Plasma Sources Sci. Technol. 9 (2000) 400–412. Printed in the UK PII: S0963-0252(00)13449-8

Transmission line balanced inductiveplasma sources

G K Vinogradov

KEM Inc., 907-8, Shimoimasuwa, Shirane-cho, Nakakomagun, Yamanashi 400-0212, Japan

E-mail: 100510.3707@compuserve.com

Received 18 October 1999, in final form 29 February 2000

Abstract. A new class of transmission line balanced inductive plasma sources havingdiscrete inductive zones is reviewed. The problems of undesirable capacitive currents,azimuthal non-uniformity and the energy efficiency of inductive plasma sources areconsidered and basically solved. The main principles of operation, discharge performanceand the most interesting experimental observations are discussed.

1. Introduction

The implementation of inductive plasma sources hasspread widely in the last decade as high-density plasmaetching/deposition tools. It was stimulated by the captivatingidea of ‘pure inductive plasma’. However, from theearly times of J J Thomson (1856–1940) it was knownthat inductive discharges generate substantial capacitivecurrents from an inductor (coil) to the plasma. Inevitably,capacitive currents must be sunk by a grounded electrodeor metal chamber. These currents impair the overallperformance of inductive plasma sources, producing wallsputtering, discharge non-uniformities and arcing. InductiveRF discharges start from the capacitive breakdown, whichgenerates harmful capacitive currents outside the plasmasource. Azimuthal discharge non-uniformities appear withlarge inductive plasma sources, when the lengths of theinductor winding increases up to the values comparableto the wavelength of the excitation RF frequency [1–3].Therefore, conventional inductive plasma sources have alimited applicability as high-power, large-volume plasmasources.

There have been different attempts undertaken in orderto suppress capacitive and transmission line problems byvarious particular measures; however, they have not resultedin any general solution. An opposite approach to theseunresolved issues is to not suppress the wave properties oftransmission 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, azimuthalnon-uniformity and energy efficiency have been basicallysolved. Moreover, the new plasma sources show uniquerobustness, flexibility and other valuable features, which arerather unexpected and extraordinary. This paper is dedicatedto briefly overviewing the basic principles of the new plasmagenerators, which have already been successfully taken upby industry.

2. Inductive plasma sources

Since the mechanisms of gas discharge generation are notself-evident but rather speculative, they do not provide asimple basis for comparison of plasma sources. A technicaldefinition of inductive plasma sources using tangible termswould be most convenient for our considerations. Therefore,the following definition will be used:

The inductive plasma source (IPS) is a gas dischargesource having an inductor (inductive power applicator)generating alternative magnetic fields in the dischargevolume.

This definition is broad and does not refer to anyparticular mechanism of discharge ignition or self-support.

2.1. Capacitive problems

Capacitive currents generated in an IPS are usuallyundesirable except for the initial gas breakdown. Playing atwofold role in the discharge physics, the capacitive currentsare necessary for discharge igniton, but harmful as theygenerate capacitive problems. All known IPSs, short helicalinductors, one-turn coils, helicon antennas and conventionalhelical resonators (HR), are unbalanced capacitively. Thatis, their capacitive equivalent structure is similar to theasymmetric capacitive discharges with a large-area groundedelectrode (chamber) and a small RF electrode representedby the inductor itself, as shown in figure 1. The capacitivecurrents entering the plasma from the inductor generatecapacitive sheaths in the processing chamber that is on thewafer.

Probe diagnostics of such systems frequently show lowplasma potentials in the chamber. It is usually supposed thatthe discharge operates in ‘pure inductive’ mode. However,the capacitive discharges with highly asymmetric electrodes,i.e. small RF/large ground, also show very low plasmapotential [6]. The main voltage drop or a self-biased sheath

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Transmission line balanced inductive plasma sources

Figure 1. Inductive plasma source and its capacitive equivalents.

appears at the small-area electrode that is at the high-voltageportion of the inductor. The RF voltage from the generatoris divided in proportion to the capacitive impedances ofthe inductor–plasma gap and discharge capacitive sheaths.Since the chamber capacitance is typically the largest, theRF fluctuation of the plasma potential here is minimal. Thenarrow entrance into the chamber provides the most powerfulplasma–ground sheath since it is in the closest vicinity of theactive discharge area.

The discharge power increases by increasing the inductorcurrent and, hence, voltage. Consequently, the capacitivecurrent from the inductors also increases. It is difficult tosuggest a priori to what extent the increase of capacitivecurrent is threatening for a particular process, since IPSshave different geometries. Therefore, we discuss here somewidely spread IPSs.

2.1.1. Single-turn inductor. A single-turn loop is thesimplest inductor having the RF voltage distribution shownin figure 2. A high-voltage end of the loop generatesthe highest capacitive current and, hence, the strongestplasma sheaths. Even this is not so pronounced in verylow-pressure discharges, but it does generate an azimuthalnon-uniformity and the discharge vessel suffers from wallsputtering. This non-uniformity can be visualized at elevatedpressures (�1 Torr).

The single-turn inductor has minimum inductanceamong inductive applicators, and the lowest inductivecoupling efficiency. Therefore, this kind of inductor shouldbe considered as the weakest inductive applicator with thehighest capacitive non-uniformity

2.1.2. Short helical inductor. A short helical inductor is acommon type of inductive applicator widely used for meltingmetals, welding, plasma torches and for low-pressure glowdischarges. A winding of the short inductor is substantiallyshorter than a quarter wavelength (λ/4) corresponding to the

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

excitation frequency, so it can be analysed without takingwave phenomena into consideration.

