Completer polarimetry for immersion lithography equipment that comprises Stokes polarimetry of illumination and
Mueller matrix polarimetry of projecting optics had been established. It was found that illumination and projecting optics
were slightly different from our expectation. These differences might affect optical proximity correction and source mask
optimization. However, no lithographer can desterilize parameter sets from the polarimetry for the use of lithography
calculation because of their formats, Stokes parameters and Mueller matrix. Conventional lithography simulators require
the Jones vector and Jones matrix only.
When the illumination was partial polarization or the projecting optics was partially polarizing or partially depolarizing,
the Jones calculus cannot support these situations. The Mueller calculus is needed for the case that involves polarizationdepolarization
and depolarization-polarization translations. Previous works showed that actual un-polarization of
illumination was somewhat polarized in the scan (y) direction and an actual catadioptric projecting optics has a little
degrees of polarizance in the slit (x) direction. On the other hand, if you took the aberration effects into the lithography
calculation, you had to use the Jones calculus. Therefore, for the lithography calculation with actual polarization data as
well as actual aberration data, a special technique is required to handle these data. This paper describes how to physically
convert Stokes parameters, which are multiplied by a general Mueller matrix, into Jones vectors. This method permits us
to use the actual polarization data to the lithography calculation.
For immersion lithography with aggressive polarization illumination settings, it is important to newly construct two
systems for diagnosing lithography tools; Stokes polarimetry of illumination and Mueller matrix polarimetry of
projection lenses. At the SPIE conference on Optical Microlithography XXI in 2008, the authors had already reported on
the former Stokes polarimetry. True polarization states of several illumination settings emerged. On the other hand, the
latter Mueller matrix polarimetry is thought more complicated than the Stokes polarimetry. Therefore, the Mueller
matrix polarimetry is reported separating into two papers. A theoretical approach to realizing the polarimetry has
reported at the SPIE conference on Lithography Asia 2009.
The test mask for the Mueller matrix polarimetry also comprises thin-plate polarizers and wide-view-angle quarter-waveplates,
both which are developed by collaboration with Kogakugiken Corporation in Japan. Mueller matrices of the
sample projecting optics are reconstructed by sixteen measurements of Stokes parameters of a light ray that reaches the
wafer plane though the test mask and the projecting optics. The Stokes parameters are measured with a polarization
measurement system already equipped on a side stage lying at the wafer plane. It took about seven hours to capture all
the images at five image heights within the static exposure field. Stokes parameters are automatically calculated from the
images and outputted from the lithography tools as a text file, and Mueller matrices are calculated by homebuilt software
in a short time. All the images were captured under the identical illumination condition that the tool manufacturer calls
"un-polarization".
It will be required for more accurate lithography simulation of complicated mask patterns then ever, under hyper-NA
(numerical aperture) projection lens and aggressive small-aperture polarized-light illumination, to construct two systems
of polarimetry; one is polarimetry for illumination, and the other is Mueller matrix polarimetry for projection lenses. The
former polarimetry already reported by the authors is necessary for us to appreciate how the true polarization state of
illumination is. The polarimeter mask described in the paper determines illumination polarization states by Stokes
parameters. The latter polarimetry is the main subject of this paper. A Mueller matrix is a translation matrix of the input
Stokes parameters to the output Stokes parameters. With the full elements of the Mueller matrix of a projection lens, the
Stokes parameters of a light at the wafer plane can be easily predicted from the Stokes parameters of any illumination
conditions. This paper proposed a new method of Mueller matrix polarimetry and a monitor mask used for 193-nm
immersion lithography tools with a polarization monitor at the wafer plane.
Ellipsometry is defined as a technique for determining the properties of a bulk material or a thin film, such as optical
index and thickness, from the measurement of a polarization state of a reflected light or a change of polarization states
between the incident and reflected lights. On the other hand, polarimetry is defined as a technique for determining a
polarization state of a light. In other words, ellipsometry uses polarization as a probe and polarimetry measures
polarization itself.
We have constructed a theory of polarimetry of illumination used in lithography equipments, fabricated a polarimeter
mask, and demonstrated it for a hyper-NA (numerical aperture) immersion lithography scanner. The polarimeter mask
comprises polarizers and quarter-wave (λ/4) plates that are crammed into a narrow space with a height of 6.35 mm. The
thin plate polarizers available at a wavelength of 193 nm are made of calcite, and the λ/4-plates insensitive to angle of
incidence are made of four thin plates, two of which are crystalline quartz; the other two are sapphire. A light traveling
through a window of the polarimeter mask reaches an image detector at the wafer level through projection optics. Stokes
parameters of the illumination light can be measured without any influence from polarization characteristics of the
projection optics between the mask and the image detector.
