Russian Microelectronics, Vol. 29, No. 6, 2000, pp. 380–390. Translated from Mikroelektronika, Vol. 29, No. 6, 2000, pp. 431–441. Original Russian Text Copyright © 2000 by Braginskii, Vasil’eva, Kovalev.
A Helicon Plasma Source O. V. Braginskii, A. N. Vasil’eva, and A. S. Kovalev Skobeltsyn Research Institute of Nuclear Physics, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia; e-mail:
[email protected] Received February 21, 2000
Abstract—The parameters of a helicon plasma source was studied for an rf power to 500 W and a magnetic field ranging from 0 to 200 G under an argon pressure of 3 mtorr. The electron density in the plasma was found to reach 1012 cm–3. Axial and radial electron distributions were studied. Helicon waves were excited by antennas of three types, a loop antenna being the most efficient. It is shown that the electron density in the plasma can significantly be increased if the system is under a nonuniform magnetic field such that its lower-value (relative to the rest of the system) part is applied to the antenna.
1. INTRODUCTION The fabrication of VLSI circuits with feature sizes of less than 0.35 µm needs plasma reactors that provide high-rate anisotropic etching and a small amount of induced defects. To obtain a desired etching anisotropy, a plasma-forming gas must be kept at a pressure of no more than several mtorr. For the density of defects to be low, the ion energy at the surface to be processed must be within 20–30 eV. At such low energies, the reasonable process rate can be achieved only if the ion concentration is high, about 1012 cm–3. In addition to this, advanced plasma reactors must provide a possibility to independently vary the density and energy of ions incident on the target. Today, the most efficient sources of a high-density low-pressure plasma are rf inductively coupled discharge (ICD) [1–3], microwave surface-wave discharge (SWD) [4], microwave EPR discharge (EPRD) [5–8], and rf helicon-wave discharge (HWD) [9–15]. Planar ICD with a pancake coil has received the widest acceptance [1–3]. Its advantages are simple structure and the absence of a magnetic field. The disadvantage of ICD and SWD is that the energy is released within a narrow near-surface plasma layer (several millimeters thick), because an electromagnetic wave rapidly decays in a plasma. This sets limits on the allowable distance between an output dielectric window and the surface to be processed. Also, for largediameter wafers, difficulties associated with gas delivery may arise. Moreover, the impedance of an ICD plasma is unstable at low pressures (~ 1mtorr). In EPRD and HWD, the energy is released throughout the plasma; hence, a more flexible approach to designing the discharge chamber. The EPRD disadvantage is the need for producing a magnetic field as high as 875 G. This is usually a challenge in practice; furthermore, the nonuniformity of the magnetic field
causes a potential difference to appear across the surface. In the case of HWD, which offers the same properties as EPRD, the magnetic field is 10 to 30 times lower and rf equipment is simpler and cheaper than microwave equipment for EPRD [6–8]. As compared with ICD, HWD is more stable and provides a higher electron concentration in the plasma for the same power consumption. That is why the use of helicon discharge in microelectronic technology is of immediate interest [16–20]. High efficiency of gas ionization by helicon waves is currently accounted for by two mechanisms. The first implies that electrons are entrapped by the field of a slow helicon wave [21, 22]. In fact, the phase velocities of helicon waves in an external field correspond to electron energies of about several tens of eV. At such energies, the ionization cross section for the majority of working gases is maximum. The second mechanism suggests that electrostatic waves, or Trievelpiece– Gould waves, are excited in a plasma [23], which, unlike helicon waves, rapidly decay. Helicon and electrostatic waves may be strongly coupled at plasma inhomogeneities, in particular, at plasma–dielectric wall boundaries [24–27]. Thus, helicon waves decay through their conversion to electrostatic waves. The latter, in turn, undergo collisional damping, passing the energy to plasma electrons. The relative effect of the two mechanisms still remains unclear. Of special practical interest are sharp changes in the electron concentration in the plasma, which is typical of HWD. The change in the electron concentration correlates with that in the rf power or magnetic field. The effect of ICD initiation conditions on the plasma parameters is essential for effective control of the plasma reactor operating mode. It is also instructive to consider the efficiency of plasma excitation by antennas of various type. Helicon waves in a plasma are usually excited by antennas of three types. The first two are
1063-7397/00/2906-0380$25.00 © 2000 MAIK “Nauka /Interperiodica”
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(a)
Matching unit
(b)
13.56-MHz generator (c)
3
2
1
Fig. 1. Experimental setup. 1, Langmuir probe; 2, ion energy analyzer; and 3, helicon magnetic field meter.
