Energy influx from an rf plasma to a substrate during plasma processing

JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 8 15 APRIL 2000

Energy influx from an rf plasma to a substrate during plasma processingH. Kerstena)

Institute for Physics, University of Greifswald, Domstrasse 10a, D-17487 Greifswald, Germany

E. Stoffels and W. W. StoffelsDepartment of Physics, TU Eindhoven, P.O. Box 513, 5600MB Eindhoven, The Netherlands

M. Otte, C. Csambal, H. Deutsch, and R. HipplerInstitue for Physics, University of Greifswald, Domstrasse 10a, D-17487 Greifswald, Germany

~Received 19 July 1999; accepted for publication 18 January 2000!

The energy influx delivered by an rf plasma to a metal substrate has been studied by a calorimetricmethod with a thermal probe. By changing the substrate voltage, the influence of the kinetic energyof the charge carriers to the thermal power could be determined. The measured energy influx for anargon plasma can be explained mainly by ions, electrons, and their recombination. In the case of anoxygen plasma, where the energy influx is under comparable conditions about 50% higher, alsoother transfer mechanisms such as surface-aided atom association and relaxation of rovibrationalstates have to be taken into consideration. ©2000 American Institute of Physics.@S0021-8979~00!05608-5#

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I. INTRODUCTION

Plasma wall interactions are of great importance inlarge variety of applications of low-temperature, lowpressure plasmas such as in etching, deposition, and sumodification of thin films. In these complex processes,thermal and energetic conditions at the substrate surfacea dominant role.

The thermal conditions at the substrate surface afelementary processes like adsorption, desorption, and dsion as well as chemical reactions~chemical sputtering, surface film reaction!.1–3 On the other hand, especially in thcase of thin film deposition, the microstructure and morphogy as well as the stoichiometry of the film depend stronon the energetic conditions at the surface.4,5 Also, surfacediffusion of adsorbed atoms can be enhanced, which resin a rearrangement of deposited atoms.6 In addition, bom-bardment of a growing film with low-energy ions results inmodification of film properties such as adhesion and residstress, etc.7

It should be emphasized that in addition to external heing, the surface temperatureTS is largely influenced by theenergy fluxJin resulting from energetic particle bombarment, chemical surface reactions and heat radiation.8,9 By asuitable variation of the experimental conditions, the diffent contributions to the substrate heating can be separand independently studied.

In the present article, we perform investigations onenergy influx~thermal power! to substrates in rather weakdischarges. In this type of discharge, used for depositioncoatings, cleaning, and conditioning of surfaces, the hload on the surface is often a critical parameter. Also the hload of microdisperse powder particles, suspended in acharge is a topic under current investigation.10,11 In Sec. II,the various heat sources and sinks of a substrate in a

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charge will be discussed. In Sec. III, the design of our thmal probe is discussed along with the plasma setup. Msurements of the relevant plasma parameters like the elecdensity and temperature are presented to allow for a gcomparison of the measured and calculated heat fluwhich is shown in the final section.

II. THEORY

When a solid comes into contact with a plasma, enetransfer takes place. The substrate is heated and, after atain time, it may reach a thermal equilibrium. This steastate is determined by a balance of energy gain fromplasma processes and energy losses by conductionradiation.12,13 The general power balance at the substrategiven by

Qin5HS1Qout, ~1!

where HS5mc(dTS /dt) denotes the enthalpy of the substrate andQout summarizes the heat losses by radiation athermal conduction by the gas and the substrate. For msubstrates thermal conduction to~or from, in case of a heatedsubstrate! the substrate holder will be the dominant heat s~source!. However, in case of an isolated substrate, liketrapped microdisperse particle floating in the discharge,is completely absent. In those cases, radiation and gas cing are the only heat sinks. As we operate at low pressuand low temperatures, both are relatively ineffective and tthe temperature of a thermally isolated object in a dischacan be elevated with respect to its surroundings.10

In the following, the different contributions to the totaenergy influxQin which are relevant under our experimentconditions will be discussed shortly. It should be mentionthat the fluxQin is the surface integral of the related enerflux densityJin over the substrate surfaceAS :

7 © 2000 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

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3638 J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Kersten et al.

Qin5EAs

JindA. ~2!

