Transmission Line Balanced Inductive Plasma Source Lmbda Resonator G Vinogradov

Plasma Sources Sci. Technol. 9 (2000) 400–412. Printed in the UK

PII: S0963-0252(00)13449-8

Transmission line balanced inductive plasma sources G K Vinogradov KEM Inc., 907-8, Shimoimasuwa, Shirane-cho, Nakakomagun, Yamanashi 400-0212, Japan E-mail: [email protected] Received 18 October 1999, in final form 29 February 2000 Abstract. A new class of transmission line balanced inductive plasma sources having discrete inductive zones is reviewed. The problems of undesirable capacitive currents, azimuthal non-uniformity and the energy efficiency of inductive plasma sources are considered and basically solved. The main principles of operation, discharge performance and the most interesting experimental observations are discussed.

1. Introduction

2. Inductive plasma sources

The implementation of inductive plasma sources has spread widely in the last decade as high-density plasma etching/deposition tools. It was stimulated by the captivating idea of ‘pure inductive plasma’. However, from the early times of J J Thomson (1856–1940) it was known that inductive discharges generate substantial capacitive currents from an inductor (coil) to the plasma. Inevitably, capacitive currents must be sunk by a grounded electrode or metal chamber. These currents impair the overall performance of inductive plasma sources, producing wall sputtering, discharge non-uniformities and arcing. Inductive RF discharges start from the capacitive breakdown, which generates harmful capacitive currents outside the plasma source. Azimuthal discharge non-uniformities appear with large inductive plasma sources, when the lengths of the inductor winding increases up to the values comparable to the wavelength of the excitation RF frequency [1–3]. Therefore, conventional inductive plasma sources have a limited applicability as high-power, large-volume plasma sources. There have been different attempts undertaken in order to suppress capacitive and transmission line problems by various particular measures; however, they have not resulted in any general solution. An opposite approach to these unresolved issues is to not suppress the wave properties of transmission lines but to use them to remove the problems. Thus, a new class of plasma sources has been proposed: transmission line balanced inductive plasma sources [4, 5]. The problems of undesirable capacitive currents, azimuthal non-uniformity and energy efficiency have been basically solved. Moreover, the new plasma sources show unique robustness, flexibility and other valuable features, which are rather unexpected and extraordinary. This paper is dedicated to briefly overviewing the basic principles of the new plasma generators, which have already been successfully taken up by industry.

Since the mechanisms of gas discharge generation are not self-evident but rather speculative, they do not provide a simple basis for comparison of plasma sources. A technical definition of inductive plasma sources using tangible terms would be most convenient for our considerations. Therefore, the following definition will be used:

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The inductive plasma source (IPS) is a gas discharge source having an inductor (inductive power applicator) generating alternative magnetic fields in the discharge volume. This definition is broad and does not refer to any particular mechanism of discharge ignition or self-support. 2.1. Capacitive problems Capacitive currents generated in an IPS are usually undesirable except for the initial gas breakdown. Playing a twofold role in the discharge physics, the capacitive currents are necessary for discharge igniton, but harmful as they generate capacitive problems. All known IPSs, short helical inductors, one-turn coils, helicon antennas and conventional helical resonators (HR), are unbalanced capacitively. That is, their capacitive equivalent structure is similar to the asymmetric capacitive discharges with a large-area grounded electrode (chamber) and a small RF electrode represented by the inductor itself, as shown in figure 1. The capacitive currents entering the plasma from the inductor generate capacitive sheaths in the processing chamber that is on the wafer. Probe diagnostics of such systems frequently show low plasma potentials in the chamber. It is usually supposed that the discharge operates in ‘pure inductive’ mode. However, the capacitive discharges with highly asymmetric electrodes, i.e. small RF/large ground, also show very low plasma potential [6]. The main voltage drop or a self-biased sheath

Transmission line balanced inductive plasma sources

Figure 2. RF voltage distribution along the single-turn loop.

Figure 1. Inductive plasma source and its capacitive equivalents.

appears at the small-area electrode that is at the high-voltage portion of the inductor. The RF voltage from the generator is divided in proportion to the capacitive impedances of the inductor–plasma gap and discharge capacitive sheaths. Since the chamber capacitance is typically the largest, the RF fluctuation of the plasma potential here is minimal. The narrow entrance into the chamber provides the most powerful plasma–ground sheath since it is in the closest vicinity of the active discharge area. The discharge power increases by increasing the inductor current and, hence, voltage. Consequently, the capacitive current from the inductors also increases. It is difficult to suggest a priori to what extent the increase of capacitive current is threatening for a particular process, since IPSs have different geometries. Therefore, we discuss here some widely spread IPSs. 2.1.1. Single-turn inductor. A single-turn loop is the simplest inductor having the RF voltage distribution shown in figure 2. A high-voltage end of the loop generates the highest capacitive current and, hence, the strongest plasma sheaths. Even this is not so pronounced in very low-pressure discharges, but it does generate an azimuthal non-uniformity and the discharge vessel suffers from wall sputtering. This non-uniformity can be visualized at elevated pressures (
1 Torr). The single-turn inductor has minimum inductance among inductive applicators, and the lowest inductive coupling efficiency. Therefore, this kind of inductor should be considered as the weakest inductive applicator with the highest capacitive non-uniformity 2.1.2. Short helical inductor. A short helical inductor is a common type of inductive applicator widely used for melting metals, welding, plasma torches and for low-pressure glow discharges. A winding of the short inductor is substantially shorter than a quarter wavelength (λ/4) corresponding to the

