plasma sources iii principles of p course notes: prof....

Plasma Sources III 47

Fig. 1. Mechanism of electron cyclo-tron heating

Fig. 2. Various microwave modepatterns and ways to couple to them.

Fig. 3. The shaded region is the reso-nance zone (L & L, p. 429).

PRINCIPLES OF PLASMA PROCESSINGCourse Notes: Prof. F.F. Chen

PART A5: PLASMA SOURCES III

VI. ECR SOURCES (L & L, Chap. 13, p. 412)

ECR discharges require a magnetic field such thatthe electrons cyclotron frequency is in resonance withthe applied microwave frequency, usually 2.45 GHz.Both the large magnetic field of 875G and the micro-wave waveguide plumbing make these reactors morecomplicated and expensive than RIE reactors. Unlessone uses tricky methods that depend on nonuniformmagnetic fields and densities, microwaves cannot pene-trate into a plasma if ωp > ω. Ατ 2.45 GHz, that meansthat the maximum density that can be produced, in prin-ciple, is 100 × (2.45/9)2 = 7.4 × 1010 cm-3 [Eq. (A1-9)].However, this does not hold in the near-field of thelaunching device, usually a horn antenna or a loop or slotcoupler. Densities of order 1012 cm-3 have been pro-duced in ECR reactors because the free-space wave-length of 2.45-GHz radiation is 12.2 cm, and the interiorof a 10 cm diam plasma is still within the near-field.This is discussed in more detail later. In cyclotron heating, electrons gyrate around the B-field at ωc; and if the microwave field also rotates at thisfrequency, an electron will be pushed forward continu-ously, gaining energy rapidly. Those electrons movingin the wrong direction will be decelerated by the field,but will eventually be turned around and be acceleratedin phase with the field. Though resonant electrons gainenergy only in their cyclotron motion perpendicular to B,they collide rapidly with other electrons and, first, be-come isotropic in their velocity distribution and, second,transfer their energy to heat the entire electron popula-tion. Since a thermal electron can lose only its smallthermal energy while an electron in the right phase cangain 100s of eV of energy while it is in resonance, thereis a net gain of energy by the distribution as a whole. Atvery low pressures, electrons can gain 1000s of eV andbecome dangerous, generating harmful X-rays when theystrike the wall. Fortunately, there are two mitigatingfactors besides collisions: electrons do not stay in theresonance zone very long because of their thermal ve-locities, and microwave sources tend to be incoherent,putting out short bursts of radiation with changing phaseinstead of one continuous wave. Actual ECR reactors in production have nonuniform

Part A548

Fig. 4. In this case, a second coil canproduce more resonance zones.

Fig. 5. This experimental device hasan annular resonance zone.

(a)

Fig. 6. Dispersion curves for (a) theO-wave, (b) the L and R waves, and

(c) the X-wave.

magnetic fields, so that B cannot be 875G everywhere.In a diverging magnetic field, there are resonance zones,usually shaped like a shallow dish, in which the field isat the resonance value. Electrons are heated when theypass through this zone, and the time spent there deter-mines the amount of heating. Note that the microwavefield does not have to be circularly polarized. A plane-polarized wave can be decomposed into the sum of aright- and a left-hand polarized wave. An electron seesthe left-polarized component as a field at 2ωc and is notheated by it; the right-hand component does the heating. A microwave signal at exactly ωc will not travel, orpropagate, through the plasma. This is because electro-magnetic (e.m.) waves are affected by the charges andcurrents in the plasma and therefore behave differentlythan in vacuum or in a solid dielectric. The relation be-tween the frequency of a wave and its wavelength λ iscall its dispersion relation. For an e.m. wave such aslight, microwave, or laser beam, the dispersion relation is

2 2 2 2pc k ω ω= −

or 22 2 2

2 2 201 pc c k

vφ

ωεε ω ω

= = = − , (1)

where k ≡ 2π / λ. In Part A1 we have already encoun-tered the dispersion relations for two electrostatic waves:the plasma oscillation (ω = ωp, which does not depend onk) and the ion acoustic wave (ω = kcs, which is linear ink). The dispersion curve for Eq. (1) is shown in Fig. 6(a)[from Chen, p. 128]. We see that if ω < ωp (the shadedregion), the wave cannot propagate. Its amplitude fallsexponentially away from the exciter and is confined to askin depth. It is evanescent. We will need this conceptlater for RF sources. This behavior is specified by Eq.(1), since k2 becomes negative for ω < ωp. Note that forω > ωp the waves travel faster than light! This is OK,since the group velocity will be less than c, and thatswhat counts.

