The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

A lithographic apparatus configured to project a patterned beam of radiation onto a target portion of a substrate is disclosed. The apparatus includes a first radiation dose detector and a second radiation dose detector, each detector comprising a secondary electron emission surface configured to receive a radiation flux and to emit secondary electrons due to the receipt of the radiation flux, the first radiation dose detector located upstream with respect to the second radiation dose detector viewed with respect to a direction of radiation transmission, and a meter, connected to each detector, to detect a current or voltage resulting from the secondary electron emission from the respective electron emission surface.

Lithographic apparatus, and device manufacturing method

Advancements in optical lithography tools, processes, and patterning materials have been critical to the continued performance increases of semiconductor devices as well as to the overall economics of the semiconductor industry.1 Reducing the wavelength of the source radiation has been a traditional pathway to increase resolution in optical lithography.1-3 In recent years, the technological challenges and the soaring costs associated with developing new exposure tools and new imaging materials have slowed the progress of wavelength scaling, evidenced by the decision not to commercialize 157 nm (F2 excimer) lithography in 2004.4 Rather than reducing the vacuum wavelength of the illumination, the semiconductor industry instead turned to scaling the effective wavelength via immersion lithography to extend the resolution capabilities of 193 nm lithography. Immersion lithography, which utilizes a coupling medium with a refractive index greater than that of air between the last lens element (LLE) and the photoresist, provides an increased depth-of-focus (DOF) and enables imaging systems with numerical apertures greater than one.5-13 This approach is economically attractive since it continues to use large amounts of the existing lithographic tooling infrastructure and patterning materials. In particular, the rapid development and commercialization of 193 nm water immersion lithography helped seal the fate of 157 nm lithography.

Advances in patterning materials for 193 nm immersion lithography.

The image display apparatus includes an observation optical system including first and second optical elements which respectively introducing first and second light fluxes from first and second image-forming elements to first and second exit pupils, and a relay optical system. The relay optical system causes third and fourth light fluxes from the second and first image-forming elements to form intermediate images and introducing them to the first and second optical elements. The observation optical system displays images corresponding to the first and second original images in mutually different viewing angle areas by introducing the first and third light fluxes to the first exit pupil through the first optical element, and displays images corresponding to the second and first original images in mutually different viewing angle areas by introducing the second and fourth light fluxes to the second exit pupil through the second optical element.

Image display apparatus

First and second virtual grates are defined as respective sets of parallel virtual lines extending across a layout area in first and second perpendicular directions, respectively. The virtual lines of the first and second virtual grates correspond to placement locations for layout features in lower and higher chip levels, respectively. Each intersection point between virtual lines of the first and second virtual grates is a gridpoint within a vertical connection placement grid. Vertical connection structures are placed at a number of gridpoints within the vertical connection placement grid so as to provide electrical connectivity between layout features in the lower and higher chip levels. The vertical connection structures are placed so as to minimize a number of different spacing sizes between neighboring vertical connection structures across the vertical connection placement grid, while simultaneously minimizing to an extent possible layout area size. The vertical connection structures may be contacts or vias.

Methods for defining contact grid in dynamic array architecture

A newly developed sub-resolution assist feature (SRAF) placement technique with two-dimensional
transmission cross coefficient (2D-TCC) is described in this paper. In SRAF placement with 2D-TCC, Hopkins'
aerial image equation with four-dimensional TCC is decomposed into the sum of Fourier transforms of diffracted
light weighted by 2D-TCC, introducing an approximated aerial image so as to place SRAFs into a given reticle
layout. SRAFs are placed at peak positions of the approximated aerial image for enhanced resolution. Since the
approximated aerial image can handle the full optical model, SRAFs can be automatically optimized to the given
optical condition to generate the optimized reticle. The validity of this technique was confirmed by experiment
using a Canon FPA6000-ES6a, 248 nm with a numerical aperture (NA) of 0.86. A binary reticle optimized by this
technique with mild off-axis illumination was used in the experiment. Both isolated and dense 100 nm contacts (k 1 
= 0.35) were simultaneously resolved with the aid of this technique.

Resolution enhancement by aerial image approximation with 2D-TCC

In this paper, a new resolution enhancement technique named 2D-TCC technique is proposed. This method can enhance resolution of line patterns as well as that of contact hole patterns by the use of an approximate aerial image. The aerial image, which is obtained by 2D-TCC calculation, expresses the degree of coherence at the image plane of a projection optic considering mask transmission at the object plane. OPC of desired patterns and placement of assist patterns can be simultaneously performed according to an approximate aerial image called a 2D-TCC map. Fast calculation due to truncation of a series in calculating an aerial image is another advantage. Results of mask optimization for various line patterns and the validity of the 2D-TCC technique by simulations and experiments are reported.

Mask optimization for arbitrary patterns with 2D-TCC resolution enhancement technique

The extendibility of 2D-TCC technique to an isolated line of 45 nm width is investigated in this paper. The 2D-TCC
technique optimizes mask patterns placing assist pattern automatically. For 45 nm line patterns, the assist pattern width
generally becomes much smaller than the exposure wavelength of 193 nm. Thus, the impact of the topography of a mask
is examined using an electro-magnetic field (EMF) simulation. This simulation indicates that unwanted assist pattern
printings are brought about by assist patterns with a smaller size than expected by the Kirchhoff's approximation. The
difference, however, can be easily solved by giving a bias to the main pattern in the optimized mask. The main pattern
bias decreases DOF very little. Furthermore, DOF simulated with a thick mask model is roughly the same as that
simulated with a thin mask model. Therefore the topography of the optimized mask does not have an influence on the
assist pattern position of the optimized mask. From these results, we have confirmed that the 2D-TCC technique can be
extended to the optimization of 45 nm line patterns. As one of the notable features, the optimized aperiodic assist pattern
greatly reduces MEEF compared with the conventional periodic assist pattern. To verify the feasibility of the 2D-TCC
technique for 45 nm line, we performed experiment with an optimized mask. Experimental results showed that DOF
increased with the number of assist pattern as simulation indicated. In addition, a defect whose length was twice that of
the assist pattern did not have an influence on CD. From these results we have confirmed that the 2D-TCC technique can
enhance the resolution of 45 nm line and has practical feasibility.

Extension of the 2D-TCC technique to optimize mask pattern layouts

There is provided an interferometer for measuring a surface shape of an optical element using interference, including a reference wave-front generating unit for generating a reference wave front for measuring the surface shape, which is provided in a target optical path, and includes an Alvarez lens.

Interferometer and interferance measurement method

A projection optical system for projecting a pattern of a first object onto a second object. The projection optical system includes a field stop provided to an optical element in the projection optical system, which is closest to the second object. The field stop is provided for shielding the outside of a pattern projected area on the second object.

Yoshiyuki Sekine

Papers

Resolution enhancement by aerial image approximation with 2D-TCC

Mask optimization for arbitrary patterns with 2D-TCC resolution enhancement technique

Extension of the 2D-TCC technique to optimize mask pattern layouts

Interferometer and interferance measurement method

Projection optical system and exposure apparatus having the same