Mechanistic Advantages of Organotin Molecular EUV Photoresists.

Extreme ultraviolet (EUV)-induced radiation exposure chemistry in organotin-oxo systems, represented by the archetypal [(R-Sn)12O14(OH)6](A)2 cage, has been investigated with density functional theory. Upholding existing experimental evidence of Sn-C cleavage-dominant chemistry, computations have revealed that either electron attachment or ionization can single-handedly trigger tin-carbon bond cleavage, partially explaining the current EUV sensitivity advantage of metal oxide systems. We have revealed that tin atoms at different parts of the molecule react differently to ionization and electron attachment and have identified such selectivity as a result of local coordination chemistry instead of the macro geometry of the molecule. An ionization-deprotonation pathway has also been identified to explain the observed evolution of an anion conjugate acid upon exposure and anion mass dependence in resist sensitivity.

Quantitative phase retrieval with arbitrary pupil and illumination.

We present a general algorithm for combining measurements taken under various illumination and imaging conditions to quantitatively extract the amplitude and phase of an object wave. The algorithm uses the weak object transfer function, which incorporates arbitrary pupil functions and partially coherent illumination. The approach is extended beyond the weak object regime using an iterative algorithm. We demonstrate the method on measurements of Extreme Ultraviolet Lithography (EUV) multilayer mask defects taken in an EUV zone plate microscope with both a standard zone plate lens and a zone plate implementing Zernike phase contrast.

Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks.

We report theoretical and experimental results for imaging of electromagnetic phase edge effects in lithography photomasks. Our method starts from the transport of intensity equation (TIE), which solves for phase from through-focus intensity images. Traditional TIE algorithms make an implicit assumption that the underlying in-plane power flow is curl-free. Motivated by our current study, we describe a practical situation in which this assumption breaks down. Strong absorption gradients in mask features interact with phase edges to contribute a curl to the in-plane Poynting vector, causing severe artifacts in the phase recovered. We derive how curl effects are coupled into intensity measurements and propose an iterative algorithm that not only corrects the artifacts, but also recovers missing curl components.

Modeling of through-focus aerial image with aberration and imaginary mask edge effects in optical lithography simulation.

Aerial image through focus in the presence of aberrations and electromagnetic edge effects modeled by adding ±π/2 phase at pattern edges is expanded by a quadratic equation with respect to focus. The quadratic equation is expressed by four coefficients that are adequately independent of both mask layout and the variations in the optical setting in projection printing, thus saving the computation cost of the quadratic fit for each individual layout edge position in a new mask pattern or variation from a nominal optical setting. The error of this method is less than 1% for any typical integrated circuit features. This accuracy holds when the defocus is less than one Rayleigh unit (0.5λ/NA(2), where λ is a wavelength and NA is the numerical aperture) and the root mean square of the existing aberration is less than 0.02λ, which encompasses current lithography practice. More importantly, the method is a foundation for future first-cut accurate algebraic imaging models that have sufficient speed for assessing the desired or undesired changes in the through-focus images of millions of features as the optical system conditions change. These optical system changes occur naturally across the image field, and aberration levels are even programmed in tuning modern tooling to compensate for electromagnetic mask edge effects.

Numerical experiment of the Shannon entropy in partially coherent imaging by Koehler illumination to show the relationship to degree of coherence.

This paper describes the Shannon entropy in a partially coherent imaging system with Koehler illumination. Numerical simulation shows that the entropy has a one-to-one relationship with the normalized mutual intensity given by the van Cittert-Zernike theorem. Analytical evaluation shows that the entropy is consistent with the definition of coherence and incoherence, which is also verified by numerical simulations. Additional numerical experiments confirm that the entropy depends on the source intensity distribution, polarization state of the source, object, and pupil. Therefore, the entropy quantitatively measures the degree of coherence of the partially coherent imaging system.

Expansion of image interaction by the eigenfunction of the transmission cross coefficient to show the interaction between features.

This paper presents a method for evaluating the image interaction of two object patterns of arbitrary shape in partially coherent imaging. The interaction is shown to be the interference of the eigenfunctions of the transmission cross coefficient at the image plane convolved with each of the object patterns. For two arbitrary patterns, the ith eigenfunction convolved with one object pattern interferes only with the ith eigenfunction convolved with the second object pattern. This method is useful for understanding how object feature shapes influence image interactions, and examples are simulated to evaluate the method. A method to determine constructive and destructive interference areas is also introduced.

Self-organized silver nanoparticles for three-dimensional plasmonic crystals.

Metal nanostructures that support surface plasmons are compelling as plasmonic circuit elements and as the building blocks for metamaterials. We demonstrate here the spontaneous self-assembly of shaped silver nanoparticles into three-dimensional plasmonic crystals that display a frequency-selective response in the visible wavelengths. Extensive long-range order mediated by exceptional colloid monodispersity gives rise to optical passbands that can be tuned by particle volume fraction. These metallic supercrystals present a new paradigm for the fabrication of plasmonic materials, delivering a functional, tunable, completely bottom-up optical element that can be constructed on a massively parallel scale without lithography.