Efficient optical proximity correction based on semi-implicit additive operator splitting

Yijiang Shen; Fei Peng; Zhenrong Zhang

doi:10.1364/OE.27.001520

1. Introduction

With the ever-growing integration intensity of semiconductor devices in the sub-22nm technology node, the undesired distortions on printed images have to be compensated by advanced resolution enhancement techniques (RETs) [1,2] including optical proximity correction (OPC) [3]. Inverse lithography technology (ILT) [4,5] which is an integral part of OPC, is requesting more aggressive optimization and image processing techniques with new computational strategies to improve computational efficiency for pixelated OPC techniques.

Pixleated OPC effectively improves lithographic imaging performance by prewarping the mask pattern and inserting the subresolution assist features (SRAFs) around the layout features [6,7]. However, with much higher degrees of optimization freedom than traditional rule-based [1] or edge-based OPC [8], the performance comes with intensive computational price, especially for sophiscated large-scale patterns. Gradient based algorithms including steepest descent [9–11], conjugate gradient [12, 13], augmented Lagrangian [14], level-set methods [15–18], depth learning methods [19], compressive sensing [20,21], model-driven convolution neural network (CNN) methods [22] and alike, have been extensively studied for pixelated OPC techniques to process a large amount of data during the optimization procedure. The simple and popular explicit (Euler forward) time-discretization schemes are widely applied in these approaches where in each iteration, the aerial images and the gradients of cost functions on pixelated masks have to be calculated. However, the stability of the optimization requests necessary small time step defined by the Courant-Friedrichs-Lewy (CFL) condition [23], therefore time-consuming computation is accumulated by the slow convergence in terms of iteration number dictated by the prohibitive time step. Alternatively, implicit time-discretization schemes which ensure unconditional stability with large time steps require the solving of a sizeable linear system of equations hence limiting its application to ILT. In this regard, implicit operator splitting schemes are developed to overcome this shortcoming including additive operator splitting (AOS) [24,25] and locally one-dimension (LOD) with first order temporal accuracy, alternative directional implicit (ADI) [26] and additive-multiplicative operator splitting (AMOS) with second order temporal accuracy [27], where arbitrary dimensional problems are reduced to consecutive one-dimensional processes for which fast recursive algorithms with linear comlexity are available.

In this paper, we develop a fast pixelated OPC using semi-implicit AOS theory. Diffusion terms to keep mask patterns piecewise smooth with sharp edegs, are incorporated as regularization into the cost function which seeks to preserve pattern fidelity. Semi-implicit time discretizaton scheme is applied to generate linear system of equations which is later reduced to two tridiagonal linear systems with AOS method, showing the advantages of epxlict and implicit schemes by combining simplicty and stablility. The tridiagonal linear systems are most efficiently solved by the Thomas algorithm with linear complexity. Significant convergence improvement is achieved by enabling large time steps in the iterations which also greatly reduces the overall computation load with much less iteration numbers.

2. Forward vector imaging model

The lithographic wafer imaging process 𝒯 {·} can be divided into two functional blocks: projection optical effects whose schematic is given in Fig. 1 and resist effects. Consider a point source at (α_s, β_s) emanating a polarized electromagnetic wave in the direction k⃗, the aerial image intensity I_a under a partially coherent illumination can be calculated by Fourier optics [28] and Abbe method [29] as

I_{a} = \frac{1}{J_{sum}} \sum_{(α_{s}, β_{s})} J (α_{s}, β_{s}) \sum_{p = x, y, z} {| H_{p}^{α_{s} β_{s}} \otimes (B^{α_{s} β_{s}} ⊙ M) |}^{2},

where ⊗ are entry-by-entry multiplication operation and convolution operation, respectively. J ∈ ℛ^N_s×N_s and M ∈ ℛ^N×N are scalar matrices representing the source pattern and mask pattern distributions,

J_{sum} = \sum_{(α_{s}, β_{s})} J (α_{s}, β_{s})

is the sum of source intensities,

H_{p}^{α_{s} β_{s}}

with p = x, y, z are referred to as the equivalent filters of the x, y, z components, and B^α_sβ_s ∈ ℛ^N×N is the approximate matrix of mask diffraction. Since it is impractical to perform rigorous electromagnetic field calculations by FDTD or RCWA, we apply a simple embodiment of the constant scattering coefficient assumption (CSCA) [30] to approximate the mask near field.