The dispersion curve becomes more complicatedwhen there is a dc magnetic field B0. For waves travel-ing along B0, the dispersion relation is

22 2

2 211

1

p

c

c k ωωω ωω

= −∓

. (2)

Here we have two cases: the upper sign is for right-hand


(b)

(c)

Fig. 7. A slotted-waveguide ECRsource.

circularly polarized (R) waves, and the bottom one forleft (L) polarization. These are shown in (b). Of interestis the R-wave, which can resonate with the electrons (thesolid line). At ωc, the curve crosses the axis; the phasevelocity is zero. As the wave comes in from the low-density edge of the plasma, it sees an increasing n, andthe point marked by ωR shifts to the right. For conven-ience consider the diagram to be fixed and the wave tocome in from the right, which is equivalent. After thewave passes ωR, it goes into a forbidden zone where k2 isnegative. The resonance zone is inaccessible from theoutside. The problem is still there if the wave propagatesacross B0 into the plasma. This is now called an ex-traordinary wave, or X-wave, whose diagram is shown in(c). Here, also, the wave encounters a forbidden zonebefore it can reach cyclotron resonance.

Fortunately, there are tricks to avoid the problemof inaccessibility: shaping the magnetic field, makingmagnetic beaches, and so on. ECR reactors can oper-ate in the near-field; that is, within the skin depth, so thatthe field can penetrate far enough. Though ECR sourcesare not in the majority, they are used for special applica-tions, such as oxide etching. There are many other in-dustrial applications, however. For instance, there areECR sources made for diamond deposition which leakmicrowaves through slots in waveguides and create mul-tiple resonance zones with permanent magnet arrays, asshown in Fig. 7. By choosing magnets of differentstrengths, the resonance zone can be moved up or down.These linear ECR sources can be arrayed to cover a largearea; as in Fig. 7 and 8. There are also microwave sources which use sur-face excitation instead of cyclotron resonance. For in-stance, the so-called surfatron sources shown in Fig. 9has an annular cavity with a plunger than can be movedto tune the cavity to resonance. The microwaves are thenleaked into the cylindrical plasma column to ionize it.The plasma is then directed axially onto a substrate.

VII. INDUCTIVELY COUPLED PLASMAS (ICPs)

1. Overview of ICPsInductively Coupled Plasmas are so called be-

cause the RF electric field is induced in the plasma by anexternal antenna. ICPs have two main advantages: 1) no

Part A550

Fig. 8. A large-area ECR source

Fig. 9. A surfatron ECR source

0z (cm )

17

(a)Fig. 11. A commercial ICP mountedon top of an experimental chamber

(Plasma-Therm)

internal electrodes are needed as in capacitively coupledsystems, and 2) no dc magnetic field is required as inECR reactors. These benefits make ICPs probably themost common of plasma tools. These devices come inmany different configurations, categorized in Fig. 10.

Symmetric ICP

TCP

Helical Resonator DPS

Fig. 10. Different types of ICPs.

In the simplest form, the antenna consists of one or sev-eral turns of water-cooled tubing wrapped around a ce-ramic cylinder, which forms the sidewall of the plasmachamber. Fig. 2 shows two commercial reactor of thistype. The spiral coil acts like an electromagnet, creatingan RF magnetic field inside the chamber. This field, inturn generates an RF electric field by Faradays Law:

∇ × = − ≡E B Bd dt/ " , (3)

B-dot being a term we will use to refer to the RF mag-netic field. This field is perpendicular to the antenna cur-rent, but the E-field is more or less parallel to the antennacurrent and opposite to it. Thus, with a slinky-shapedantenna, the E-field in the plasma would be in the azi-muthal direction.

