NUMERICAL INVESTIGATION ON THE CHARACTERISTICS OF POWER DEPOSITION IN HELICON PLASMA
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摘要: 螺旋波等离子体凭借其高电离率、高密度等优势, 在半导体制造与电推进领域具有重要应用价值. 针对现有研究难以解析实验中多波耦合模式下功率沉积机制这一科学难题, 本研究基于HELIC数值模拟, 系统探究trivelpiece-gould(TG)波与helicon(H)波的本征模式竞争规律及其在低、高阶波耦合模式下的功率沉积特性. 通过构建参数化径向密度剖面模型(梯度参数s = 2.1 ~ 3.4, 峰化参数t = 1.8 ~ 2.5), 并结合自洽求解Maxwell-Boltzmann耦合方程组的数值方法, 实现了多波模式跳变过程的动态重构. 结果表明: 在低阶波模式(W1, ne = 2.0 × 1012 cm−3)下, TG波通过径向电场局域化机制贡献61.8%的边界电子加热效率, 而H波中心区功率沉积占比仅38.2%; 当激发高阶本征模(W2-W4, ne = 4.0 × 1012 ~ 1.1 × 1013 cm−3)时, TG波边缘阻尼效应导致其功率占比骤降至16.5%, 此时H波通过轴向驻波共振实现中心区83.5%的功率沉积主导, 并诱导等离子体密度分布从边缘峰化(s = 2.1)向中心聚集(s = 3.4)的模态转变. 研究结果为精确调控螺旋波等离子体参数分布及模式选择提供了重要理论支撑, 对优化半导体刻蚀均匀性和电推进器比冲性能具有直接指导意义.Abstract: Helicon plasma has significant application value in semiconductor manufacturing and electric propulsion fields, with its advantages of high ionization rate and high density. The scientific challenge of existing research is difficult to analyze the power deposition mechanism under the multi-wave coupling modes. This study systematically explores the competition rules of the eigenmodes of Trivelpiece-Gould (TG) waves and Helicon (H) waves and their power deposition characteristics in low and high-order wave coupling modes based on HELIC numerical simulation. By constructing a parameterized radial density profile model (with the gradient parameter s ranging from 2.1 to 3.4 and the peaking parameter t ranging from 1.8 to 2.5), and combining with the numerical method of self-consistently solving the coupled Maxwell-Boltzmann equations, the dynamic reconstruction of the multi-wave mode hopping process has been achieved. The results show that in the low-order wave mode (W1, ne = 2.0 × 1012 cm−3), TG waves contribute 61.8% of the boundary electron heating efficiency through the radial electric field localization mechanism, while the power deposition in the central region of H waves only accounts for 38.2%; when the high-order modes (W2-W4, ne = 4.0 × 1012 ~ 1.1 × 1013 cm−3) are excited, the edge damping effect of TG waves leads to a sudden drop in its power contribution to 16.5%, and at this time, H waves achieve 83.5% of the power deposition in the central region through axial standing wave resonance, and induce a modal transition of the plasma density distribution from the peripheral peak formation (s = 2.1) to central aggregation (s = 3.4). The research results provide important theoretical support for the precise regulation of the parameter distribution and mode selection of helicon plasmas. It has direct guiding significance for optimizing the uniformity of semiconductor etching and the specific impulse performance of electric thrusters.
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Keywords:
- helicon plasma /
- TG-H wave coupling /
- eigenmodes /
- power deposition
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引 言
螺旋波作为磁化有界等离子体中传播的哨声波, 其频率介于电子与离子回旋频率之间, 主要包含弱阻尼螺旋波(H波)和强阻尼trivelpiece-gould波(TG波)两种本征模式. 螺旋波等离子体源凭借低温、低气压和高密度等特性, 广泛应用于等离子体材料处理工艺[1-3], 如半导体刻蚀、薄膜沉积等, 同时在电推进领域因其无电极损耗、高电离效率等优势展现出重要应用前景[4-6].