Modern low-pressure discharges for microelectronicsneed very large volumes. The winding length of inductorsis growing as it is scaled up by the increasing wafer size.The inductor winding length is increasing, but the ratio (coillength)/(diameter) is decreasing so that it is deviating far froman elongated solenoid shape. An inductive (transformer)coupling efficiency of the short inductor is proportional to thenumber of turns N in a helix. That is, the coupling efficiencyof the short helical inductor is about N times higher that thatof a single turn, so it can efficiently work on much largerinductive loads, producing higher density plasmas.

The helical coils generate high sheath voltages inthe plasma sources, but they show much better azimuthaluniformity increasing with the number of turns in the helix.The total capacitive current from a helical inductor to plasmais, certainly, higher than that of the single turn.

2.1.3. Pancake inductor. A spiral or pancake inductor haslong been known in inductive heating, welding and therapy.The attractiveness of this inductor for gas discharges canbe explained by the possibility to design plasma sourcesgeometrically similar to parallel-plate capacitive discharges,while generating high-density inductive plasma at lowgas pressures [7]. The pancake applicators are made asArchimedes spirals or a collection of concentric co-planarrings of decreasing diameter. A flat spiral generates strongermagnetic field at the axis in comparison with a single-turnloop.

The flat inductor is usually separated from the dischargevolume by a dielectric window, usually quartz, which istransparent for both magnetic and electric fields. Thiswindow must be thick in order to withstand atmosphericpressure. The larger the discharge diameter, the thicker isthe window. The capacitive currents from the coil generate astrong capacitive electric sheath at the window, especially atthe high-voltage portion of the coil which is usually locatednear the centre. This sheath is a cause of window sputtering.A flat split grounded shield is usually inserted between theinductor and window to limit the capacitive current to theplasma.

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Potential RF electric fields from helical IPSs can also beshielded [8–10]. However, this way is not free from seriousdrawbacks, 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 usefuland practical but palliative remedy in treating the capacitiveproblems of IPSs.

There are several ways of decreasing the sheath voltageat the grounded surfaces in a capacitive discharge: increaseRF frequency, decrease an area of a RF driving electrode orbalance the RF excitation in respect to ground. The balancingof symmetric RF capacitive discharges has been shown to beworthwhile for Langmuir probe measurements [11, 12]. Thefundamental excitation frequency in the balanced dischargesubstantially decreases down to a few per cent. Therefore,the symmetric capacitively balanced discharge has the sheathpower at the ground substantially decreased. The balancedRF feed is used in some industrial discharges for generatingradicals in a volume.

2.2. Transmission line problems

The problem of large (long) inductors affecting the dischargeuniformity was recognized only a few years ago [1–3]. Thecoil current is not uniform along the long winding, becauseits length becomes comparable to a wavelength of the RFpower, 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 inductiveplasma sources.

The concept of electrical transmission lines [13] isused to describe long electrical structures carrying electricalpower. The uniform transmission lines cannot only bestraight wires, but also spirals. A transmission line witha coaxial helical inner and cylindrical outer conductor isa coaxial helical transmission line [14]. About half acentury of history of these lines started with the microwavedevices called travelling wave lamps and klystrons. Manytheoretical and experimental problems have been solved inorder to implement these devices into the technology ofmicrowave radars [15–19]; therefore, many of them arereadily applicable.

Large inductor coils inevitably show the transmissionline effect: standing waves [1, 2]. One problem is thatthe standing wave has to be taken into account in orderto optimize the inductor geometry for compensating anazimuthal current distribution. Another problem, whichhas yet to be taken into consideration, is that enlargingthe inductive coil beyond λ/4 does not increase the totalmagnetic momentum of the inductor, but rather decreasesit by generating an opposite portion of the magnetic fielddue to the phase change along the line. Therefore, anyfurther enlargement brings about wave phenomena, whichdrastically change the physical nature of the inductor and,hence, its interaction with the discharge. In other words,

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 connectedto the shield (grounded), open and/or RF fed [4].

there is no simple way to built efficient inductors longer thanλ/4 just by increasing the coil length.

Figure 3 shows voltage and current distributions alongthe transmission line resonators, each having differentelectric lengths and termination. The zero-voltage ends arethe grounded ends. When the line length exceeds λ/4, thecurrent 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 isopposite magnetic momenta. This physical feature hasnever been recognized in respect to the mechanisms ofdischarge excitation in the HR plasma sources. It wascommonly assumed that all helical resonators are similardischarge devices and which differs only by size, geometryand resonating frequencies.

The resonating helical lines of different electric lengthsand termination must generate drastically different gasdischarges having previously unknown electromagneticstructures. For instance, it is possible to use the wavestructures in order to design electrically and/or magneticallybalanced resonator IPSs using correspondingly adjustedwave segments.

3. Helical transmission line plasma sources withmultiple inductive zones

We have the following definition:

Transmission line inductive plasma sources are thosehaving large self-resonating inductors, which can be definedas transmission lines.

