Accounting for mask topography effects in source-mask optimization for advanced nodes

Coskun, Tamer H.; Dai, Huixiong; Huang, Hsu-Ting; Kamat, Vishnu G.; Ngai, Chris

doi:10.1117/12.879704

Cited by 4 publications

(3 citation statements)

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“…Here we compute the derivatives of the cost function in Eqs. (11) and (12). Due to the discrete nature of the source and mask, the differential operator∂ /∂ M and ∂ /∂ J are approximated by numerical differences.…”

Section: A Appendix: Gradients Derivationmentioning

confidence: 99%

“…Several well known numerical algorithms of solving Maxwell's equations, such as finite-difference time domain (FDTD) [8], rigorous coupled wave analysis (RCWA) [9] or the waveguide method [10] are used to model the light propagation through the mask in optical lithography. Unfortunately, the convergence of rigorous methods depends on mesh setting, accuracy requirements and boundary conditions [11]. As a consequence, high accuracy is achieved at a large computational cost, which limits the wide adoption of rigorous 3D mask modeling for practical large layout simulations in advanced resolution enhancement techniques (RETs) such as source and mask optimization (SMO) [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Robust source and mask optimization compensating for mask topography effects in computational lithography

Li¹,

Lam²

2014

Opt. Express

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Mask topography effects need to be taken into consideration for a more accurate solution of source mask optimization (SMO) in advanced optical lithography. However, rigorous 3D mask models generally involve intensive computation and conventional SMO fails to manipulate the mask-induced undesired phase errors that degrade the usable depth of focus (uDOF) and process yield. In this work, an optimization approach incorporating pupil wavefront aberrations into SMO procedure is developed as an alternative to maximize the uDOF. We first design the pupil wavefront function by adding primary and secondary spherical aberrations through the coefficients of the Zernike polynomials, and then apply the conjugate gradient method to achieve an optimal source-mask pair under the condition of aberrated pupil. We also use a statistical model to determine the Zernike coefficients for the phase control and adjustment. Rigorous simulations of thick masks show that this approach provides compensation for mask topography effects by improving the pattern fidelity and increasing uDOF.

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Section: A Appendix: Gradients Derivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust source and mask optimization compensating for mask topography effects in computational lithography

Li¹,

Lam²

2014

Opt. Express

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“…1 Rigorous 3D mask experiments have confirmed that mask topography is a leading cause due to the fact that the thickness of the mask absorber produces phase errors among different diffraction orders. 2,3 Unfortunately, the rigorous electromagnetic field (EMF) modeling used to describe light diffraction from the mask generally involves intensive computation, 4 which limits the wide adoption of rigorous 3D mask modeling for practical large layout simulations in advanced resolution enhancement techniques (RETs) such as source and mask optimization (SMO). 5,6 Additionally, although SMO is a powerful and effective technique which provides more flexibility regarding both the mask design and illumination configuration adjustment, [7][8][9][10] it is inadequate to control the phase in the lens pupil.…”

Section: Introductionmentioning

confidence: 99%

Joint optimization of source, mask, and pupil in optical lithography

Lam

2014

SPIE Proceedings

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Mask topography effects need to be taken into consideration for more advanced resolution enhancement techniques in optical lithography. However, rigorous 3D mask model achieves high accuracy at a large computational cost. This work develops a combined source, mask and pupil optimization (SMPO) approach by taking advantage of the fact that pupil phase manipulation is capable of partially compensating for mask topography effects. We first design the pupil wavefront function by incorporating primary and secondary spherical aberration through the coefficients of the Zernike polynomials, and achieve optimal source-mask pair under the condition of aberrated pupil. Evaluations against conventional source mask optimization (SMO) without incorporating pupil aberrations show that SMPO provides improved performance in terms of pattern fidelity and process window sizes.

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