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Spatial distribution of charged particles in a magnetic neutral loop discharge etcher: experimental results and numerical simulations
Surface and Coatings Technology 166 (2003) 135–140
Spatial distribution of charged particles in a magnetic neutral loop discharge etcher: experimental results and numerical simulations Youl-Moon Sunga,*, Tatsuya Sakodab a
Department of Electrical and Electronic Engineering, Miyazaki University, 1-1 Gakuen Kibana Dai Nishi, Miyazaki 889-2192, Japan b Sojo University, Kumamoto 860-0082, Japan Received 25 April 2002; accepted in revised form 28 October 2002
Abstract This paper reports a result of rather sophisticated measurement in a magnetic neutral loop discharge (NLD) etcher system. The spatial profiles of electron temperature Te and density ne were measured for an extended region including the downstream of the source using laser Thomson scattering technique. Also, based on these profiles and ion current density measured by a double probe, experimental and numerical investigation for the entire structure of electron behavior was performed. The results showed that the high-density plasma produced around the magnetic neutral loop (NL) is transferred from the NL region to the downstream region along magnetic force lines. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Processing plasma; Neutral loop discharge (NLD); Downstream; Thomson scattering; Double probe
1. Introduction Neutral loop discharge (NLD) plasma w1–4x has attracted much attention as a new plasma source that satisfies uniform processing requirements over a large area with a high processing rate. The NLD etcher system uses a separatrix configuration of the magnetic field, in which a magnetic neutral loop (NL) is produced perpendicular to the magnetic field lines. A radio frequency (RF) inductive field is applied to the NL, and then the ring shape plasma is generated. Controlling the position of electromagnetic coils and their current values can easily vary the position and the diameter of the NL. Thus, by controlling the position and diameter of the plasma, uniform processing can be realized. The heating mechanism of the NLD was theoretically analyzed by Yoshida and Uchida w2x proposing a simple slab model, where the absorption mechanism of energy from the RF electric field through non-linear meandering motion of electrons was investigated. Also, Yoshida et al. have reported some new results of the theoretical studies on the electron heating in magnetic null regions w3–5x. In *Corresponding author. Tel.yfax: q81-985-58-7350. E-mail address: [email protected] (Y.-M. Sung).
order to understand the processes of the NLD plasma formation, laser Thomson scattering w6,7x measurements of electron temperature and density profiles have previously been performed at the plasma source region w8x. Population densities at excited levels of atoms were also measured using laser-induced fluorescence spectroscopy w9x. From these measurements, it was found that electron heating and ionization at the NL is essential for the formation of the NLD plasma. In numerical studies carried out w11–13x, analyses of the electron behavior were performed using a two-dimensional model. The results helped reveal the existence of the optimum conditions for the formation of NLD plasma w13x. Threedimensional numerical analysis of the distribution of the electron temperature (Te) and electron density (ne) in a NLD etcher system was also performed. Results from the three-dimensional modeling showed that the experimental inward radial shift of the ne peak is mainly due to structural factors such as, the non-symmetrical mirror field and the wall effect w11x. In addition, variations of the production region of plasmas produced under various conditions of the magnetic field, the RF electric field and the frequency were measured by a combination of laser spectroscopy and optical emission spectroscopy
0257-8972/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 7 7 8 - 8
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Fig. 1. Schematic arrangement of the experimental apparatus.
