Eytan Barouch

OPTIMASK: an OPC algorithm for chrome and phase-shift mask design

A mask correction algorithm (OPTIMASK) has been designed and implemented. Its main ingredients are optical proximity correction (OPC) and optical design rule checker (ODRC). The algorithm is based on the lithographic notion that a mask has to print throughout its defocus budget, taking into account multiple defocus planes. In each defocus plane the aerial image is computed using FAIM, and the design failures are reported via ODRC. The mask correction is subjected to physical restrictions that do not allow any feature couplings to occur. The union of the failures at all defocus values determines the first step taken in correcting the mask. Then a (constrained) Newton optimization scheme is applied to optimize line shrinkage, linewidth control, and corner rounding errors. All the tools needed to optimize a specific layer within a particular cell and return the optimized layer to the original mask file have been implemented. Several examples will be shown.

Large-area optical design rule checker for logic PSM application

An aerial optical design rule checker (ODRC) that will handle large areas is used to validate the automatic CAD software used for application of alternating Phase Shift Mask technology to logic devices. An automatic alternating aperture layout algorithm developed internally by Advanced Micro Devices is applied to 0.24 to 0.50 micrometers electrical designs. The layout is then verified for different stepper and defocus values by the ODRC which utilizes the simulated aerial image to compare directly to the electrical design database. Entire databases are handled by fracturing the database into optically isolated areas or by using a sliding window technique. Small areas up to 420 um per side can be done with single processor workstations with at least 512 megabyte of memory. Larger problems require multiprocessor computers with at least 16 gigabyte of memory. Full circuit analysis should be done on systems with at least 64 gigabyte of memory in order to accomplish solving the problem in a reasonable time frame.

Using advanced simulation to aid microlithography development

An early historical overview is first presented here on the use of simulation in optical microlithography, along with a description of the general physical models. This paper then turns to more recent development work in microlithography simulation, which has followed several very different tracts. Three of the most important areas are discussed here. The first involves improvements in the underlying physical models, such as advances beyond the Kirchhoff boundary condition in optical diffraction theory, as well as a deeper understanding into the chemistry and physical behavior of photoresist materials. Such work guides basic understanding both in the optics and photoresist areas. At the other extreme, phenomenological models are being advanced to enable simulation results on large scales to be placed in the hands of device and circuit designers. Finally, optimization of the large number of allowable parameters is a pervasive problem that has received much attention and interest by the engineering community.

Derivation and Simulation of Higher Numerical Aperture Scalar Aerial Images

The application of scalar diffraction theory to a projection optics system is examined here for somewhat higher numerical aperture conditions upon removing the paraxial, or small angle, approximation that is typically made. A detailed derivation is given that notes the key physical assumptions originally contained in work by others on vector imaging theory. The asymptotic limit of large lenses and focal length sizes to object and image sizes is explicitly carried out, while keeping numerical apertures and magnification fixed. Numerical results of the resulting equations are presented for a variety of imaging conditions, including phase shift masks and modified illumination.

Exact solution of Dill's model equations for positive photoresist kinetics

The equations of Dill for bleaching of photoactive compound in positive photoresists have been solved analytically in closed form. As an application, the contrast γ, has been evaluated explicitly in the absence of reflection from the substrate.

Extending scalar aerial image calculations to higher numerical apertures

The usual formula for the scalar aerial image of an isolated object due to a projection lens system has been generalized beyond the paraxial approximation in an attempt to extend scalar diffraction theory to include numerical aperture (NA) values up to about 0.6. Beyond this regime, or certainly beyond NA=0.7, polarization effects need to be included, thereby demanding a full vector treatment and invalidating the present scalar formulation. A key point to the present scalar result without the paraxial approximation is the predicted functional dependence of the aerial image on magnification as NA increases. A second key point is that the usual scaling of λ/NA for the object dimensions and λ/NA2 for defocus become invalid for high NA systems. Numerical results of illustrative test cases are shown.

Effect of adsorbed layers on the van der Waals interaction between particles and bubbles in aqueous media

Abstract The effect of adsorbed layers on van der Waals interactions between alumina particles and bubbles in aqueous media was investigated. This system is important in flotation studies. In the absence of adsorbed layers, the interaction shows repulsion. When the alumina particles and bubbles are covered with adsorbed layers, the interaction energy changes from repulsion to attraction at small separations. The Vold and Lifshitz equations for a planar case yielded nearly identical results. However, when the interacting particles are spheres, certain differences have been obtained using the two approaches. It has been shown that the effect of adsorbed layers on the van der Waals energy is less significant than the hydrophobic interaction reported in the literature.

Double-layer interactions of unequal spheres. Part 1.—The effect of electrostatic attraction with particles of like sign of potential

The Poisson–Boltzmann equation for two unequal spheres with fixed surface potentials is analysed. When both potentials are of the same sign but of different magnitude it is shown that the electrostatic energy decreases owing to the fact that a portion of the surfaces may be attractive even though the rest of the surfaces may be repulsive. This effect depends on the separation, as well as on the difference in the potentials and the sizes of the two spheres.

Limitation of the Kirchhoff boundary conditions for aerial image simulation in 157-nm optical lithography

The aerial images of half-wavelength features with 0/spl deg/ and 180/spl deg/ phases obtained by using the Kirchhoff boundary conditions are compared with those obtained by using rigorous electromagnetic field computation for 248-nm lithography and 157-nm lithography. The discrepancies between the aerial images computed by the two methods are large at both wavelengths, but they are much larger for TM polarization at the wavelength /spl lambda/=157 nm. These discrepancies are due to diffraction effects in the aperture regions, which are more pronounced at /spl lambda/=157 nm because of the larger ratio of the thickness of the chromium absorber to the wavelength required at /spl lambda/=157 nm for a given attenuation factor. This shows that diffraction effects in the aperture regions must be included when simulating aerial images in 157-nm lithography.

Illuminator optimization for projection printing

In this paper we report a new algorithm designed to enable printability and enhanced defocus budget at half and sub- half wavelength feature sizes. An integral part of this algorithm is the optimization of aerial image contrast, performed in stages, for an algorithmically determined set of contrast cost functions. The optimization is performed on the geometric shape of the condenser filter, herein referred to as the illuminator. Combining (1) illuminator optimization, (2) reticle proximity correction, and (3) attenuated phase shift masks allows one to perform corrections to aggressive SRAM mask designs with features sizes as small as 140 nm, when employing 248 nm illumination, as well as 125 nm feature sizes of lines and spaces. We also present optimizations for 80 nm lines, with 120 nm spaces using 193 nm illumination.