Fig. 1 Schematic of forward lithography.

Download Full Size | PDF

The resist effect can be approximated by a sigmoid logarithmic function $sig (x) = \frac{1}{1 + e^{- a (x - t_{r})}}$ , where a is the steepness of the sigmoid function and t_r is the threshold. Putting together, the wafer image I can be written as

I = 𝒯 {M} = sig (I_{a}) .

3. Semi-implicit additive operator splitting

3.1. Optimization framework

The goal of ILT is to synthesize an optimal mask M̂ ∈ ℛ^N×N which minimizes the mismatch between the target pattern I₀ ∈ ℛ^N×N and 𝒯 {M} over all locations. From Eqs. (1) and (2), we can see that inverse lithography is generally ill-posed which can possibly be solved by incorporating scalar functionals quantifying mask patten qualities. Since nonlinear diffusion such as the Malik and Perona model [31] and the CLMC filter [32,33] does not penalize discontinuities thus enabling piecewise smooth mask patterns with sharp edges at the transition regions, we opt to used it in this work to formulate the inverse lithography problem as

{\begin{cases} \partial_{t} ω = \nabla \cdot (g ({| \nabla ω |}^{2}) | \nabla ω |) \\ \int_{Ω} {(𝒯 {M} - I_{0})}^{2} d x = ε \end{cases},

where ω is transformed with

M = \frac{1 + cos ω}{2}

to reduce the binary constraint on M, ∇ denotes gradient, Ω is an open and bounded domain of ℛ² which contains ω. ε describes the approximation between the printed pattern 𝒯 {M} and the desired target pattern I₀ with smaller ε indicating better approximation. Diffusivity g is a smooth nonincreasing function which in this paper is defined as [25]

g (s) = {\begin{matrix} 1 & (s \leq 0) \\ 1 - \exp [\frac{- 3.315}{{(s / λ_{1})}^{4}}] & (s > 0) \end{matrix},

however, other diffusivity functions can be readily applied.

The diffusion equation ∂_tω = ∇ · (g (|∇ω|²) |∇ω|) in Eq. (3) is designed to keep piecewise smooth mask patterns with sharp edegs [25], while a close to zero ε tries to minimize the sum of the mismatches between the printed image I = 𝒯 {M} and the desired one I₀ over all locations. With λ being the Lagrangian multiplier, the Euler-Lagrange equation of Eq. (3) is

- λ \nabla \cdot (g ({| \nabla ω |}^{2}) | \nabla ω |) + α (x) = 0,

where α(x) and λ are computed as

\begin{array}{l} α (x) = \frac{1}{2} \frac{\partial}{\partial ω} {(I - I_{0})}^{2} = & - \frac{a sin ω}{2 J_{sum}} ⊙ \sum_{(α_{s}, β_{s})} J (α_{s}, β_{s}) \sum_{p = x, y, z} Real [{(B^{α_{s} β_{s}})}^{*} ⊙ \\ ({(H_{p}^{α_{s} β_{s}})}^{* ○} \otimes {E_{p}^{α_{s} β_{s}} ⊙ (I - I_{0}) ⊙ I ⊙ (1 - I)})] \end{array}

and

λ = {‖ α (x) ‖}_{2}^{2} \cdot {[\int_{Ω} α (x) \nabla \cdot (g ({| \nabla ω |}^{2}) | \nabla ω |) d x]}^{- 1},

with * being the conjugate operation, ○ flipping the matrix in the argument in both up-down and right-left directions, 1 ∈ ℝ^N×N being the all-ones matrix and

E_{p}^{α_{s} β_{s}} = H_{p}^{α_{s} β_{s}} \otimes (B^{α_{s} β_{s}} ⊙ M)

.

3.2. Time-dependent scheme

Equation (5) can be solved by a time-dependent scheme, yielding

\partial_{t} ω = - α (x, t) + λ \nabla \cdot (g ({| \nabla ω |}^{2}) | \nabla ω |),

in which t is the artificial time. Equation (8) emulates the level-set evolution in [15] where piecewise smoothing with sharp edges are maintained by the nonliner diffusivity g and the constraints are included in α(x, t) to prevent the distortion in 𝒯 {M} from I₀ which is otherwise named as the “balloon force” in [23].