excitation frequency, so it can be analysed without taking wave phenomena into consideration. Modern low-pressure discharges for microelectronics need very large volumes. The winding length of inductors is growing as it is scaled up by the increasing wafer size. The inductor winding length is increasing, but the ratio (coil length)/(diameter) is decreasing so that it is deviating far from an elongated solenoid shape. An inductive (transformer) coupling efficiency of the short inductor is proportional to the number of turns N in a helix. That is, the coupling efficiency of the short helical inductor is about N times higher that that of a single turn, so it can efficiently work on much larger inductive loads, producing higher density plasmas. The helical coils generate high sheath voltages in the plasma sources, but they show much better azimuthal uniformity increasing with the number of turns in the helix. The total capacitive current from a helical inductor to plasma is, certainly, higher than that of the single turn. 2.1.3. Pancake inductor. A spiral or pancake inductor has long been known in inductive heating, welding and therapy. The attractiveness of this inductor for gas discharges can be explained by the possibility to design plasma sources geometrically similar to parallel-plate capacitive discharges, while generating high-density inductive plasma at low gas pressures [7]. The pancake applicators are made as Archimedes spirals or a collection of concentric co-planar rings of decreasing diameter. A flat spiral generates stronger magnetic field at the axis in comparison with a single-turn loop. The flat inductor is usually separated from the discharge volume by a dielectric window, usually quartz, which is transparent for both magnetic and electric fields. This window must be thick in order to withstand atmospheric pressure. The larger the discharge diameter, the thicker is the window. The capacitive currents from the coil generate a strong capacitive electric sheath at the window, especially at the high-voltage portion of the coil which is usually located near the centre. This sheath is a cause of window sputtering. A flat split grounded shield is usually inserted between the inductor and window to limit the capacitive current to the plasma. 401

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Potential RF electric fields from helical IPSs can also be shielded [8–10]. However, this way is not free from serious drawbacks, because the electrostatic shield (ES): (1) dramatically suppresses discharge ignition; (2) increases the external size or decreases the useful internal discharge volume; and (3) impairs the inductive coupling by picking up some portion of inductive current. Consequently, the ES should be considered as a useful and practical but palliative remedy in treating the capacitive problems of IPSs. There are several ways of decreasing the sheath voltage at the grounded surfaces in a capacitive discharge: increase RF frequency, decrease an area of a RF driving electrode or balance the RF excitation in respect to ground. The balancing of symmetric RF capacitive discharges has been shown to be worthwhile for Langmuir probe measurements [11, 12]. The fundamental excitation frequency in the balanced discharge substantially decreases down to a few per cent. Therefore, the symmetric capacitively balanced discharge has the sheath power at the ground substantially decreased. The balanced RF feed is used in some industrial discharges for generating radicals in a volume. 2.2. Transmission line problems The problem of large (long) inductors affecting the discharge uniformity was recognized only a few years ago [1–3]. The coil current is not uniform along the long winding, because its length becomes comparable to a wavelength of the RF power, and it is no longer possible to ignore wave phenomena. Further increase in wafer size needs larger coils and, hence, the problem is becoming a threat for conventional inductive plasma sources. The concept of electrical transmission lines [13] is used to describe long electrical structures carrying electrical power. The uniform transmission lines cannot only be straight wires, but also spirals. A transmission line with a coaxial helical inner and cylindrical outer conductor is a coaxial helical transmission line [14]. About half a century of history of these lines started with the microwave devices called travelling wave lamps and klystrons. Many theoretical and experimental problems have been solved in order to implement these devices into the technology of microwave radars [15–19]; therefore, many of them are readily applicable. Large inductor coils inevitably show the transmission line effect: standing waves [1, 2]. One problem is that the standing wave has to be taken into account in order to optimize the inductor geometry for compensating an azimuthal current distribution. Another problem, which has yet to be taken into consideration, is that enlarging the inductive coil beyond λ/4 does not increase the total magnetic momentum of the inductor, but rather decreases it by generating an opposite portion of the magnetic field due to the phase change along the line. Therefore, any further enlargement brings about wave phenomena, which drastically change the physical nature of the inductor and, hence, its interaction with the discharge. In other words, 402

Figure 3. RF current I (dashed line) and voltage V (full line) amplitude distributions on helical inductors: (a) ‘short’ inductor; (b) quarter-wave HR; (c) half-wave HR; (d) full-wave λ-HR; (e) half-wave dipole-HR with open ends. Coil ends are connected to the shield (grounded), open and/or RF fed [4].

there is no simple way to built efficient inductors longer than λ/4 just by increasing the coil length. Figure 3 shows voltage and current distributions along the transmission line resonators, each having different electric lengths and termination. The zero-voltage ends are the grounded ends. When the line length exceeds λ/4, the current changes a phase, that is a direction, crossing zero. A conventional half-wave HR shown in figure 3(c) has two inductive zones with opposite currents, that is opposite magnetic momenta. This physical feature has never been recognized in respect to the mechanisms of discharge excitation in the HR plasma sources. It was commonly assumed that all helical resonators are similar discharge devices and which differs only by size, geometry and resonating frequencies. The resonating helical lines of different electric lengths and termination must generate drastically different gas discharges having previously unknown electromagnetic structures. For instance, it is possible to use the wave structures in order to design electrically and/or magnetically balanced resonator IPSs using correspondingly adjusted wave segments. 3. Helical transmission line plasma sources with multiple inductive zones

We have the following definition: Transmission line inductive plasma sources are those having large self-resonating inductors, which can be defined as transmission lines. The electromagnetic structure of helical transmission lines was described about 50 years ago [15–19], when a considerable study was given to microwave electronics of radar applications. A model, enlarged ten times, of the actual helix was constructed and the field distribution, excited by oscillations in the frequency interval between 375 and 120 MHz, was investigated by means of a miniature sliding and rotating probe [19]. The axial field at a distance r from the axis was found to agree quite well with an expression on the assumption that the field is quasi-static: f (z, r) = f (z, r0 )