Nagoya-type [28] and Boswell-type [16] antennas, which are, respectively, one and two turns in a plane parallel to the magnetic field. They generate clockwiseand counterclockwise-polarized helicon waves with an azimuth number m = ±1. The third antenna type is a loop lying in a plane perpendicular to the magnetic field and generating azimuth-symmetric waves (M = 0). Experimental results obtained with these antennas placed on various equipment are difficult to compare. Therefore, the performance of the antennas placed on the same equipment will be considered. As a rule, helicon waves are excited in a uniform cylindrical magnetic field. In the work, we will study plasma excitation in a nonuniform field. 2. EXPERIMENTAL SETUP A helicon plasma source is shown in Fig. 1. The plasma was excited in a 40-cm-long glass tube of diameter 15 cm. The tube is connected to a 24-cm-long steel chamber of diameter 26 cm. The assembly is placed into a constant magnetic field produced by three coils (a–c) of diameter 32 cm. The intercoil distance was 30 cm, and the magnetic field was varied between 0 and RUSSIAN MICROELECTRONICS
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200 G. The coils produced both a uniform (within ±10%) magnetic field throughout the volume and desired field gradients in the tube and chamber. Helicon waves were excited by special-shaped antennas. We used Boswell- and Nagoya-type antennas, as well as a loop antenna made of two turns around the tube (i.e., their plane was perpendicular to the tube axis). The first two generated helicon waves with M = 1, while the last one, with M = 0. The length and diameter of the first two antennas were 17 and 16 cm, respectively. The third one was 2 cm long, and its diameter was 16 cm. The antennas were connected (through matching units) to an rf generator (700 W, 13.56 MHz). Parameters to be measured were incident and reflected powers and rf voltage across the antennas. In the experiments, the reflected-to-incident power ratio did not exceed 7%. The metal screen around the setup had a diameter of 50 cm. The discharge chamber was evacuated to a pressure of 10–5 torr. An argon flow through the chamber was kept at a pressure of 3 mtorr. The electron concentration and plasma potential in the chamber were measured with a Langmuir probe (diameter 300 µm, length 2 mm). The probe was free to move both axially and radially. The electron concentra-
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BRAGINSKII et al. Ne × 10 –11 /cm3 2.6 32 G 2.4
44 G 54 G
2.2
64 G 2.0 74 G 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 0
100
200
300
400
500
600
W
Fig. 2. Ne vs. plasma-generating rf power for various magnetic fields.
tion N was derived from the saturation ion current at the probe potential 100 V: mi N = ( I sat /0.54eA ) -----, Te
(1)
where Isat is the saturation ion current, e is the electron charge, A is the probe surface area, mi is the mass of an ion, and Te is the electron temperature. The energy spectrum of ions was recorded with a three-grid analyzer. The 40-µm-mesh grids of diameter 15 mm made of cadmium–tungsten alloy were spaced at 2 mm intervals. This analyzer was also used to check the electron concentration and plasma potential measurements.
The rf magnetic field of a helicon wave (the Bz component aligned with the constant field) was measured with a magnetic probe. It consisted of a turn (molybdenum wire 0.2 mm in diameter) of diameter 15 mm, which was placed normally to the constant field and can be moved along the discharge axis. The probe signal was applied to an oscilloscope through a cable terminated by a resistance equal to the wave impedance. The probe voltage V(t) is given by 2 1 d Bz ( t ) V ( t ) = πR --- ---------------, c dt
(2)
where Bz(t) is the z component of the magnetic field of a helicon wave and R is the radius of the probe turn. The advantage of this probe is that its potential is suffiRUSSIAN MICROELECTRONICS
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Bz, G 1.0 100 W
4
0.9
200 W 300 W
0.8
1
400 W
3 0.7
0.6
0.5
2
0.4
0.3 0
5
10
15
20
25
30
35 Z, cm
Fig. 3. Z component of the rf field of the helicon wave at different distances to the antenna.