w12x. The results of these measurements were consistent with the theoretically predicted dependencies of electron heating on the magnetic field strength, the RF electric field and the frequency of the RF source. However, the conditions required for the formation of the NLD plasma were not fully understood because the above analyses were almost all based on the results obtained under restricted experimental conditions. In order to expand the use of the NLD etcher for the fabrication of ultralarge scale integrated circuits, it is necessary to understand electron behavior from the NL to the downstream region including the entire plasma structure. For this reason, laser Thomson scattering measurements of electron density and temperature at the downstream region were performed. The ion fluxes were also measured using a double probe in order to understand the plasma flow from the plasma source region to the downstream region. Also, computer based simulations with our threedimensional model w12x were used to examine the experimental results that we have obtained. Based on the above results, we discuss the structure of NLD plasma and the electron behavior from the NL to the downstream region. 2. Experiment and methods Fig. 1 shows the schematic diagram of the NLD etcher device and the measurements system. Three electromagnetic coils were placed co-axially around the vacuum chamber made of stainless steel with its inner diameter of 308 mm. Two electromagnetic coils (coils 1 and 2 in Fig. 1) has an internal diameter of 390 mm and 60 turns. Coil 3 has 120 turns with an inner diameter of 320 mm. In forming the NL, coils 1 and 3 (I1 and I3) have their currents flowing in the same direction
while coil 2 (I2) flows in the opposite direction. For a NL with a radius of RNLs100 mm, the coil currents were set the particular condition of I1s66.8 A, I2s193 A and I3s115 A. In Fig. 1, z direction corresponds to the distribution of the vertical magnetic strength along the chamber axis, and zs0 mm represents the location of the NL plane. The magnetic field strength Br0 at the center (rs0 mm) of the plane that contained the NL at zs0 mm was approximately 4 mTorr w8x. A one-turn RF antenna, with a radius of 130 mm, insulated from the plasma by a quartz glass tube with a cross-sectional diameter of 10 mm, was placed inside the chamber. The distance from the RF antenna to the position of the NL plane was 20 mm in the axial direction of the chamber. The RF power was 400 W and the discharge gas was argon at 3 mTorr for the experiments reported herein. The light source for laser Thomson scattering measurements was a Nd:YAG laser which had an energy of 0.5 Jypulse, a pulse duration of 5 ns and a repetition rate of 10 Hz. The laser beam was passed through the downstream region at zs250 mm in radial direction. The scattering light was collected by a lens (detection solid angle 0.03 sr), and was directed into a double monochromator. Radial measurements of electron density and temperature were performed along the laser beam path from the center to rs140 mm. A photoncounting technique was used for the scattered signal detection. The detection limit of electron density was approximately 5=1016 my3. Laser Thomson scattering technique directly measures the electron velocity distribution function along the scattering vector, in the limit of incoherent scattering which is well satisfied in the present conditions. Therefore, it yields unambiguous and reliable results. However, the laser Thomson scattering technique needs some contrivances such as Brewster windows, a series of baffles and a viewing dump in order to prevent the light scattered by the windows from entering the detection optics. For this reason, the laser Thomson scattering measurements in our experimental system were performed at zs0 and 250 mm. A z-shaped double probe, which minimizes measurement errors from the magnetic field effect, was used to measure the ion current density distributions related to the plasma structure at zs25, 100 and 250 mm, thereby facilitating measurements in the radial direction. The probe tips made of tungsten with a diameter of 0.4 mm, length of 4 mm and were separated by a piece of ceramic material for electrical insulation. Fig. 2 and Fig. 3 show the calculated distribution of magnetic field strength and magnetic field lines in the vertical cross-section (r–z plane). Here the radius, rs (x 2qy 2)1y2 and the NL radius RNL was 100 mm. The co-ordinates of the null point (Bs0 G) was at rs100 mm, zs0 mm, (i.e. in the r–z plane). When the frequency of the RF source is 13.56 MHz, the resonance magnetic field strength B0 (smev ye; me: electron mass,
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Fig. 2. Distribution of magnetic field strength in the chamber for RNLs100 mm.
v: angular frequency of the RF source) that satisfies the electron cyclotron resonance condition is approximately 0.5 mTorr. L, defined as the spatial extent of Bs0yB0, was 5.4 mm. It is predicted that electron undergoes a non-linear meandering motion in the region of y2Lr-2L under the typical operating condition of the NLD plasma w2,10x. 3. Experimental results Measured radial profiles of electron temperature Te for the case of NL radius RNLs100 mm and the RF power of 400 W, are shown in Fig. 4. The measurement points were the NL plane (zs0 mm) and downstream region (zs250 mm) where the radial distribution of magnetic field strength is almost flat and its strength was approximately 3 mTorr. The z-axis is the center axis of the chamber as shown in Fig. 1. As can be seen from this figure, the measured Te radial profile obtained at the NL plane (zs0 mm) has a peak on the NL. This peak value of the temperature was 2.3 eV at rs0 mm and minimum value was 1.5 eV at rs60 mm. In addition, the Te values are high in the range of "L around the NL, which corresponds to the magnetic filed strength in the range of 0–0.5 mTorr (B0). This is consistent with the prediction of theoretical analysis that the electron heating is caused via the meandering motion of electrons w9,11x. On the other hand, the measured Te profile obtained from the downstream region (zs250 mm) has a slight peak at approximately rs90–100 mm. As compared with the profiles obtained on the NL plane, profiles at zs250 mm are relatively flat. However, the peaked profiles are maintained even at the downstream region.
Fig. 3. Distribution of magnetic force line in the chamber for RNLs 100 mm.