Rather than apply the RF current at one end of theantenna and take it out at the other, one can design ahelical resonator, which is a coil with an electricallength that resonates with the drive frequency. The an-tenna then is a tank circuit, and applying the RF at onepoint will make the current oscillate back and forth fromone end of the antenna to the other at its natural fre-quency. Such a resonant ICP is shown in Fig. 13.


Fig. 12. A similar ICP by Prototech.

Fig. 13. Diagram and photo of a heli-cal resonator (Prototech).

Fig. 14. Diagram of a TCP and a simulation by M. Kushner(U. Illinois, Urbana).

Another configuration called the TCP (TransformerCoupled Plasma) uses a top-mounted antenna in theshape of a flat coil, like the heating element on an elec-tric stove. This design is meant to put RF energy into thecenter of the plasma, near the axis. Fig. 14 shows a dia-gram of a Lam Research TCP together with a computersimulation of its plasma. This will be discussed furtherlater. If one combines an azimuthal winding with a spiralwinding, the result is a dome-shaped antenna, which isused by Applied Materials in their DPS (DetachedPlasma Source) reactors (Figs. 15, 16). These sourcesare farther removed from the wafers, allowing the plasmato diffuse and become more uniform. In addition to inductive coupling, there can also becapacitive coupling, since a voltage must be applied atleast to one end of the antenna to drive the RF currentthrough it. Since this voltage is not uniformly distrib-uted, as it is in a plane-parallel capacitive discharge, itcan cause an asymmetry in the plasma density. On theother hand, this voltage can help to break down theplasma, creating enough density for inductive couplingto take hold.

Part A552

(a)

(b)

Fig. 15. A DPS ICP reactor (AppliedMaterials).

Fig. 17. Diagram of a Faraday shield

Fig. 16. Parts of a DPS reactor (Applied Materials).

Some machines shield out the capacitive couplingby inserting a Faraday shield between the antenna andthe chamber. Such a shield is simply a thin sheet ofmetal which can be grounded. However, slits must becut in the shield to allow the inductive field to penetrateit. These slits are perpendicular to the direction of thecurrent flow in the antenna; then induced currents in theshield that would otherwise create a B-dot field opposingthat of the antenna would be unable to flow withoutjumping across a gap. Such a shield is particularly im-portant in helical resonators, since the standing wave inthe antenna can cause very large voltages to develop. AFaraday shield can be seen in Fig. 13, and a diagram of itis shown in Fig. 17. Another essential feature is theelectrostatic chuck, or ESC, which can be seen in Fig.15. This uses electric charges to hold the wafer flat andwill be discussed later. Antennas do not present much resistance to thepower supply, but when the plasma is created, the RFenergy is absorbed, and this appears as a resistance to thepower supply. Currents in the plasma induce a back-emfinto the antenna circuit, making the power supply workharder, and this extra work appears as plasma heat. Thepart of the back-emf that is in phase with the antennacurrent appears as an added antenna resistance, and thepart that is 90° out of phase appears as added or reducedinductance. Normally, the plasma density is low enoughthat the currents in the plasma are too small to affect theinductance much. Since most power supplies must bematched to a 50-Ω load, a matchbox or tuning circuit isneeded to transform the impedance of the antenna to50Ω, even under changing plasma loads. This will be


x

x

x

x

x

Jo

J

B

skin wallantenna

Fig. 18. Illustrating the currents in theantenna and in the skin layer.

discussed quantitatively later.

2. Normal skin depthJust as a plasma can distribute its charges so as

to shield out an applied voltage, it can also generate cur-rents to shield out an applied magnetic field. In Eq. (1)we saw that electromagnetic waves cannot propagatethrough a plasma if ω < ωp. More precisely, let the e.m.wave vary as cos[i(kx − ωt)] = Reexp[i(kx − ωt)]. (Wenormally use exponential notation, in which the Re isunderstood and is omitted.) If k is imaginary, as it is inICPs, in which ω << ωp, the wave will vary as

Im( ) cosk xe tω− as it propagates in the x direction. Theevanescent wave does not oscillate but decays exponen-tially upon entering the plasma. In the case of mostICPs, f = 13.56 MHz while ωp is measured in GHz, sothat ω << ωp, and Eq. (1) can be approximated by k2 =−ωp

2/c2, and Im(k) = ωp/c. The wave then varies asexp(−x/δs − iωt], where the characteristic decay length,called the exponentiation distance or e-folding length, is1/Im(k). This decay length is defined as the skin depthδs:

δ δ ωs c pc= ≡ / . (4)

The quantity δc is called the collisionless skin depth andis the same as δs here because we have so far neglectedcollisions. Note that δc depends on n½; the current layerdoing the shielding can be thinner if the plasma is dense.The diagram shows that as the current J in the antennaincreases, a B-field is induced in the plasma, and this inturn drives a shielding current in the opposite direction.This current decays away from the wall with an e-foldingdistance ds.