The electromagnetic structure of helical transmissionlines was described about 50 years ago [15–19], when aconsiderable study was given to microwave electronics ofradar applications. A model, enlarged ten times, of theactual helix was constructed and the field distribution, excitedby oscillations in the frequency interval between 375 and120 MHz, was investigated by means of a miniature slidingand rotating probe [19]. The axial field at a distance r fromthe axis was found to agree quite well with an expression onthe assumption that the field is quasi-static:

f (z, r) = f (z, r0)I0(2πr/λh)

I0(2πr0/λh)sin(2πz/λh)

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

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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 wavelengthin the helical transmission line.

Figure 4 shows the experimental field pattern of the axialfield with strong longitudinal variations, when the parameter2πr0/λh = 3.3 for λ = 82 cm and λh = 6.6 cm. This fieldpattern is very far from a solenoid distribution. A resonatingpart of the helical transmission line, which has a lengthequal to any integer multiple of λ/4, should be consideredas a longitudinally non-uniform inductive applicator. Thelongitudinal periodic structure is the key to controlling theinductor–plasma coupling and the mechanisms of dischargeignition and power distribution.

3.1. Transmission line capacitive balancing of inductiveplasma sources

A resonating section of the lossless transmission line hasstanding waves of voltage and current as shown in figure 5,where positive and negative amplitudes show phase andanti-phase half-waves. Each phase voltage portion canhave an anti-phase counterpart. The total transmission linesegment is capacitively balanced or unbalanced in respectto ground, depending on the number of phase and anti-phase λ/4 portions comprising the segment. The method ofcapacitive balancing of the transmission line resonators canbe designated as lambda balancing. That is, the capacitivebalance can be adjusted by adjusting the wavelength to theelectric length of the resonator or its resonant frequency.Correspondingly, a minimum-length capacitively balancedresonator is a λ/2 open-ended segment or a half-wave dipole.A minimum-length close-end capacitively balanced section isa full-wave or λ-resonator (λ-R) [20]. The resonators havingone end open and another closed are unbalanced.

Higher order resonances satisfy the capacitive balancecondition for the dipole sections having an electrical lengthof nλ/2, where n = 1, 2, . . . . This class of resonatorshas a zero-potential central point of symmetry for the oddand maximum voltage central point for the even harmonics.These devices do not belong to the conventional helicalresonators, which have both short or one open end. Theycan be designated as a particular class of dipole-resonators.

The balanced resonators with both ends grounded, theλ-Rs, have an electric length of nλ. These resonators allhave a zero-voltage centre of symmetry and are balancedtotally, that is not only capacitively but also magnetically:

Figure 5. Voltage (full curve) and current (dotted curve) standingwave amplitude distributions in the resonating section of a longtransmission line: capacitively balanced segments correspondingto 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 conventionalshort-ended λ/2-resonators having an even number of λ/2segments.

The main role of the magnetic portions of thetransmission line inductive sources is generating the circularelectric fields in the discharge volume. It is now wellunderstood that there are multiple anti-phase inductive zonesin the helical transmission lines. The conventional half-wave HR has two separate inductive zones with oppositemagnetic momenta. This feature of helical resonators, whichis crucially important for the discharge physics, has only justbeen appreciated [4, 5].

3.2. Discrete inductive zones in transmission lineinductive plasma sources

The number of inductive zones in a transmission line sourceis equal to the number of mono-phase current segments orcurrent maxima. That is, for the quarter-wave HR (one openend) having electric length of ( 1

4 +n/2)λ, wheren = 0, 1, . . . ,

the number of inductive zones is equal to (n + 1). Only theclosed-ended inductive zone is a λ/4 zone, another n zonesare of λ/2 type.

The short-ended inductors having electric length equalto ( 1

2 + n/2)λ, where n = 0, 1, 2, . . . , have the number ofinductive zones equal to (n + 2). The two end zones of theseinductors are of λ/4 type; the inside zones are all λ/2 type.

Any change of the electrical length by a λ/4 quantumaffects the basic field structure. It changes, in turn, the

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inductor–plasma interaction because of both an inductiveand a capacitive transformation of the plasma source and,what is also important, the three-dimensional self-consistentconductive structure of the discharge plasma. The dischargetransformations change the electrical nature of the resonatorload and can show second-order phase transitions anddischarge self-organization at elevated gas pressures.

The dipole-resonators have the number of inductivezones 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) inductivezones, where two of them are always λ/2 type.

Conventional quarter and half wavelength HR sourcesare particular examples of transmission line plasma sourceswith one and two λ/4 inductive zones, respectively. Bothresonators are capacitively unbalanced. Being high-Q (quality factor) resonators, they generate very highvoltages on the coils and, hence, generate the strongestcapacitive inductor–plasma–ground currents among allhelical inductors.

Helicon inductors, usually called antennas, aresometimes very large. Commonly used antennas are half-wavelength long wires shaped in several empirical ways.Antennas longer than λ/2 have never been tried, becauseoptimization of antenna design has been carried out onlyby trial and error [21]. The λ/2 wires of helicons, beingcapacitively unbalanced, generate high-voltage capacitivesheaths and capacitive inductor–plasma–ground currents.This is, probably, the cause of high-energy electrons andions found in helicon discharges but not the cause of ‘wavesurfing’. The possibility of the balanced transformer RFfeed for a helicon discharge has been mentioned [22].This reduces the maximum antenna–plasma voltage by afactor of two, thus also reducing the undesired capacitivecurrent coupled to plasma by a factor of two [22]. Thetransmission line properties of large helicon antennas arenot well understood. They can be dramatically improvedby utilizing the described principles of transmission linebalance.

