Research Progress on the Imaging of Three-Dimensional Mask for Extreme Ultraviolet Lithography

Zinan Zhang; Sikun Li; Xiangzhao Wang

doi:10.3788/LOP202259.0922021

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 9 >Page 0922021 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 9, 0922021 (2022)

Research Progress on the Imaging of Three-Dimensional Mask for Extreme Ultraviolet Lithography

Zinan Zhang^1、2, Sikun Li^1、2, and Xiangzhao Wang^1、2、*

Author Affiliations

¹Laboratory of Information Optics and Opt-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.3788/LOP202259.0922021 Cite this Article Set citation alerts

Zinan Zhang, Sikun Li, Xiangzhao Wang. Research Progress on the Imaging of Three-Dimensional Mask for Extreme Ultraviolet Lithography[J]. Laser & Optoelectronics Progress, 2022, 59(9): 0922021 Copy Citation Text

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Abstract

Extreme ultraviolet (EUV) lithography is the most advanced lithography technology, and guarantees the development of the chip to higher integration degree. High imaging quality is the premise to ensure the performance of the EUV lithography system, while the reflective three-dimensional (3D) mask and the special imaging optics bring more challenges in improving the imaging quality of EUV lithography. The research of the imaging of 3D mask is the basis to improve the imaging quality, and the 3D mask imaging model is an important research tool. In this paper, combined with the research work of our group, the principle of the imaging of 3D mask for EUV lithography is briefly introduced and the typical 3D mask models are reviewed. Then the researches on the imaging quality of 3D mask for EUV lithography are introduced. Finally, the research tendency of this field is prospected.

Keywords

diffraction extreme ultraviolet lithography imaging quality lithography three-dimensional mask model

I ({\hat{x}}_{i}, {\hat{y}}_{i}) = \int_{- \infty}^{+ \infty} \int S (\hat{f}, \hat{g}) \{{|\int_{- \infty}^{+ \infty} \int H (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) B ({\hat{f}}^{'}, {\hat{g}}^{'}) e x p [- j 2 π ({\hat{x}}_{i} {\hat{f}}^{'} + {\hat{y}}_{i} {\hat{g}}^{'})] d {\hat{f}}^{'} d {\hat{g}}^{'}|}^{2}\} d \hat{f} d \hat{g}

，（1）

S (\hat{f}, \hat{g}) = \frac{1}{π σ^{2}} c i r c (\frac{\sqrt[]{{\hat{f}}^{2} + {\hat{g}}^{2}}}{σ}) = \{\begin{matrix} \frac{1}{π σ^{2}}, & \sqrt[]{{\hat{f}}^{2} + {\hat{g}}^{2}} \leq σ \\ 0, & o t h e r w i s e \end{matrix}

。（2）

H (\hat{f}, \hat{g}) = \{\begin{matrix} R (\hat{f}, \hat{g}) T (\hat{f}, \hat{g}) e x p [- j \frac{2 π}{λ} W (\hat{f}, \hat{g})], & \sqrt[]{{\hat{f}}^{2} + {\hat{g}}^{2}} \leq 1 \\ 0, & o t h e r w i s e \end{matrix}

，（3）

I ({\hat{x}}_{i}, {\hat{y}}_{i}) = \int_{- \infty}^{+ \infty} \int S (\hat{f}, \hat{g}) [{|\int_{- \infty}^{+ \infty} \int \begin{array}{l} V (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) J (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) {V^{'}}^{- 1} (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) \\ H (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) B ({\hat{f}}^{'}, {\hat{g}}^{'}) e x p [- j 2 π ({\hat{x}}_{i} {\hat{f}}^{'} + {\hat{y}}_{i} {\hat{g}}^{'})] d {\hat{f}}^{'} d {\hat{g}}^{'} \end{array}|}^{2}] d \hat{f} d \hat{g}

，（4）

T C C ({\hat{f}}^{'}, {\hat{g}}^{'}; {\hat{f}}^{″}, {\hat{g}}^{″}) = \int_{- \infty}^{+ \infty} \int S (\hat{f}, \hat{g}) H (\hat{f} + {\hat{f}}^{'}, \hat{g} + {\hat{g}}^{'}) H^{*} (\hat{f} + {\hat{f}}^{″}, \hat{g} + {\hat{g}}^{″}) d \hat{f} d \hat{g}

。（5）

I ({\hat{x}}_{i}, {\hat{y}}_{i}) = \int_{- \infty}^{+ \infty} \int \int \int T C C ({\hat{f}}^{'}, {\hat{g}}^{'}, {\hat{f}}^{″}, {\hat{g}}^{″}) B ({\hat{f}}^{'}, {\hat{g}}^{'}) B^{*} ({\hat{f}}^{″}, {\hat{g}}^{″}) e x p \{- j 2 π [{\hat{x}}_{i} ({\hat{f}}^{'} - {\hat{f}}^{″}) + {\hat{y}}_{i} ({\hat{g}}^{'} - {\hat{g}}^{″})]\} d {\hat{f}}^{'} d {\hat{g}}^{'} d {\hat{f}}^{″} d {\hat{g}}^{″}

