Collisional-radiative model for on-line analysis of C4F8/O2/Ar plasma optical emission spectroscopy

ZHANG Zhanling; ZHU Ximing; WANG Lu; ZHAO Yu; YANG Xihong

doi:10.7498/aps.74.20251182

Abstract

Octafluorocyclobutane (C₄F₈)-based fluorocarbon plasmas have become a cornerstone of nanometre-scale etching and deposition in advanced semiconductor manufacturing, owing to their tunable fluorine-to-carbon (F/C) ratio, high density of reactive radicals, and superior material selectivity. In high-aspect-ratio pattern transfer, optical emission spectroscopy (OES) enables in-situ monitoring by correlating the density of morphology-determining radicals with their characteristic spectral signatures, thereby providing a viable pathway for the simultaneously optimizing pattern fidelity and process yield. A predictive plasma model that integrates kinetic simulation with spectroscopic analysis is therefore indispensable. In this study, a C₄F₈/O₂/Ar plasma model tailored for on-line emission-spectroscopy analysis is established. First, the comprehensive reaction mechanism is refined through a systematic investigation of C₄F₈ dissociation pathways and the oxidation kinetics of fluorocarbon radicals. Subsequently, the radiative-collisional processes for the excited states of F, CF, CF₂, CO, Ar and O are incorporated, establishing an explicit linkage between spectral features and radical densities. Under representative inductively coupled plasma (ICP) discharge conditions, the spatiotemporal evolution of the aforementioned active species is analyzed and validated against experimental data. Kinetic back-tracking is employed to elucidate the formation and loss mechanisms of fluorocarbon radicals and ions, and potential sources of modelling uncertainty are discussed. This model has promising potential for application in real-time OES monitoring during actual etching processes.

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Authors and contacts

Corresponding author: ZHU Ximing, zhuximing@hit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. U22B2094).

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[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]
[56]
[57]
[58]

Cited By

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编号	公式	注释
E1	$\begin{array}{cc}\dfrac{{{\text{d}}{n_k}}}{{{\text{d}}t}} = \displaystyle\sum\nolimits_V {R_V^ + } (k) - \displaystyle\sum\nolimits_V {R_V^ - (k)} \\\qquad + \displaystyle\sum\nolimits_S {R_S^ + (k)} - \displaystyle\sum\nolimits_S {R_S^ - (k)} = 0 \end{array}$	$ {n_k} $: 物质 k 密度; $ R_V^ + (k) $: 物质 k 气相生成速率; $ R_V^ - (k) $: 物质 k 气相损失速率; $ R_S^ + (k) $: 物质 k 表面生成速率; $ R_S^ - (k) $: 物质 k 表面损失速率
E2	$ {R_V} = {K_V}\displaystyle\sum\nolimits_v {{n_v}};\;\; R_V^{{\text{rad}}} = A {n_v} $	$ {K_V} $: 气相反应速率系数; $ {n_v} $: 气相反应物密度; $ R_V^{{\text{rad}}} $: 气相自发辐射速率; A: 爱因斯坦系数
E3	$\begin{array} {cc} {K_V} = a T_{\text{e}}^b\exp \left( { - {c}/{{{T_{\text{e}}}}}} \right) ; \\ K_V^{{\text{exc}}} = \displaystyle\int_0^\infty {\sigma ({E_{\text{e}}})\sqrt {\dfrac{{2{E_{\text{e}}}}}{{{m_{\text{e}}}}}} f({E_{\text{e}}}){\text{d}}{E_{\text{e}}}} \end{array} $	$ {T_e} $: 电子温度; a, b, c : Arrhenius公式参数; $ K_V^{{\text{exc}}} $: 气相激发反应速率系数; E_e: 电子能量; m_e: 电子质量; $ \sigma ({E_{\text{e}}}) $: 激发截面; $ f({E_{\text{e}}}) $: 电子能量分布
E4	$ {R_{\text{S}}} = {K_{\text{S}}}{n_{\text{s}}} $	$ {n_{\text{s}}} $: 表面损失物质密度
E5	$ K_S^{\text{n}} = {\left[ {\dfrac{{{\varLambda ^2}}}{{{D_{\text{n}}}}} + \dfrac{{2 V(2 - \gamma )}}{{S{u_{\text{n}}}\gamma }}} \right]^{ - 1}} $	$ K_S^{\text{n}} $: 中性粒子表面损失系数; $ {D_{\text{n}}} $: 扩散系数; $ \gamma $: 表面黏附系数; $ {u_{\text{n}}} $: 平均热速度; V, S : 反应腔室体积和表面积
E6	$ {\varLambda ^{ - 2}} = {\left( {{{\pi}}/{l}} \right)^2} + {\left( {{{2.405}}/{r}} \right)^2} $	$ \varLambda $: 有效扩散长度; l, r : 反应腔室高度和半径
E7	$ K_{\text{S}}^{+} = 2{u_{\text{B}}}\left( {{{h_{\text{l}}}}}/{l} + {{{h_{\text{r}}}}}/{r}\right) $	$ K_{\text{S}}^{+} $: 离子表面损失系数; $ {u_{\text{B}}} $: 玻姆速度;
E8	${h_{\text{l}}} = 0.86{\left[ {3.0 + {l}/({{2\lambda }})} \right]^{-1/2}}$	${h_{\text{l}}}$: 轴向边界-中心离子密度比; $\lambda $: 平均自由程
E9	$ h_{\text{r}}=0.80\left(4.0 + {r}/{\lambda}\right)^{-1/2} $	${h_{\text{r}}}$: 径向边界-中心离子密度比