3.3. Two basic capacitively balanced transmission lineplasma sources

From a practical point of view, inductive plasma sourcesshould not have too large coils. That is, the most promisingrealizations are the shortest capacitively balanced inductors,which are the half-wave open-ended Dipole-resonator andthe short-ended full-wave λ-R plasma sources. The full-wavedipole-resonator has about the same size inductor as the λ-R, however, the grounded ends of the λ-R are convenient inpractice.

3.3.1. λ-R inductive plasma source. The λ-R plasmasource is schematically shown in figure 6 [5]. Figure 7shows the equivalent schemas of the λ-R discharge [24]. Theinductor is represented as four similar λ/4 coils connectedin series fed from two equivalent push–pull RF generators.Three inductive excitation zones are located at the currentmaxima. Two central λ/4 coils are in-phase, thus comprising

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

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

a λ/2 coil keeping the same direction of the distributedelectric current. This coil thus produces twice as large aninduction field in comparison with the side quarter-wavecoils.

Two side λ/4 coils are both anti-phase in respect to thecentral λ/2 portion. The magnetic fields generated by thecentral coil and every side coil are repulsive. They produceinductive electric fields and circular discharge currents inopposite directions. Consequently, the inductive plasmatoroids produced by these currents can never collapse intoone. That is, the plasma toroids are strictly localized intheir corresponding inductive zones, and their positions donot depend on the discharge parameters but are determinedsolely by the standing wave structure.

The capacitive structure is more or less self-explanatory.Part of the push–pull balance electric field is shunted outsidethe discharge tube due to the high serial inter-turn capacitanceCs . Capacitive currents from the inductor flow to thedischarge through a wide (about 40 mm) inductor–wall airgap denoted as Ci−w. The plasma–wall sheath is beyond

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

the dotted line indicating the tube wall. The sheath is thinand, hence, of low impedance because of high-density plasmagenerated in the inductive zones. The bulk plasma stronglyshunts the push–pull capacitive currents thus decreasing RFplasma potential fluctuations in the discharge centre up to afew volts [23–25] at 2 kW discharge power.

The bulk plasma does not spread beyond the excitationcoil under the elevated pressure of about �1 Torr. Atlow pressures, the plasma diffuse downstream the plasma.However, even under these conditions the parasitic capacitivesheath near the ground surface is invisible up to a fewkilowatts of the discharge power.

It would be useful to compare the λ-R source, comprisingof four equal λ/4 coils, versus the conventional quarter-waveHR source under the same discharge conditions and similarload configurations. Suppose the two plasma sources infigure 8 have similar coil geometry.

Let us consider a cylindrical discharge load as a one-turnclosed resistive loop. In the λ-R source, this load is heatedby circulating currents generated by the four λ/4 coils. Weassume these coils produce equal additive inductive powersin the discharge, which is consistent with our experimentalobservations. The quarter-wave HR, in its turn, must generatethe same total power from a single λ/4 coil. Both voltage andcurrent on that coil must be doubled in order to transmit thatpower. In other words, the high voltage on the λ-R sourcecoil must be at least twice as low provided the same inductivepower is generated in the discharge.

The capacitive currents of the λ-R source balancesreactively within the source volume and are also partlyabsorbed in the discharge. This portion of the total dischargepower does not go outside the plasma source. In contrast,the capacitive current of the quarter-wave HR source flowsfrom the bulk plasma into the ground capacitive sheath,thus delivering an essential portion of the capacitive poweroutside the source, that is on the chamber wall and processingwafers. These are well known capacitive problems: wallsputtering contamination and wafer damage. Very highground capacitive currents flow from a half-wave HR plasmasource even its RF voltage is lower than that of a quarter-wave HR source. The most severe sputtering occurs on thecircumferential metal surface of the bottom flange of theplasma source.

In summary, the λ-R not only keeps the capacitivecurrents, and hence their power, inside the plasma source,but also generates much lower capacitive current density inthe discharge wall sheaths in comparison with conventionalquarter- and half-wave HR discharges. These features

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

partially explain why the transmission line capacitivelybalanced plasma sources demonstrate incredibly high processperformance and stability.

3.3.2. γ-dipole plasma source. A γ -dipole IPS is aresonating half-wavelength open-ended coil with a centralunbalanced RF feeder. This structure can be thought ofas created from a well known half-wave dipole vibratorconverted into a helix. The central feed from an unbalanced,i.e. coaxial, cable is known as a gamma-match. This meansthat both RF and ground ends of the coaxial cable areconnected at about the centre of the dipole. This is the originof the term γ -dipole plasma source.

The equivalent scheme of the γ -dipole discharge canbe shown as just a central half-wave segment of theλ-R equivalent schema, as shown in figure 9 denotingcorresponding capacitors as capacitive impedances: Zs ,inductor serial; Zi−w, inductor–wall; Zsh, sheath. The maindifference from the λ-R discharge is that the bulk plasmahas only the central inductive zone. All the discharge power,inductive and capacitive, is concentrated in a single compactarea generating two to five times denser plasmas than theλ-R discharge, which has a much longer discharge volume.Certainly, the push–pull capacitive currents are essentiallyshorter in the centre plasma and balanced. It is theorizedthat the high-conductivity inductive plasma toroid providesan electrostatic self-shielding. Any capacitive problemsin the aluminium downstream chamber could not be evenintentionally generated in the range of RF power up to5000 W, with gas pressure between 1 and 50 000 mTorr, for Aror O2 discharges: no arcs, no sparks and no visible capacitivesheath.