Using Eq. (A1-9) for fp, we find that δc for a 1012

cm-3 plasma is of order 0.5 cm. We would expect thatvery little RF power will get past the skin layer and reachthe center of the plasma, perhaps 10 cm away. This isthe reason stove-top antennas were invented. However,it is found, amazingly, that even antennas of the first typein Fig. 10 can produce uniform densities across thewhole diameter. This is one of the mysteries of RFsources and has given this field the reputation of being ablack art. A possible explanation will be given later.

ICPs, however, are not collisionless, and onemight think that the skin depth would be increased bycollisions. To account for collisions of frequency νc, weneed merely replace Eq. (1) with

Part A554

0

1

10

100

0 1 10 100 1000n (1011 cm-3)

ds (c

m)

1003010531

p (mTorr)Argon, 2 MHz, Te = 3 eV

(a)

0

5

10

15

20

1 10 100p (mTorr)

ds (c

m)

654321

Te (eV)n = 1011 cm-3, f = 2 MHz

(b)

Fig. 19. (a) Classical skin depth vs.density at various neutral pressures.(b) Effect of argon pressure on skindepth at various electron tempera-tures.

c ki

p

c

2 2

2

2

1ω

ωω ω ν

= −+( )

. (5)

The complex denominator makes it hard to see how theskin depth is changed, but we can look for an approxi-mation. Since ω ≈ 9 × 107 sec-1, νen = 3 × 1013<σv>en

p(mTorr), σ ≈ 5 × 10−16 cm2, and v ≈ 108 cm/sec (forKTe ≈ 4 eV), we find that νc < ω for p < 60 mTorr. If νc

<< ω, we can expand the denominator in a Taylor series,obtaining

12 2 2 2 21 1c c

p pi ic k ν νω ω ωω ω

− ≈ − + ≈ − −

.

Here we have taken ωp2 >> ω2, which is well satisfied.

Taking the square root by Taylor expansion, we nowhave

21

21 , | Im( ) | 1 O2

p c cs c

ik i kc

ω ν νδ δω ω

− ≈ ± − = ≈ + .

We see that the real part of k has acquired a small valueas a result of collisions, but the imaginary part is un-changed to first order in νc/ω unless our assumption of νc

<< ω breaks down. At the mTorr pressures that ICPsoperate at, the skin depth is quite well approximated byδc.

With a computer, it is easy to solve Eq. (5) usingthe collision data given in Part A2, and some results areshown in Fig. 19. These were computed for f = 2 MHz,used by some ICPs, rather than the more usual 13.56MHz, in order to increase ν /ω and bring out the effect ofcollisions more clearly. We see in (a) that ds decreaseswith √n as expected, but it hits a lower limit imposed bycollisions. In (b), we see that the increase of ds withpressure depends on Te, which affects νc = nn <σv>.

3. Anomalous skin depthIn plasma physics, classical treatments like the

above are often doomed to failure, since plasmas aretricky and more often than not are found experimentallyto disobey the simple laws of electromagnetics. Theycan do this by deviating from strict Maxwelliandistributions and generating internal currents and chargesthat are not included in simple formulations. However,in this case, observations show that Eq. (5) is correct . . .up to a point. Fig. 20 shows data taken in the ICP of Fig.11 with a magnetic probe measuring the RF magnetic


0.01

0.1

1

10

100

-15 -10 -5 0 5 10 15R (cm)

|Bz|

(mV)

51020Calc

p (mTorr)

(a)

0

1

2

3

0 5 10 15r (cm)

n,

KTe,

|Bz

|

8

12

16

20

Vs (V

olts

)nKTeBzVs

(b)

Fig. 20. (a) Decay of the RF fieldexcited by a loop antenna. (b)Profiles of n (1011 cm-3), KTe (eV),plasma potential Vs (V), and Bz(arbitrary units) in an ICP discharge in10 mTorr of argon, with Prf = 300W at2 MHz.