In general, the total energy influxJin is the sum of thefluxes due to electrons (Je), ions (Ji), neutrals (Jn), andphotons (Jphot). Each of these fluxes consists of several cotributions. The electrons and ions hitting a substrate trantheir kinetic energy, moreover recombination energy isleased when a positive ion and electron recombine atsurface. In our case with cold gas and cold substrates,kinetic energy of neutrals can be neglected, but neutralstransfer internal energy from electronic and rovibrationalcitation (Jinter). Furthermore gas molecules can associwith another gas phase species at the surface (Jass) or reactwith the surface (Jchem). Heating by photons can occur bblackbody radiation from heated surfaces or by plasma pduced photons. In our case, there are no heated surfacethe metal substrate reflects virtually all photons in the visiregion. At our operating pressure and power, the plasmoptically dense for resonant radiation and therefore the tmal load of UV photons hitting the substrate is also neggible. Note that this is not necessarily true in other plasconfigurations or in case of opaque, nonreflecting substraConcluding, the total heat influx is given by

Jin5Je1Jion1Jinter1Jass1Jchem. ~3!

In the following, we shall estimate these contributionsmore detail. In general, the mean kinetic ion energy is demined by the ion energy distribution function~IEDF! at thesurface. At elevated pressures, the energy distribution ofions arriving at the substrate is affected by collisions insheath in front of the substrate. At low pressures inpresent experiment~1 Pa!, the maximum ion energy is detemined mainly by the free fall energye0Vbias, whereVbias isthe potential drop from the plasma glow to the substrwhich corresponds to the difference between the plasmatential Vpl and the substrate potentialVS with respect toground:

Vbias5Vpl2VS . ~4!

It should be emphasized that the simple expressionEq. ~4! for the mean kinetic energy of the ions striking thsubstrate is applicable in most cases of plasma procesOnly if the IEDF for the ions near the substrate is much mcomplex, the assumption ofe0Vbias for the kinetic energy isno longer justified. In an argon discharge, charge tranreactions readily occur in the sheath region. In this case,of the ion energy (e0Vbias) is transferred to a neutral. However, as the neutral has a directional velocity towardssubstrate, still most energy will be transferred to the sstrate and the simple expression of Eq.~4! holds. In additionto the directed kinetic energy of the ions, which originafrom acceleration in the electrical field in front of the sustrate, the ions also have thermal energy. However, thiscan be neglected because the ions are nearly at roomperature. Hence, the contribution of the kinetic energy ofions (Ji

kin) which can be expressed as a product of theflux density j i and their mean energyEi is given by


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Jikin5 j iEi5 j ie0~Vpl2VS!

5nevambe0~Vpl2VS!

5neAkTe

miexp$20.5%e0~Vpl2VS!, ~5!

where we have approximated the ambipolar diffusionnevamb

in Eq. ~5! by the Bohm flux14

j i5neAkTe

miexp$20.5%. ~6!

Under low-pressure conditions (p,10 Pa), the Bohmequation is applicable for argon discharges, because inpresheath almost no collisions occur. The Bohm equayields the ion fluxj i by knowing the ion densityni , whichequals the electron densityne at the sheath edge. This approach is also valid in presence of negative ions, like inoxygen discharge. However, in that case the Bohm flux@Eq.~6!# is governed by the ion temperature.15

In addition to kinetic energy, ions transfer a part of thepotential energy when striking a surface. For metallic sustrates, the neutralization of ions is caused by long-rainteractions and may be accompanied by the emissionsecondary electrons. The resulting contributionJi

rec to theenergy balance of the substrate due to the recombinatio

Jirec5 j iErec. ~7!

Each incident ion releases its ionization potentialEion

minus the work function of the metalF, as an electron has tobe released from the metal surface before recombinationcase of secondary electron emission, also their work funchas to be supplied. The released recombination energyErec isgiven by

Erec5Eion2F. ~8!

Data forEion andF, respectively, may be taken from thliterature.16 In principle, Eq.~8! should still be corrected bythe difference between the adsorption energy of the ionthe desorption energy of the resulting neutral, but this ctribution is rather low. As stated above, it is assumed thatresulting neutral is in its ground state, especially for molelar ions, this is not necessarily true and appropriate chanin Eion should be made in this case.

The cooling effect by sputtering of substrate material calso be ignored. Because in our case, the energye0Vbias ofthe impinging ions is always smaller than 100 eV, the spuyield Y is rather small (Y<0.1). Therefore, the flux of sputtered surface atoms, which may contribute to an energyof the substrate, is negligible.

The electrons have to overcome the bias voltageVbias infront of the substrate in order to reach the substrate surand to transfer their energy. The kinetic energy of the plaselectrons arises from the integration over the EEDF frVbias up to infinity. Moreover, every electron hitting the suface will release an energy equivalent to the work functionthe material. In case of a Maxwellian electron energy disbution ~EEDF!, the energetic influxJe thus reads


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3639J. Appl. Phys., Vol. 87, No. 8, 15 April 2000 Kersten et al.