Taking into account about 100% energy efficiency ofthis source as a resonator (measured unloaded Q ≈ 3200at 27 MHz), we conclude that it can be classified as a superinductive plasma source. Indeed, there are no more inductiveplasma sources which could theoretically or practicallyprovide a higher or even close power efficiency in generatinga bulk plasma.

3.3.3. RF matching. Helical transmission line plasmasources, including conventional HR, can be directly matchedto a 50 � coaxial cable [26–29]. Since the resonator itselfdoes not consume any RF power, the plasma is the only active

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load. Therefore, an energy efficiency of these IPS is virtually100% from a cable. The λ-R plasma sources used in thecommercial ‘λ-Strip’ equipment manufactured by KEM Inc(formerly RAMCO, MC Electronics) typically is set up forabout 5–10 W reflected power from a 50 � coaxial cable fedby the maximum power (generator limitation) of 2, 2.7 or5 kW at 27 MHz.

The author is aware of some unfortunate attempts tobuild and evaluate the λ-R plasma sources using conventionalfixed frequency RF generators and matching boxes. It isworth mentioning here that the resonator sources are notsimilar to conventional inductive sources in respect to thematching with fixed frequency generators. If the λ-R itselfdoes not match exactly the excitation frequency under theplasma loaded conditions, that is it cannot be fed directlyfrom a coaxial cable, it will never operate in a λ-R dischargemode with any matching devices. The external matchingelements do not change the electrical length and, hence, theresonating frequency of the line; they can only compensatean input impedance mis-match to some extent at the point ofconnection (tap position). An apparent matching observed inthis case is just an indication that the matching box and theplasma source together comprises a resonating system. It canbe very far from the resonator’s eigenfrequency. Therefore,the resonators having a resonance frequency different fromthat of the RF generator cannot be matched in principle.Conventional inductive sources can use an external matchingnetwork because their inductors themselves do not resonateat the excitation frequency. They are only a part of the wholeresonating system, which includes an external matching box.

In a practical situation the RF frequency usually variesin a range of about 1–2% in order to match a resonator IPS.That is, the wavelength matches the coil length. The exacttap position cannot be calculated because of the effect ofthe discharge conditions. It is typically located at abouta 0.1–0.3 turn distance from the ground point of the coilin our experiments. This distance can be easily found byexperimenting. It is shorter in the case of highly conductiveplasmas (Ar, N2), and longer for highly resistive media likeelectronegative molecular plasmas (O2, CF4).

3.3.4. Ionization and dissociation efficiency. There aremany opinions concerning the ionization and dissociationefficiency of different plasmas: capacitive, inductive,microwave, dc, etc. The fundamental problem of thesimilarity of different plasmas and the overall efficiency ofthe plasma sources are two problems of differing natures.In other words, the specific plasma efficiency, which isa fundamental concept, and the total discharge efficiency,which is a technical concept, do not correspond to eachother. Many research works have been aimed at proving that‘inductive plasmas’ show superior efficiency in comparisonwith ‘capacitive’ or ‘microwave plasmas’ in respect to ‘RFor dc plasma’. Some workers have tried to prove superiorionization in a particular plasma source and others superiordissociation for a similar source depending on the applicationpurpose. However, there are very few scientifically approvedmethodologies and little experimental evidence [30, 31].

We assume a simple but rather solid basis to comparedifferent discharges: the total absorbed power in the bulk

plasma. It is well known that the electron density in abulk uniform plasma is roughly proportional to the specificabsorbed power. Both ionization and dissociation rates areabout proportional to the electron density provided the EEDFis unchanging. Two plasma sources being fed from similarRF generators can be reasonably compared by the portion ofthe total power absorbed in the bulk plasma without regardfor the mechanisms of plasma generation.

The total losses of the RF power occur mainly inthree places: (1) a matching box, about 10–50% [32];(2) capacitive losses outside the plasma source, that is in theprocess chamber (considered as losses because undesirable),about 10–30%; (3) capacitive sheaths inside the plasmasource, about 10–20% (for ion acceleration, i.e. for surfacebombardment). The third channel is not a completely lostenergy, because some part goes for the electron heating by thesheaths. These estimations are to be considered as qualitativeranges only, but are useful for overall comparisons of differentplasma sources.

The transmission line sources operate without amatching box and do not produce capacitive plasmas outsidethe source. Taking essentially lower voltages on thecapacitive sheaths inside the source into consideration, onecan obtain a correct idea about the energy efficiency. By andlarge, a balanced transmission line plasma source achievesa higher or much higher energy efficiency in comparisonwith any other RF inductive source [24]. Consequently, suchplasma sources should demonstrate noticeably higher processrates in comparison with other inductive sources with thesame RF power consumed from a RF generator. On the otherhand, the same performance can be achieved with smaller RFgenerators.

