Michael Totzeck

Phase-singularities in 2D diffraction fields and interference microscopy

Abstract Phase singularities in two-dimensional diffraction fields and interference microscopy images of deep topometrical sub-wavelength structures are discussed using a scalar model system, measurements and a rigorous computation of diffraction fields and images. Both coherent and partially coherent illumination are considered. A simple relation between transverse plane screw-type phase-singularities and longitudinal edge-type phase-singularities is derived. Phase-singularities in the image are attributed to electromagnetic near-field phase-singularities of the edge-type. Although image phase-singularities yield supersteep edges in the measured topometry, the Rayleigh resolution limit is still valid.

Polarization influence on imaging

We give a general introduction into polarized imaging and report on a Jones pupil approach for a complete evaluation of the resulting optical performance. The Jones pupil assigns a Jones matrix to each point of the exit pupil, describing the impact of both the global phase and the polarization on imaging. While we already can learn much about the optical system by taking a close look at the Jones pupil-and starting imaging simulations from it-a quantitative assessment is necessary for a complete evaluation of imaging. To do this, we generalize the concept of scalar Zernike aberrations to Jones-Zernike aberrations by expansion of the Jones pupil into vector polynomials. The resulting method is nonparaxial, i.e., the effect of the polarization-dependent contrast loss for high numerical apertures is included. The aberrations of the Jones matrix pupil are a suitable tool to identify the main drivers determining polarization performance. Furthermore, they enable us to compare the polarized and unpolarized performance of such a characterized lithographic system.

Polarization effects associated with hyper-numerical-aperture (>1) lithography

The use of immersion technology will extend the lifetime of 193-nm technology by enabling numerical apertures (NAs) much greater than 1.0. The ultimate limits of NA are explored by analysis of polarization effects at the reticle and imaging effects at the wafer. The effect of reticle birefringence with polarized illumination is explored. The effects on critical dimension (CD) uniformity are mitigated if the maximum birefringence is <5 nm/cm. Hertzian or micropolarization due to the size of the reticle structures is examined through rigorous simulation. For the regime of interest, 20- to 50-nm imaging, it is found that dense features on a Cr binary reticle will polarize the light into the TE component upward of 15%. Below this regime, the light becomes polarized in the TM direction. The use of polarization in the illuminator for imaging will result in substantial gains in exposure latitude and mask error factor (MEF) when the NA~1.3 with 45-nm lines at 193 nm, with overall polarization effects increasing with decreasing k1. The end-of-line pullback for 2-D patterns is reduced by the use of TE polarization in the illuminator. The interaction between the reticle-induced polarization and the illumination polarization is shown to be significant when an analysis is done using rigorous mask simulation instead of the more common Kirchhoff approximation. The impact of birefringence in the lens is analyzed using Jones pupil matrices to create a local polarization error in the pupil. The photoresist process is shown to interact with polarization. Different photoresists will show varying degrees of sensitivity to polarization variation.

Orientation Zernike polynomials: a useful way to describe the polarization effects of optical imaging systems

We introduce the new concept of orientation Zernike polynomials, a base function representation of retardation and diattenuation in close analogy to the wavefront description by scalar Zernike polynomials. We show that the orientation Zernike polynomials provide a complete and systematic description of vector imaging using high numerical aperture lithography lenses and, hence, a basis for an in depth understanding of both polarized and unpolarized imaging, and its modeling.

Rigorous coupled-wave analysis calculus of submicrometer interference pattern and resolving edge position versus signal-to-noise ratio

The signal-to-noise ratio required to obtain 10-nm accuracy in the measurement of lateral position is studied with an interference microscope. Evaluations are performed using the rigorous coupled-wave analysis (RCWA) modal approach and Hopkins image formation theory.

How to describe polarization influence on imaging (Invited Paper)

We give a general introduction into polarized imaging and report on a Jones-pupil approach for a complete evaluation of the resulting optical performance. The Jones pupil assigns a Jones matrix to each point of the exit pupil describing the impact of both the global phase and the polarization on imaging. While we can learn already a lot about the optical system by taking a close look at the Jones pupil - and starting imaging simulations from it - a quantitative assessment is necessary for a complete evaluation of imaging. To do this, we generalize the concept of scalar Zernike aberrations to Jones-Zernike aberrations by expansion of the Jones pupil into vector polynomials. The resulting method is non-paraxial, i.e. the effect of the polarization dependent contrast loss for high numerical apertures is included. The aberrations of the Jones-matrix pupil are a suitable tool to identify the main drivers determining the polarization performance. Furthermore, they enable us to compare the polarized and the unpolarized performance of the such characterized lithographic system.