DownLoad: CSV

类别	物种
离子	$ \mathrm{CF}_3^+ $, ${\mathrm{CF}}_2^+ $, CF⁺, Ar⁺
自由基	CF₃, CF₂, CF, COF, F, C, O
中性产物	C₂F₄, CF₄, F₂, COF₂, CO, CO₂
原料气体	C₄F₈, O₂, Ar

DownLoad: CSV

类别	物种
Ar^*	Ar(1s₅)-Ar(1s₂), Ar(2p₁₀)-Ar(2p₁)
O^*	O(2p.¹D), O(2p.¹S), O(3s.³S^o), O(3s.⁵S^o), O(3p.³P), O(3p.⁵P), O(3p.³D^o), O(3p.⁵D^o)
F^*	F(3s.²P), F(3s.⁴P), F(3s.²D), F(3p.²S^o), F(3p.⁴S^o), F(3p.²P^o), F(3p.⁴P^o), F(3p.²D^o), F(3p.⁴D^o)
CF^*	CF(a⁴Σ^–), CF(A²Σ), CF(b⁴Π), CF(B²Δ), CF(C²Σ^–)
${\mathrm{CF}}^*_2 $	CF₂(A¹B₁), CF₂(X¹A₂), CF₂(X³A₂), CF₂(X³B₁), CF₂(X³B₂)
CO^*	CO(a³Π), CO(A¹Π), CO(b³Σ), CO(B¹Σ)