Fig. 21. Monte Carlo calculation of aelectron trajectory in an RF field with(blue) and without (black) the Lorentzforce. The dotted line marks the col-lisional skin depth.

field Bz. In the outer 10 cm of the cylinder, the semilogplot shows |Bz| decreasing exponentially away from thewall with a scalelength corresponding to ds. (The exactsolution here is a Bessel function because of thecylindrical geometry.) However, as the wave reaches theaxis, it goes through a null and a phase reversal, as if itwere a standing wave. This behavior is entirelyunexpected of an evanescent wave, and suchobservations gave rise to many theoretical papers onwhat is called anomalous skin depth. Fast, ionizingelectrons are created in the skin layer, where the E-fieldis strong. These velocities, however, are along the walland do not shoot the electrons toward the interior. Mosttheorists speculate that thermal motions take theseprimary electrons inward and create the small reversedB-field there. This effect, however, should decrease withpressure, and Fig. 20a shows that the opposite is true.The explanation is still in dispute. In Fig. 20b, theexponential decay of Bz is seen on a linear scale. Alsoshown is the plasma density, which peaks near the axis.Since the RF energy, proportional to Bz

2, is concentratednear the wall, as the Te profile confirms, it is puzzlingwhy the density should peak at the center and not at thewall. We have explained this effect recently by tracingthe path of an individual electron as it travels in and outof the skin layer over many periods of the RF. Anexample is shown in Fig. 21. The result depends onwhether or not the Lorentz force LF e= − ×v B isincluded. This is a nonlinear term, since both v and Bare small wave quantities. This force is in the radialdirection and causes the electron to hit the wall at steeperangles. The electrons are assumed to reflect from thesheath at the wall. The steeper angles of incidence allowthe fast electrons to go radially inwards rather than

018036054072090010801260

RF phase(degrees)

Part A556

Fig. 22. The Ec curve, a very usefulone in discussing energy balance anddischarge equilibrium (L & L, p. 81).

Fig. 23. Drawing of a TCP from theU.S. Patent Office.

skimming the surface in the skin layer. Only when FL isincluded do the electrons reach the interior with enoughenergy to ionize. This effect, which requires non-Maxwellian electrons as well as nonlinear forces, canexplain why the density peaks at the center even whenthe skin layer is thin. Because of such non-classicaleffects, ICPs can be made to produce uniform plasmaseven if they do not have antenna elements near the axis.

4. Ionization energy.How much RF power does it take to maintain a

given plasma density? There are three factors to con-sider. First, not all the power delivered from the RF am-plifier is deposited into the plasma. Some is lost in thematchbox, transmission line, and the antenna itself,heating up these elements. A little may be radiated awayas radio waves. The part deposited in the plasma isgiven by the integral of J ⋅E over the plasma volume. Ifthe plasma presents a large load resistance and thematching circuit does its job, keeping the reflected powerlow, more than 90% of the RF power can reach theplasma. Second, there is the loss rate of ion-electronpairs, which we have learned to calculate from diffusiontheory. Each time an ion-electron pair recombines on thewall, their kinetic energies are lost. Third, energy isneeded to make another pair, in steady state. The thresh-old energy for ionization is typically 15 eV (15.8 eV forargon). However, it takes much more than 15 eV, on theaverage, to make one ionization because of inelastic col-lisions. Most of the time, the fast electrons in the tail ofthe Maxwellian make excitation collisions with the at-oms, exciting them to an upper state so that they emitradiation in spectral lines. Only once in a while will acollision result in an ionization. By summing up all thepossible transitions and their probabilities, one finds thatit takes more like 50−200 eV to make an ion-electronpair, the excess over 15 eV being lost in radiation. Thegraph of Fig. 22 by V. Vahedi shows the number of eVspent for each ionization as a function of KTe.

