Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11475038).
Received Date:14 January 2019
Accepted Date:20 March 2019
Available Online:01 May 2019
Published Online:20 May 2019
Abstract:Inductively coupled plasmais widely used in semiconductor and display process because of its desirable characteristics such as high plasma density, simple structure and independently controllable ion energy. The driving frequency is a significant parameter that generates and maintains the plasma. However, the effects of different driving frequencies on the radial distribution of the plasma parameters are hardly investigated. So a large area cylindrical inductively coupled plasma source driven separately by 2 MHz and 13.56 MHz is investigated. In order to perform a comprehensive investigation about the effect of driving frequency, the radially resolved measurements of electron density, electron temperature and density of metastable state atoms for the argon discharge are systematically analyzed by Langmuir double probe and optical emission spectroscopy at various power values and gas pressures. It is found that input power values at high frequency (13.56 MHz) and low frequency (2 MHz) have different effects on plasma parameters. When discharge is driven at high frequency, the electron density increases obviously with the increase of power. However, when discharge is driven at low frequency, the electron temperature increases evidently with the increase of power. This can be explained by calculating the skin depths in high and low frequency discharge. When the discharge is driven at high frequency, the induced electromagnetic field is higher than that at low frequency, and the single electron obtains more energy. It is easier to ionize, so the energy is mainly used to increase the electron density. When the discharge is driven at low frequency, the skin layer is thicker, the number of heated electrons is larger, and the average energy of electrons is increased, so the energy is mainly used to raise the electron temperature. At a gas pressure of 10 Pa, the electron density shows a ‘convex’ distribution and increases with the increase of input power for both the high-frequency and low-frequency discharge. While the distributions of electron temperature are obviously different. When the discharge is driven at high frequency, the electron temperature is relatively flat in the center of the chamber and slightly increases on the edge. When the discharge is driven at low frequency, the electron temperature gradually decreases along the radial position. This is due to the one-step ionization in the high-frequency discharge and the two-step ionization in the low-frequency discharge. In order to prove that the low-frequency discharge is dominated by two-step ionization, the spectral intensities of the argon plasma under the same discharge conditions are diagnosed by optical emission spectroscopy. The number density of metastable states is calculated by the branch ratio method. The results are consistent with the analyses. At a gas pressure of 100 Pa, the electron density increases and then decreases with the increase of radial distance, and the overall distribution shows a " saddle shape” for high frequency and also for low frequency discharge. Although the uniformity of electron density improves with the gas pressure, the uniformity at low frequency is better than that at high frequency. The reason can be attributed to the fact that the skin layer of low frequency is thicker and the heating area is wider. Keywords:inductively coupled plasma/ Langmuir double probe/ optical emission spectroscopy/ plasma parameters
固定气压为10 Pa, 在输入功率为200, 400, 600, 800, 1000 W时, 测量轴向位置z = 10 cm, r = 0 cm处, 电子密度和电子温度随输入功率的变化情况如图3所示. 为了保证实验数据的准确性, 每个数据点都是至少三次测量结果的平均, 并通过计算数据的标准差得出了相应的误差棒. 图 3 气压为10 Pa时, 在z = 10 cm, r = 0 cm处, 13.56 MHz/2 MHz放电中等离子体参数随功率的变化 (a)电子密度; (b)电子温度 Figure3. (a) The electron density and (b) electron temperature of 13.56 MHz/2 MHz discharge at different power. The gas pressure is fixed at 10 Pa and the measurement position is z = 10 cm, r = 0 cm.
固定气压为10 Pa, 驱动频率分别为13.56 MHz和2 MHz, 在输入功率为400, 600, 800, 1000 W时, 测量了径向平面(z = 10 cm)上电子密度和电子温度的分布. 图5(a)和图5(b)分别为高频和低频放电时, 电子密度随径向位置的变化. 图 5 气压为10 Pa时, z = 10 cm处, 13.56 MHz/2 MHz放电中电子密度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz Figure5. The radial distribution profiles of electron density for (a) 13.56 MHz and (b) 2 MHz discharge. The gas pressure is fixed at 10 Pa and the measurement plane is z = 10 cm.