Fig. 5 shows radial profiles of electron density ne obtained at zs0 mm and 250 mm, respectively. As can be seen from this figure, the ne profile obtained at zs0 mm has a peak at a radius of 30 mm inward from the NL. The peak value of density was 7=1017 my3 and minimum value was 4=1017 my3 at rs0 mm. The reason why the ne peak appears at the radius inward from the NL was discussed in w11x. The measured ne profile obtained at zs250 mm has a slight peak at approximately rs80 mm. The peaked profiles are also maintained at the downstream region. This indicates that changing the diameter and position of the NL at the
Fig. 4. Measured radial profiles of the electron temperature.
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Fig. 5. Measured radial profiles of the electron density.
plasma source region can also control the plasma condition in the downstream region. The location of magnetic force line from the NL region along z-axis and measured radial profiles of ion current density obtained at zs25, 100 and 250 mm are shown in Fig. 6. The horizontal error bar is due to the setting error of a double probe. It can be seen from this figure that the peak positions of the measured ion flux profiles at zs25, 100 and 250 mm are rs95, 75 and 90 mm, respectively. Considering the horizontal error, each individual peak position of ion flux profile exists on the magnetic force line from the NL region. In the NLD plasma, the ionization zone is concentrated around the NL, and electron heating and ionization on the NL is essential for the formation of plasma w9x. It was found that ion flux produced around the NL is transferred from the NL region to the downstream region along magnetic force line.
electromagnetic induction relation. The RF electric field E can be deduced from the application of Maxwell’s equation, ==Bsjvm0´E. The magnetic field B can be obtained three-dimensionally from the calculation of the vector potential A, using BsrotA. In the calculations, the current i, which flows through the RF antenna was measured using a Rogowski type current probe and was 6.3 A in amplitude. The RF-induced electric field can be related to the equation Bzsm0Hz by using the z component of Faraday’s law. The above-mentioned calculation to obtain the induced RF field can be well applied under the vacuum field condition, however, it is insufficient to obtain the electric field under the plasma condition. The magnitude of the field decays more rapidly within the plasma since the electron plasma frequency vpe is greater than 13.56 MHz. This implies that the electromagnetic wave is cutoff inside the plasma. Therefore, it was necessary to consider the decay length d, which was obtained experimentally using the magnetic induction probe w14x. Assuming that Eus Eu0e y6z2q(r0yr)2yd—where r0 is the radius of the antenna—and inserting this into the final induced electric field equation yields the electric field. The decay length d of the electric field, which was 35 mm, was determined from the measurement of the RF magnetic field. Furthermore, collisions between electron and Ar atoms were considered. Elastic and inelastic (excitation and ionization) collisions were considered. Monte Carlo method was used to determine the kind of collision and the direction of motion thereafter. The calculations were made on the assumption that electrons are lost by recombination on reaching the chamber walls. Fig. 7 shows examples of the electron orbits in the r–z plane for the case of RNLs100 mm. The initial
4. Numerical model and simulation The experimental results showed the plasma flow from the NL region to the downstream region. In order to reveal the above plasma flow, a three-dimensional calculation model of electron behavior was constructed. The conventional NLD model w2,13x paid attention to the electron behavior around the NL and, therefore, three-dimensional distributions of electric field and magnetic field were not considered. The configuration of our three-dimensional model has been described in detail in w11x, and is briefly described as follows: the motion of an electron and magnetic field can be expressed using the Lorentz equation and Biot–Savart law. The electric field generated by the RF antenna, located in the plane where rs130 mm, zsy5 mm was calculated from the
Fig. 6. Measured radial profiles of the ion current density.
Y.-M. Sung, T. Sakoda / Surface and Coatings Technology 166 (2003) 135–140
Fig. 7. Examples of the simulated electron orbits for RNLs100 mm.
points of electrons at zs0 mm plane were set at rs45, 60, 80, 100 and 120 mm. Each initial electron velocity referred to each measured electron temperature w4x of 1.5 to 2.3 eV on the NL plane. As can be seen from Fig. 7, the actual magnetic field configuration greatly affects the electron behavior. Electrons having the initial points in the range of 90–110 mm flows from the NL region to downstream region with a spiral motion along the magnetic force lines after the characteristic meandering motions around the NL. The electron motion restricted around the NL is similar to the results obtained by the conventional NLD model w10,13x. Also, electrons having the initial points at rs45 and 60 mm, flow along the magnetic force lines without the characteristic motions for obtaining energy, i.e. electron energy does not change significantly when the electron is placed beyond the radius of "2L. Fig. 8 shows the calculation result of the average electron energy distribution of 104 particles in the r–z plane for the case of RNLs100 mm. The initial points of electrons were set at the NL plane. The initial velocity of electrons were set at vxsvysvzs1=105 mys. Each particle, however, had a different direction of motion and position and obeyed the equation, mdvydtsye(Eq v=B). It can be found that electrons heated with the characteristic meandering motion around the NL and these high energetic electrons around NL region flowed downstream. Electrons gained energy from the electric field through such motion and, therefore, the NL is essential for the formation of the plasma, which has been experimentally confirmed by measurements of the electron temperature and population densities at excited levels of atoms on the NL plane w9x. Therefore, it is concluded that the obtained profiles of the electron
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Fig. 8. Calculation result of the average electron energy distribution in the r–z plane for the case of RNLs100 mm.