5. Transformer Coupled Plasmas (TCPs)As shown in Fig. 23, a TCP is an ICP with an

antenna is shaped into a flat spiral like the heater on anelectric stove top. It sits on top of a large quartz plate,which is vacuum sealed to the plasma chamber belowcontaining the chuck and wafer. The processing cham-ber can also have dipole surface magnetic fields, and theantenna may also have a Faraday shield consisting of a


(a)

(b)

(c)

(d)

plate with radial slots. According to our previous discus-sion, the induced electric field in the plasma is in theazimuthal direction, following the antenna current.Electrons are therefore driven in the azimuthal directionto produce the ionization. As in other ICPs, the skindepth is of the order of a few centimeters, so the plasmais generated in a layer just below the quartz plate. Fig.24a shows the compression of the RF field by theplasmas shielding currents. The plasma then diffusesdownwards toward the wafer. In the vicinity of the an-tenna, its structure is reflected in irregularities of plasmadensity, but these are smoothed out as the plasma dif-fuses. There is a tradeoff between large antenna-waferspacing, which gives better uniformity, and small spac-ing, which gives higher density. Being one of the firstcommercially successful ICPs, TCPs have been studiedextensively; results of modeling were shown in Fig. 14.Densities of order 1012 cm-3 can be obtained (Fig. 24c).Magnetic buckets have been found to improve theplasma uniformity. There is dispute about the need for aFaraday shield: though a shield in principle reducesasymmetry due to capacitive coupling, it makes it harderto ignite the discharge. If the antenna is too long or thefrequency too high, standing waves may be set up in theantenna, causing an uneven distribution of RF power.The ionization region can be extended further from theantenna by launching a waveeither an ion acousticwave or an m = 0 helicon wave, but such TCPs have notbeen commercialized. The spiral coil allows the TCPdesign to be expanded to cover large substrates; in fact,very large TCPs, perhaps using several coils, have beenproduced for etching flat-panel displays.

TCPs and ICPs have several advantages over RIEreactors. There is no large RF potential in the plasma, sothe wafer bias is not constrained to be high. This biascan be set to an arbitrary value with a separate oscillator,so the ion energy is well controlled. The ion energiesalso are not subject to violent changes during the RF cy-cle. These devices have higher ionization efficiency, sohigh ion fluxes can be obtained at low pressures. It iseasier to cover a large wafer uniformly. In remote-source or detached-source operation, it is desired to haveas little plasma in contact with the wafer as possible; theplasma is used only to produce the necessary chemicalradicals. This is not possible with RIE devices. Com-pared with ECR machines, ICPs are much simpler andcheaper, because they require no magnetic field or mi-crowave power systems.

Part A558

Fig. 24. (a) RF field pattern withoutand with plasma; (b) radial profiles ofBr at various distances below the an-tenna, showing the symmetry; (c)density vs. RF power at various pres-sures; (d) plasma uniformity with andwithout a magnetic bucket. [from L &L, p. 400 ff.]

Fig. 25. The standard (left) and al-ternate (right) matching networks.

6. Matching circuitsThe matching circuit is an important part of an

ICP. It consists of two tunable vacuum capacitors, whichtend to be large and expensive, mounted in a box withinput and output connectors. At RF frequencies, wiresare not simply wires, since every length of wire has anappreciable inductance; hence, the way the connectionsand ground plane are arranged inside the matchbox re-quires RF expertise. In addition, industrial plasma reac-tors have automatch circuits, which sense the way thecapacitors have to be tuned to match the load and havelittle motors that automatically turn the tuning knobs.Design of matching circuits can be done with commer-cial network analyzers which plot out the Smith chartthat is familiar to electrical engineers. However, wehave derived analytic formulas which students can usewithout the expensive equipment (Chen, UCLA ReportPPG-1401, 1992). The capacitors, called the loading capacitor CL (C1in the diagram) and the tuning capacitor CT (C2), can bearranged in either the standard or an alternate configura-tion. Let R0 be the characteristic impedance of the poweramplifier and the transmission lines (usually 50Ω), andlet R and X be respectively the resistance and reactanceof the load, both normalized to R0. For instance for aninductive load with inductance L, X is ωL/R0. These willchange when the plasma is created. For the standard cir-cuit, the capacitances are

′ = − −

′ = − − ′ −

C R R

C X R CL

T L

[ ( ) ] /

[ ( ) / ]