从图5中可以看出, 高频和低频分别放电时, 在功率一定的条件下, 电子密度的径向分布均呈现“凸型”分布, 这是因为等离子体具有抗磁性, 感应电场主要分布在靠近天线的位置, 因此电子加热主要发生在腔室边缘, 而被涡旋电场加热的电子可以在较短时间内穿过趋肤层并获得能量[29,30], 之后在能量完全损失之前到达腔体内, 并与中性粒子发生非弹性碰撞产生电子, 各个方向的电子都向腔室中心堆积; 另外, 由于实验中采用的放电腔室, 其轴向长度为370 mm, 径向宽度为260 mm, 长宽比大于1, 电子更容易在径向边缘与腔室壁发生复合损失, 而到达轴向边缘比较困难, 因此, 在轴向积累了较多的电子, 最终导致电子分布呈现中间高, 边缘低的“凸型”分布. 在相同的条件下, 测量了电子温度的径向分布如图6所示, 由图可知, 在气压和输入功率相同的情况下, 高频放电中电子温度的径向分布较为平缓, 在腔室边缘略有上升, 这是由于电子主要通过腔室壁上的线圈感应而来的交变电磁场获得能量, 之后向腔室中心运动的过程中, 与中性粒子发生非弹性碰撞损失能量, 且低能电子不能克服腔室中心的双极性电势到达边缘加热[16]; 而由于低频放电中感应产生的电场较弱, 单个电子在边缘获得的能量较少, 发生直接电离比较困难, 在腔室边缘获得能量之后先发生反应, ${\rm{Ar}} + {\rm{e}}\left( {11.4{\rm{ eV}}} \right) \to {\rm{A}}{{\rm{r}}^*} + {\rm{e}}$, 产生了大量${\rm{A}}{{\rm{r}}^*}$损失了较多的能量, 之后这些亚稳态粒子继续向腔室中心运动的过程中与电子碰撞电离, ${\rm{A}}{{\rm{r}}^*} + {\rm{e}}\left( {4.2{\rm{ eV}}} \right) \to {\rm{A}}{{\rm{r}}^ + } + 2{\rm{e}}$, 因此导致电子温度的径向分布为中间高, 边缘低的“凸型”分布. 图 6 气压为10 Pa时, 高低频放电中电子温度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz Figure6. The radial distribution profiles of electron temperature for (a) 13.56 MHz and (b) 2 MHz discharge. The gas pressure is fixed at 10 Pa and the measurement plane is z = 10 cm.
为了验证上述过程, 在相同的实验条件下, 通过测量发射光谱, 计算了波长为811.5 nm和750.4 nm的两条谱线的强度比, 比值随径向位置的变化如图7所示. 图 7 气压为10 Pa时, 高低频放电中亚稳态的径向分布 (a)高频13.56 MHz; (b)低频2 MHz Figure7. The radial distribution profiles of metastable states for (a) 13.56 MHz and (b) 2 MHz discharge at 10 Pa.
为了进一步研究高气压下频率对等离子体参数的影响, 将气压升高为100 Pa, 驱动频率分别为13.56 MHz和2 MHz, 在输入功率为400, 600, 800, 1000 W时, 测量了径向平面(z = 10 cm)上电子密度和电子温度的分布. 图8(a)和图8(b)分别为13.56 MHz和2 MHz放电时, 电子密度随径向位置的变化. 图 8 气压为100 Pa时高低频放电中电子密度的径向分布 (a)频率为13.56 MHz; (b)频率为2 MHz Figure8. The radial distribution profiles of electron density (a) 13.56 MHz and (b) 2 MHz discharge. The gas pressure is fixed at 100 Pa and the measurement plane is z = 10 cm.
从图8中可以看出, 无论在高频还是低频放电条件下, 电子密度的径向分布均为“马鞍形”, 峰值在R = 10—12 cm之间, 与图5中10 Pa条件下高频和低频放电中电子密度的径向分布相比, 其均匀性得到了改善, 但低频的均匀性优于高频. 图9所示为计算了不同气压下高频和低频放电中不均匀度随输入功率的变化, 与上述分析一致. 其中不均匀度可以衡量一个测量平面内电子密度的空间分布状况, 不均匀度越小代表该平面内电子密度的空间分布越均匀. 其表达式如下: 图 9 气压为10 Pa和100 Pa时, 在z = 10 cm处, 高低频放电中径向不均匀度随功率的变化 Figure9. Thenonuniformity at different power for 13.56 MHz/2 MHz discharge. The gas pressure is fixed at 10 Pa and 100 Pa, the measurement plane is z = 10 cm.
