Polarization influence on imaging

Totzeck, Michael; Gräupner, Paul; Heil, Tilmann; Göhnermeier, Aksel; Dittmann, O. J.; Krähmer, D. S.; Kamenov, V. P.; Ruoff, Johannes; Flagello, Donis G.

doi:10.1117/1.2049187

Cited by 23 publications

(13 citation statements)

References 10 publications

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“…, N 2 , p, q = 1 or 2, p = (p + 1) mod 2, q = (q + 1) mod 2, and f ( ω (2(i−1)+p)(2(j−1)+q) ) is described in Eqn. (26). In Eqn.…”

Section: Generalized Wavelet Penalty For Two-phase Psm Optimizationmentioning

confidence: 95%

Gradient-based resolution enhancement optimization methods based on vector imaging model

Dong

2012

SPIE Proceedings

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Recently, a set of gradient-based optical proximity correction (OPC) and phase shifting mask (PSM) optimization methods have been developed to solve for the inverse lithography problem under scalar imaging models, which are only accurate for numerical apertures (NA) less than approximately 0.4. However, as the lithography technology node enters the 45nm realm, immersion lithography systems with hyper-NA (NA>1) are now extensively used in the semiconductor industry. For the hyper-NA lithography systems, the vector nature of the electromagnetic field must be taken into account, leading to the vector imaging models. Thus, the OPC and PSM optimization approaches developed under the scalar imaging models are inadequate to enhance the resolution in the immersion lithography systems. This paper focuses on developing gradient-based OPC and PSM optimization algorithms under vector imaging models. The mask optimization framework is first formulated, in which the imaging process of the optical lithography system is represented by an integrative and analytic vector imaging model. The steepest descent algorithm is then used to optimize the mask iteratively. Subsequently, a generalized wavelet penalty (GWP) is proposed to improve the manufacturability of the mask, and results in smaller pattern errors and CD errors than the traditional wavelet penalty (WP). Finally, a set of algorithm acceleration techniques are exploited to speed up the proposed algorithms.

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“…, N 2 , p, q = 1 or 2, p = (p + 1) mod 2, q = (q + 1) mod 2, and f ( ω (2(i−1)+p)(2(j−1)+q) ) is described in Eqn. (26). In Eqn.…”

Section: Generalized Wavelet Penalty For Two-phase Psm Optimizationmentioning

confidence: 95%

Gradient-based resolution enhancement optimization methods based on vector imaging model

Dong

2012

SPIE Proceedings

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“…However, high-NA optics affects the polarization of the light close to the pupil edge where the highest spatial frequencies propagate, thereby influencing the imaging of the sharpest mask-elements. 28 This effect is critical in PIIL because the interfering/imaging beams propagate off-axis where the polarization changes are stronger. The subsequent changes in polarization have also a significant impact on the absolute contrast, the contrast uniformity, and the lattice symmetry of the interference pattern.…”

Section: Multibeam High-na Vector Volume Interference/image Modelingmentioning

confidence: 99%

Pattern-integrated interference lithography: Vector modeling and 1D, 2D, and 3D device structures

Leibovici¹,

Gaylord²

2013

Journal of Vacuum Science & Technology B, Nanotechnology an

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“…a Y-dipole with X-polarization for horizontal features whereas a C-QUAD or annular illumination with X,Y-polarization, for example, has non-ideal components. Depolarization also occurs due to birefringence in the quartz mask substrate and the lens (6,7) and to the mask feature when the polarization axis crosses a feature gap that is on the order, or less, of the wavelength. (8) The effect is simulated in Prolith, whereby a monopole is scanned across the x-axis of the lens, for X or Y polarization, and the reflectivity calculated at different points.…”

Section: Iic Depolarization Effectsmentioning

confidence: 99%

Reflection control for line features of multiple pitches at hyper NA

Reilly¹,

Wagner²,

Montgomery³

et al. 2008

Advances in Resist Materials and Processing Technology XXV

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This study combines simulation and experiment to compare the impact that changing BARC thickness around some nominal value has on the resist profile, on an underlying reflective surface. Process window and profile effects are an important part of understanding how a BARC interacts with the resist's parameters to affect the latitude in the light of imperfect reflection control. Reflectivity simulations are made using MATLAB ® and Prolith™ that show the effect of choosing refractive index and thickness in a multi-layer bottom anti-reflecting coating (BARC). Trends are identified for the better operating values for the index as well as specific values that meet the criterion for organic BARC in a front end application on a reflective substrate. Experimental profiles are compared to simulation using a calibrated resist model for nominal, better and ideal BARC stacks. Reflectivity, as a function of angle in resist, is convolved with the diffraction intensity distribution. This reflection, determined by a pitch's diffraction angle, identifies what can become problematic in setting up a process. Depolarization causes are discussed and while their impact affects image formation, there is little difference in reflection. II. INTRODUCTIONPrinting features near the resolution limit of hyper-NA exposure systems has many challenges, one of which is reflection control. The angle at which light rays pass through the absorbing films of the stack is dependent upon the mask pitch. This effect becomes limiting below 65 nm half-pitch for single BARC layers because reflectivity varies significantly with pitch. At the same time, resist thickness is scaled thinner; therefore the BARC needs to become even thinner. Increasing the BARC index (n BARC ) has been shown to decrease its required thickness, but limiting reflection to very low values for all pitches cannot be done with a single BARC film.(1) Prior work has demonstrated dual BARCs provide lower reflection down to 1%.(2) Below that, additional strategies are needed for low light reflection through pitch. This work extends the effort on reducing reflectivity to below 0.2% while also keeping the BARC thickness to below that expected for the resist.Reflectivity plays a role in resist profile as a function of focus and exposure and hence, process latitude. Estimates for the maximum allowable reflectivity on a flat substrate ranges from 0.5% to less than 0.1% across any portion of the lens. (3) While the physical resist parameters, especially photoacid diffusivity(4), also directly impact the standing wave amplitude seen on the sidewall and interface of the profile, the main thrust of this work is the examination of optical reflectivity effects. IIa. Reflectivity and PitchThe angle of any light ray, and thus its position in the pupil plane, is determined by the angle at which it diffracts through the mask. For the zero order and m th order the angle is: θ 0 (deg) ≈ (180/π)sin -1 (σNA/n) θ m (deg) ≈ θ 0 +(180/π)sin -1 (mλ/pitch) , m = +1 at resolution limit Downloaded From: http://proce...

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Polarization influence on imaging

Cited by 23 publications

References 10 publications

Gradient-based resolution enhancement optimization methods based on vector imaging model

Gradient-based resolution enhancement optimization methods based on vector imaging model

Pattern-integrated interference lithography: Vector modeling and 1D, 2D, and 3D device structures

Reflection control for line features of multiple pitches at hyper NA

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