I0 (2πr/λh ) sin(2π z/λh ) I0 (2πr0 /λh )

where z is the distance parallel to the axis, r0 is the mean radius of helix, I0 (x) is the modified Bessel function of zero

Transmission line balanced inductive plasma sources

Figure 4. Lines of equal axial field strength approximately in a plane through the axis of a helix [19].

order and λh is not a free space λ but the reduced wavelength in the helical transmission line. Figure 4 shows the experimental field pattern of the axial field with strong longitudinal variations, when the parameter 2π r0 /λh = 3.3 for λ = 82 cm and λh = 6.6 cm. This field pattern is very far from a solenoid distribution. A resonating part of the helical transmission line, which has a length equal to any integer multiple of λ/4, should be considered as a longitudinally non-uniform inductive applicator. The longitudinal periodic structure is the key to controlling the inductor–plasma coupling and the mechanisms of discharge ignition and power distribution. 3.1. Transmission line capacitive balancing of inductive plasma sources A resonating section of the lossless transmission line has standing waves of voltage and current as shown in figure 5, where positive and negative amplitudes show phase and anti-phase half-waves. Each phase voltage portion can have an anti-phase counterpart. The total transmission line segment is capacitively balanced or unbalanced in respect to ground, depending on the number of phase and antiphase λ/4 portions comprising the segment. The method of capacitive balancing of the transmission line resonators can be designated as lambda balancing. That is, the capacitive balance can be adjusted by adjusting the wavelength to the electric length of the resonator or its resonant frequency. Correspondingly, a minimum-length capacitively balanced resonator is a λ/2 open-ended segment or a half-wave dipole. A minimum-length close-end capacitively balanced section is a full-wave or λ-resonator (λ-R) [20]. The resonators having one end open and another closed are unbalanced. Higher order resonances satisfy the capacitive balance condition for the dipole sections having an electrical length of nλ/2, where n = 1, 2, . . . . This class of resonators has a zero-potential central point of symmetry for the odd and maximum voltage central point for the even harmonics. These devices do not belong to the conventional helical resonators, which have both short or one open end. They can be designated as a particular class of dipole-resonators. The balanced resonators with both ends grounded, the λ-Rs, have an electric length of nλ. These resonators all have a zero-voltage centre of symmetry and are balanced totally, that is not only capacitively but also magnetically:

Figure 5. Voltage (full curve) and current (dotted curve) standing wave amplitude distributions in the resonating section of a long transmission line: capacitively balanced segments corresponding to capacitively balanced inductive plasma sources are indicated.

the total magnetic momentum is to be about zero. The λ-Rs, in an electrical sense, are a particular case of conventional short-ended λ/2-resonators having an even number of λ/2 segments. The main role of the magnetic portions of the transmission line inductive sources is generating the circular electric fields in the discharge volume. It is now well understood that there are multiple anti-phase inductive zones in the helical transmission lines. The conventional halfwave HR has two separate inductive zones with opposite magnetic momenta. This feature of helical resonators, which is crucially important for the discharge physics, has only just been appreciated [4, 5]. 3.2. Discrete inductive zones in transmission line inductive plasma sources The number of inductive zones in a transmission line source is equal to the number of mono-phase current segments or current maxima. That is, for the quarter-wave HR (one open end) having electric length of ( 41 +n/2)λ, where n = 0, 1, . . . , the number of inductive zones is equal to (n + 1). Only the closed-ended inductive zone is a λ/4 zone, another n zones are of λ/2 type. The short-ended inductors having electric length equal to ( 21 + n/2)λ, where n = 0, 1, 2, . . . , have the number of inductive zones equal to (n + 2). The two end zones of these inductors are of λ/4 type; the inside zones are all λ/2 type. Any change of the electrical length by a λ/4 quantum affects the basic field structure. It changes, in turn, the 403

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inductor–plasma interaction because of both an inductive and a capacitive transformation of the plasma source and, what is also important, the three-dimensional self-consistent conductive structure of the discharge plasma. The discharge transformations change the electrical nature of the resonator load and can show second-order phase transitions and discharge self-organization at elevated gas pressures. The dipole-resonators have the number of inductive zones equal to the number of λ/2 segments in the resonator. The dipole-resonators generate only λ/2 inductive zones. Every even mode resonance is also magnetically balanced. The λ-Rs with an electrical length of nλ have (n+2) inductive zones, where two of them are always λ/2 type. Conventional quarter and half wavelength HR sources are particular examples of transmission line plasma sources with one and two λ/4 inductive zones, respectively. Both resonators are capacitively unbalanced. Being highQ (quality factor) resonators, they generate very high voltages on the coils and, hence, generate the strongest capacitive inductor–plasma–ground currents among all helical inductors. Helicon inductors, usually called antennas, are sometimes very large. Commonly used antennas are halfwavelength long wires shaped in several empirical ways. Antennas longer than λ/2 have never been tried, because optimization of antenna design has been carried out only by trial and error [21]. The λ/2 wires of helicons, being capacitively unbalanced, generate high-voltage capacitive sheaths and capacitive inductor–plasma–ground currents. This is, probably, the cause of high-energy electrons and ions found in helicon discharges but not the cause of ‘wave surfing’. The possibility of the balanced transformer RF feed for a helicon discharge has been mentioned [22]. This reduces the maximum antenna–plasma voltage by a factor of two, thus also reducing the undesired capacitive current coupled to plasma by a factor of two [22]. The transmission line properties of large helicon antennas are not well understood. They can be dramatically improved by utilizing the described principles of transmission line balance. 3.3. Two basic capacitively balanced transmission line plasma sources From a practical point of view, inductive plasma sources should not have too large coils. That is, the most promising realizations are the shortest capacitively balanced inductors, which are the half-wave open-ended Dipole-resonator and the short-ended full-wave λ-R plasma sources. The full-wave dipole-resonator has about the same size inductor as the λR, however, the grounded ends of the λ-R are convenient in practice. 3.3.1. λ-R inductive plasma source. The λ-R plasma source is schematically shown in figure 6 [5]. Figure 7 shows the equivalent schemas of the λ-R discharge [24]. The inductor is represented as four similar λ/4 coils connected in series fed from two equivalent push–pull RF generators. Three inductive excitation zones are located at the current maxima. Two central λ/4 coils are in-phase, thus comprising 404

Figure 6. A schematic cross sectional view of the experimental λ-R plasma source.