4. Some experimental observations

The experimental set-up and some results on the probe andoptical emission diagnostics and visual observations havebeen described in details elsewhere [4, 23–26]. Figure 6shows the main configuration of the λ-R plasma source,which was also used for generating half-wave HR, three-half-wave HR and 2λ-R modes. The γ -dipole source wasused with a 235 mm diameter, 300 mm long quartz tube,as shown in figure 10. It was fed from a coaxial cable atabout the centre point of the coil. The ground was connecteda few centimetres away from the fed point (more detailswill be shown in figure 14). The same coil with one endground and another open was also used for quarter-waveHR experiments. It should be mentioned, however, that theresonance frequencies of helical resonators, which are shortsegments of ideal long transmission lines, do not correspondwell to the integer multiples of the fundamental frequency.This has been explained by the deviation of the magnetic fieldconfiguration from the ideal infinite line. Two transmissionlines were used in order to compare six plasma sources, eachof which can also generate particular discharge modes. Sometests were performed on the industrial 200 and 300 mm waferashers.

The 0.005–2.25 kW RF power at 10–80 MHz frequencywas supplied to the resonators by using a 50 � coaxialcable directly from a wide-band tube amplifier IFI-410 with

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

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

a sign wave signal generator HP-8648A. Commercial RFgenerators of 4.5 or 5 kW RF power (Kyosan and Adtec), at27 MHz, were used in some experiments. RF signals from thedischarges were monitored by a digital 2 GS/s oscilloscopeTEK360P

4.1. Capacitively balanced plasma sources

4.1.1. λ-resonator. Visual observations of thetransmission line discharges impress by direct visualizationsof their electromagnetic structure. Both capacitive andinductive current channels are well seen in large dischargevolumes.

Figure 11 shows the experimentally measured resonanceaxial RF magnetic field under the plasma-unloaded conditionin the standard 235 mm discharge tube of the λ-R source[33]. It is seen that the magnetic field is essentially strongernear the wall. There are three distinct inductive zones:two λ/4 and one central λ/2. One can see an additionalweak zone in the bottom aluminium flange. This field isgenerated by a return current induced by the bottom partof the inductor in the nearest conductive flange. The fieldstructure corresponds to the theoretical models. The RFfields are substantially shielded inside the conductive bulkplasma, when a gas discharge is ignited. The axial magneticfields generate corresponding circular electric fields of thelocalized inductive discharges. The location of the inductivezones is therefore strictly fixed and does not depend on thedischarge parameters. Magnetic field zeros correspond to thehigh-voltage maxima on the helix.

Interestingly, the configuration of the RF electric fieldsin the λ-R is similar to the picture indicating helicon waves[21]. Indeed, looking at figure 12, showing azimuthal andradial 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. Thevertical localized capacitive currents, similar to thoseobserved in the λ-R discharge [4, 5], can be easily generatedin argon gas under a pressure of 10–50 Torr. A very distinctlongitudinal split of the luminous channel of the inductiveplasma toroid can be observed with the power increase.A further increase makes the plasma toroid flatten to a50–60 mm wide belt shape. It is also possible to generate astable floating and swinging plasma toroid, whose diameteris noticeably, about 30%, smaller than the discharge tube.We have never observed such wonderful creations in otherdischarges. This observation is, probably, explained by awider profile of the magnetic field lines generated by thedipole coil in comparison with the inside λ/2 segment oflonger inductors compressed by the opposite magnetic fieldsof the adjacent coil segments.

In the lambda coil, for example, the central magneticfield is removed to a great extent from the axis to the wall.Therefore, the central plasma toroid in the λ-R coil cannotdecrease its perimeter without loosing a large portion of themagnetic flux necessary to support the inductive currents.In the γ -dipole plasma source, the toroid can shrink itsdiameter because the lost portion of magnetic flux is almostcompensated by the lost length of the current channel.

4.2. Capacitively unbalanced plasma sources

The unbalanced quarter-, half-, and three-half-wave HRplasma sources were tested under a wide range of conditions.They generate well the visible capacitive discharges ontothe ground surface. Such visualization under the elevatedpressure shows the discharge currents and the spatialdistribution of the RF power. It is clearly seen that thecapacitive power comprises an essential portion of the totaldischarge power.

The quarter- and half-wave HR discharges generate oneand two inductive toroids, respectively. They are located atthe coil ends in correspondence with the RF current standingwave pattern.

In the pressures range of about 0.6–0.8 Torr thecapacitive currents and the chaotic arcing in the downstreammetal chamber are typical. The aluminium flange supportingthe resonator suffers from sputtering. This flange probablysinks the main portion of the capacitive current from thesource which is very close to the highly conductive area.The arcs at 2–3 kW RF power are so strong that they producealuminium oxide particles from the locally melted spots onthe aluminium surface.

The three-half-wave HR discharge is interesting forphenomenal inductive–capacitive interactions. Verticalsaddle-type inductive plasma toroids, shown in figure 13,can be observed in the three-half-wave HR discharge mucheasier than in the λ-R discharge. The mechanism of theseamazing discharge creations is explained as follows. Adense magnetic flux between the neighbour coil segmentswith opposite currents crosses the helix and discharge wall.Consequently, part of this flux can be captured by a closedconductive path like a plasma toroid located on the wall.

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Figure 12. Standing wave field patterns in the λ-R 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 fourinductive toroids: two full-wave and two quarter-wave. It isworth mentioning that this discharge has smaller capacitiveproblems than the conventional λ/2 or λ/4 HR discharges.The three-half-wave HR is only partially unbalanced forabout 30%, because it has totally balanced λ-segment.