Typical implentations of Eq. (8) are based on an explicit or forward Euler scheme which requires very small time-steps, severely limiting its efficiency. Consequently, if we employ discrete times t_k = kτ with τ being time-step size and reprensent ω by a vector ∈ ℛ^N²×1 by stacking the rows or columns of ω and i corresponds to some grid node x_i hence denoting the approximation of ω(x_i, t_k) by $ω_{i}^{k}$ , Eq. (8) reads in its semi-implicit formulation as

ω_{i}^{k + 1} = ω_{i}^{k} + τ λ \sum_{j \in 𝒩 (i)} \frac{g_{j}^{k} + g_{i}^{k}}{2 h^{2}} (ω_{j}^{k + 1} - ω_{i}^{k}) + τ α (i, k),

where h is the grid size, 𝒩(i) denotes the 4-neighbors of the pixel i. Equation (9) can be written in the matrix-vector formation as

ω^{k + 1} = ω^{k} + τ α^{k} + τ \sum_{l \in {x, y}} A_{l} (ω^{k}) ω^{k + 1},

with α^k being the vector notation for α(i, k) and A_l (ω^k) = [a_ijl (ω^k)] is given by

a_{i j l} (ω^{k}) = {\begin{array}{l} \frac{g_{i}^{k} + g_{j}^{k}}{2 h^{2}} & [j \in 𝒩_{l} (i)] \\ - \sum_{n \in 𝒩_{l} (i)} & \frac{g_{i}^{k} + g_{n}^{k}}{2 h^{2}} & (j = i) \\ 0 & (else) \end{array},

with 𝒩_l(i) being the 2-neighbors of the pixel i with respect to the l coordinate. The solution of ω^k+1 requires to solve the linear system of equations

ω^{k + 1} = {(I - τ \sum_{l \in {x, y}} A_{l} (ω^{k}))}^{- 1} (ω^{k} + τ α^{k}),

where I denotes the unit matrix. It should be noted that the system matrix in Eq. (12) is strictly diagonally dominate therefore invertible. However, comparing with vector-matrix notation of the explicit schemes

ω^{k + 1} = (I + τ \sum_{l \in {x, y}} A_{l} (ω^{k})) ω^{k} + τ α^{k}

with prohibitive time-step τ, it does not necessarily imply the superiority of the semi-implict schemes in Eq. (12). Althoug the structure of the system matrix in Eq. (12) depends on pixel numbering, it is not possible to order the pixels in such a way that all nonvanishing matrix element in ith row are bounded diagonally revealing much larger bandwidth.

Solving Eq. (12) with Gaussian elimination and iterative methods leads to immense storage and computation, consequently, the additive operator splitting (AOS) is applied to decompose the two dimensional problem to two one dimensional ones to give

ω^{k + 1} = \frac{1}{2} \sum_{L = 1}^{2} {(I - L τ A_{l} (ω^{k}))}^{- 1} (ω^{k} + τ α (x, k)),

in which L = 1 and L = 2 relates to l = x and l = y coordinates respectively. With the system matrices I −lτA_l(ω^k) being strictly diagonally dominate tridiagonal, the linear systems in l ∈ x, y direction of the AOS scheme in Eq. (14) can be computed very effectively with the Thomas Algorithm (TDMA) [34] which has linear complexity and easy implementation.

4. Simulation results

Numerical simulations are performed on an immersion lithographic imaging system with wavelength λ = 193nm, NA = 1.35, spatial resolution δx = δy = 4nm/pixel, the steepness and threshold of sigmoid function being a = 80 and t_r = 0.25. The system is illuminated by a partially coherent annular source J with σ_in = 0.6 and σ_out = 0.9. J and two desired target pattern I₀₁ and I₀₂ are given in Fig. 2. All the computations are implemented in MATLAB with 3.6 GHz CPU and 16 GB memory.

Fig. 2 From left to right are annular illumination source J with σ_in = 0.6 and σ_out = 0.9, desired target pattern I₀₁ and desired target pattern I₀₂.