temperature, density and ion current density at the downstream region are a reflection of profiles at the plasma source region. For plasma processing, such as etching, changing the diameter and position of the NL at the plasma source region can effectively perform deposition and surface treatment at the substrate region. In our simulation process of electron behavior, the three-dimensional electron motion was calculated by considering the three-dimensional configurations of magnetic and electric fields although all simulation results were indicated by a two-dimensional form with r–z axis. The word ‘3-D’ is somewhat inappropriate and our asymmetric model must be said to be two-dimensional. However, it is considered that the large problem does not occur by substituting the two-dimensional form for the three-dimensional calculation results of electron motions because the structure of NLD is almost the doughnut-shaped ring of symmetry form. Also, it is necessary to distinguish from our previous two-dimensional model w10,13x where electron trajectory was calculated by considering the two-dimensional configurations of magnetic and electric fields. Therefore, we will call this simulation three-dimensional for this paper. The real three-dimensional expression of the simulation results will soon be examined. 5. Conclusions Laser Thomson scattering measurements of electron density and temperature were performed at the NL and downstream region in order to understand the full details of electron behavior and plasma structure. The measured profiles of electron temperature and density at the downstream region have slight peaks. At the same time,
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the ion fluxes were measured using a double probe, and the electron orbits from the NL region to the downstream region were evaluated by using a three-dimensional model. The three-dimensional simulation had a potential to support the validity of the obtained results experimentally. From the measurements of ion current density and the calculations of the electron behavior, it was found that their peaks produced around the NL were transferred along magnetic force lines from the NL region. Acknowledgments The authors wish to thank Professors K. Muraoka and K. Uchino of Kyushu University for their valuable contribution. They would also like to thank to Dr T. Uchida of ULVAC Japan Ltd. and Prof. Z. Yoshida of the University of Tokyo for their useful comments. They are grateful to Professors C. Honda and M. Otsubo of Miyazaki University for their kind cooperation. References w1x H. Tsuboi, M. Itoh, M. Tanabe, T. Hayashi, T. Uchida, Jpn. J. Appl. Phys. 34 (1995) 2476.
w2x Z. Yoshida, T. Uchida, Jpn. J. Appl. Phys. 34 (1995) 4213. w3x Z. Yoshida, H. Asakura, H. Kakuno, J. Morikawa, K. Takemura, S. Takizawa, T. Uchida, Phys. Rev. Lett. 81 (1998) 2458. w4x I.Y. Kostyukov, J.M. Rax, Phys. Plasmas 7 (2000) 185. w5x R. Numata, Z. Yoshida, Phys. Rev. Lett. 88 (2002) 045003. w6x T. Hori, M.D. Bowden, K. Uchino, K. Muraoka, M. Maeda, J. Vac. Sci. Tech. A14 (1) (1996) 144. w7x K. Muraoka, K. Uchinol, M.D. Bowden, Plasma Phys. Cont. Fusi. 40 (1998) 1221. w8x T. Sakoda, H. Iwamiya, K. Uchino, K. Muraoka, M. Itoh, T. Uchida, Jpn. J. Appl. Phys. 36 (1997) L67. w9x T. Sakoda, T. Miyao, K. Uchino, K. Muraoka, Jpn. J. Appl. Phys. 36 (1997) 6981. w10x Y.M. Sung, K. Uchino, K. Muraoka, T. Sakoda, J. Vac. Sci. Technol. A 18 (2000) 2149. w11x Y. Okraku-Yirenkyi, Y.M. Sung, M. Otsubo, C. Honda, T. Sakoda, J. Vac. Sci. Technol. A 19y5 (2001) 2590. w12x T. Sakoda, Y.O. Yirenkyi, Y.M. Sung, M. Otsubo, C. Honda, Jpn. J. Appl. Phys. 40 (2001) 6607. w13x Y. Okraku-Yirenkyi, Y.-M. Sung, M. Otsubo, C. Honda, T. Sakoda, Surf. Coatings Technol. 149 (2–3) (2002) 185. w14x J. Hopwood, C.R. Guarnieri, S.J. Whitehair, J.J. Cuomo, J. Vac. Sci. Technol. A 11y1 (1993) 147.