螺旋波等离子体放电过程呈现典型的3个放电模式: 容性耦合(CCP)、感性耦合(ICP)及波耦合(W)模式[7-10]. 不同模式对应等离子体参数(如电子密度、发射光谱强度)与电路参数(如射频电流)的阶跃式变化, 并伴随放电形貌的显著差异. 值得关注的是, 实验观测表明波耦合模式本身亦可细分为多种本征模式[11-15], 其本质源于轴向与径向本征模的耦合效应, 而能量沉积机制的空间异性直接导致等离子体参数分布的差异性, 这对工艺调控具有决定性影响. 尽管CCP与ICP模式的能量耦合机制已形成共识[16-18], 但关于螺旋波模式的功率沉积机理仍存争议.
早期研究基于朗道阻尼理论解释螺旋波的高效电子加热[19-20]. 然而, 该模型无法合理解释实验观测的高电离效率与热电通量间的矛盾[21]. 后续研究发现, 具有准静电特性且短波长的TG波在等离子体边缘区域通过强局域化阻尼实现高效功率吸收, 而长波长的H波则主导中心区域的能量沉积[22-26]. 这一理论虽能解释边界电离现象, 却难以阐明实验中普遍存在的中心峰值密度分布与强轴向辐射特征[22-24]. 对此, Carter等[27]指出当电子密度超过临界阈值(ne ≥ 5 × 1012 cm−3)时, TG波因强阻尼效应无法穿透核心区, 此时H波的轴向聚焦机制成为中心功率沉积的主导因素. Piotrowicz等[28-29]进一步提出, H波通过驻波共振将能量直接沉积于轴心区域, 从而形成中心峰化密度分布. Eom等[30]则系统论证了磁场强度对TG-H波耦合机制的调控作用: 高磁场条件下TG波模式抑制, H波主导的轴向加热导致密度分布由边缘峰化向中心聚集转变. Isayama等[31]的最新研究揭示了TG/H波功率比与密度剖面形态的定量关联, 为多模式耦合理论提供了实验依据. 尽管如此, 关于不同本征波模式下TG波与H波对功率沉积的竞争机制仍缺乏系统性理论框架, 特别是实验中观测到的多波模式跳变现象(如密度突变[11-13])尚未得到合理解释.
当前, 针对螺旋波多模式耦合的数值模拟研究仍存在显著空白: 现有模型多基于实验中观察到的单一波模式的简化假设, 难以真实反映实验中复杂的多波场耦合效应. 为此, 本研究采用HELIC仿真软件[32-36], 结合前期实验观测的多波模式跳变数据[11-12], 系统探究不同本征波模式下的功率沉积特性. 通过调节等离子体密度与温度的空间分布参数, 定量解析TG/H波耦合机制对电场分布、电子加热路径的分区特性(边界局域化加热与中心加热)以及密度剖面的模态跃迁规律(边缘峰化↔中心聚集)的影响规律, 为揭示螺旋波等离子体的多尺度耦合物理提供新的研究思路.
1. 计算模型与数值方法
1.1 控制方程与耦合算法
本研究基于HELIC全波仿真平台[32-36], 重点构建螺旋波多模式耦合的功率沉积动力学模型. 通过自洽耦合Maxwell方程组与Boltzmann方程, 建立包含H波与TG波本征模式激发—传播—耗散链式过程的数值分析体系. 该模型采用特征边界条件求解六维耦合微分方程, 其数值算法的建立基于3个核心假设: (1)静磁场轴向均匀分布假设; (2)等离子体输运过程与粒子源项的准稳态近似; (3)轴向均匀系统条件. 虽未计入动态粒子平衡过程, 但在波场耦合机理研究方面具有独特优势. 关于程序物理模型的详细介绍, 可参考Chen-Arnush奠基理论[32-33], 本文重点论述电磁场方程与粒子动力学方程的多尺度耦合机制.
