multiplied by the pupil function of lens846,
pj=sin θo,j+sin θi,j, j=1,2 . . . ,  (24)
and the definition of θo,jand θi,jare shown in FIG.5. Angles θo,jand θi,jare conjugate angles of principle rays of beam j in the object and image space of lens846. The definition of pjis shown in FIG.6.

It is evident from Eqs. (19) and (20) that the resolution of phase φ1in terms of a change in a direction of an optical beam is increased as the length 23/2(d1−d2) is increased. However, the usable range for 23/2(d1−d2) is defined by the spatial frequency bandwidth of the Fourier transform of |h(p1)2as shown by Eq. (23).

The optimum value for 23/2(d1−d2) is generally equal to approximately one half a characteristic spatial dimension of a beam transmitted by a respective pupil. Consider, for example, the case of a rectangular pupil of dimension b in the plane ofFIG. 3for both beam854and beam856at lens846and the amplitudes of beams854and856being uniform across respective pupils. For this case, |h(p1)|2is a sinc function squared, i.e., (sin x/x)2, and the Fourier transform of |h(p1)|2is a triangle function, Λ. Triangle function, Λ, has a maximum value of 1 for 23/2(d1−d2)=0 and has a value of 0 for 23/2(d1−d2)≧b. Therefore, amplitude A1=0 for 23/2(d1−d2)≧b and the resolution of phase φ1in terms of a change in a direction of an optical beam is 0 for 23/2(d1−d2)=0. Thus the optimum value for 23/2(d1−d2) is in this case approximately b/2. The actual optimum value for 23/2(d1−d2) will depend on the criterion used to define an optimum operating condition with respect to a signal-to-noise ratio, for example. For the case where the components of beam712have Gaussian intensity profiles, the optimum value for 23/2(d1−d2) will be approximately w where w is the radius at which the intensity of beam712has a value equal to 1/e of the intensity at beam712at its center.

For an example of a beam having a Gaussian intensity profile with 2 w=5.0 mm, θ1=45 degrees, and λ1=633 nm, the sensitivity of the phase φ1to changes in dφ1and dφ3expressed in differential form is given by the equationd⁢⁢φ1=k1⁢w⁡[d⁢⁢ϕ1+d⁢⁢ϕ32]=-2.5×104⁡[d⁢⁢ϕ1+d⁢⁢ϕ32].(25)

Note, as evident from Eq. (25), that the sensitivity of the change in phase φ1with respect to changes in angles dφ1and dφ3is independent of the index of refraction n. This is an important property of the first embodiment of the angle interferometer. In particular, the sensitivity of the change in phase φ1with respect to changes in angles dφ1and dφ3has a sensitivity to temperature changes that is independent in first order to thermal induced changes in the refractive index of the optical elements of beam-shearing assembly830and only dependent on thermal coefficients of expansion of the optical elements of beam-shearing assembly830. The thermal coefficients of the elements of beam-shearing assembly830can be selected to be less than ≦0.5 ppm/° C. For similar reasons, the zero value of φ1also exhibits a corresponding low sensitivity to changes in temperature of beam-shearing assembly830.

The two primary quantities that place restrictions on the range of average value [dφ1+dφ3]/2 that can be accommodated by the first embodiment are the magnitude of the difference [dφ1−dφ3]/2 and the size of the sensitive area of detector860. The amplitude of the heterodyne signal will be reduced by a factor of approximately 2 whenw⁢⁢k1⁡[[d⁢⁢ϕ1-d⁢⁢ϕ3]2]≈1.
The higher terms in dφ1and dφ3that are omitted in Eq. (25) can be easily determined from Eq. (19) if required for a particular end use application.

A second embodiment of beam-shearing assembly830is shown diagrammatically in FIG.7and comprises two prisms8330and8332and polarization beam-splitter interface8340. A first component of input beam712is transmitted twice by polarization beam-splitter interface8340and reflected by facets of prisms8330and8332to form output beam8350. A second component of input beam712is reflected twice by polarization beam-splitter interface8340and reflected by facets of prisms8330and8332to form output beam8352.

The two prisms8330and8332and polarization beam-splitter interface8340exhibit properties the same as a Penta prism with respect to relationship of the direction of propagation of beam712and the directions of propagation for beams8350and8352. Prisms8330and8332are preferably isomorphic with relative sizes selected to introduce a beam shear Sa3between beams8350and8352. The optical paths in refractive media are substantially the same for beam8350and8352. The remaining descriptions of beams8350and8352are the same as the corresponding portion of the descriptions given for beams850and852of the first embodiment with shear Sa1replaced by shear Sa3. The description of input beam712inFIG. 7is the same as the description of input beam712of the first embodiment shown in FIG3.

Details of additional angular displacement interferometers are disclosed in PCT Publication WO 00/66969 by Henry A. Hill and published Nov. 9, 2000, the contents of which is incorporated herein by reference, and the aforementioned U.S. patent application Ser. No. 10/272,034. Furthermore, techniques described in U.S. patent application Ser. No. 10/287,898, entitled “INTERFEROMETRIC CYCLIC ERROR COMPENSATION,” by Henry A. Hill, filed Nov. 5, 2002 may be incorporated into the described embodiment to compensate for cyclic errors in the output beams of the zero-shear single-pass interferometers used to determine linear and angular displacements of plane mirror object60without departing from the scope and spirit of the present invention

As is well known in the art, lithography is a critical part of manufacturing methods for making semiconducting devices. For example, U.S. Pat. No. 5,483,343 outlines steps for such manufacturing methods. These steps are described below with reference to FIGS.9and10.FIG. 9is a flow chart of the sequence of manufacturing a semiconductor device such as a semiconductor chip (e.g., IC or LSI), a liquid crystal panel or a CCD. Step1151is a design process for designing the circuit of a semiconductor device. Step1152is a process for manufacturing a mask on the basis of the circuit pattern design. Step1153is a process for manufacturing a wafer by using a material such as silicon.