Spatial distribution of charged particles in a magnetic neutral loop discharge etcher: experimental results and numerical simulations Youl-Moon Sunga,*, Tatsuya Sakodab a
Department of Electrical and Electronic Engineering, Miyazaki University, 1-1 Gakuen Kibana Dai Nishi, Miyazaki 889-2192, Japan b Sojo University, Kumamoto 860-0082, Japan Received 25 April 2002; accepted in revised form 28 October 2002
Abstract This paper reports a result of rather sophisticated measurement in a magnetic neutral loop discharge (NLD) etcher system. The spatial profiles of electron temperature Te and density ne were measured for an extended region including the downstream of the source using laser Thomson scattering technique. Also, based on these profiles and ion current density measured by a double probe, experimental and numerical investigation for the entire structure of electron behavior was performed. The results showed that the high-density plasma produced around the magnetic neutral loop (NL) is transferred from the NL region to the downstream region along magnetic force lines. 䊚 2002 Elsevier Science B.V. All rights reserved. Keywords: Processing plasma; Neutral loop discharge (NLD); Downstream; Thomson scattering; Double probe
1. Introduction Neutral loop discharge (NLD) plasma w1–4x has attracted much attention as a new plasma source that satisfies uniform processing requirements over a large area with a high processing rate. The NLD etcher system uses a separatrix configuration of the magnetic field, in which a magnetic neutral loop (NL) is produced perpendicular to the magnetic field lines. A radio frequency (RF) inductive field is applied to the NL, and then the ring shape plasma is generated. Controlling the position of electromagnetic coils and their current values can easily vary the position and the diameter of the NL. Thus, by controlling the position and diameter of the plasma, uniform processing can be realized. The heating mechanism of the NLD was theoretically analyzed by Yoshida and Uchida w2x proposing a simple slab model, where the absorption mechanism of energy from the RF electric field through non-linear meandering motion of electrons was investigated. Also, Yoshida et al. have reported some new results of the theoretical studies on the electron heating in magnetic null regions w3–5x. In *Corresponding author. Tel.yfax: q81-985-58-7350. E-mail address: [email protected] (Y.-M. Sung).
order to understand the processes of the NLD plasma formation, laser Thomson scattering w6,7x measurements of electron temperature and density profiles have previously been performed at the plasma source region w8x. Population densities at excited levels of atoms were also measured using laser-induced fluorescence spectroscopy w9x. From these measurements, it was found that electron heating and ionization at the NL is essential for the formation of the NLD plasma. In numerical studies carried out w11–13x, analyses of the electron behavior were performed using a two-dimensional model. The results helped reveal the existence of the optimum conditions for the formation of NLD plasma w13x. Threedimensional numerical analysis of the distribution of the electron temperature (Te) and electron density (ne) in a NLD etcher system was also performed. Results from the three-dimensional modeling showed that the experimental inward radial shift of the ne peak is mainly due to structural factors such as, the non-symmetrical mirror field and the wall effect w11x. In addition, variations of the production region of plasmas produced under various conditions of the magnetic field, the RF electric field and the frequency were measured by a combination of laser spectroscopy and optical emission spectroscopy
0257-8972/03/$ - see front matter 䊚 2002 Elsevier Science B.V. All rights reserved. PII: S 0 2 5 7 - 8 9 7 2 Ž 0 2 . 0 0 7 7 8 - 8
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Fig. 1. Schematic arrangement of the experimental apparatus.