4.3. Capacitive currents from inductive resonatorplasma sources

It was found that the plasma potential fluctuations of the λ-Rdischarge are rich with very high-frequency harmonics ofthe excitation frequency [23]. The λ-R discharge does notusually generate the second harmonic the strongest, as in thecase of a balanced capacitive discharge, but rather the third,or sometimes, even the fifth. This phenomenon could beexpected from the analysis of the electric equivalent schemeof the transmission line discharges that have more than tworectifying capacitive sheaths which are not symmetric withrespect to the ground.

We have measured the RF fluctuations of theplasma potential, using the dc insulated capacitive probe[25], and capacitive plasma–ground currents [33] forseveral transmission line discharges of similar geometricalconfigurations and discharge parameters in order to assuresimilar conditions. The RF potential of an electrically

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

floating wafer separated by a capacitive gap from the groundplaten was also examined. Some preliminary results will beshown below.

The experimental set-up for capacitive current measure-ments is shown in figure 14. The current was monitoredusing a current monitor PearsonTM model 5895 operable ina frequency range up to 70 MHz within about ±10% unifor-mity. The transmission characteristics of this monitor werecalibrated using a network analyser HP-8712C up to about250 MHz, in order to estimate a very high frequency range.The transformer shows up to a ten-decibel increase in trans-mission at higher frequencies following a deep valley at about70–90 MHz.

4.3.1. RF capacitive inductor–ground current. Fig-ures 15 and 16 show, as a function of absorbed power, the totalrms capacitive current inductor–ground through the bottomof the plasma source for three discharges: half-wave HR, λ-Rand γ -dipole. This capacitive current represents the majorpart of the total capacitive current. The power deposited inthe process chamber by the capacitive currents is about twoorders of magnitude smaller in the balanced plasma source incomparison with the unbalanced source. Figure 16 shows aqualitatively similar picture for a lower pressure discharge inargon. The capacitive current in the λ-R discharge does notgrow with the power increase. These experiments supportprevious suggestions about the nature of capacitive compen-sation in transmission line discharges.

Returning to figures 15 and 16, we should recall that thecomparisons 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 thevoltage drop on the capacitive sheaths should be higher atthe lower frequency, this increases the ratio of the power

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

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

deposited on the capacitive sheaths in different plasmasources.

4.3.2. Harmonic composition of capacitive currents.The ground capacitive currents of some inductive plasmasources were measured [34]. The harmonic compositionof the RF fluctuations of the plasma potential has notbeen studied in capacitive discharges [12], although it wasanalysed in the feed RF power of inductive sources [35].The harmonic composition demonstrates a very complicatednature, which has yet to be explored. This is likely, sincethere were no ground electrodes inserted in the symmetriccapacitive discharges [11, 12] as our large grounded chamberbringing about longitudinal asimmetry.

Figures 17 and 18 show typical RF signals for λ-Rand γ -dipole discharges picked-up by an oscilloscope. Thefundamental harmonic always dominates in unbalanceddischarges. The balanced λ-R and γ -dipole dischargesdemonstrate FFT spectra, where the third or sometimes eventhe fifth, but not the second, harmonic is the highest. Thisis not expected to be from an analogy with the symmetriccapacitive discharge.

These resonator discharges can even redistribute thecapacitive power into the tenth (!) frequency harmonic asshown in figure 18. Remarkably, in this particular case thehighest tenth harmonic is very clear in the inductor itself.

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

Figure 18. Very high frequency harmonics appear not only in theplasma 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 is25 ns.

This probably means that this high harmonic coincides withone of the high resonating modes. Therefore, it is amplifiedin the resonator itself.

The high-frequency harmonics of the capacitive currentor plasma potential fluctuations do not coincide withthe eigenfrequencies of the inductors. The dischargecapacitive harmonics are just integer multiples of thefundamental frequency, which are generated solely, to afirst approximation, by the rectifying capacitive sheaths.The resonating modes of the inductors depend not only onthe mode number (that integer multiple) but on the spatialconfiguration of the electromagnetic fields of any particularmode. The shorter the inductor, the stronger is the deviationof the eigenfrequencies from that determined by the integermultiple. This is the reason why the resonating modes do notcoincide with the strictly fixed discharge harmonics generatedon the equivalent plasma sheath diodes.

In the case of frequency coincidence between a highfundamental integer multiple and a high self-resonatingmode, the resonator redistributes power into this mode.

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Wave phenomena of this sort have not yet been observed.The redistribution of power is especially noticeable in verylow gas pressure discharges at �1 mTorr, not only in thebalanced but also in the unbalanced resonators. However, wenever observed this phenomenon at about 1 Torr and higherpressures because of a high resistivity of the bulk plasmadamping high-order resonances. This study is currently inprogress.

4.4. Practical realizations of γ-dipole and λ-R plasmasources

Several capacitively balanced plasma sources were built andtested in the course of research and development. Plasmasources for 200 and 300 mm wafer processing were examinedin a wide range of discharge conditions. The smallest sourcehas a 180 mm diameter discharge tube, the largest one a330 mm diameter. Table 1 is composed in order to comparethe two basic balanced plasma sources.