在角频率为ω的时谐电磁场假设下, Maxwell方程组可表述为
$$ \left. \begin{gathered} \nabla \times {\boldsymbol{E}} = - {\mathrm{i}}\omega {\boldsymbol{B}} \\ \nabla \times {\boldsymbol{B}} = {\mu _0}({\boldsymbol{J}} + {\mathrm{i}}\omega {\varepsilon _0}{\boldsymbol{E}}) \\ \end{gathered} \right\} $$ (1) 其中, $ {\boldsymbol{J}} = - {\mathrm{e}}{n_{\text{e}}}{{\boldsymbol{\upsilon}} _{\mathrm{e}}} $为电子传导电流密度. 在螺旋波频段(ω ~ 107 Hz), 离子惯性效应可忽略, 仅需考虑电子动力学响应. 结合轴向均匀性假设(∂/∂z = 0), 方程可简化为二维柱对称形式(r−z平面).
电子速度分布函数$ {f_{\text{e}}}\left( {{\boldsymbol{r}},{\boldsymbol{\upsilon}} ,{{t}}} \right) $可通过线性化Boltzmann方程描述
$$ \frac{{\partial {f_{\text{e}}}}}{{\partial t}} + {\boldsymbol{\upsilon}} \cdot \nabla {f_{\text{e}}} - \frac{{\mathrm{e}}}{{{m_{\text{e}}}}}({\boldsymbol{E}} + {\boldsymbol{\upsilon}} \times {\boldsymbol{B}}) \cdot {\nabla _\vartheta }{f_{\text{e}}} = {\left(\frac{{\delta {f_{\text{e}}}}}{{\delta t}}\right)_{{\text{coll}}}} $$ (2) 采用小扰动近似分解: $ {f_{\text{e}}} = {f_{\text{e}}}_0 + {f_{\text{e}}}_1 $, 其中fe0为麦克斯韦平衡分布, fe1为射频场扰动项($ | {{f_{\text{e}}}_1} | \ll | {{f_{\text{e}}}_0} | $). 引入BGK碰撞模型后, 碰撞项简化为$ {(\delta {f_{\text{e}}}/\delta t)_{{\text{coll}}}} = - {\nu _{{\mathrm{e}}n}}({f_{\text{e}}} - {f_{\text{e}}}_0) $, 其中$ {\nu _{\text{e}n}} $为电子-中性粒子碰撞频率. 在时谐场条件下($ {f_{\text{e}}}_1 \propto {{\mathrm{e}}^{j\omega t}} $), 方程线性化为
$$ j\omega {f_{\text{e}}}_1 + {\boldsymbol{\upsilon}} \cdot \nabla {f_{\text{e}}}_1 - \frac{{\mathrm{e}}}{{{m_{\text{e}}}}}({\boldsymbol{E}} + {\boldsymbol{\upsilon}} \times {{\boldsymbol{B}}_0}) \cdot {\nabla _\vartheta }{f_{{\text{e0}}}} = - {\nu _{\text{e}n}}{f_{\text{e}}}_1 $$ (3) 式中, B0为轴向静磁场. 通过求解此方程可获得电子电流密度的扰动响应$ {\boldsymbol{J}} = - {\mathrm{e}}\displaystyle\int {{\boldsymbol{\upsilon}} {f_{\text{e}}}_1{{\mathrm{d}}^3}\vartheta } $.
两大控制方程的耦合通过以下迭代过程实现: (1)给定初始等离子体参数(ne, Te), 求解Boltzmann方程获得J(E); (2)将电流密度代入Maxwell方程组更新电磁场分布; (3)采用Newton-Raphson算法实现场与等离子体响应的自洽解, 收敛判据设定为max(|ΔE|/|E|) < 10−5.