w12x. The results of these measurements were consistent with the theoretically predicted dependencies of electron heating on the magnetic field strength, the RF electric field and the frequency of the RF source. However, the conditions required for the formation of the NLD plasma were not fully understood because the above analyses were almost all based on the results obtained under restricted experimental conditions. In order to expand the use of the NLD etcher for the fabrication of ultralarge scale integrated circuits, it is necessary to understand electron behavior from the NL to the downstream region including the entire plasma structure. For this reason, laser Thomson scattering measurements of electron density and temperature at the downstream region were performed. The ion fluxes were also measured using a double probe in order to understand the plasma flow from the plasma source region to the downstream region. Also, computer based simulations with our threedimensional model w12x were used to examine the experimental results that we have obtained. Based on the above results, we discuss the structure of NLD plasma and the electron behavior from the NL to the downstream region. 2. Experiment and methods Fig. 1 shows the schematic diagram of the NLD etcher device and the measurements system. Three electromagnetic coils were placed co-axially around the vacuum chamber made of stainless steel with its inner diameter of 308 mm. Two electromagnetic coils (coils 1 and 2 in Fig. 1) has an internal diameter of 390 mm and 60 turns. Coil 3 has 120 turns with an inner diameter of 320 mm. In forming the NL, coils 1 and 3 (I1 and I3) have their currents flowing in the same direction
while coil 2 (I2) flows in the opposite direction. For a NL with a radius of RNLs100 mm, the coil currents were set the particular condition of I1s66.8 A, I2s193 A and I3s115 A. In Fig. 1, z direction corresponds to the distribution of the vertical magnetic strength along the chamber axis, and zs0 mm represents the location of the NL plane. The magnetic field strength Br0 at the center (rs0 mm) of the plane that contained the NL at zs0 mm was approximately 4 mTorr w8x. A one-turn RF antenna, with a radius of 130 mm, insulated from the plasma by a quartz glass tube with a cross-sectional diameter of 10 mm, was placed inside the chamber. The distance from the RF antenna to the position of the NL plane was 20 mm in the axial direction of the chamber. The RF power was 400 W and the discharge gas was argon at 3 mTorr for the experiments reported herein. The light source for laser Thomson scattering measurements was a Nd:YAG laser which had an energy of 0.5 Jypulse, a pulse duration of 5 ns and a repetition rate of 10 Hz. The laser beam was passed through the downstream region at zs250 mm in radial direction. The scattering light was collected by a lens (detection solid angle 0.03 sr), and was directed into a double monochromator. Radial measurements of electron density and temperature were performed along the laser beam path from the center to rs140 mm. A photoncounting technique was used for the scattered signal detection. The detection limit of electron density was approximately 5=1016 my3. Laser Thomson scattering technique directly measures the electron velocity distribution function along the scattering vector, in the limit of incoherent scattering which is well satisfied in the present conditions. Therefore, it yields unambiguous and reliable results. However, the laser Thomson scattering technique needs some contrivances such as Brewster windows, a series of baffles and a viewing dump in order to prevent the light scattered by the windows from entering the detection optics. For this reason, the laser Thomson scattering measurements in our experimental system were performed at zs0 and 250 mm. A z-shaped double probe, which minimizes measurement errors from the magnetic field effect, was used to measure the ion current density distributions related to the plasma structure at zs25, 100 and 250 mm, thereby facilitating measurements in the radial direction. The probe tips made of tungsten with a diameter of 0.4 mm, length of 4 mm and were separated by a piece of ceramic material for electrical insulation. Fig. 2 and Fig. 3 show the calculated distribution of magnetic field strength and magnetic field lines in the vertical cross-section (r–z plane). Here the radius, rs (x 2qy 2)1y2 and the NL radius RNL was 100 mm. The co-ordinates of the null point (Bs0 G) was at rs100 mm, zs0 mm, (i.e. in the r–z plane). When the frequency of the RF source is 13.56 MHz, the resonance magnetic field strength B0 (smev ye; me: electron mass,
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Fig. 2. Distribution of magnetic field strength in the chamber for RNLs100 mm.
v: angular frequency of the RF source) that satisfies the electron cyclotron resonance condition is approximately 0.5 mTorr. L, defined as the spatial extent of Bs0yB0, was 5.4 mm. It is predicted that electron undergoes a non-linear meandering motion in the region of y2Lr-2L under the typical operating condition of the NLD plasma w2,10x. 3. Experimental results Measured radial profiles of electron temperature Te for the case of NL radius RNLs100 mm and the RF power of 400 W, are shown in Fig. 4. The measurement points were the NL plane (zs0 mm) and downstream region (zs250 mm) where the radial distribution of magnetic field strength is almost flat and its strength was approximately 3 mTorr. The z-axis is the center axis of the chamber as shown in Fig. 1. As can be seen from this figure, the measured Te radial profile obtained at the NL plane (zs0 mm) has a peak on the NL. This peak value of the temperature was 2.3 eV at rs0 mm and minimum value was 1.5 eV at rs60 mm. In addition, the Te values are high in the range of "L around the NL, which corresponds to the magnetic filed strength in the range of 0–0.5 mTorr (B0). This is consistent with the prediction of theoretical analysis that the electron heating is caused via the meandering motion of electrons w9,11x. On the other hand, the measured Te profile obtained from the downstream region (zs250 mm) has a slight peak at approximately rs90–100 mm. As compared with the profiles obtained on the NL plane, profiles at zs250 mm are relatively flat. However, the peaked profiles are maintained even at the downstream region.
Fig. 3. Distribution of magnetic force line in the chamber for RNLs 100 mm.
