Numerical simulation of state parameter distributions and extreme ultraviolet radiation in laser-produced tin plasma

MIN Qi; WANG Guodong; HE Chaowei; HE Siqi; LU Haidong; LIU Xingbang; WU Yan-Hong; SU Maogen; DONG Chenzhong

doi:10.7498/aps.74.20241321

Abstract
The laser-produced Sn plasma light source is a critical component in advanced extreme ultraviolet (EUV) lithography. The power and stability of EUV radiation within a 2% bandwidth centered at 13.5 nm are key indicators that determine success of the entire lithography process .The plasma state parameter distributions and the EUV radiation spectrum for a laser-produced Sn plasma light source are numerically simulated in this work. The radiative opacity of Sn plasma within the 12–16 nm range is calculated using a detailed-level-accounting model in the local thermodynamic equilibrium approximation. Next, the temperature distribution and the electron density distribution of plasma generated by nanosecond laser pulses interacting with both a Sn planar solid target and a liquid droplet target are simulated using the radiation hydrodynamics code for laser-produced plasma, RHDLPP. By combining the radiative opacity data with the plasma state data, the spectral simulation subroutine SpeIma3D is employed to model the spatially resolved EUV spectra for the planar target plasma and the angle-resolved EUV spectra for the droplet target plasma at a 60-degree observation angle. The variation of in-band radiation intensity at 13.5 nm within the 2% bandwidth as a function of observation angle is also analyzed for the droplet-target plasma. The simulated plasma state parameter distributions and EUV spectral results closely match existing experimental data, demonstrating the ability of RHDLPP code to model laser-produced Sn plasma EUV light sources. These findings provide valuable support for the development of EUV lithography and EUV light sources.

Keywords:
extreme ultraviolet lithography light source /

laser-produced tin plasma /

radiation hydrodynamics code /

extreme ultraviolet spectra
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图 1 激光等离子体辐射流体力学程序RHDLPP的程序框架图

Figure 1. Framework for the radiation hydrodynamics code RHDLPP.

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图 2 SpeIma3D程序模拟激光等离子体光谱的示意图^[35]

Figure 2. Schematic diagram of the spectrum of a laser-produced plasma simulated by the SpeIma3D program^[35].

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图 3 不同$ \left({T}_{{\mathrm{e}}}, {n}_{{\mathrm{e}}}\right) $下离子电荷态分布的对比结果, 其中红色柱状图代表 LTE条件下基于细致能级的结果(LTE-DLA), 蓝色柱状图代表LTE条件下基于屏蔽氢近似的结果(LTE-SH), 灰色柱状图代表non-LTE条件下基于屏蔽氢近似的结果

Figure 3. Comparison of ion charge state distributions under different $ \left({T}_{{\mathrm{e}}}, {n}_{{\mathrm{e}}}\right) $ conditions. The red bar chart represents results based on DLA model under LTE conditions (LTE-DLA), the blue bar chart represents results based on the screened hydrogenic approximation under LTE conditions (LTE-SH), and the gray bar chart represents results based on the screened hydrogenic approximation under non-LTE conditions.

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图 4 密度为0.002 g/cm³, 温度为(a) 32 eV和(b) 20 eV 时Sn等离子体的EUV 辐射不透明度

Figure 4. EUV Radiative opacity of Sn plasmas at a density of 0.002 g/cm³ and temperatures of (a) 32 eV, (b) 20 eV.

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图 5 延迟时间10.5 ns时, 模拟和实验测量的激光Sn等离子体(a)温度和(b)电子密度在距离靶面130, 200, 300 μm 处沿着r轴的分布

Figure 5. Simulated and experimentally measured distributions of laser-produced Sn plasma (a) temperature and (b) electron density along the r-axis are presented at distances of 130, 200, and 300 μm from the target surface, with a delay time of 10.5 ns.

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图 6 不同延迟时间下模拟的Sn等离子体温度和质量密度在r = 0处沿着z轴的分布

Figure 6. Simulated distribution of Sn plasma temperature and mass density along the z-axis at r = 0 for various delay times.

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图 7 距离靶面130, 200, 300 μm 处激光Sn等离子体的EUV光谱^[18]

Figure 7. The EUV spectra of laser-produced Sn plasma at 130, 200, and 300 μm from the target surface^[18].

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图 8 (a) 距离靶面130, 200, 300 μm 处激光Sn等离子体归一化的EUV实验光谱^[18]以及(b) Sn⁷⁺—Sn¹⁴⁺离子的归一化发射率

Figure 8. (a) Normalized EUV experimental spectra of laser-produced Sn plasma at distances of 130, 200, and 300 μm from the target surface^[18], and (b) normalized emissivity of Sn⁷⁺—Sn¹⁴⁺ ions.