其中$\sigma $为碰撞截面, M为氩原子的质量, ${\nu _{{\rm{ee}}}}$为电子与电子的碰撞频率, ${\nu _{{\rm{en}}}}$为电子与中性粒子的碰撞频率, ${T_{\rm{e}}}$为电子温度[1,2]. 我们认为高频和低频放电中电子密度的径向分布均呈现“马鞍形”的原因是:随着气压的增加, 中性粒子数密度增多, 由(6)式可得随着气压的升高, 中性粒子的数密度增加, 电子的平均自由程减小, 与中性粒子的碰撞频率增加, 单位体积内产生更多的带电粒子, 因此电子密度增加. 经过计算得出电子的能量弛豫长度如图10所示, 随气压的升高, 电子的能量弛豫长度急剧下降, 在线圈周围加热的电子, 在极短的自由程内与中性粒子发生非弹性碰撞, 产生大量电子, 因此在R = 10—12 cm之间出现峰值, 这些损失了大量能量的电子, 继续向腔室中心运动时, 只能电离部分中性粒子, 所以腔室中心电子密度较低[16]. 图 10 气压为10 Pa和100 Pa时, 13.56 MHz/2 MHz放电中电子能量弛豫长度随功率的变化 Figure10. The electron energy relaxation length versus input power for 13.56 MHz/2 MHz discharge. The gas pressure is fixed at 10 Pa and 100 Pa.
图11(a)和图11(b)为相同条件下电子温度的径向分布, 其中高频驱动时电子温度的分布情况与低频有较大差异. 高频放电时, 腔室边缘处的电子温度高于中心. 这是由于电子在腔室边缘获得能量后, 向中心运动的过程中与中性粒子发生非弹性碰撞, 导致能量损失. 其次, 由于与中性粒子发生非弹性碰撞产生了更多的电子, 电子与电子、电子与中性粒子之间的碰撞频率增加, 因此从边缘到中心电子温度缓慢下降[28]. 然而, 当低频驱动时, 电子温度随着径向距离的增加先缓慢增加之后下降, 在R = 10—12 cm范围内出现峰值, 通过计算得${I_{811}}/{I_{750}}$比值的空间分布仍与电子温度的径向分布相反, 这与前文所述的原因一致, 进一步证明了高频放电中以直接电离为主, 低频放电中以多步电离为主. 图 11 气压为100 Pa时高低频放电中电子温度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz Figure11. The radial distribution profiles of electron temperature (a) 13.56 MHz and (b) 2 MHz discharge. The gas pressure is fixed at 100 Pa and the measurement plane is z = 10 cm.
图 1 柱状感性耦合等离子体源的实验装置图
图 2 频率为13.56 MHz, 气压为10 Pa, 输入功率为400 W, 腔室中心(r = 0 cm)处氩等离子体发射光谱全谱
图 3 气压为10 Pa时, 在z = 10 cm, r = 0 cm处, 13.56 MHz/2 MHz放电中等离子体参数随功率的变化 (a)电子密度; (b)电子温度
图 4 气压为10 Pa时, 13.56 MHz/2 MHz放电中趋肤深度随功率的变化
图 5 气压为10 Pa时, z = 10 cm处, 13.56 MHz/2 MHz放电中电子密度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz
图 6 气压为10 Pa时, 高低频放电中电子温度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz
图 7 气压为10 Pa时, 高低频放电中亚稳态的径向分布 (a)高频13.56 MHz; (b)低频2 MHz
图 8 气压为100 Pa时高低频放电中电子密度的径向分布 (a)频率为13.56 MHz; (b)频率为2 MHz
图 9 气压为10 Pa和100 Pa时, 在z = 10 cm处, 高低频放电中径向不均匀度随功率的变化
图 10 气压为10 Pa和100 Pa时, 13.56 MHz/2 MHz放电中电子能量弛豫长度随功率的变化
图 11 气压为100 Pa时高低频放电中电子温度的径向分布 (a)高频13.56 MHz; (b)低频2 MHz