Je5neA kTe

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e0Vbias

kTeJ 2kTe . ~9!

The energy, which the electrons lose by overcomingbias potential, is stored as potential energy in the elecfield and consumed by accelerating ions hitting the substand by secondary electrons accelerated towards the plaThis effect is taken into account by the work functionF inEq. ~8!. Both summands of the electron energy~2kTe , F!are of the same order of magnitude.

Using the general equations~4!–~9! listed above, ananalysis of the charged plasma components will yield,principle, the surface heating caused by positive ionselectrons. In case of electronegative plasmas like oxygnegative ions also have to be considered. Because oflow temperature, they can only reach the substrate if thera large positive bias. Therefore, in general, negative ionsbe neglected in the thermal balance of a substrate. Asenergy flux of the charged species strongly depends onbias potential of the substrate@Eqs.~5! and~9!#, it is possibleto separate their contribution from other heat sourcesradiation, chemical reactions, neutrals, and charge carrby variation of the bias potential.

The contribution of the various neutral gas componestrongly depends on the gas composition and the plasmaditions. In a process plasma containing reactive speci~N2,O2, etc.!, surface-aided atomic association and heteroneous exothermic reactions occur. Evidence for substheating by exothermic reactions on the processed surfacebeen reported, for example, in case of plasma etchingsilicon with fluorine containing compounds17 and duringplasma cleaning of contaminated metal surfaces.18 In thecase of atomic recombination as a special surface reacprocess, the fraction of the energy transferred to the solidbeen described for example in Ref. 19. The percentage orecombination energy, which is used for surface heating,ies with the chemical composition of the surface. Furthmore, relaxation of internal energy~electronic and rovibra-tional excitations! adds to the thermal influx to a substratEnergy transfer of argon metastable atoms and rovibtionally excited molecular species to microdisperse particfloating in the discharge has been suggested by StoffelsStoffels.20

The energy influx by internal energy transferJinter, atomrecombinationJass and exothermic reactionsJchem is de-scribed by

Jass5 j OGOEdiss5GO

1

2nOA8kTg

pmOEdiss, ~10!

in which G is the energy transfer, association, or reactprobability of the neutrals on the substrate surface andj itsflux density. The latter can be determined accurately, ifspecies density and its diffusion properties are known.21 Theindex O indicates the quantities for oxygen. At low presures, a rough estimate is obtained by simply multiplyingglobal species densityn with its thermal velocity v: j5nv.

If the chemical reactions result in layer formation, ocan easily estimateJchemfrom the growth rateRdep, the mass


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densityr of the layer, and the average specific enthalpy ghox .

Jchem5Rdeprhox . ~11!

Analogous formulas can be easily derived in case of etcha substrate, in which the reaction products are volatile.

The thermal load on a substrate resulting from plasphotons can be calculated by integrating the product of pton flux Fpl(n), photon energyhv, and absorption coefficienof the surfaceA(hn) over the complete spectral range.

Jphot5E Fpl~n!hnA~hn!dn. ~12!

The photon flux has to be estimated using a radiative plamodel.

The different energetic contributions calculated on tbasis of the equations mentioned above can be compwith the total energy influxJin measured by the probmethod described below. This comparison gives insight ithe processes involved and about the dominant mechandetermining the thermal balance of a substrate duringplasma treatment.

III. EXPERIMENT

A. Energy flux measurements by a thermal probe

The integral energy influx from the plasma towards tsubstrate can be measured by a simple thermal probe.22 Pre-viously, Thornton23 and Wendtet al.24 have proposed a similar procedure for the determination of the total heat influx.schematic sketch of the setup is shown in Fig. 1. The pris mounted on a manipulator arm to allow for horizontal avertical scans. It can be also rotated, in order to measdirectional fluxes, e.g., secondary electrons coming fromrf electrode or infrared photons from a heated surface.

In our experiments, the heat flux measurements areried out by observing the rate of temperature risedTS /dt ofa copper substrate~diameter: 3.4 cm, areaAS518 cm2,thickness: 0.02 cm! which is spot welded to a thermocoup~type j! and placed within a solid shield. The substrateonly connected to the thermocouple and a wire for additiobiasing. No other contact to the shield and holder is reali

FIG. 1. Schematic of the experimental setup.


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in order to minimize thermal conduction. Because of its laheat capacity the shield is at a constant environmental tperatureTenv during the time of the measurement.

