The 3D modeling of high numerical aperture imaging in thin films

A modelling technique is described which is used to explore three dimensional (3D) image irradiance distributions formed by high numerical aperture (NA is greater than 0.5) lenses in homogeneous, linear films. This work uses a 3D modelling approach that is based on a plane-wave decomposition in the exit pupil. Each plane wave component is weighted by factors due to polarization, aberration, and input amplitude and phase terms. This is combined with a modified thin-film matrix technique to derive the total field amplitude at each point in a film by a coherent vector sum over all plane waves. Then the total irradiance is calculated. The model is used to show how asymmetries present in the polarized image change with the influence of a thin film through varying degrees of focus

The evaluation of positive photoresist speed

The feasibility of photographic speed values for positive photoresist is evaluated. Speed is defined as the reciprocal of exposure necessary to produce a desired response. An outline of the microlithographic process, the chemistry of positive resist, and previous exposure models precede the experimental body of work to facilitate understanding of the photoresist system. The experimental method proposes a mathematical model describing the resist response to exposure. Photographic speed values result from this model. They are tested for sensitivity to process changes using Analysis of Variance. One speed definition is chosen as a possible standard and process control. It is based on the exposure required to produce a resist thickness of .4 microns above the under-lying substrate

Laser beam modeling in optical storage systems

A computer model has been developed that simulates light propagating through an optical data storage system. A model of a laser beam that originates at a laser diode, propagates through an optical system, interacts with a optical disk, reflects back from the optical disk into the system, and propagates to data and servo detectors is discussed

Reduced basis method for source mask optimization

Image modeling and simulation are critical to extending the limits of leading edge lithography technologies used for IC making. Simultaneous source mask optimization (SMO) has become an important objective in the field of computational lithography. SMO is considered essential to extending immersion lithography beyond the 45nm node. However, SMO is computationally extremely challenging and time-consuming. The key challenges are due to run time vs. accuracy tradeoffs of the imaging models used for the computational lithography. We present a new technique to be incorporated in the SMO flow. This new approach is based on the reduced basis method (RBM) applied to the simulation of light transmission through the lithography masks. It provides a rigorous approximation to the exact lithographical problem, based on fully vectorial Maxwell's equations. Using the reduced basis method, the optimization process is divided into an offline and an online steps. In the offline step, a RBM model with variable geometrical parameters is built self-adaptively and using a Finite Element (FEM) based solver. In the online step, the RBM model can be solved very fast for arbitrary illumination and geometrical parameters, such as dimensions of OPC features, line widths, etc. This approach dramatically reduces computational costs of the optimization procedure while providing accuracy superior to the approaches involving simplified mask models. RBM furthermore provides rigorous error estimators, which assure the quality and reliability of the reduced basis solutions. We apply the reduced basis method to a 3D SMO example. We quantify performance, computational costs and accuracy of our method.Comment: BACUS Photomask Technology 201

Comparison of Scalar and Vector Diffraction Modelling for Deep-UV Lithography

As deep-UV projection system complexity increases to pursue 0.25 micron resolution, the adequacy of diffraction theory using scalar models is of concern. Approximations that are suitable for low NA reduction systems do not hold true for higher NAs. Furthermore, scalar models treat all illumination as polarized perpendicular to the plane of incidence. Feature interaction effects from the polarized radiation of an excimer laser both in a projection system and within a photoresist film cannot be accounted for. Vector diffraction theory has been utilized more appropriately for modelling in these situations, but deviations of scalar predictions from those made with vector models do not warrant abandonment. This paper will describe investigations into scalar and vector diffraction modelling for 248 nm lithography. An experimental design approach was used to study the effects and interactions of coherence, polarization, and numerical aperture on a resist feature response. An exposure latitude response to achieve 1 0% linewidth control with +1- 0.3 micron of defocus was utilized. Both vector and scalar diffraction models were used to simulate process runs. Experimental comparisons were made using a variable NA, variable coherence deep-UV projection system, adapted for control of polarization at the aperture of the mask. Exposure latitude response surfaces are presented, along with details on isolated process runs

Optical lithography into the millennium: Sensitivity to aberrations, vibration and polarization

ABSTRACT Various factors, such as lens aberrations, system vibration and the choice of illumination polarization can degrade the level of modulation, and hence, image quality. This paper discusses the sensitivity of multiple feature types to these factors. It is shown that aberration sensitivity increases linearly with decreasing resolution, scaled to the Rayleigh criteria. An analysis of the vibration tolerance is done for transverse and axial vibration planes, where the effects on the process window and CD uniformity are measured. The vibration is shown to decrease the process window greater for low contrast images and is shown to scale directly with the resolution. The new millennium will usher in optical systems with very high NA lenses (>0.75 NA) for 248 nm, 193 nm and 157 nm. This paper re-examines the role of the polarization on required specifications of the exposure tool optics. It is found that tight polarization specifications with <10% residual polarization will be needed for future systems

High numerical aperture imaging in homogeneous thin films.

This dissertation investigates imaging phenomena by lenses of high relative numerical aperture (NA) in the first layer of a homogeneous thin film stack. The imaging is described by a high NA model that combines elements of vector imaging theory with traditional thin-film optics. Various examples are studied with an emphasis on analyzing the polarization effects of the illumination. Experiments are shown that verify aspects of the model. A brief review of the development of high NA imaging theory is given. The use of the Debye approximation dominates most of the previous work. Investigation of imaging in thin films has been limited to the area of micro-photolithography, where verification studies are done in photoresist. High NA imaging in films is described in terms of matrix formalism. The image is based on the Debye approach in which the vector field is characterized as a plane wave decomposition for each Cartesian component of the electric field, E. This is used to describe propagation from object to entrance pupil, from entrance pupil to exit pupil, and from exit pupil to thin-film stack. If the first film of the stack is located at or near focus, the amplitude and phase of each plane wave, weighted by factors due to polarization, aberration and object diffraction, are used as input into thin-film equations to calculate the local field volume. The image distribution within the film is described by the absorbed electric energy distribution, which is proportional to |E|². The overall effect of the film is shown to significantly reduce vector effects and asymmetries in the image. This is mainly due to the reduction of NA in the film by refraction. The image of a tri-bar object with an extreme NA of 0.95 is simulated. The differences between two orthogonal polarizations are shown to be small. This is attributed to the large contribution due to the central zone of the pupil. The behavior is shown to be similar to three-beam interference. Modification of this simulation with a annular pupil results in image behavior that is very similar to two-beam interference with increased image differences between two polarizations. Two-beam and three-beam interference is shown to be derived from the general imaging equation, resulting in concise analytic vector equations. Experimental verification in photoresist film is shown using a cross-sectioning technique that highlights the image distribution. Structural artifacts within the simulated image are identified in experimental scanning electron microscope photographs. Large differences are seen between S and P polarized illumination