Achromatic nulling interferometer based on a geometric spin-redirection phase

Nulling interferometry aims to perform destructive interference achromatically. It is used to detect a faint source near a bright one and to provide dark field, an annular pupil, and rotational shear. A nulling out-of-plane interferometer that utilizes the geometric phase of spin redirection is proposed. The degree of nulling is determined by beam collimation and angular orientation of mirrors. Simulations and experiments are in reasonable agreement.

The impact of projection lens polarization properties on lithographic process at hyper-NA

The continuous implementation of novel technological advances in optical lithography is pushing the technology to ever smaller feature sizes. For instance, it is now well recognized that the 45nm node will be executed using state-of-the-art ArF (193nm) hyper-NA immersion-lithography. Nevertheless, a substantial effort will be necessary to make imaging enhancement techniques like hyper-NA immersion technology, polarized illumination or sophisticated illumination modes routinely available for production environments. In order to support these trends, more stringent demands need to be placed on the lithographic optics. Although this holds for both the illumination unit and the projection lens, this paper will focus on the latter module. Today, projection lens aberrations are well controlled and their lithographic impact is understood. With the advent of imaging enhancement techniques such as hyper-NA immersion lithography and the implementation of polarized illumination, a clear description and control of the state of polarization throughout the complete optical system is required. Before polarization was used to enhance imaging, the imaging properties at each field position of the lens could be fully characterized by 2 pupil maps: a phase map and a transmission map. For polarized imaging, these two maps are replaced by a 2x2 complex Jones matrix for each point in the pupil. Although such a pupil of Jones matrices (short: Jones pupil) allows for a full and accurate description of the physical imaging, it seems to lack transparency towards direct visualization and lithographic imaging relevance. In this paper we will present a comprehensive method to decompose the Jones pupils into quantities that represent a clear physical interpretation and we will study the relevance of these quantities for the imaging properties of lithography lenses.

Challenges with hyper-NA (NA>1.0) polarized light lithography for sub λ/4 resolution

The use of immersion technology will extend the lifetime of 193nm and 157nm lithography by enabling numerical apertures (NA) much greater than 1.0. This paper explores the effects that will occur when the high NA systems are augmented with polarization.. Specifically we show that there are strong interactions between the polarization induced by the reticle and polarization in the optics. This has a direct impact on the across-field specification of the polarization of the optical system as it causes a large variation in the imaging impact in photoresist. The impact of lens and reticle birefringence on the imaging is also analyzed. We show that reticle birefringence should not be a major concern when the birefringence is maintained to 2nm/cm - 4nm/cm levels. The lens can be modeled by a Jones matrix approach, where multiple pupils must be defined for each polarization state. We show the impact of the optical components by using a rigorous photoresist simulation on the process window of sub-50nm features using NA>1.3. The simulator uses a full Maxwell equation solver for the mask, polarized illumination, a Jones matrix approach for the pupil, and a photoresist simulation with calibrated model. The photoresist process is also shown to interact with polarization. Different photoresist will show varying degrees of sensitivity to polarization variation.

Edge localization of subwavelength structures by use of polarization interferometry and extreme-value criteria

A polarization interferometric method is presented for the quantitative microscopy of topographical structures with subwavelength linewidths. A liquid-crystal phase shifter is inserted into the imaging optics of a reflected-light microscope, and the principles of phase-shifting interferometry are applied to measuring the phase and the contrast of the TE-polarized image (E parallel edge) with the TM-polarized image (E perpendicular edge) as the reference. This common-path interferometric method provides selective edge detection for line structures because the polarization difference is localized at the structure edges. Two different threshold criteria for linewidth determination are discussed: distance of the contrast minima and distance of the points of the steepest phase change. Linewidths as small as 300 nm were measured at a 635-nm wavelength. The dependence on the illumination numerical aperture, as well as on the material, the width, and the depth of the structure, is investigated both experimentally and by rigorous numerical simulations.