The measurement of the total energy influxQin is basedon the determination of the difference between the timerivatives of the substrate temperatureTs during heating~‘‘plasma on’’! and cooling~‘‘plasma off’’ !. Examples oftypical temperature curvesTS(t) which have been obtainefor an Ar plasma (p51 Pa,P515 W) at three different substrate voltages are presented in Fig. 2.

The general power balance at the substrate is givenEq. ~1!. The losses are always small in comparison toincoming fluxes due to the plasma process. During the hing phase ~plasma on: Qin.0! HS is determined byHS~heat!5Qin2Qout and during the cooling phase~plasmaoff: Qin50! by HS~cool!52Qout. By taking these expressions into Eq.~1!, the difference yields the energy influx:

Qin5HS~heat!2HS~cool!5mcH S dTS

dt Dheat

2S dTS

dt Dcool

JT

.

~13!

If the slopesdTS /dt are determined at the same temperatT and assuming no change of the environmental temperaTenv, which is achieved by short measurement times,expression within the brackets of Eq.~13! is a quantity pro-portional to the thermal power at the substrate. In ordeobtain absolute values ofQin , the specific heat of the substrate~thermal probe! was determined by a known thermpower as described in Ref. 25 toCS50.65 J/K.

The measured energy influx is an integral value comping the various contributions as kinetic energy of charge criers, recombination heat, reaction heat, etc. By measuthe energy fluxes at different substrate voltagesVS , the con-tributions of ions and electrons from the other sources canseparated. For this purpose, the thermal probe~substrate! canbe biased externally by a dc voltage. Simultaneously,electrical current to the substrate is measured and one obthe substrate characteristic, which is similar to a usual prcharacteristic. In Fig. 3, the thermal probe characteristic in1 Pa argon and oxygen rf plasma is shown. At sufficiennegative substrate voltages, the currentI S changes only

FIG. 2. TS(t) curves as measured during the Ar plasma proc(p51 Pa,P515 W) for three substrate voltages~0, 246, 295 V!.


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slightly with increasing voltageVS . From the characteristicsin Fig. 3, an ion saturation current of about 1 mA andfloating potential ofVfl'23 V can be obtained for the argoplasma.

B. The plasma setup

In order to test the thermal probe, a commonly usasymmetric, capacitively coupled rf discharge was used.plasma glow is located in the region between the planeminum rf electrode (D5130 mm) and the upper part of thspherically shaped reactor vessel (D5400 mm) which servesas grounded electrode, see Fig. 1.

The 13.56 MHz rf power is supplied by a generat~Dressler CESAR1310! in combination with an automaticmatching network~Dressler VM700!. The rf voltage wasvaried between 300 and 900 V, resulting in a dischapower of 10–100 W. The turbopump~Pfeiffer TMU260C!which allows for a base pressure of 1024 Pa is connected tothe vessel by a butterfly valve, the gas pressure was vabetween 0.5 and 5 Pa by the valve and by using a flcontroller ~MKS!. Argon and oxygen, respectively, werused as process gases.

C. Plasma diagnostics

In order to compare the measured energy fluxes wsimple model assumptions, the internal plasma parametethe rf discharge have been investigated by plasma diagtics as analytical charge coupled device~CCD! photometryand Langmuir-probe measurements,26 respectively.

A CCD camera~SBIG ST-6! coupled with a photoelectrical filter ~CRI VIS2-05! was used to determine the sheawidth in front of the powered electrode by measuring tspatial emission profile at several wavelengths. This giinformation on the local variations in the electron enerdistribution function, with a high spatial accuracy~0.2 mm!.

The Langmuir-probe characteristics have been obtaiby a source meter~Keithley SM2400!. The probe~diameter:47 mm, length: 12 mm! could be moved axially through thplasma bulk into the plasma glow near the sheath, see FiDuring a measurement, the probe voltage is stepwisecreased and the electrical probe current is recorded from

sFIG. 3. Current–voltage characteristic of the substrate~thermal probe! forargon and oxygen.


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ion acceleration region up to the electron acceleration regThe electron energy distribution function~EEDF! can thendirectly be determined from the second derivative of theV– Icharacteristics.27 Figure 4 shows examples for the secoderivative for argon at 0.75 Pa and 10 W taken at sevdistances above the electrode which yield Maxwellian disbutions. The values of the electron densityne and the meanelectron energyue(kTe) as well as the plasma and floatinpotentials (Vpl ,Vfl) have been determined from the probecurrent–voltage characteristics.