Figure 7. Electrical equivalent schema of the λ-R inductive plasma source.

a λ/2 coil keeping the same direction of the distributed electric current. This coil thus produces twice as large an induction field in comparison with the side quarter-wave coils. Two side λ/4 coils are both anti-phase in respect to the central λ/2 portion. The magnetic fields generated by the central coil and every side coil are repulsive. They produce inductive electric fields and circular discharge currents in opposite directions. Consequently, the inductive plasma toroids produced by these currents can never collapse into one. That is, the plasma toroids are strictly localized in their corresponding inductive zones, and their positions do not depend on the discharge parameters but are determined solely by the standing wave structure. The capacitive structure is more or less self-explanatory. Part of the push–pull balance electric field is shunted outside the discharge tube due to the high serial inter-turn capacitance Cs . Capacitive currents from the inductor flow to the discharge through a wide (about 40 mm) inductor–wall air gap denoted as Ci−w . The plasma–wall sheath is beyond

Transmission line balanced inductive plasma sources

Figure 8. A comparison of the λ-R and conventional quarter-wave HR inductive plasma sources.

the dotted line indicating the tube wall. The sheath is thin and, hence, of low impedance because of high-density plasma generated in the inductive zones. The bulk plasma strongly shunts the push–pull capacitive currents thus decreasing RF plasma potential fluctuations in the discharge centre up to a few volts [23–25] at 2 kW discharge power. The bulk plasma does not spread beyond the excitation coil under the elevated pressure of about 1 Torr. At low pressures, the plasma diffuse downstream the plasma. However, even under these conditions the parasitic capacitive sheath near the ground surface is invisible up to a few kilowatts of the discharge power. It would be useful to compare the λ-R source, comprising of four equal λ/4 coils, versus the conventional quarter-wave HR source under the same discharge conditions and similar load configurations. Suppose the two plasma sources in figure 8 have similar coil geometry. Let us consider a cylindrical discharge load as a one-turn closed resistive loop. In the λ-R source, this load is heated by circulating currents generated by the four λ/4 coils. We assume these coils produce equal additive inductive powers in the discharge, which is consistent with our experimental observations. The quarter-wave HR, in its turn, must generate the same total power from a single λ/4 coil. Both voltage and current on that coil must be doubled in order to transmit that power. In other words, the high voltage on the λ-R source coil must be at least twice as low provided the same inductive power is generated in the discharge. The capacitive currents of the λ-R source balances reactively within the source volume and are also partly absorbed in the discharge. This portion of the total discharge power does not go outside the plasma source. In contrast, the capacitive current of the quarter-wave HR source flows from the bulk plasma into the ground capacitive sheath, thus delivering an essential portion of the capacitive power outside the source, that is on the chamber wall and processing wafers. These are well known capacitive problems: wall sputtering contamination and wafer damage. Very high ground capacitive currents flow from a half-wave HR plasma source even its RF voltage is lower than that of a quarterwave HR source. The most severe sputtering occurs on the circumferential metal surface of the bottom flange of the plasma source. In summary, the λ-R not only keeps the capacitive currents, and hence their power, inside the plasma source, but also generates much lower capacitive current density in the discharge wall sheaths in comparison with conventional quarter- and half-wave HR discharges. These features

Figure 9. Capacitive equivalent schema of the γ -dipole plasma

source.

partially explain why the transmission line capacitively balanced plasma sources demonstrate incredibly high process performance and stability. 3.3.2. γ -dipole plasma source. A γ -dipole IPS is a resonating half-wavelength open-ended coil with a central unbalanced RF feeder. This structure can be thought of as created from a well known half-wave dipole vibrator converted into a helix. The central feed from an unbalanced, i.e. coaxial, cable is known as a gamma-match. This means that both RF and ground ends of the coaxial cable are connected at about the centre of the dipole. This is the origin of the term γ -dipole plasma source. The equivalent scheme of the γ -dipole discharge can be shown as just a central half-wave segment of the λ-R equivalent schema, as shown in figure 9 denoting corresponding capacitors as capacitive impedances: Zs , inductor serial; Zi−w , inductor–wall; Zsh , sheath. The main difference from the λ-R discharge is that the bulk plasma has only the central inductive zone. All the discharge power, inductive and capacitive, is concentrated in a single compact area generating two to five times denser plasmas than the λ-R discharge, which has a much longer discharge volume. Certainly, the push–pull capacitive currents are essentially shorter in the centre plasma and balanced. It is theorized that the high-conductivity inductive plasma toroid provides an electrostatic self-shielding. Any capacitive problems in the aluminium downstream chamber could not be even intentionally generated in the range of RF power up to 5000 W, with gas pressure between 1 and 50 000 mTorr, for Ar or O2 discharges: no arcs, no sparks and no visible capacitive sheath. Taking into account about 100% energy efficiency of this source as a resonator (measured unloaded Q ≈ 3200 at 27 MHz), we conclude that it can be classified as a super inductive plasma source. Indeed, there are no more inductive plasma sources which could theoretically or practically provide a higher or even close power efficiency in generating a bulk plasma. 3.3.3. RF matching. Helical transmission line plasma sources, including conventional HR, can be directly matched to a 50  coaxial cable [26–29]. Since the resonator itself does not consume any RF power, the plasma is the only active 405