The discharge power was limited to 5 kW by the available27 MHz generator. We have tested the smallest plasma sourcefor the 5 kW power absorbed in the discharge (reflectionbelow 5–10 W). This gives a scaling idea for the maximumpower of larger sources. Plasma diagnostics have beencarried out on the 235 mm λ-R plasma source [23, 25]. Othersources were not tested systematically. All the sources wereexamined in real scale (200 and 300 mm wafers) industrialequipment. This also gave a reliable basis for comparisonand justified our estimations by the processing results.

The very low level of the discharge power equal to about5–20 W given in the input power range is real and wellmeasured with a systematic error of �20%. The balancedresonators allow one to sustain a very low power stablebulk capacitive discharge in the regime of a high impedancecurrent generator. From another side, the highest pressureof the range is realized in inductive or multiple contractedcapacitive discharges depending on the gas.

A variety of industrial applications, high radical and/orhigh ion flux, can employ transmission line balanceddischarges. It is not difficult with these sources to achievecontrollable convex, flat or concave ion or radical densityprofiles. At present, these plasma sources are used in super-fast damage-free automatic photoresist ashers/etchers. As anexample, the photoresist ashing rate in a 100% O2 dischargeon the 300 mm wafer is up to 10 µm min−1 at 250 ◦Cwithin about ±3% typical uniformity using the λ-R plasmasource, so that the total throughput is limited solely by thewafer transfer system. The γ -dipole source overcomes thisperformance 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.

5. Schematic comparison of inductive plasmasources

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

to compare them and select the most suitable one forparticular needs, because there is no basis for comparisonbut rather explanations of experimental or process dataand plasma heating mechanisms. Some authors usethe arguments concerning fundamental plasma parameters,directly applying them to the discharges, which apparentlyare much more complicated objects then the idealizeduniform plasmas. Similarly, some fundamental resultsderived from the simplest ideal situations or particularnoble gas discharges, for example the EEDF, are directlyapplied to interpret complicated chemistries with even morecomplicated heterogeneous processes. Therefore, onlyan overall discharge performance of different inductiveplasma sources is considered here, mainly from a practicalengineering point of view. They are considered as electricmeans for delivering the input power from a RF generatorinto the bulk plasma. This comparison is based on theexperimental facts and objective considerations as well asthe author’s personal experience.

Table 2 shows a schematic comparison and the total rankof several real and hypothetical inductive plasma sourcesapplied to a reference 235 mm diameter cylinder dischargetube 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 beentested on the same discharge tube and chamber providingdirect evidence for a comparison.

The capacitive damage relates to the semiconductorprocessing and is usually estimated using antenna structureswith MOS capacitors well known in microelectronics. Theignition function is estimated as the minimum RF powernecessary to initiate the gas discharge at a 100 mTorr pressurein argon. The power window means the whole range of astable discharge; it certainly does not overlap with the wholepressure range. The same is true for the pressure window,it does not cover the whole power range. The azimuthaluniformity is estimated experimentally by electrostaticprobes and by a qualitative comparison of integral distributedcircular inductive currents and azimuthally distributed highvoltage in the inductors.

The size limit just means a qualitative estimation of thepossibility to enlarge the current plasma source (from thereference 235 mm) or scale it down. This is the most uncertainparameter and it is not included in the total rank. The specificpower is qualitatively estimated from the total power lossesoutside the plasma source for matching, and inside mainly forthe capacitive sheaths. The discharges were compared on aone-by-one basis inside one parameter column. The relativeerror of the total rank should be considered within about twopoints. The total rank here does not mean that the last twotransmission line balanced plasma sources are the best optionfor any particular application. It does mean that the sum ofall marks for these sources is at a maximum.

6. Conclusion

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

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

γ -dipole λ-Resonator

Inductive structure One toroid Three separate toroidsPlasma diameter (mm)a 180 235 200 235 280 330Coil height (mm) 70 65 230 230 260 250Coil diameter (mm) 240 330 260 330 340 400Pressure range (mTorr)b 1–50 000Excitation frequency (MHz) 27Input power, experimental (kW)c 0.005–4.5Max. power, estimated (kW) 10 20Discharge volume (l)d 2 3 7 10 16 21Max. specific power (W cm−3) 2.5 1.6 0.6 0.5 0.3 0.2Electron density (1 × 1011 cm−3) 30 20 5 4 3 2Plasma potential (V) 17–25Applications STRIP,ETCH High ion density

STRIP, CVD High radical density

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

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

Capacitive BulkInductors problems, Power Pressure Azimuthal Size limit energy Specific Total(coil, antenna) damage Ignition window window uniformity down/upa efficiencyb power rankc

Single turn x oo oo o x ooo/o x oo 7/3Pancake coil x oo ooo o o o/oo oo oo 11/1E-shielded oo x oo oo oo o/oo o ooo 12/1Helical short coil x oo ooo oo oo ooooo/oo ooo ooo 15/1Helical resonator x oooo ooo ooo ooo ooo/oo ooo ooo 19/1E-shielded HR oooo x ooo oooo ooooo oo/o oooo oooo 24/1Helicon x ooo ooo x oo oo/oo ooo ooo 14/2λ-Resonator oooo oooo ooooo oooo ooooo oo/ooo ooooo ooo 30/0γ -dipole oooo oooo ooooo ooooo ooooo oooo/ooooo ooooo ooooo 34/0

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

with controllable characteristics for dry processing. Theconcepts of transmission line balance and discrete inductivezones opens an interesting prospect for new inductive plasmasources for laboratory and industrial use.

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