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图 9 延迟时间为4, 7, 10, 13 ns时, 模拟得到的Sn液滴等离子体的温度(第一行)和密度(第二行)的二维分布, 图中激光自左向右沿着z轴入射

Figure 9. Two-dimensional distributions of temperature (first row) and density (second row) of Sn droplet plasma, obtained from simulations, when the delay times is 4, 7, 10, and 13 ns. In the panel, the laser propagates along the z-axis from left to right.

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图 10 观测视线与激光入射方向成60º角时, 实验测量的^[12] (黑色实线)、Torretti等^[12]模拟的(红色实线)以及本文利用RHDLPP程序模拟的(蓝色实线) Sn液滴等离子体的EUV光谱

Figure 10. The EUV spectra for the Sn droplet plasma, including the experimentally measured data^[12] (black solid line), the simulation by Torretti et al. ^[12](red solid line), and the simulation performed in this paper using the RHDLPP program (blue solid line). The spectra are observed at a 60º angle relative to the direction of laser incidence.

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图 11 Sn液滴等离子体在13.5 nm, 2%带宽内的归一化辐射强度随观测角的变化, 其中红色实心圆表示本文的模拟结果, 蓝色虚线表示拟合曲线

Figure 11. Variation of the normalized radiation intensity of the Sn droplet plasma at 13.5 nm with a 2% bandwidth as a function of the observation angle. The red solid circles represent the simulation results from this paper, while the blue dashed lines correspond to the fitted curves.

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表 1 14组$ \left({T}_{{\mathrm{e}}}, {n}_{{\mathrm{e}}}\right) $下的比值R、电离温度$ {T}_{Z} $、LTE条件下基于细致能级的平均电荷态$ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-1} $、LTE条件下基于屏蔽氢近似的平均电荷态$ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-2} $及non-LTE条件下基于屏蔽氢近似的平均电荷态$ {\left\langle{Z}\right\rangle}_{{\mathrm{n}}{\mathrm{o}}{\mathrm{n}}-{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}} $

Table 1. Ratios R, ionization temperatures $ {T}_{Z} $, average charge states $ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-1} $ based on DLA model under LTE conditions, $ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-2} $ based on the screened hydrogenic approximation under LTE conditions, and $ {\left\langle{Z}\right\rangle}_{{\mathrm{n}}{\mathrm{o}}{\mathrm{n}}-{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}} $ based on the screened hydrogenic approximation under non-LTE conditions for 14 sets of $ \left({T}_{{\mathrm{e}}}, {n}_{{\mathrm{e}}}\right) $ values.

序号	$ {T}_{{\mathrm{e}}}/ $eV	$ {n}_{{\mathrm{e}}} $/cm^–3	$ R $	$ {T}_{Z} $/eV	$ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-1} $	$ {\left\langle{Z}\right\rangle}_{{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}-2} $	$ {\left\langle{Z}\right\rangle}_{{\mathrm{n}}{\mathrm{o}}{\mathrm{n}}-{\mathrm{L}}{\mathrm{T}}{\mathrm{E}}} $
1	38	5.10×10²⁰	1.00754	37.72	12.57	12.60	12.60
2		2.05×10²⁰	1.01839	37.31	13.20	13.35	13.34
3		5.97×10¹⁹	1.05867	35.89	13.91	14.09	14.08
4	32	5.07×10²⁰	1.00418	31.87	11.10	11.14	11.13
5		1.26×10²⁰	1.01645	31.48	12.39	12.58	12.57
6		5.34×10¹⁹	1.03737	30.85	13.17	13.25	13.23
7	28	3.18×10²⁰	1.00418	27.88	10.44	10.41	10.41
8		1.15×10²⁰	1.0114	27.68	11.32	11.46	11.46
9		4.31×10¹⁹	1.02944	27.20	12.14	12.39	12.37
10	23	1.00×10²⁰	1.00664	22.85	9.87	9.82	9.81
11		5.26×10¹⁹	1.0125	22.72	10.37	10.39	10.38
12		2.23×10¹⁹	1.02862	22.36	11.00	11.11	11.10
13	20	4.77×10¹⁹	1.00851	19.83	9.40	9.30	9.29
14	20	1.06×10¹⁹	1.0364	19.30	10.42	10.44	10.43

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表 2 COWAN计算采用的Sn¹¹⁺—Sn¹⁴⁺离子的组态列表

Table 2. Configuration list of Sn¹¹⁺ to Sn¹⁴⁺ ions.

