Masato Shibuya

Exact sine condition in the presence of spherical aberration

Considering the real pupil curvatures, a new exact sine condition in the presence of spherical aberration is derived and its validity is confirmed by ray traces. This sine condition is useful for lens design and lens evaluation.

Resolution enhancement techniques for optical lithography and optical imaging theory

Production of a fine pattern is necessary to get a high integration degree of integrated circuits. The conventional methods which utilize high numerical aperture and short wavelength exposure are limited by designing and manufacturing of a practical lens and make the focus depth narrow. Resolution enhancement techniques (RETs) have, therefore, been required and proposed. This paper introduces a phase-shifting mask, a typical RET, points out the problems and inconsistencies of conventional optical imaging theory and explains the image formation concept of expansion of plane waves. Essentially using this concept, an attempt is also made to describe some other typical RETs with potential.

Mathematical treatment of condenser aberrations and their impact on linewidth control

While condenser aberrations under Koehler illumination were previously treated in the literature their mathematical derivation did not take conservation of radiance into consideration. Here we make use of a more rigorous derivation of the mutual intensity where the source deformation term is treated in the context of radiance conservation. The derivation predicts that condenser aberrations lead to radiance invariance while aberrations have a direct bearing on illumination uniformity and the angular extent of the local effective source. This result significantly contrasts with the previously established conclusion in the literature that condenser aberrations lead to a modification of the source radiance but preserves irradiance in the reticle plane. Source aberrations of first and third order are derived and then systematically explored both analytically and numerically. Aberration impact on linewidth control are further considered and quantified from the aerial image perspective. It is shown that third order coma has the most significant impact on CD control as a result of the asymmetry in the deformation of the source shape. Similarly coma also significantly impacts overall mask illumination uniformity.

The relation between offence against the sine condition in the presence of spherical aberration and lateral aberration

Abstract We have already derived the sine condition in the presence of spherical aberration which coincides with that proposed by Marx. In this paper, a new relation between offence against the sine condition in the presence of spherical aberration and lateral aberration is derived and is examined by a numerical calculation of ray traces.

The Non-isoplanatic Image Equation and the Effect of Not Satisfying the Sine Condition in the Scanning Microscope

Abstract By considering lack of agreement with the sine condition and using the concept of image formation by interference of plane waves, we derive a new equation for non-isoplanatic image formation. Moreover, applying this equation and considering alignment errors between optical elements, a new equation for the image formation of the object-scan type scanning microscope is derived. This type of microscope also includes laser-disc optical systems. Effects of the sine condition not being satisfied both for the illumination lens and for the collector lens are discussed.

Resolution versus depth of focus in the resolution-enhanced optical system for lithography

Practical resolution of optical lithography is often defined as the minimum feature size which can be fabricated with acceptable depth of focus. It can be predicted by calculating diffraction image contrast in various defocused plane. However since large volume of calculation is required to know image contrast under partially coherent illumination, evaluation of optical lithography systems with regard to use of the practical resolution is time consuming and does not give us quick and clear forecast on optimum optical parameters for a given lithography specifications. In this paper, we propose an analytical and intuitive method for getting image contrast in defocused planes, by use of the theory of interference fringe formation. By using this method, relations among defocus, numerical aperture, wavelength, coherence factor and image contrast are derived analytically and these parameters can be optimized for given lithography methods, which employ not only the conventional but also various resolution-enhanced methods, such as annular illumination, phase-shift, illumination control and others.