Step1154is a wafer process which is called a pre-process wherein, by using the so prepared mask and wafer, circuits are formed on the wafer through lithography. To form circuits on the wafer that correspond with sufficient spatial resolution those patterns on the mask, interferometric positioning of the lithography tool relative the wafer is necessary. The interferometry methods and systems described herein can be especially useful to improve the effectiveness of the lithography used in the wafer process.

Step1155is an assembling step, which is called a post-process wherein the wafer processed by step1154is formed into semiconductor chips. This step includes assembling (dicing and bonding) and packaging (chip sealing). Step1156is an inspection step wherein operability check, durability check and so on of the semiconductor devices produced by step1155are carried out. With these processes, semiconductor devices are finished and they are shipped (step1157).

FIG. 10is a flow chart showing details of the wafer process. Step1161is an oxidation process for oxidizing the surface of a wafer. Step1162is a CVD process for forming an insulating film on the wafer surface. Step1163is an electrode forming process for forming electrodes on the wafer by vapor deposition. Step1164is an ion implanting process for implanting ions to the wafer. Step1165is a resist process for applying a resist (photosensitive material) to the wafer. Step1166is an exposure process for printing, by exposure (i.e., lithography), the circuit pattern of the mask on the wafer through the exposure apparatus described above. Once again, as described above, the use of the interferometry systems and methods described herein improve the accuracy and resolution of such lithography steps.

Step1167is a developing process for developing the exposed wafer. Step1168is an etching process for removing portions other than the developed resist image. Step1169is a resist separation process for separating the resist material remaining on the wafer after being subjected to the etching process. By repeating these processes, circuit patterns are formed and superimposed on the wafer.

The interferometry systems described above can also be used in other applications in which the relative position of an object needs to be measured precisely. For example, in applications in which a write beam such as a laser, x-ray, ion, or electron beam, marks a pattern onto a substrate as either the substrate or beam moves, the interferometry systems can be used to measure the relative movement between the substrate and write beam.

As an example, a schematic of a beam writing system1200is shown in FIG8. A chamber1201houses beam writing system1200. A source1210generates a write beam1212, and a beam focusing assembly1214directs the radiation beam to a substrate1216supported by a movable stage1218. To determine the relative position of the stage, an interferometry system1220directs a reference beam1222to a mirror1224mounted on beam focusing assembly1214and a measurement beam1226to a mirror1228mounted on stage1218. Since the reference beam contacts a mirror mounted on the beam focusing assembly, the beam writing system is an example of a system that uses a column reference. Interferometry system1220can be any of the interferometry systems described previously. Changes in the position measured by the interferometry system correspond to changes in the relative position of write beam1212on substrate1216. Interferometry system1220sends a measurement signal932to controller1230that is indicative of the relative position of write beam1212on substrate1216. Controller1230sends an output signal934to a base1236that supports and positions stage1218. In addition, controller1230sends a signal1238to source1210to vary the intensity of, or block, write beam1212so that the write beam contacts the substrate with an intensity sufficient to cause photophysical or photochemical change only at selected positions of the substrate. Controller1230can be housed within chamber1201, can be mounted on the outside of the chamber, or can be located at some location remote from chamber1201.

Furthermore, in some embodiments, controller1230can cause beam focusing assembly1214to scan the write beam over a region of the substrate, e.g., using signal1244. As a result, controller1230directs the other components of the system to pattern the substrate. The patterning is typically based on an electronic design pattern stored in the controller. In some applications the write beam patterns a resist coated on the substrate and in other applications the write beam directly patterns, e.g., etches, the substrate.

An important application of such a system is the fabrication of masks and reticles used in the lithography methods described previously. For example, to fabricate a lithography mask an electron beam can be used to pattern a chromium-coated glass substrate. In such cases where the write beam is an electron beam, the beam writing system encloses the electron beam path in a vacuum. Also, in cases where the write beam is, e.g., an electron or ion beam, the beam focusing assembly includes electric field generators such as quadrapole lenses for focusing and directing the charged particles onto the substrate under vacuum. In other cases where the write beam is a radiation beam, e.g., x-ray, UV, or visible radiation, the beam focusing assembly includes corresponding optics and for focusing and directing the radiation to the substrate.

A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. For example, although the embodiment described herein is with reference to a lithography system, the disclosed techniques can be used in other interferometry applications where the accuracy of the interferometry measurement may be compromised by time-varying optical properties of gas in the interferometer measurement and/or reference beam.

Furthermore, although the described interferometry system includes two displacement measuring interferometers and two angular displacement interferometers, other embodiments can include more or fewer than two displacement measuring interferometers and two angular displacement interferometers. For example, in embodiments where the orientation of the measurement object remains stationary, or where variations of the orientation of the measurement object are monitored independent of the interferometry system, the effect of time-varying optical properties of gas can be compensated by monitoring a single measurement beam.