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load. Therefore, an energy efficiency of these IPS is virtually 100% from a cable. The λ-R plasma sources used in the commercial ‘λ-Strip’ equipment manufactured by KEM Inc (formerly RAMCO, MC Electronics) typically is set up for about 5–10 W reflected power from a 50  coaxial cable fed by the maximum power (generator limitation) of 2, 2.7 or 5 kW at 27 MHz. The author is aware of some unfortunate attempts to build and evaluate the λ-R plasma sources using conventional fixed frequency RF generators and matching boxes. It is worth mentioning here that the resonator sources are not similar to conventional inductive sources in respect to the matching with fixed frequency generators. If the λ-R itself does not match exactly the excitation frequency under the plasma loaded conditions, that is it cannot be fed directly from a coaxial cable, it will never operate in a λ-R discharge mode with any matching devices. The external matching elements do not change the electrical length and, hence, the resonating frequency of the line; they can only compensate an input impedance mis-match to some extent at the point of connection (tap position). An apparent matching observed in this case is just an indication that the matching box and the plasma source together comprises a resonating system. It can be very far from the resonator’s eigenfrequency. Therefore, the resonators having a resonance frequency different from that of the RF generator cannot be matched in principle. Conventional inductive sources can use an external matching network because their inductors themselves do not resonate at the excitation frequency. They are only a part of the whole resonating system, which includes an external matching box. In a practical situation the RF frequency usually varies in a range of about 1–2% in order to match a resonator IPS. That is, the wavelength matches the coil length. The exact tap position cannot be calculated because of the effect of the discharge conditions. It is typically located at about a 0.1–0.3 turn distance from the ground point of the coil in our experiments. This distance can be easily found by experimenting. It is shorter in the case of highly conductive plasmas (Ar, N2 ), and longer for highly resistive media like electronegative molecular plasmas (O2 , CF4 ). 3.3.4. Ionization and dissociation efficiency. There are many opinions concerning the ionization and dissociation efficiency of different plasmas: capacitive, inductive, microwave, dc, etc. The fundamental problem of the similarity of different plasmas and the overall efficiency of the plasma sources are two problems of differing natures. In other words, the specific plasma efficiency, which is a fundamental concept, and the total discharge efficiency, which is a technical concept, do not correspond to each other. Many research works have been aimed at proving that ‘inductive plasmas’ show superior efficiency in comparison with ‘capacitive’ or ‘microwave plasmas’ in respect to ‘RF or dc plasma’. Some workers have tried to prove superior ionization in a particular plasma source and others superior dissociation for a similar source depending on the application purpose. However, there are very few scientifically approved methodologies and little experimental evidence [30, 31]. We assume a simple but rather solid basis to compare different discharges: the total absorbed power in the bulk 406

plasma. It is well known that the electron density in a bulk uniform plasma is roughly proportional to the specific absorbed power. Both ionization and dissociation rates are about proportional to the electron density provided the EEDF is unchanging. Two plasma sources being fed from similar RF generators can be reasonably compared by the portion of the total power absorbed in the bulk plasma without regard for the mechanisms of plasma generation. The total losses of the RF power occur mainly in three places: (1) a matching box, about 10–50% [32]; (2) capacitive losses outside the plasma source, that is in the process chamber (considered as losses because undesirable), about 10–30%; (3) capacitive sheaths inside the plasma source, about 10–20% (for ion acceleration, i.e. for surface bombardment). The third channel is not a completely lost energy, because some part goes for the electron heating by the sheaths. These estimations are to be considered as qualitative ranges only, but are useful for overall comparisons of different plasma sources. The transmission line sources operate without a matching box and do not produce capacitive plasmas outside the source. Taking essentially lower voltages on the capacitive sheaths inside the source into consideration, one can obtain a correct idea about the energy efficiency. By and large, a balanced transmission line plasma source achieves a higher or much higher energy efficiency in comparison with any other RF inductive source [24]. Consequently, such plasma sources should demonstrate noticeably higher process rates in comparison with other inductive sources with the same RF power consumed from a RF generator. On the other hand, the same performance can be achieved with smaller RF generators. 4. Some experimental observations

The experimental set-up and some results on the probe and optical emission diagnostics and visual observations have been described in details elsewhere [4, 23–26]. Figure 6 shows the main configuration of the λ-R plasma source, which was also used for generating half-wave HR, threehalf-wave HR and 2λ-R modes. The γ -dipole source was used with a 235 mm diameter, 300 mm long quartz tube, as shown in figure 10. It was fed from a coaxial cable at about the centre point of the coil. The ground was connected a few centimetres away from the fed point (more details will be shown in figure 14). The same coil with one end ground and another open was also used for quarter-wave HR experiments. It should be mentioned, however, that the resonance frequencies of helical resonators, which are short segments of ideal long transmission lines, do not correspond well to the integer multiples of the fundamental frequency. This has been explained by the deviation of the magnetic field configuration from the ideal infinite line. Two transmission lines were used in order to compare six plasma sources, each of which can also generate particular discharge modes. Some tests were performed on the industrial 200 and 300 mm wafer ashers. The 0.005–2.25 kW RF power at 10–80 MHz frequency was supplied to the resonators by using a 50  coaxial cable directly from a wide-band tube amplifier IFI-410 with

Transmission line balanced inductive plasma sources

Figure 10. A schematic cross section of the γ -dipole plasma

source.