We have constructed a theory of polarimetry of illumination used in 193-nm lithography equipments, fabricated a
polarimeter mask, and demonstrated it for a hyper-NA (numerical aperture) lithography scanner. The polarimeter mask
comprises newly- developed polarizers and quarter-wave (λ/4) plates. The thin plate polarizers are made of calcite
(CaCO3), and the λ/4 plates are composed of two crystalline quartz (α-SiO2) plates and two sapphire (Al2O3) plates. A
light traveling through a window of the polarimeter mask reaches an image detector at the wafer level through projection
optics. Whereas the polarization states of the projection optics are unknown to us, Stokes parameters of the illumination
light are formulated without any influence from the projection optics.
A new focus monitor reticle is proposed to measure field curvature and even wave-front aberrations. A grating pattern comprising opaque line, naked line and (pi) /2-phase-shifted groove with their width ratio equivalent to 2/1/1 makes either of first-order rays of diffraction disappear entirely. The other first-order ray interferes with the zeroth-order ray to form interference fringes with the ability of moving proportional to a defocus. This paper describes basic characteristics of the reticle and demonstration for a krypton fluoride (KrF) excimer laser scanner with a numerical aperture (NA) of 0.73 as an application of the reticle. Using overlapped exposures and an overlay inspection tool, the measurement of field curvature verified to achieve high accuracy of several nanometers or better. Besides, even wave-front aberrations up to six-foil were characterized with a high degree of accuracy.
Measurement techniques for higher order aberrations of a projection optical system in photolithographic exposure tools have been established. Even-type and odd-type aberrations are independently obtained from printed grouped lines on a wafer by three-beam interference under highly coherent illumination. Even-type aberrations, i.e. spherical aberration and astigmatism, are derived from the best focus position of vertical, horizontal and orthogonal grouped lines by an optical microscope. Odd-type aberrations, i.e. coma and trefoil, are obtained by detecting relative shifts of fine grouped lines to a large pattern by an overlay inspection tool. The qualitative diagnosis for lens aberrations was demonstrated to a krypton fluoride excimer laser scanner.
Coma aberration of projection optics and asymmetric illumination degrade a resist profile symmetricity and enhanced a placement error which depend on pattern size, density and feature. Relative displacements between 2.0 micrometer isolated lines and sub-micron periodic lines are measured to characterize the coma aberration and the illumination telecentricity. A conventional overlay inspection tool and bars-in-bars marks are used for this evaluation. It is difficult to measure the placement error of periodic patterns because their inner patterns have a different placement error from their both ends. The differences in line- width between both ends of periodic lines are caused by the differences in placement errors between their inner and their both ends patterns. The measurement marks for periodic lines are fabricated by the double exposure of two marks. When the resist patterns are imaged by the interference of only three diffracted beams, the coma aberration of Zernike's polynomials can be calculated by the simple expressions from the measurement results. We derived the condition of coherency (sigma) and pattern pitch P which satisfy the imaging of only three diffracted beams. The coma aberration is estimated to be 0.12 wavelength at maximum for the exposure system we applied. In this method, the focus is not so important for the accurate measurement because the measurement data remain constant at any foci. It takes only one hour to estimate the coma aberration completely including a sample making (sample making: 0.5 h, measurement/evaluation: 0.5 h). The relative pattern shifts between large patterns and fine patterns could be usually caused by not only coma aberration but also illumination optics. The telecentricity of the illumination optics is also discussed in this paper.
A laboratory reflectometer with a laser produced plasma source and a constant deviation angle monochromator is used as an ellipsometer to evaluate a transmission multilayer phase shifter. With use of the phase shifter, all normalized Stokes parameters of the incident beam to the reflectometer from the monochromator were measured.
Soft-x-ray transmission multilayers have been designed and fabricated for use as polarizing elements. Polarization performance of the multilayers has been studied at a photon energy of 97 eV by rotating analyzer ellipsometry with a multilayer reflection polarizer. The transmission multilayers were found to be a good polarizer of 99.2% polarizance and a phase shifter of 90 degree(s) retardation with equal transmission ratio (5:3) and high throughput around 10%.
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