功率沉积密度的定量分析通过Poynting矢量散度计算实现
$$ {P}_{\text{abs}}(r,z) = \frac{1}{2}\mathrm{Re}({\boldsymbol{J}}\cdot {{\boldsymbol{E}}}^{\ast }) $$ (4) 式中, 电流密度J包含两种物理机制的贡献: H波主要源于电磁模式的极化电流项$ {{\boldsymbol{J}}_{\text{H}}} = - {\mathrm{i}}\omega {\varepsilon _0}\left( {{\varepsilon _{\text{r}}} - 1} \right){\boldsymbol{E}} $, 其色散关系满足$ {\omega ^2} = \omega _{{\text{pe}}}^2 + {c^2}k_z^2 $[37](kz < 0.5 cm−1, B0 > 100 G, ne ~ 5.0 × 1012 cm−3[27]), 表现为长波长特性(λz > 12 cm), 轴向相位速度υph ≈ 0.8c; TG波贡献主要对应准静电模式的传导电流项$ {{\boldsymbol{J}}_{{\text{TG}}}} = {\sigma _{{\text{TG}}}}{\boldsymbol{E}} $, 满足准静电近似色散关系$ \omega = \sqrt {\omega _{{\text{pe}}}^2 + 3\upsilon _{t{\mathrm{e}}}^2 k_{\text{r}}^{\text{2}}} $[37](kz > 0.7 cm−1, ne < 1.0 × 1013 cm−3), 呈现短波长特性(λz < 8 cm), 径向波数kr ∝ ne1/2.
通过引入等效电导率张量, 式(4)可重构为波模竞争方程
$$ P(r) = \frac{1}{2}{{\mathrm{Re}}} \left({\sigma _{\text{H}}}{\left| {E_{\text{r}}^{{\text{(H)}}}} \right|^2} + {\sigma _{{\text{TG}}}}{\left| {E_{\text{r}}^{{\text{(TG)}}}} \right|^2}\right) $$ (5) 其中, σH和σTG分别为H波和TG波的等效电导率; Er(H)源于电磁场横向分量, 满足$ \nabla \times {\boldsymbol{E}} = - \partial {\boldsymbol{B}}/\partial t $, 主导中心区能流($ {{\boldsymbol{S}}_{\mathrm{H}}} \propto {E_{\mathrm{r}}}^{({\mathrm{H}})}{B_\theta } $); Er(TG)由电荷分离引起, 满足$ \nabla \cdot {\boldsymbol{E}} = \rho /{\varepsilon _0} $, 其幅值与局域密度梯度$ \partial {n_{\text{e}}}/\partial r $成正比, 导致边缘区域电场局域化.
该计算方法充分考虑了电磁场能量与等离子体响应的非线性相互作用, 为功率沉积机理研究提供了可靠的理论工具.
1.2 关键参数设置
基于前期实验观测的多模式密度分布特征[11-12], 我们构建了参数化径向密度剖面
$$ n\left( r \right) = {n_0}{\left[ {1 - {{\left( {\frac{r}{\varpi }} \right)}^s}} \right]^t},\quad \varpi = \frac{{{r_0}}}{{{{\left[ {1 - {{({f_{{r_0}}})}^{1/t}}} \right]}^{1/s}}}} $$ (6) 式中, n0是等离子体中心的密度, s和t分别控制密度梯度的陡峭度与峰化程度; fr0表示r = r0的相对密度nr0 / n0. 如图1所示, 通过调节(s,t)参数组合可精确重构实验中观测到的典型模式特征: 低阶波模式(W1)对应缓变梯度分布(s = 2.1, t = 1.8), 高阶波模式(W2 ~ W4)呈现边界陡降特征(如W2: s = 3.4, t = 2.5). 这种梯度敏感性的量化表征为研究波模竞争机制提供了关键输入[35,38].