离子	组态
Sn¹¹⁺	4s²4p⁶ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d4f5p, 4d5s², 4d5p², 4d5d², 4d5p5d };
	4s²4p⁵ + {4d³4f, 4d³5p, 4d³5f, 4d²4f5s, 4d²4f5d, 4d²5s5p};
	4s²4p⁴ + {4d⁵, 4d⁴5s, 4d⁴5d, 4d³4f², 4d³4f5p};
	4s²4p³ + {4d⁵4f, 4d⁵5p, 4d⁴4f5s, 4d⁴4f5d };
	4s4p⁶ + {4d⁴, 4d³5s, 4d³5d, 4d²4f², 4d²4f5p};
	4s4p⁵ + {4d⁴4f, 4d⁴5p, 4d³4f5s, 4d³4f5d}.
	4s²4p⁶ + {4d²4f, 4d²5p, 4d²5f, 4d4f5s, 4d4f5d, 4d5s5p};
	4s²4p⁵ + {4d⁴, 4d³5s, 4d³5d, 4d²4f², 4d²5s², 4d²4f5p, 4d²5s5d};
	4s²4p⁴ + {4d⁴4f, 4d⁴5p, 4d³4f5s, 4d³4f5d};
	4s²4p³ + {4d⁶, 4d⁵5s, 4d⁵5d, 4d⁴4f², 4d⁴4f5p};
	4s4p⁶ + {4d³4f, 4d³5p, 4d²4f5s, 4d²4f5d};
	4s4p⁵ + {4d⁵, 4d⁴5s, 4d⁴5d, 4d³4f², 4d³4f5p}.
Sn¹²⁺	4s²4p⁶ + {4d², 4d5s, 4d5d, 4f², 4f5p, 5s², 5p², 5d², 5p5d};
	4s²4p⁵ + {4d²4f, 4d²5p, 4d²5f, 4d4f5s, 4d4f5d, 4d5s5p};
	4s²4p⁴ + {4d⁴, 4d³5s, 4d³5d, 4d²4f², 4d²4f5p};
	4s²4p³ + {4d⁴4f, 4d⁴5p, 4d³4f5s, 4d³4f5d};
	4s4p⁶ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d4f5p};
	4s4p⁵ + {4d³4f, 4d³5p, 4d²4f5s, 4d²4f5d}.
	4s²4p⁶ + {4d4f, 4d5p, 4d5f, 4f5s, 4f5d, 5s5p};
	4s²4p⁵ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d5s², 4d4f5p, 4d5s5d};
	4s²4p⁴ + {4d³4f, 4d³5p, 4d²4f5s, 4d²4f5d};
	4s²4p³ + {4d⁵, 4d⁴5s, 4d⁴5d, 4d³4f², 4d³4f5p};
	4s4p⁶ + {4d²4f, 4d²5p, 4d4f5s, 4d4f5d};
	4s4p⁵ + {4d⁴, 4d³5s, 4d³5d, 4d²4f², 4d²4f5p}.
Sn¹³⁺	4s²4p⁶ + {4d, 5s, 5d};
	4s²4p⁵ + {4d4f, 4d5p, 4d5f, 4f5s, 4f5d, 5s5p};
	4s²4p⁴ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d4f5p};
	4s²4p³ + {4d³4f, 4d³5p, 4d²4f5s, 4d²4f5d};
	4s4p⁶ + {4d², 4d5s, 4d5d, 4f², 4f5p};
	4s4p⁵ + {4d²4f, 4d²5p, 4d4f5s, 4d4f5d}.
	4s²4p⁶ + {4f, 5p, 5f};
	4s²4p⁵ + {4d², 4d5s, 4d5d, 4f², 5s², 4f5p, 5s5d};
	4s²4p⁴ + {4d²4f, 4d²5p, 4d4f5s, 4d4f5d};
	4s²4p³ + {4d⁴, 4d³5s, 4d³5d, 4d²4f², 4d²4f5p};
	4s4p⁶ + {4d4f, 4d5p, 4f5s, 4f5d};
	4s4p⁵ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d4f5p}.
Sn¹⁴⁺	4s²4p⁶;
	4s²4p⁵ + {4f, 5p, 5f};
	4s²4p⁴ + {4d², 4d5s, 4d5d, 4f², 4f5p};
	4s²4p³ + {4d²4f, 4d²5p, 4d4f5s, 4d4f5d};
	4s4p⁶ + {4d, 5s, 5d};
	4s4p⁵ + {4d4f, 4d5p, 4f5s, 4f5d}.
	4s²4p⁵ + {4d, 5s, 5d};
	4s²4p⁴ + {4d4f, 4d5p, 4f5s, 4f5d};
	4s²4p³ + {4d³, 4d²5s, 4d²5d, 4d4f², 4d4f5p};
	4s4p⁶ + {4f, 5p};
	4s4p⁵ + {4d², 4d5s, 4d5d, 4f², 4f5p}.

DownLoad: CSV

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