Figure 11. Axial RF magnetic field in the λ-R plasma source.

a sign wave signal generator HP-8648A. Commercial RF generators of 4.5 or 5 kW RF power (Kyosan and Adtec), at 27 MHz, were used in some experiments. RF signals from the discharges were monitored by a digital 2 GS/s oscilloscope TEK360P 4.1. Capacitively balanced plasma sources 4.1.1. λ-resonator. Visual observations of the transmission line discharges impress by direct visualizations of their electromagnetic structure. Both capacitive and inductive current channels are well seen in large discharge volumes. Figure 11 shows the experimentally measured resonance axial RF magnetic field under the plasma-unloaded condition in the standard 235 mm discharge tube of the λ-R source [33]. It is seen that the magnetic field is essentially stronger near the wall. There are three distinct inductive zones: two λ/4 and one central λ/2. One can see an additional weak zone in the bottom aluminium flange. This field is generated by a return current induced by the bottom part of the inductor in the nearest conductive flange. The field structure corresponds to the theoretical models. The RF fields are substantially shielded inside the conductive bulk plasma, when a gas discharge is ignited. The axial magnetic fields generate corresponding circular electric fields of the localized inductive discharges. The location of the inductive zones is therefore strictly fixed and does not depend on the discharge parameters. Magnetic field zeros correspond to the high-voltage maxima on the helix. Interestingly, the configuration of the RF electric fields in the λ-R is similar to the picture indicating helicon waves [21]. Indeed, looking at figure 12, showing azimuthal and radial field patterns along the axis, we assume this similarity. This is a standing wave field pattern of the λ-R.

4.1.2. γ -dipole plasma source. The γ -dipole discharge, having the simplest balanced electromagnetic structure, dopes not demonstrate so many visual phenomena. The vertical localized capacitive currents, similar to those observed in the λ-R discharge [4, 5], can be easily generated in argon gas under a pressure of 10–50 Torr. A very distinct longitudinal split of the luminous channel of the inductive plasma toroid can be observed with the power increase. A further increase makes the plasma toroid flatten to a 50–60 mm wide belt shape. It is also possible to generate a stable floating and swinging plasma toroid, whose diameter is noticeably, about 30%, smaller than the discharge tube. We have never observed such wonderful creations in other discharges. This observation is, probably, explained by a wider profile of the magnetic field lines generated by the dipole coil in comparison with the inside λ/2 segment of longer inductors compressed by the opposite magnetic fields of the adjacent coil segments. In the lambda coil, for example, the central magnetic field is removed to a great extent from the axis to the wall. Therefore, the central plasma toroid in the λ-R coil cannot decrease its perimeter without loosing a large portion of the magnetic flux necessary to support the inductive currents. In the γ -dipole plasma source, the toroid can shrink its diameter because the lost portion of magnetic flux is almost compensated by the lost length of the current channel. 4.2. Capacitively unbalanced plasma sources The unbalanced quarter-, half-, and three-half-wave HR plasma sources were tested under a wide range of conditions. They generate well the visible capacitive discharges onto the ground surface. Such visualization under the elevated pressure shows the discharge currents and the spatial distribution of the RF power. It is clearly seen that the capacitive power comprises an essential portion of the total discharge power. The quarter- and half-wave HR discharges generate one and two inductive toroids, respectively. They are located at the coil ends in correspondence with the RF current standing wave pattern. In the pressures range of about 0.6–0.8 Torr the capacitive currents and the chaotic arcing in the downstream metal chamber are typical. The aluminium flange supporting the resonator suffers from sputtering. This flange probably sinks the main portion of the capacitive current from the source which is very close to the highly conductive area. The arcs at 2–3 kW RF power are so strong that they produce aluminium oxide particles from the locally melted spots on the aluminium surface. The three-half-wave HR discharge is interesting for phenomenal inductive–capacitive interactions. Vertical saddle-type inductive plasma toroids, shown in figure 13, can be observed in the three-half-wave HR discharge much easier than in the λ-R discharge. The mechanism of these amazing discharge creations is explained as follows. A dense magnetic flux between the neighbour coil segments with opposite currents crosses the helix and discharge wall. Consequently, part of this flux can be captured by a closed conductive path like a plasma toroid located on the wall. 407

G K Vinogradov

Figure 12. Standing wave field patterns in the λ-R plasma source.

Figure 14. Experimental arrangement for RF capacitive current measurements; γ -dipole plasma source.

Figure 13. An example of the standing wave plasma structure: evolution of saddle-type inductive toroids.

The three-half-wave HR discharge generates four inductive toroids: two full-wave and two quarter-wave. It is worth mentioning that this discharge has smaller capacitive problems than the conventional λ/2 or λ/4 HR discharges. The three-half-wave HR is only partially unbalanced for about 30%, because it has totally balanced λ-segment. 4.3. Capacitive currents from inductive resonator plasma sources It was found that the plasma potential fluctuations of the λ-R discharge are rich with very high-frequency harmonics of the excitation frequency [23]. The λ-R discharge does not usually generate the second harmonic the strongest, as in the case of a balanced capacitive discharge, but rather the third, or sometimes, even the fifth. This phenomenon could be expected from the analysis of the electric equivalent scheme of the transmission line discharges that have more than two rectifying capacitive sheaths which are not symmetric with respect to the ground. We have measured the RF fluctuations of the plasma potential, using the dc insulated capacitive probe [25], and capacitive plasma–ground currents [33] for several transmission line discharges of similar geometrical configurations and discharge parameters in order to assure similar conditions. The RF potential of an electrically 408