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图 1 数值模拟采用的参数化径向密度剖面及其与实验数据的一致性验证: Langmuir探针测量数据(散点; 0.3 Pa, Ar, 500 G; 800, 1200, 1500和2000 W分别对应W1 ~ W4)与参数化拟合曲线(实线)Figure 1. The parametric radial density profile used in the numerical simulation and the verification of its consistency with the experimental data: Langmuir probe measurement data (scatter points; 0.3 Pa, Ar, 500 G; 800, 1200, 1500 and 2000 W correspond to W1 ~ W4 respectively) and the parametric fitting curves (solid lines)电子温度剖面采用双参数调控模型
$$ \frac{T}{{{T_0}}} = {f_{{r_0}}} + (1 - {f_{{r_0}}}){\left[ {1 - {{\left( {\frac{r}{{{r_0}}}} \right)}^{{s_t}}}} \right]^{{t_t}}},\quad {f_{{r_0}}} = \frac{{{T_{{r_0}}}}}{{{T_0}}} $$ (7) 其中, st控制近轴区温度梯度; tt决定边缘温度衰减速率; T0是等离子体中心温度; Tr0是边缘温度. 通过实验确定典型参数组合st = 1.2和tt = 2.3[11-12], 确保温度场与密度场的物理自洽性.
本研究构建的几何-电磁耦合约束体系严格遵循实验装置原型参数[9-13]: 等离子体约束在半径r0 = 3 cm的石英管内, 外绕半螺旋天线(rA = 3.5 cm、长度dA = 15.5 cm), 整体置于rc = 15 cm的金属真空腔(图2). 电磁边界处理采用Mur二阶吸收边界条件精确抑制腔壁寄生反射, 射频馈入系统通过L型阻抗匹配网络实现13.56 MHz驱动功率的高效馈入(驻波比 < 1.5). 该建模策略通过物理原型参数的全尺度复现, 确保仿真与实验的严格空间一致性.
2. 结果与分析
图3显示不同等离子体密度下的功率沉积径向分布特征(B0 = 500 G).
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图 3 不同等离子体密度下功率沉积的径向分布; B0 = 500 G; ne = 6.3 × 1011, 2.0 × 1012 ~ 1.1 × 1013 cm−3, 对应ICP、低(W1)和高阶(W2 ~ W4)波模式Figure 3. The radial distribution of power deposition under different plasma densities; B0 = 500 G; ne = 6.3 × 1011, 2.0 × 1012 ~ 1.1 × 1013 cm−3, corresponding to the ICP, low (W1), and high-order (W2 ~ W4) wave modes实验观测表明[11], 当ne = 6.3 × 1011 cm−3(ICP模式)时, 功率沉积源于射频磁场感应的欧姆加热, 呈现显著的边缘局域化特征(边界区占比 > 95%). 此时等离子体密度呈现均匀或空心分布, 源于边界产生的粒子沿磁力线快速扩散的输运机制[16, 39]. 当密度升至2.0 × 1012 cm−3时, 系统进入低阶波(W1)耦合状态: TG波在边界区的功率沉积占比降至61.8%, 而H波在中心区贡献38.2%的功率吸收. 这种双峰分布表明H-TG波形成协同加热机制, 但TG波仍占主导地位. 值得注意的是, 当径向密度梯度陡峭化(梯度参数s从2.1增至3.4)时, 高阶波模式(W2 ~ W4; ne = 4.0 × 1012 ~ 1.1 × 1013 cm−3)呈现显著的模态跃迁: 中心区功率沉积占比提升至83.5% (如W2), 同时边界功率沉积强度下降61%. 该现象揭示TG波在高密度梯度下发生强朗道阻尼, 导致H波通过轴向驻波共振主导中心能量沉积[38].
图4揭示了磁场强度对功率沉积分布的调控规律(ne = 8 × 1012 cm−3). 当B0 = 50 G (ICP模式)时, 功率沉积再次呈现边界局域性( > 92%). 随着磁场增强至B0 = 100 G(低阶波模式), 中心区出现明显的H波沉积峰(占比41.8%). 当B0 > 300 G时(高阶波模式), 中心沉积强度随磁场呈超线性增长, 在B0 = 700 G时达到峰值占比278%. 这表明强磁场条件下, H波的波长缩短效应增强了其与等离子体本征模的相位匹配, 从而提升中心能量的耦合效率.