ciently large (at the diameter 15 mm), while plasma disturbance is weak (since small is the area contacting with the plasma at the wire thickness 0.2 mm) [29]. 3. RESULTS AND DISCUSSION Figure 2 plots the electron concentration Ne in the plasma against the plasma-generating rf power for various magnetic fields (uniform throughout the volume). By plasma-generating power, we mean the difference between the powers incident on and reflected from the matching unit. The electron concentration was measured at a distance of 30 cm from the antenna center. The curves in Fig. 2 can be divided into three sections. Initially, Ne smoothly grows with power, then a much sharper rise is observed, and finally Ne reaches its steady-state value, becoming virtually power-independent. A helicon wave forms at the second, sharp-rise section. As the magnetic field increases, the helicon wave is generated at higher powers but the final electron concentration grows. The peak and subsequent slight decrease in Ne are associated with the Ne redistriRUSSIAN MICROELECTRONICS
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bution within the distance 30 cm between the antenna and point of measurement. Figure 3 is evidence in favor of the assumption that a drastic rise in the electron concentration in Fig. 2 is related to the generation of a helicon wave in the plasma. It depicts the amplitude of the varying magnetic field Bz vs. distance to the center of the loop antenna for various rf plasma-generating powers and a fixed constant magnetic field of 40 G. At 100 W, the wave rapidly decays (curve 1) because of screening the electromagnetic field of the antenna. At 200, 300, and 400 W, a standing helicon wave arises. Its amplitude grows with power. The length of the helicon wave is about 28 cm. Figure 4 compares the dependences of the electron concentration on magnetic field for antennas of the three types. In all instances, the plasma generating power is 300 W and the distance between the antenna center and point of measurement, 30 cm. For both antennas generating waves with M = 1, the curves has two peaks. For a wave with M = 0, the curve has one broad maximum. At fields in the range 30–80 G, the
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BRAGINSKII et al. Ne × 10 –11 cm–3 1.7 Nagoya Loop Boswell
1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
20
40
60
80
100
120
140
160 180 200 Magnetic field, G
Fig. 4. Ne vs. magnetic field for the three different antennas.
loop antenna leads to much greater Ne than the Boswell and Nagoya ones. Hence, it holds more promise when used in plasma reactors. In Fig. 5a, the values of Ne are plotted against magnetic field H for varying distance to the antenna center, and Fig. 5b shows the dependence of Ne on the distance to the center at various magnetic fields. All the dependences were obtained for the Nagoya antenna and a plasma-generating power of 300 W. Figures 6a and 6b display analogous curves for the loop antenna. As follows from Fig. 5a, near the antenna, Ne peaks at H ~ 40 G and then sharply drops. As the distance from the antenna increases, Ne after the peak drops smoother and the second peak appears at H ~ 80 G. For the loop antenna (Fig. 6a), the dependences are similar but Ne peaks at the lower (~25 G) field. At large distances to the antenna, Ne exhibits one peak at H ~ 60 Gs. It is also seen from Figs. 5b and 6b that, for high magnetic fields, the electron concentration decreases more slowly with distance.
For the plasma-generating power 300 W, Fig. 6 implies that the optimum magnetic field in the vicinity of the loop antenna is ~20 G. For a 20-cm distance to the antenna, the optimum field lies between 50 and 60 G. These two conditions can be combined by locally reducing the field near the antenna, i.e., by using a nonuniform magnetic field in the plasma. To do this, we switched off coil (a). As a result, the chamber was under the uniform field due to coils (b) and (c), while the antenna was under the nonuniform field whose strength near the antenna was roughly half that in the chamber. The electron concentration Ne vs. magnetic field for the case of the nonuniform field is shown in Fig. 7a. Here, the field values in the center of the chamber are given. Near the antenna, the field is half as large. The curves were taken for the plasma-generating power 300 W. Comparing Fig. 7a with Figs. 5a and 6a, one notices that the runs of electron concentration in the uniform and nonuniform fields diverge considerably. The value of Ne does not drop markedly even near the antenna. At a distance of 22 cm, Ne monotonically rises. For the same field configuration, Fig. 7b shows Ne vs. RUSSIAN MICROELECTRONICS
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Ne × 10 –11 cm–3 (a) 2.0
Z = 4.5 cm Z = 10.0 cm Z = 22.0 cm
1.5
1.0
0.5
0
0
50
100
150 200 Magnetic field, G
Ne × 10 –11 cm–3 2.2 (b) 20 G 40 G 70 G 140 G
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0
1
2
3
4
5
Z, cm
Fig. 5. (a) Ne vs. magnetic field for various distances to the Nagoya antenna and (b) Ne vs. distance to the Nagoya antenna for various magnetic fields. RUSSIAN MICROELECTRONICS
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BRAGINSKII et al. Ne × 10 –11 cm–3 7 (a) 6
Z = 4.5 cm Z = 10.0 cm Z = 15.0 cm Z = 22.0 cm
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4
3
2
1
0 Ne × 6
0
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100
150 200 Magnetic field, G
10 –11 cm–3 (b)
5 20 G 40 G 70 G 140 G
4
3
2
1
0
5
10
15
20
25 Z, cm
Fig. 6. (a) Ne vs. magnetic field for various distances to the loop antenna and (b) Ne vs. distance to the loop antenna for various magnetic fields. RUSSIAN MICROELECTRONICS
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Ne × 10 –11cm–3 (a)
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4 Z = 4.5 cm Z = 10.0 cm Z = 22.0 cm
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0 0
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150
200 Magnetic field, G
Ne × 10 –11 cm–3 10 G 30 G 70 G 140 G
(b)
9 8 7 6 5 4 3 2 1 0 5
10
15
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25 Z, cm
Fig. 7. (a) Ne vs. nonuniform magnetic field for various distances to the loop antenna and (b) Ne vs. distance to the loop antenna for various strengths of the nonuniform magnetic field. RUSSIAN MICROELECTRONICS
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BRAGINSKII et al. Ne × 10 –11 cm–3 5.4 1 2 3 4 5
5.2 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6
–1
0
1
2
3
4
5
6
7
8 R, cm
Fig. 8. Radial distribution of Ne: 1 and 2, uniform field 60 and 40 G, respectively; 3–5, nonuniform field.