DownLoad: CSV

反应编号	反应式	速率系数/(cm³·s^–1)			参考文献
反应编号	反应式	a	b	c	参考文献
电子碰撞反应
R1	e + C₄F₈ → 2C₂F₄ + e	9.58 × 10^–8	0.042	8.572	[12]
R2	e + C₂F₄ → 2CF₂ + e	1.32 × 10^–8	0.412	6.329	[12]
R3	e + CF₄ → CF₃ + F + e	2.10 × 10^–9	0.936	12.004	[35]
R4	e + CF₃ → CF₂ + F + e	7.94 × 10^–8	–0.452	12.100	[12]
R5	e + CF₂ → CF + F + e	1.16 × 10^–8	–0.380	–14.350	[12]
R6	e + CF → C + F + e	4.51 × 10^–8	–0.110	8.941	[12]
R7	e + F₂ → 2F + e	1.08 × 10^–8	–0.296	4.464	[12]
R8	e + COF₂ → COF + F + e	3.20 × 10^–9	0.013	10.300	[36]
R9	e + CO₂ → CO + O + e	2.90 × 10^–9	0.302	12.100	[37]
R10	e + CO → C + O + e	1.54 × 10^–8	0.270	14.600	[38]
R11	e + O₂ → 2O + e	1.71 × 10^–8	–1.270	7.310	[39]
R12	e + CF₄ → ${\mathrm{CF}}_3^+ $ + F + 2e	2.29 × 10^–8	0.680	18.304	[35]
R13	e + CF₃ → ${\mathrm{CF}}_2^+ $ + F + 2e	7.02 × 10^–9	0.430	16.280	[12]
R14	e + CF₂ → CF⁺ + F + 2e	5.43 × 10^–9	0.561	14.290	[12]
R15	e + ${\mathrm{CF}}_3^+ $ → CF₂ + F	6.54 × 10^–8	–0.500	0.025	[13]
R16	e + ${\mathrm{CF}}_2^+ $ → CF + F	6.54 × 10^–8	–0.500	0.025	[13]
R17	e + CF⁺ → C + F	6.54 × 10^–8	–0.500	0.025	[13]
R18	e + CF₃ → ${\mathrm{CF}}_3^+ $ + 2e	1.36 × 10^–9	0.796	9.057	[12]
R19	e + CF₂ → ${\mathrm{CF}}_2^+ $ + 2e	1.10 × 10^–8	0.393	11.370	[12]
R20	e + CF → CF⁺ + 2e	5.48 × 10^–9	0.556	9.723	[12]
R21	e + Ar → Ar⁺ + 2e	7.35 × 10^–8	0.208	19.100	[40]
电荷交换反应
R22	$ {\mathrm{CF}}_2^+$ + CF → ${\mathrm{CF}}_3^+ $ + C	2.06 × 10^–9	0	0	[13]
R23	${\mathrm{CF}}_2^+ $ + C → CF⁺ + CF	1.04 × 10^–9	0	0	[13]
R24	CF⁺ + CF₃ → ${\mathrm{CF}}_3^+ $ + CF	1.71 × 10^–9	0	0	[13]
R25	CF⁺ + CF₂ → ${\mathrm{CF}}_2^+ $ + CF	1.00 × 10^–9	0	0	[13]
R26	Ar⁺ + CF₄ → ${\mathrm{CF}}_3^+ $ + F + Ar	4.80 × 10^–10	0	0	[13]
R27	Ar⁺ + CF₃ → ${\mathrm{CF}}_2^+ $ + F + Ar	5.00 × 10^–10	0	0	[13]
R28	Ar⁺ + CF₂ → CF⁺ + F + Ar	5.00 × 10^–10	0	0	[13]
氧化反应
R29	CF₃ + O → COF₂ + F	3.30 × 10^–11	0	0	[13]
R30	CF₂ + O → COF + F	3.10 × 10^–11	0	0	[13]
R31	CF + O → CO + F	6.60 × 10^–11	0	0	[13]
R32	COF + O → CO₂ + F	9.30 × 10^–11	0	0	[13]
R33	COF + COF → COF₂ + CO	1.00 × 10^–11	0	0	[13]
R34	C + CO₂ → 2CO	1.00 × 10^–15	0	0	[41]
R35	COF + CF₃ → COF₂ + CF₂	1.00 × 10^–11	0	0	[13]
R36	COF + CF₂ → COF₂ + CF	3.00 × 10^–13	0	0	[13]
R37	COF + CF₃ → CO + CF₄	1.00 × 10^–11	0	0	[13]
R38	COF + CF₂ → CO + CF₃	3.00 × 10^–13	0	0	[13]
重组反应
R39	F + CF₃ → CF₄	2.00 × 10^–11	0	0	[13]
R40	F + CF₂ → CF₃	1.80 × 10^–11	0	0	[13]
R41	F + CF → CF₂	9.96 × 10^–11	0	0	[13]
R42	F₂ + CF₃ → CF₄ + F	1.90 × 10^–14	0	0	[13]
R43	F₂ + CF₂ → CF₃ + F	8.30 × 10^–14	0	0	[13]

DownLoad: CSV

反应编号	反应式	速率系数
原子扩散
R44	O → $\dfrac{1}{2} $O₂	4.20 × 10³ s^–1
R45	F → $\dfrac{1}{2} $F₂	3.2 × 10² s^–1
离子扩散
R46	${\mathrm{CF}}_3^+ $ → CF₃	6.73 × 10³ s^–1
R47	${\mathrm{CF}}_2^+ $ → CF₂	7.91 × 10³ s^–1
R48	CF⁺ → CF	1.00 × 10⁴ s^–1
R49	Ar⁺ → Ar	8.85 × 10³ s^–1
等效表面反应
R50	C₂F₄ + C₂F₄ → C₄F₈	1.00 × 10^–11 cm³/s
R51	CF₂ + CF₂ → C₂F₄	1.00 × 10^–11 cm³/s
R52	C + F → CF	1.00 × 10^–11 cm³/s

DownLoad: CSV

参数	Kimura和Noto	Lee等^[56]
ICP腔室尺寸
半径/mm	80	80
高度/mm	80	130
放电工况
气压/mTorr	30	10
功率/W	140	700
气流/sccm	40	40
等离子参数
电子温度/eV	2.93—3.05	3.60—4.25
电子密度/cm^–3	5.48 × 10¹⁰— 1.00 × 10¹¹	5.00 × 10¹⁰— 6.20 × 10¹⁰

DownLoad: CSV

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Vol. 74, Issue 23 - 2025-12-05

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