Fig. 5 shows radial profiles of electron density ne obtained at zs0 mm and 250 mm, respectively. As can be seen from this figure, the ne profile obtained at zs0 mm has a peak at a radius of 30 mm inward from the NL. The peak value of density was 7=1017 my3 and minimum value was 4=1017 my3 at rs0 mm. The reason why the ne peak appears at the radius inward from the NL was discussed in w11x. The measured ne profile obtained at zs250 mm has a slight peak at approximately rs80 mm. The peaked profiles are also maintained at the downstream region. This indicates that changing the diameter and position of the NL at the
Fig. 4. Measured radial profiles of the electron temperature.
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Fig. 5. Measured radial profiles of the electron density.
plasma source region can also control the plasma condition in the downstream region. The location of magnetic force line from the NL region along z-axis and measured radial profiles of ion current density obtained at zs25, 100 and 250 mm are shown in Fig. 6. The horizontal error bar is due to the setting error of a double probe. It can be seen from this figure that the peak positions of the measured ion flux profiles at zs25, 100 and 250 mm are rs95, 75 and 90 mm, respectively. Considering the horizontal error, each individual peak position of ion flux profile exists on the magnetic force line from the NL region. In the NLD plasma, the ionization zone is concentrated around the NL, and electron heating and ionization on the NL is essential for the formation of plasma w9x. It was found that ion flux produced around the NL is transferred from the NL region to the downstream region along magnetic force line.
electromagnetic induction relation. The RF electric field E can be deduced from the application of Maxwell’s equation, ==Bsjvm0´E. The magnetic field B can be obtained three-dimensionally from the calculation of the vector potential A, using BsrotA. In the calculations, the current i, which flows through the RF antenna was measured using a Rogowski type current probe and was 6.3 A in amplitude. The RF-induced electric field can be related to the equation Bzsm0Hz by using the z component of Faraday’s law. The above-mentioned calculation to obtain the induced RF field can be well applied under the vacuum field condition, however, it is insufficient to obtain the electric field under the plasma condition. The magnitude of the field decays more rapidly within the plasma since the electron plasma frequency vpe is greater than 13.56 MHz. This implies that the electromagnetic wave is cutoff inside the plasma. Therefore, it was necessary to consider the decay length d, which was obtained experimentally using the magnetic induction probe w14x. Assuming that Eus Eu0e y6z2q(r0yr)2yd—where r0 is the radius of the antenna—and inserting this into the final induced electric field equation yields the electric field. The decay length d of the electric field, which was 35 mm, was determined from the measurement of the RF magnetic field. Furthermore, collisions between electron and Ar atoms were considered. Elastic and inelastic (excitation and ionization) collisions were considered. Monte Carlo method was used to determine the kind of collision and the direction of motion thereafter. The calculations were made on the assumption that electrons are lost by recombination on reaching the chamber walls. Fig. 7 shows examples of the electron orbits in the r–z plane for the case of RNLs100 mm. The initial
4. Numerical model and simulation The experimental results showed the plasma flow from the NL region to the downstream region. In order to reveal the above plasma flow, a three-dimensional calculation model of electron behavior was constructed. The conventional NLD model w2,13x paid attention to the electron behavior around the NL and, therefore, three-dimensional distributions of electric field and magnetic field were not considered. The configuration of our three-dimensional model has been described in detail in w11x, and is briefly described as follows: the motion of an electron and magnetic field can be expressed using the Lorentz equation and Biot–Savart law. The electric field generated by the RF antenna, located in the plane where rs130 mm, zsy5 mm was calculated from the
Fig. 6. Measured radial profiles of the ion current density.
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Fig. 7. Examples of the simulated electron orbits for RNLs100 mm.
points of electrons at zs0 mm plane were set at rs45, 60, 80, 100 and 120 mm. Each initial electron velocity referred to each measured electron temperature w4x of 1.5 to 2.3 eV on the NL plane. As can be seen from Fig. 7, the actual magnetic field configuration greatly affects the electron behavior. Electrons having the initial points in the range of 90–110 mm flows from the NL region to downstream region with a spiral motion along the magnetic force lines after the characteristic meandering motions around the NL. The electron motion restricted around the NL is similar to the results obtained by the conventional NLD model w10,13x. Also, electrons having the initial points at rs45 and 60 mm, flow along the magnetic force lines without the characteristic motions for obtaining energy, i.e. electron energy does not change significantly when the electron is placed beyond the radius of "2L. Fig. 8 shows the calculation result of the average electron energy distribution of 104 particles in the r–z plane for the case of RNLs100 mm. The initial points of electrons were set at the NL plane. The initial velocity of electrons were set at vxsvysvzs1=105 mys. Each particle, however, had a different direction of motion and position and obeyed the equation, mdvydtsye(Eq v=B). It can be found that electrons heated with the characteristic meandering motion around the NL and these high energetic electrons around NL region flowed downstream. Electrons gained energy from the electric field through such motion and, therefore, the NL is essential for the formation of the plasma, which has been experimentally confirmed by measurements of the electron temperature and population densities at excited levels of atoms on the NL plane w9x. Therefore, it is concluded that the obtained profiles of the electron
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Fig. 8. Calculation result of the average electron energy distribution in the r–z plane for the case of RNLs100 mm.