，（6）

T C C ({\hat{f}}^{'}, {\hat{g}}^{'}, {\hat{f}}^{″}, {\hat{g}}^{″}) \approx \sum_{k}^{K} μ_{k} Φ_{k} ({\hat{f}}^{'}, {\hat{g}}^{'}) Φ_{k}^{*} ({\hat{f}}^{″}, {\hat{g}}^{″})

，（7）

I ({\hat{x}}_{i}, {\hat{y}}_{i}) = {\sum_{k}^{K} μ_{k} |ℱ^{- 1} \{Φ_{k} ({\hat{f}}^{'}, {\hat{g}}^{'}) B ({\hat{f}}^{'}, {\hat{g}}^{'})\}|}^{2}

，（8）

\begin{matrix} B ({\hat{f}}_{i}^{}, {\hat{g}}_{i}^{}; {\hat{f}}^{'}, {\hat{g}}^{'}) = \\ \sum_{j} w_{j} B [{\hat{f}}_{j}^{s}, {\hat{g}}_{j}^{s}; {\hat{f}}^{'} - ({\hat{f}}_{i}^{} - {\hat{f}}_{j}^{}), {\hat{g}}^{'} - ({\hat{g}}_{i}^{} - {\hat{g}}_{j}^{})] \end{matrix}

，（9）

\{\begin{array}{l} \nabla \cdot D (t) = ρ_{v} (t) \\ \nabla \cdot B (t) = 0 \\ \nabla \times E (t) = - \frac{\partial B (t)}{\partial t} \\ \nabla \times H (t) = J (t) + \frac{\partial D (t)}{\partial t} \end{array}

，（10）

B_{a} = t_{a} s i n c (m) + (t_{b} - t_{a}) d s i n c (m d) + \frac{2 δ_{e}}{p} c o s (π m d)

，（11）

R_{m} = r_{m} e x p (- j \frac{2 π}{λ} 2 d_{m} c o s γ_{m})

，（12）

B (α_{n}, β_{n}) = \int ϕ_{1} (α_{i}, β_{i}) B_{a} (α_{m} - α_{i}, β_{m} - β_{i}) ϕ_{2} (α_{m}, β_{m}) R_{m} (γ_{m}) \times ϕ_{2} (α_{m}, β_{m}) B_{a} (α_{n} - α_{m}, β_{n} - β_{m}) ϕ_{2} (α_{n}, β_{n}) d α_{m} d β_{m},

（13）

B_{a} = t_{a} s i n c (m) + (t_{b} - t_{a}) F_{p} (θ_{e}, θ_{m}) d s i n c (m d) + \frac{2 δ_{e}}{p} G_{p} (θ_{e}, θ_{m}) c o s (π m d)

，（14）

B_{a} = ℱ \{t_{a} + (t_{b} - t_{a}) ⊙ M + δ_{e} ⊙ Λ (M)\}

，（15）

B_{r} = ϕ_{1} ⊙ B_{a} ⊙ ϕ_{2} ⊙ R_{m}

，（16）

B (i, j) = \sum_{p} \sum_{q} B_{r} (p, q) ϕ_{2} (p, q) B_{a} (i - p, j - q) ϕ_{2} (i, j)

，（17）

B = (B_{r} ⊙ ϕ_{2}) \otimes B_{a} ⊙ ϕ_{2}

，（18）

B = (ϕ_{1} ⊙ B_{a} ⊙ ϕ_{2} ⊙ R_{m} ⊙ ϕ_{2}) \otimes B_{1} ⊙ ϕ_{2} ⊙ ϕ_{d}

。（19）

Δ w = \frac{2 d_{a} t a n θ_{e}}{R_{o}}, Δ x = \frac{d_{a} t a n θ_{e}}{R_{o}}

，（20）

B_{0} = 2 r_{m} \int_{0}^{α} s i n c^{2} (\frac{π w δ}{λ}) c o s (\frac{2 π}{λ} D α_{i} δ) d δ

，（21）

Δ w = \frac{2 D^{2} α_{i}^{2} α}{λ} - \frac{2 π^{2} D^{4} α_{i}^{4} α^{3}}{9 λ^{3}}

。（22）

Δ x = \frac{(d_{a} + d_{m}) α_{i}}{R_{o}}

。（23）

Zinan Zhang, Sikun Li, Xiangzhao Wang. Research Progress on the Imaging of Three-Dimensional Mask for Extreme Ultraviolet Lithography[J]. Laser & Optoelectronics Progress, 2022, 59(9): 0922021

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