Download Full Size | PDF

OPC results with target pattern I₀₁ are presented in Fig. 3. In the columns of Fig. 3 from left to right lie the illuminated input mask pattern M, the aerial image I_a and the wafer image I, and rows (a), (b) and (c) show the imaging results with I₀₁, the synthesized masks computed with the explicit time-scheme SGD method (which hereafter, will be abbreviated as the SGD method when there is no ambiguity) and the proposed approach, respectively. The time-step τ₁ in the SGD method is defined optimally as 0.1 after repeated tests for convergence, where τ₁ < 0.1 will slow down the convergence and τ₁ > 0.1 is likely to diverge the updating process. The time-step in the proposed approach is set as a much larger 0.85. While severe wafer image distorton is observed in row (a) of Fig. 3 which has to be compensated by OPC, pattern fidelities in row (b) and (c) are greatly improved with the SGD method and the proposed approach from pattern error (PE) 4631 to 464 and 413, respectively. The SGD method is updated similarly to Eq. (13) without the diffusion equation in Eq. (3) as

ω^{k + 1} = ω^{k} + τ_{1} α^{k},

minimizing the pattern error which is a common practice among existing gradient based methods. It is worth mentioning that the inverse lithography problem is non-convex with multiple local minima and solving the problem with numerical schemes there is no guarantee of reaching the global minimum. However, ILT is an ill-posed problem and it is often not necessary to arrive at the local minimum. Moreover, the proposed approach calculates the diffusion equation in Eq. (3) to keep the sharp edges between piecewise smooth layout features in favor of increasing image contrast in 𝒯 {M}, hence slightly outperform the SGD method in terms of pattern fidelity.

Fig. 3 Simulation results with I₀₁ as target pattern illuminated by J in Fig. 2. Columns from left to right: the illuminated input mask pattern M, the aerial image I_a and the wafer image I. Rows (a), (b) and (c) present the simulation results with the desired pattern I₀₁, and synsthesized mask with the SGD method with optimal step-size τ₁ = 0.1 and the synthesized mask with the proposed approach with time-step τ₁ = 0.85 as the inputs, respectively.

Download Full Size | PDF

Mask updating in each iteration by solving the linear systems of equations in Eq. (14) using the Thomas Algorithm with the semi-implict time scheme, although very efficient, is comparatively slower than that with the explict time scheme. However, the overall convergence performance with the proposed approach is greatly improved with much larger time step τ₁ thereby much less number of iterations. Such comparsions are given in Fig. 4 where the convergence performance of SGD with τ₁ = 0.1 and the proposed approach with τ₁ = 0.1, 0.25, 0.4, 0.55, 0.7, 0.85 are presented. It is observed that with the same τ₁ = 0.1 the proposed apprach converges slower and with τ₁ = 0.25, the performances of the proposed approach and the SGD method are comparable. The τ₁ of the proposed approach can reach beyond 0.85, still ensuring fast and stable convergence. Figure 5 illustrated the time-efficiency of the proposed approach with τ₁ = 0.85 and the SGD method with τ₁ = 0.1, where it takes 0.28 and 0.98 hours for the proposed approach and the SGD method to converge, respectively.

Fig. 4 Convergence performance using the SGD method with τ₁ = 0.1 and the proposed approach with τ₁ = 0.1, 0.25, 0.4, 0.55, 0.7, 0.85.

Download Full Size | PDF

Fig. 5 Time efficiency of the proposed approach with τ₁ = 0.85 and the SGD method with τ₁ = 0.1 in Fig. 3.

Download Full Size | PDF

The proposed approach is further applied to another target pattern I₀₂ in Fig. 2 illuminated by J with the OPC results illustrated in Fig. 6. In row (a) with I₀₂ as input when no OPC is involved, pattern fidelity is greatly degraded in terms of PE 7371. Aerial and wafer images illuminating synthesized mask patterns by the SGD method with τ₁ = 0.1 and the proposed approach τ₁ = 0.85 are presented in row (b) and (c) respectively, with improved PEs 1079 and 814. The runtimes of the simulations in rows (b) and (c) of Fig. 6 are depicted Fig. 7, showing the convergence of the proposed approach in 0.26 hours which is a significant improvement from the the 0.98 hours with the SGD method by employing much large τ₁ with the semi-implict time-scheme.