floating wafer separated by a capacitive gap from the ground platen was also examined. Some preliminary results will be shown below. The experimental set-up for capacitive current measurements is shown in figure 14. The current was monitored using a current monitor PearsonTM model 5895 operable in a frequency range up to 70 MHz within about ±10% uniformity. The transmission characteristics of this monitor were calibrated using a network analyser HP-8712C up to about 250 MHz, in order to estimate a very high frequency range. The transformer shows up to a ten-decibel increase in transmission at higher frequencies following a deep valley at about 70–90 MHz. 4.3.1. RF capacitive inductor–ground current. Figures 15 and 16 show, as a function of absorbed power, the total rms capacitive current inductor–ground through the bottom of the plasma source for three discharges: half-wave HR, λ-R and γ -dipole. This capacitive current represents the major part of the total capacitive current. The power deposited in the process chamber by the capacitive currents is about two orders of magnitude smaller in the balanced plasma source in comparison with the unbalanced source. Figure 16 shows a qualitatively similar picture for a lower pressure discharge in argon. The capacitive current in the λ-R discharge does not grow with the power increase. These experiments support previous suggestions about the nature of capacitive compensation in transmission line discharges. Returning to figures 15 and 16, we should recall that the comparisons were made at different excitation frequencies. Both λ-R and γ -dipole discharges were operating at 27 MHz, while the half-wave HR was at about 17 MHz. Since the voltage drop on the capacitive sheaths should be higher at the lower frequency, this increases the ratio of the power

Transmission line balanced inductive plasma sources

Figure 15. RF capacitive currents in oxygen gas discharges for three transmission line plasma sources: half-wave HR, γ -dipole, λ-R.

Figure 17. Oscillograms of the (a) voltage on the resonator, (b) total ground capacitive current and (c) FFT spectrum of the capacitive current in the λ-R; O2 , 0.1 Torr, 2 kW RF power absorbed in the discharge. Note, the time scale is 50 ns.

Figure 16. RF capacitive currents in argon gas discharges for half-wave HR and λ-R.

deposited on the capacitive sheaths in different plasma sources. 4.3.2. Harmonic composition of capacitive currents. The ground capacitive currents of some inductive plasma sources were measured [34]. The harmonic composition of the RF fluctuations of the plasma potential has not been studied in capacitive discharges [12], although it was analysed in the feed RF power of inductive sources [35]. The harmonic composition demonstrates a very complicated nature, which has yet to be explored. This is likely, since there were no ground electrodes inserted in the symmetric capacitive discharges [11, 12] as our large grounded chamber bringing about longitudinal asimmetry. Figures 17 and 18 show typical RF signals for λ-R and γ -dipole discharges picked-up by an oscilloscope. The fundamental harmonic always dominates in unbalanced discharges. The balanced λ-R and γ -dipole discharges demonstrate FFT spectra, where the third or sometimes even the fifth, but not the second, harmonic is the highest. This is not expected to be from an analogy with the symmetric capacitive discharge. These resonator discharges can even redistribute the capacitive power into the tenth (!) frequency harmonic as shown in figure 18. Remarkably, in this particular case the highest tenth harmonic is very clear in the inductor itself.

Figure 18. Very high frequency harmonics appear not only in the plasma but in the resonator itself: (a) voltage on the inductor; (b) the total ground capacitive current of the γ -dipole discharge; (c) FFT spectrum of the capacitive current. Note, the time scale is 25 ns.

This probably means that this high harmonic coincides with one of the high resonating modes. Therefore, it is amplified in the resonator itself. The high-frequency harmonics of the capacitive current or plasma potential fluctuations do not coincide with the eigenfrequencies of the inductors. The discharge capacitive harmonics are just integer multiples of the fundamental frequency, which are generated solely, to a first approximation, by the rectifying capacitive sheaths. The resonating modes of the inductors depend not only on the mode number (that integer multiple) but on the spatial configuration of the electromagnetic fields of any particular mode. The shorter the inductor, the stronger is the deviation of the eigenfrequencies from that determined by the integer multiple. This is the reason why the resonating modes do not coincide with the strictly fixed discharge harmonics generated on the equivalent plasma sheath diodes. In the case of frequency coincidence between a high fundamental integer multiple and a high self-resonating mode, the resonator redistributes power into this mode. 409

G K Vinogradov

Wave phenomena of this sort have not yet been observed. The redistribution of power is especially noticeable in very low gas pressure discharges at 1 mTorr, not only in the balanced but also in the unbalanced resonators. However, we never observed this phenomenon at about 1 Torr and higher pressures because of a high resistivity of the bulk plasma damping high-order resonances. This study is currently in progress. 4.4. Practical realizations of γ -dipole and λ-R plasma sources Several capacitively balanced plasma sources were built and tested in the course of research and development. Plasma sources for 200 and 300 mm wafer processing were examined in a wide range of discharge conditions. The smallest source has a 180 mm diameter discharge tube, the largest one a 330 mm diameter. Table 1 is composed in order to compare the two basic balanced plasma sources. The discharge power was limited to 5 kW by the available 27 MHz generator. We have tested the smallest plasma source for the 5 kW power absorbed in the discharge (reflection below 5–10 W). This gives a scaling idea for the maximum power of larger sources. Plasma diagnostics have been carried out on the 235 mm λ-R plasma source [23, 25]. Other sources were not tested systematically. All the sources were examined in real scale (200 and 300 mm wafers) industrial equipment. This also gave a reliable basis for comparison and justified our estimations by the processing results. The very low level of the discharge power equal to about 5–20 W given in the input power range is real and well measured with a systematic error of 20%. The balanced resonators allow one to sustain a very low power stable bulk capacitive discharge in the regime of a high impedance current generator. From another side, the highest pressure of the range is realized in inductive or multiple contracted capacitive discharges depending on the gas. A variety of industrial applications, high radical and/or high ion flux, can employ transmission line balanced discharges. It is not difficult with these sources to achieve controllable convex, flat or concave ion or radical density profiles. At present, these plasma sources are used in superfast damage-free automatic photoresist ashers/etchers. As an example, the photoresist ashing rate in a 100% O2 discharge on the 300 mm wafer is up to 10 µm min−1 at 250 ◦ C within about ±3% typical uniformity using the λ-R plasma source, so that the total throughput is limited solely by the wafer transfer system. The γ -dipole source overcomes this performance for about 50–60% with the same RF generator. Other damage-free isotropic processes are also realized: super-fast isotropic etching of silicon (12–16 µm min−1 at 100 ◦ C); light etch of p-Si/BPSG (25–50 nm min−1 , uniformity ±2%); highly selective low-k materials ashing, back side nitride etching, etc.