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图 4 不同磁场下功率沉积的径向分布; ne = 8 × 1012 cm−3; B0 = 50, 100 ~ 700 G, 对应ICP、低(W1)和高阶(W2 ~ W4)波模式Figure 4. The radial distribution of power deposition under different magnetic fields; ne = 8 × 1012 cm−3; B0 = 50, 100 ~ 700 G, corresponding to the ICP, low (W1), and high-order (W2 ~ W4) wave modes图5的不同波模式下轴向功率沉积分布显示: 在低阶波模式(ne = 2.0 × 1012 ~ 3.0 × 1012 cm−3)下, 沉积峰位于天线下游z = 0 ~ 40 cm区间, 与实验观测的轴向发光强度分布高度吻合[12]. 高阶模式(ne = 8.0 × 1012 ~ 9.0 × 1012 cm−3)则呈现双峰结构, 第二沉积峰出现在z ~ 25 cm处, 对应轴向波数kz ~ 0.4 cm−1的驻波共振效应(图6(b)). 定量分析表明, 高阶模的功率沉积强度较低阶模提升2.3倍, 这与密度梯度诱导的波场重构密切相关.
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图 5 不同波模式下功率沉积的轴向分布; 虚线表示天线中心; ne = 2.0 × 1012 ~ 3.0 × 1012, 8.0 × 1012 ~ 9.0 × 1012 cm−3, 对应低(W1)和高阶(W4)波模式Figure 5. The axial distribution of power deposition under different wave modes; The dashed line represents the center of the antenna; ne = 2.0 × 1012 ~ 3.0 × 1012, 8.0 × 1012 ~ 9.0 × 1012 cm−3, corresponding to the low (W1) and high-order (W4) wave modes![]()
图 6 在低阶模式和高阶波模式下功率沉积随轴向波数的变化Figure 6. The variation of power deposition with the axial wave number in the low-order mode and the high-order wave modes图6揭示了轴向波数kz对功率沉积的调制规律及其模式依赖性.
在低阶波模式(ne = 1.5 × 1012 ~ 2.5 × 1012 cm−3)下, 相对吸收功率谱呈现单峰结构(图6(a)), 其峰值位置稳定在kz ~ 0.2 cm−1处, 与实验测量的低阶本征模轴向波数误差小于5%[11-12]. 数值模拟显示, 当ne = 1.5 × 1012 cm−3增至2.5 × 1012 cm−3时, 峰值功率密度提升1.2倍, 表明低阶模的激发效率与密度呈正相关.
高阶波模式(ne = 8.0 × 1012 ~ 10 × 1012 cm−3)则呈现显著的双峰特征(图6(b)). 基模(kz ~ 0.2 cm−1): 其峰值功率随密度增加逐渐减小, 当ne = 1.0 × 1013 cm−3时功率贡献率降至12.7%; 高阶模(kz ~ 0.4 cm−1): 峰值功率随密度几乎线性增长, 在ne = 1.0 × 1013 cm−3时占据77.8%的沉积主导地位.
图7的径向电场分布揭示关键物理机制: 低阶W1波模式下, 边界区(r > 2.8 cm)电场强度Er较高(TG波主导), 相较于H波贡献区(r < 2 cm)提升2.8倍. TG波通过准静电场与密度梯度(s = 2.1)耦合, 激发强径向电场$ E_{\text{r}}^{{\text{(TG)}}} \propto {{\nabla {n_{\text{e}}}} \mathord{\left/ {\vphantom {{\nabla {n_{\text{e}}}} {{n_{\text{e}}}}}} \right. } {{n_{\text{e}}}}} \cdot {T_{\text{e}}} $(泊松方程推导), 此阶段电子加热以边界区碰撞耗散为主. 高阶波(W2 ~ W4)模式下, 中心区Er显著增强, 如W4相比W1模式: Er提升了约6倍, 且中心区Er幅值提升至边界区的1.3倍, 表明H波通过电磁模式转换实现高效能量沉积. H波通过电磁模式转换增强中心区场耦合$ \nabla \times {\boldsymbol{E}} = - \partial {\boldsymbol{B}}/\partial t $(法拉第定律主导), 该过程触发波-粒共振加热, 电子温度分布从边界峰化转变为中心强聚焦[9,12].