1 1 2 2

1

2

1, (6)

where CL′ ≡ ωCLR0, etc. For the alternate circuit wehave

′ = ′ = −C R B C X B TL T/ , ( ) / 2 , (7)

where

T R X B R T R2 2 2 2 2≡ + ≡ −, ( ) . (7a)

Note that these two circuits are actually identical: toswitch from standard to alternate, you merely haveto swap the input and output terminals. The alternatecircuits usually requires smaller capacitors with highervoltage ratings. These formulas do not include the cablethat connects the matchbox to the antenna. Any cablelength longer than a foot or so can make a big differencein the tuning; for instance, it can change in inductive load


(a)

(b)

Fig. 26. (a) A monopolar ESC; (b) abipolar ESC. What is seen is actuallythe coolant paths (from Applied Mate-rials).

to a resistive load. This is because a ¼ wavelength of a13.56 MHz wave in the cable is only about 5 m, and thereflected signal arriving back at the tuning circuit wouldbe changed in phase significantly by a cable length of afraction of a meter. How to handle transmission lines iscovered in PPG-1401. Note in Eq. (6) that a capacitiveload would have negative X, and then CT would becomenegative; that is, it would require an inductor rather thana capacitor. Indeed, RIE discharges cannot be matchedby purely capacitive tuning circuits; an inductor has to beadded inside the matchbox. This inductor can be just awire loop a couple of inches in diameter, but the coilmust not be distorted or moved by the user, because thatwould change its inductance.

7. Electrostatic chucks (ESCs)In plasma processing, photons and ions impinge

on the wafer and heat it up. It is important to have anefficient way to remove the heat. A flow of He gas, agood heat transfer agent, is used on the back side of thewafer to cool the wafer. Originally, the wafer was heldonto the chuck with mechanical fingers at the edges.This not only made the available area smaller but alsoallowed the wafer to bulge upwards under the He pres-sure, thus compromising its planarity. Electrostaticchucks have been developed to overcome these prob-lems. In an ESC, a DC voltage is put on the chuck,charging it up. An opposite charge is attracted to theback side of the wafer, and these opposite charges attracteach other, holding the wafer flat against the chuck at allpoints. To introduce the He, grooves are milled into thechuck. The back side of the wafers are rough enoughthat gas entering these grooves can seep beneath the wa-fer and remove heat from the whole surface.

There are two types of ESC. Monopolar chuckshave the same voltage applied to the entire chuck. Thereturn path is through the plasma; that is, if a positivecharge, say, is put on the chuck, the originally neutralwafer would have negative charges attracted to its backside and positive charges repelled to its front side.There, the charges are neutralized by electrons from theplasma. Thus, a monopolar chuck can function only ifthe plasma is on. There are problems with timing, be-cause one has to make sure the wafer is not released toosoon after plasma turnoff, and the wafer has to be firmlyheld as the plasma is turned on. The advantage of mo-nopolar chucks is that it is easy to release the wafer. Bi-polar chucks are divided into regions which get chargedto opposite potentials. The return path in the wafer is

Part A560

Fig. 27. Design curves for electro-static chucks (from PMT, Inc.)

then through the wafers cross section from one region tothe next. The plasma is not necessary for the chuck tohold. The problem is that it is hard to get rid of thecharging after the process is over to release the wafer;materials of just the right dielectric constant and conduc-tivity have to be used in bipolar chucks. An ESC consists of a flat plate (with grooves) cov-ered with a layer of dielectric. On top of that is an airgap, which is just the roughness of the wafer, and thenthe wafer itself. The holding pressure of the chuck de-pends on the thickness tgap of the air gap, and also on theratio ε / t, where ε is the dielectric constant of the dielec-tric layer of thickness t. For given values of these pa-rameters, the holding pressure (in Torr) will increasewith chuck voltage. Dielectric constants vary from 3-4for polyimide insulators to 9-11 for alumina or sapphire.Chuck voltages can vary from 100 to 5000V. Since theplasma potential oscillates at the RF and bias frequen-cies, the required chuck voltage can also vary with RFpower. Figure 27 shows the variation of clamping forcewith gap thickness and voltage with ε / t.

plasma sources iii principles of p course notes: prof....

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