to compare them and select the most suitable one for particular needs, because there is no basis for comparison but rather explanations of experimental or process data and plasma heating mechanisms. Some authors use the arguments concerning fundamental plasma parameters, directly applying them to the discharges, which apparently are much more complicated objects then the idealized uniform plasmas. Similarly, some fundamental results derived from the simplest ideal situations or particular noble gas discharges, for example the EEDF, are directly applied to interpret complicated chemistries with even more complicated heterogeneous processes. Therefore, only an overall discharge performance of different inductive plasma sources is considered here, mainly from a practical engineering point of view. They are considered as electric means for delivering the input power from a RF generator into the bulk plasma. This comparison is based on the experimental facts and objective considerations as well as the author’s personal experience. Table 2 shows a schematic comparison and the total rank of several real and hypothetical inductive plasma sources applied to a reference 235 mm diameter cylinder discharge tube mounted on the downstream metal processing chamber. Some of these sources, including a short inductor, quarter-, half- and three-half-wave HR, λ-R and γ -dipole have been tested on the same discharge tube and chamber providing direct evidence for a comparison. The capacitive damage relates to the semiconductor processing and is usually estimated using antenna structures with MOS capacitors well known in microelectronics. The ignition function is estimated as the minimum RF power necessary to initiate the gas discharge at a 100 mTorr pressure in argon. The power window means the whole range of a stable discharge; it certainly does not overlap with the whole pressure range. The same is true for the pressure window, it does not cover the whole power range. The azimuthal uniformity is estimated experimentally by electrostatic probes and by a qualitative comparison of integral distributed circular inductive currents and azimuthally distributed high voltage in the inductors. The size limit just means a qualitative estimation of the possibility to enlarge the current plasma source (from the reference 235 mm) or scale it down. This is the most uncertain parameter and it is not included in the total rank. The specific power is qualitatively estimated from the total power losses outside the plasma source for matching, and inside mainly for the capacitive sheaths. The discharges were compared on a one-by-one basis inside one parameter column. The relative error of the total rank should be considered within about two points. The total rank here does not mean that the last two transmission line balanced plasma sources are the best option for any particular application. It does mean that the sum of all marks for these sources is at a maximum. 6. Conclusion

5. Schematic comparison of inductive plasma sources

There are many technical papers about inductive plasma sources. It is, however, very difficult for the end user 410

I have covered in this paper only the most interesting, in my opinion, aspects of the subject, which are not yet fully understood. The transmission line plasma sources, as a whole, represent a new class of gas discharge devices

Transmission line balanced inductive plasma sources Table 1. Two basic types of transmission line balanced plasma sources.

γ -dipole Inductive structure Plasma diameter (mm)a Coil height (mm) Coil diameter (mm) Pressure range (mTorr)b Excitation frequency (MHz) Input power, experimental (kW)c Max. power, estimated (kW) Discharge volume (l)d Max. specific power (W cm−3 ) Electron density (1 × 1011 cm−3 ) Plasma potential (V) Applications STRIP,ETCH STRIP, CVD

λ-Resonator

One toroid Three separate toroids 235 200 235 280 330 65 230 230 260 250 330 260 330 340 400 1–50 000 27 0.005–4.5 10 20 2 3 7 10 16 21 2.5 1.6 0.6 0.5 0.3 0.2 30 20 5 4 3 2 17–25 High ion density High radical density

180 70 240

a

Discharge tube diameter. Depends on gas. c Limited by available RF generator. d Inside the coil. b

Table 2. Schematic comparison of 235 mm diameter inductive plasma sources. ‘x’, negative ranking; ‘o’, minimum positive ranking.

Inductors (coil, antenna)

Capacitive problems, damage

Single turn Pancake coil E-shielded Helical short coil Helical resonator E-shielded HR Helicon λ-Resonator γ -dipole

x x oo x x oooo x oooo oooo

a b c

Ignition

Power window

Pressure window

Azimuthal uniformity

Size limit down/upa

Bulk energy efficiencyb

Specific power

Total rankc

oo oo x oo oooo x ooo oooo oooo

oo ooo oo ooo ooo ooo ooo ooooo ooooo

o o oo oo ooo oooo x oooo ooooo

x o oo oo ooo ooooo oo ooooo ooooo

ooo/o o/oo o/oo ooooo/oo ooo/oo oo/o oo/oo oo/ooo oooo/ooooo

x oo o ooo ooo oooo ooo ooooo ooooo

oo oo ooo ooo ooo oooo ooo ooo ooooo

7/3 11/1 12/1 15/1 19/1 24/1 14/2 30/0 34/0

Down- and up-side scalability from the current 235 mm discharge size. Energy transfer into the bulk plasma. ‘Size limit’ is not included.

with controllable characteristics for dry processing. The concepts of transmission line balance and discrete inductive zones opens an interesting prospect for new inductive plasma sources for laboratory and industrial use.

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