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图 7 不同等离子体密度下(波模式)等离子体径向电场的分布Figure 7. The distribution of the radial electric field of the plasma under different plasma densities (wave modes)3. 结 论
本研究通过数值模拟, 系统揭示螺旋波等离子体多模式耦合的功率沉积特性, 主要结果如下.
(1)建立了TG-H波功率竞争定量模型: 低阶波模式以TG波边界局域化加热为主(占比61.8%), 高阶波模式则由H波主导中心共振加热(占比83.5%), 实现能量沉积路径的可控切换.
(2)发现密度梯度调控规律: 径向密度梯度参数s > 3.4时触发TG波边缘阻尼增强效应, 使H波中心区域功率沉积效率大大提升, 诱导密度剖面从边缘峰化向中心聚集转变.
(3)阐明波场耦合特性: 轴向波数kz ~ 0.4 cm−1对应高阶本征模驻波共振, 其功率沉积强度较基模提高2.3倍, 且轴向双峰结构与实验密度分布高度一致.
本模型为半导体刻蚀均匀性控制和电推进器比冲优化提供了新的设计准则. 后续研究将引入动态粒子输运模型, 完善波场-等离子体实时耦合理论体系.
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图 1 数值模拟采用的参数化径向密度剖面及其与实验数据的一致性验证: Langmuir探针测量数据(散点; 0.3 Pa, Ar, 500 G; 800, 1200, 1500和2000 W分别对应W1 ~ W4)与参数化拟合曲线(实线)
Figure 1. The parametric radial density profile used in the numerical simulation and the verification of its consistency with the experimental data: Langmuir probe measurement data (scatter points; 0.3 Pa, Ar, 500 G; 800, 1200, 1500 and 2000 W correspond to W1 ~ W4 respectively) and the parametric fitting curves (solid lines)
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图 3 不同等离子体密度下功率沉积的径向分布; B0 = 500 G; ne = 6.3 × 1011, 2.0 × 1012 ~ 1.1 × 1013 cm−3, 对应ICP、低(W1)和高阶(W2 ~ W4)波模式
Figure 3. The radial distribution of power deposition under different plasma densities; B0 = 500 G; ne = 6.3 × 1011, 2.0 × 1012 ~ 1.1 × 1013 cm−3, corresponding to the ICP, low (W1), and high-order (W2 ~ W4) wave modes
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图 4 不同磁场下功率沉积的径向分布; ne = 8 × 1012 cm−3; B0 = 50, 100 ~ 700 G, 对应ICP、低(W1)和高阶(W2 ~ W4)波模式
Figure 4. The radial distribution of power deposition under different magnetic fields; ne = 8 × 1012 cm−3; B0 = 50, 100 ~ 700 G, corresponding to the ICP, low (W1), and high-order (W2 ~ W4) wave modes
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图 5 不同波模式下功率沉积的轴向分布; 虚线表示天线中心; ne = 2.0 × 1012 ~ 3.0 × 1012, 8.0 × 1012 ~ 9.0 × 1012 cm−3, 对应低(W1)和高阶(W4)波模式
Figure 5. The axial distribution of power deposition under different wave modes; The dashed line represents the center of the antenna; ne = 2.0 × 1012 ~ 3.0 × 1012, 8.0 × 1012 ~ 9.0 × 1012 cm−3, corresponding to the low (W1) and high-order (W4) wave modes
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图 6 在低阶模式和高阶波模式下功率沉积随轴向波数的变化
Figure 6. The variation of power deposition with the axial wave number in the low-order mode and the high-order wave modes
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