Fig. 6 Simulation results with I₀₂ as target pattern illuminated by J in Fig. 2. Columns from left to right: the illuminated input mask pattern M, the aerial image I_a and the wafer image I. Rows (a), (b) and (c) present the simulation results with the desired pattern I₀₂, and synsthesized mask with the SGD method with optimal step-size τ₁ = 0.1 and the synthesized mask with the proposed approach with time-step τ₁ = 0.85 as the inputs, respectively.

Download Full Size | PDF

Fig. 7 Time efficiency of the proposed approach with τ₁ = 0.85 and the SGD method with τ₁ = 0.1 in Fig. 6.

Download Full Size | PDF

Semi-implicit discretization scheme in Eq. (14) is applied to explicit SGD method in Eq. (13) to show the validity of the proposed approach. While there are other gradient-based approaches such as conjugate gradient, level-set methods, depth-learning methods and so on, application of the semi-implicit schemes can be tailored to these approaches to expect similar convergence improvement.

5. Conclusion

In this paper, we investigate the application of semi-implicit time discretization schemes with additive operator splittering (AOS) to the numerical solution of mask synthesis in optical lithography. Nonlinear diffusion enabling piecewise smoothing is incorporated into the optimization framework which is further addressed by solving linear systems of equations with semi-implicit time discretization. Subsequently, the linear system is decomposed into two tridiagonal linear system of equations with respect to pattern coordinates which are solved very efficiently by the Thomas algorithm. Simulation results merit the significant efficiency improvement by the proposed approach enabling large time-steps under the premise of stable convergence. The theoretical and numerical analysis of the proposed approach enhance the algorithmic understanding of the applicability of implicit time discretization to OPC problems in next-generation immersion lithography.

Funding

National Natural Science Foundation of China (61875041); Natural Science Foundation of Guangdong Province, China (2016A030313709, 2015A030310290); Guangzhou Municipal Science and Technology Project, China (201607010180); Natural Science Foundation of Guangxi Province (2013GXNSFCA019019, 2017GXNSFAA198227).

References

1. A. K.-K. Wong, Resolution Enhancemenant Techniques in Optical Lithography (SPIE Press, 2001). [CrossRef]

2. L. W. Liebmann, S. M. Mansfield, A. K.-K. Wong, M. A. Lavin, W. C. Leipold, and T. G. Dunham, “TCAD development for lithography resolution enhancement,” IBM. J. Res. Dev. 45(5), 651–665 (2010). [CrossRef]

3. A. K.-K. Wong, Optical Imaging in Projection Microlithography (SPIE Press, 2005). [CrossRef]

4. Y. L. Linyong Pang and D. Abrams, “Inverse lithography technology (ILT): What is the impact to the photomask industry?” Proc. SPIE 6283, 6283X (2006).

5. A. Poonawala and P. Milanfar, “Mask design for optical microlithography – an inverse imaging problem,” IEEE. T. Image. Process 16(3), 774–788 (2007). [CrossRef]

6. Xu Ma and Gonzalo R. Arce, “Pixel-based simultaneous source and mask optimization for resolution enhancement in optical lithography,” Opt. Express 17(7), 5783–5793 (2009). [CrossRef] [PubMed]

7. X. Ma and G. R. Arce, Computational Lithography, Wiley Series in Pure and Applied Optics, 1st ed. (John Wiley and Sons, 2010). [CrossRef]

8. P. Gao, A. Gu, and A. Zakhor, “Optical Proximity Correction with Principal Component Regression,” Proc. SPIE 6924, 69243N (2008). [CrossRef]

9. Y. Peng, J. Zhang, Y. Wang, and Z. Yu, “Gradient-based source and mask optimization in optical lithography,” IEEE. T. Image. Process 20(10), 2856–2864 (2011). [CrossRef]

10. X. Ma, C. Han, Y. Li, L. Dong, and G. R. Arce, “Pixelated source and mask optimization for immersion lithography,” J. Opt. Soc. Am. A 30(1), 112–123 (2013). [CrossRef]