temperature, density and ion current density at the downstream region are a reflection of profiles at the plasma source region. For plasma processing, such as etching, changing the diameter and position of the NL at the plasma source region can effectively perform deposition and surface treatment at the substrate region. In our simulation process of electron behavior, the three-dimensional electron motion was calculated by considering the three-dimensional configurations of magnetic and electric fields although all simulation results were indicated by a two-dimensional form with r–z axis. The word ‘3-D’ is somewhat inappropriate and our asymmetric model must be said to be two-dimensional. However, it is considered that the large problem does not occur by substituting the two-dimensional form for the three-dimensional calculation results of electron motions because the structure of NLD is almost the doughnut-shaped ring of symmetry form. Also, it is necessary to distinguish from our previous two-dimensional model w10,13x where electron trajectory was calculated by considering the two-dimensional configurations of magnetic and electric fields. Therefore, we will call this simulation three-dimensional for this paper. The real three-dimensional expression of the simulation results will soon be examined. 5. Conclusions Laser Thomson scattering measurements of electron density and temperature were performed at the NL and downstream region in order to understand the full details of electron behavior and plasma structure. The measured profiles of electron temperature and density at the downstream region have slight peaks. At the same time,
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the ion fluxes were measured using a double probe, and the electron orbits from the NL region to the downstream region were evaluated by using a three-dimensional model. The three-dimensional simulation had a potential to support the validity of the obtained results experimentally. From the measurements of ion current density and the calculations of the electron behavior, it was found that their peaks produced around the NL were transferred along magnetic force lines from the NL region. Acknowledgments The authors wish to thank Professors K. Muraoka and K. Uchino of Kyushu University for their valuable contribution. They would also like to thank to Dr T. Uchida of ULVAC Japan Ltd. and Prof. Z. Yoshida of the University of Tokyo for their useful comments. They are grateful to Professors C. Honda and M. Otsubo of Miyazaki University for their kind cooperation. References w1x H. Tsuboi, M. Itoh, M. Tanabe, T. Hayashi, T. Uchida, Jpn. J. Appl. Phys. 34 (1995) 2476.
w2x Z. Yoshida, T. Uchida, Jpn. J. Appl. Phys. 34 (1995) 4213. w3x Z. Yoshida, H. Asakura, H. Kakuno, J. Morikawa, K. Takemura, S. Takizawa, T. Uchida, Phys. Rev. Lett. 81 (1998) 2458. w4x I.Y. Kostyukov, J.M. Rax, Phys. Plasmas 7 (2000) 185. w5x R. Numata, Z. Yoshida, Phys. Rev. Lett. 88 (2002) 045003. w6x T. Hori, M.D. Bowden, K. Uchino, K. Muraoka, M. Maeda, J. Vac. Sci. Tech. A14 (1) (1996) 144. w7x K. Muraoka, K. Uchinol, M.D. Bowden, Plasma Phys. Cont. Fusi. 40 (1998) 1221. w8x T. Sakoda, H. Iwamiya, K. Uchino, K. Muraoka, M. Itoh, T. Uchida, Jpn. J. Appl. Phys. 36 (1997) L67. w9x T. Sakoda, T. Miyao, K. Uchino, K. Muraoka, Jpn. J. Appl. Phys. 36 (1997) 6981. w10x Y.M. Sung, K. Uchino, K. Muraoka, T. Sakoda, J. Vac. Sci. Technol. A 18 (2000) 2149. w11x Y. Okraku-Yirenkyi, Y.M. Sung, M. Otsubo, C. Honda, T. Sakoda, J. Vac. Sci. Technol. A 19y5 (2001) 2590. w12x T. Sakoda, Y.O. Yirenkyi, Y.M. Sung, M. Otsubo, C. Honda, Jpn. J. Appl. Phys. 40 (2001) 6607. w13x Y. Okraku-Yirenkyi, Y.-M. Sung, M. Otsubo, C. Honda, T. Sakoda, Surf. Coatings Technol. 149 (2–3) (2002) 185. w14x J. Hopwood, C.R. Guarnieri, S.J. Whitehair, J.J. Cuomo, J. Vac. Sci. Technol. A 11y1 (1993) 147.