distance to the antenna at various fields. Figures 5b–7b imply that the curves run in a similar way for low (from 10 to 30 G) fields. For those above 60 G, the concentration peaks at a distance of 10 cm. This is not observed for the uniform field. Moreover, at high fields, a decrease in the electron concentration with increasing distance is not very sharp. Eventually, at the distances 10 and 20 cm, the electron concentration exceeds that in the uniform field at the same distances and rf power, 300 W, by a factor of 3 and 7, respectively. Thus, under a nonuniform field, the electron concentration rises and its peak approaches the surface to be processed. It should be noted that the field configuration in the plasma affects both the longitudinal and radial distributions of the electron concentration. Figure 8 shows how the magnetic field configuration influences the dependence of the electron concentration on the distance to the discharge axis. The curves were taken for the loop antenna and rf power 300 W. In the nonuniform field, the radial distribution of electrons can obviously be made both narrower (curve 3) and broader (curves 4, 5) than in the uniform case (curves 1, 2).
It seems likely that, under a nonuniform magnetic field, the plasma is redistributed along the tube so that the electron concentration in the high field range rises. In our experiments, the frequency ω of the rf generator, magnetic field strength H, electron concentration Ne, and gas pressure obey the condition ν ! ω < ωc ! ω p ,
(3)
where ωÒ = eH/m c and ω = 4πe2Ne/m are the cyclotron and plasma frequencies, respectively, and ν is the rate of electron–atom and electron–ion collisions. With condition (3) satisfied, the dispersion relation for helicon waves can be written as [9] 2 2 ωp k c -, --------- = ---------------------------------------2 ω ( ω c cos θ – ωγ ) ω 2
2
(4)
2
where k2 = k l + k r , kl and kr are the longitudinal (along magnetic field) and radial components of the wave vector, cosθ = kl /k, γ = 1 + i(ν/ω), and c is the velocity of light. As follows from Fig. 3, the length of the longitudinal wave equals 28 cm and varies with the applied rf power only slightly. Hence, we can put kl = 2π/28. RUSSIAN MICROELECTRONICS
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Under helicon wave resonance, kr is derived from the relationship kr = 3.83/R, where R is the plasma tube radius. For resonance conditions, the relationship between Ne and H is obtained from (4): 2 2 k c m eH k N e = -------------2- ----------- ----l – γ . 4πe mcω k
7.
(5)
The electron concentration is seen to grow with field. In a discharge chamber of complex configuration like ours, the resonance may be not very sharp. Yet, Ne is expected to grow in the high-strength part of a magnetic field by extracting electrons from the low-strength one. Another reason for an increase in the electron concentration in a nonuniform field appears to be a combination of high plasma excitation efficiency at low strengths and high plasma transfer efficiency at high strengths.
8.
9.
10.
11.
CONCLUSION The parameters of the plasma excited by helicon waves of three types were studied. A loop antenna is shown to be more advantageous. The dependences of the electron concentration on the rf power and external magnetic field were obtained. Both axial and radial distributions of electrons were derived. It was found that the electron concentration in the operating discharge region can be increased by applying a nonuniform field so that the antenna is in the low-strength part of the field. For an rf power of 500 W and a magnetic field strength of 70 G, the electron concentration attains 1012 cm–3.
12.
13.
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15.
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