11. N. Jia and E. Y. Lam, “Pixelated source mask optimization for process robustness in optical lithography,” Opt. Express 19(20), 19384–19398 (2011). [CrossRef]

12. W. Lv, S. Liu, Q. Xia, X. Wu, Y. Shen, and E. Y. Lam, “Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step,” J. Vac. Sci. Technol. B 31(4), 041605 (2013). [CrossRef]

13. J. Li and E. Y. Lam, “Robust source and mask optimization compensating for mask topography effects in computational lithography,” Opt. Express 22(8), 9471 (2014). [CrossRef]

14. J. Li, S. Liu, and E. Y. Lam, “Efficient source and mask optimization with augmented lagrangian methods in optical lithography,” Opt. Express 21(7), 8076–8090 (2013). [CrossRef]

15. Y. Shen, N. Wong, and E. Y. Lam, “Level-set-based inverse lithography for photomask synthesis,” Opt. Express 17(26), 23690–23701 (2009). [CrossRef]

16. Y. Shen, N. Jia, N. Wong, and E. Y. Lam, “Robust level-set-based inverse lithography,” Opt. Express 19(6), 5511–5521 (2011). [CrossRef]

17. Y. Shen, “Level-set based mask synthesis with a vector imaging model,” Opt. Express 25(18), 21775 (2017). [CrossRef]

18. Y. Shen, “Lithographic source and mask optimization with narrow-band level-set method,” Opt. Express 26(8), 10065–10078 (2018). [CrossRef]

19. F. Peng and Y. Shen, “Source and mask co-optimization based on depth learning methods,” in 2018 China Semiconductor Technology International Conference (CSTIC), (2018), pp. 1–3.

20. X. Ma, D. Shi, Z. Wang, Y. Li, and G. R. Arce, “Lithographic source optimization based on adaptive projection compressive sensing,” Opt. Express 25(6), 7131–7149 (2017). [CrossRef]

21. X. Ma, Z. Wang, Y. Li, G. R. Arce, L. Dong, and J. Garcia-Frias, “Fast optical proximity correction method based on nonlinear compressive sensing,” Opt. Express 26(11), 14479–14498 (2018). [CrossRef]

22. X. Ma, Q. Zhao, H. Zhang, Z. Wang, and G. R. Arce, “Model-driven convolution neural network for inverse lithography,” Opt. Express 26(25), 32565–32584 (2018). [CrossRef]

23. S. Osher and N. Paragios, Geometric Level Set Methods in Imaging, Vision, and Graphics (Springer, 2003).

24. J. Weickert, Scale-Space Theory in Computer Vision (Springer, 1997).

25. J. Weickert, B. M. T. H. Romeny, and M. A. Viergever, “Efficient and reliable schemes for nonlinear diffusion filtering,” IEEE. T. Image. Process 7(3), 398–410 (1998). [CrossRef]

26. D. W. Peaceman and J. H. H. Rachford, “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3(1), 28–41 (1955). [CrossRef]

27. D. Barash, T. Schlick, M. Israeli, and R. Kimmel, “Multiplicative operator splittings in nonlinear diffusion: From spatial splitting to multiple timesteps,” J. Math. Imaging. Vis. 19(1), 33–48 (2003). [CrossRef]

28. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Science, 1996).

29. M. Born and E. Wolf, Principle of Optics (Cambridge University, 1999). [CrossRef]

30. T. V. Pistor, A. R. Neureuther, and R. J. Socha, “Modeling oblique incidence effects in photomasks,” Proc. SPIE 4000, 228–237(2000). [CrossRef]

31. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE. T. Pattern. Anal. 12(7), 629 (1990). [CrossRef]

32. F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992). [CrossRef]

33. L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion II,” SIAM J. Numer. Anal. 29(3), 845–866 (1992). [CrossRef]

34. S. D. Conte and C. deBoor, Elementary Numerical Analysis (McGraw-Hill Science, 1972).

Efficient optical proximity correction based on semi-implicit additive operator splitting

Abstract

1. Introduction

2. Forward vector imaging model

3. Semi-implicit additive operator splitting

3.1. Optimization framework

3.2. Time-dependent scheme

4. Simulation results

5. Conclusion

Funding

References

Cited By

Figures (7)

Equations (15)

Optics Express