IV. RESULTS AND DISCUSSION

A. Plasma parameters

The interpretation of the substrate heating by chargeriers requires the determination of the electron and ion dsity (ne ,ni), the plasma and the floating potential (Vpl ,Vfl),and the electron temperature (kTe). In the present study, thinternal plasma parameters have been measured in thestrate region by analytical CCD photometry and Langmuprobe measurements as described above.

The sheath position has been determined by the Cphotometry technique. For example, the extension ofsheath thicknessdsh for an argon plasma has been estimafor two different excitation levels at 420 nm (1s5– 3p9) and668 nm (1s4– 2p1). Figure 5 shows an example of the mesured sheath widthdsh for p51 Pa in dependence on thepower. The accuracy of the determination ofdsh is 60.2 mm.Since the required energy for the excitation of the 2p level~13.48 eV! is lower than the excitation energy for the 3plevel ~14.5 eV!, the glow in the 668 nm line can be observcloser to the electrode. This observation, which is knownSeeliger’s rule of glow edge,28 is due to the kinetic energy og electrons originating from the electrode and acceleratethe sheath. The larger the distance from the electrode,more kinetic energy the electrons gain for exciting collisio

In Fig. 5, the sheath widths measured by the CCmethod are also compared with values obtained

FIG. 4. Second derivative of Langmuir-probe characteristics, whichmeasure for the EEDF obtained at different heights above the rf elect(p50.75 Pa,P510 W).


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Langmuir-probe measurements. In this case,dsh was definedas the distance from the electrode where theV– I character-istic of the Langmuir-probe failed. This means that withindistance of about 20 mm in front of the electrode~sheath!,the second derivative of the probe characteristic, whichneeded to determine the EEDF as well as the electron denand the electron temperature, is strongly disturbed andevaluation of the probe characteristic becomes impossiBoth methods yield reliable values for the sheath thicnesses, but obviously the CCD method is more accuratesystematic measurements, a weak dependence on thecharge power~Fig. 5!, and a strong influence of the pressuon dsh could be observed. In all cases the sheath thicknesin the order of a centimeter.

In addition, by using a balance equation,29 the internalplasma parameters for an Ar plasma could also be obtaiUnder the assumption that charge carrier formation occmainly by direct impact ionization within the plasma gloand by measuring the external discharge quantities asamplitude of the rf voltage (Vpp;Vrf), the dc-bias voltage(Vdc) and the sheath thickness in front of the hot electrothe model yields the electron temperaturekTe and electrondensityne .

The floating potential isVfl523 V and the plasma potential Vpl is in the order of 15 V for argon and about 20for oxygen plasma, respectively. The plasma potenchanges only slightly within the plasma glow. Figureshows the variation of the plasma potential in an argplasma as a function of the axial distance from the rf eltrode. As mentioned above, the position where the potendrops dramatically and the evaluation of the EEDF fails cbe identified as the sheath edge and it coincides withoptically determined sheath edge position~Fig. 5!. A quitesimilar behavior can be observed in the axially measuelectron temperature, shown in Fig. 7. At the sheath edthere are hardly any electrons from the plasma glow. Melectrons are secondary electrons, heated in the sheatgion. Thus,kTe increases strongly towards the rf electrodwhile the electron densityne drops. The values at substraposition~3.25 cm!, which are important for the calculationsare 3.5 eV for the argon plasma and about 5.2 eV for

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FIG. 5. Observed sheath thicknessdsh in front of the rf electrode for twowavelengths and determined by a Langmuir-probe for different rf powThe argon gas pressure was 1 Pa.


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oxygen plasma. For a Maxwellian EEDF, the electron teperature can also be simply estimated by the differencetween floating and plasma potential:

Vfl2Vpl5kTe

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miD<0. ~14!

This formula yields for argon (Vfl2Vpl5218 V,me /mi

51.431025), an electron temperature of 3.5 eV. By usinthe relevant values for oxygen, one obtainskTe54.6 eV.Comparison with the measurement supports the assumpof a Maxwellian EEDF at least for the argon plasma.

The electron densityne for argon at a power of 15 Wand a pressure of 1 Pa, which were the standard dischconditions in energy flux measurements, is about3109 cm23 ~Fig. 8!. The values for the electron density antheir dependence on discharge power determined byLangmuir-probe measurements are also confirmed by thetical measurements on the basis of the sheath model.

B. Argon plasma

In the case of an argon plasma, we will initially considthe energetic contributions due to kinetic energy ofcharge carriers@Eqs. ~5! and ~9!# and their recombination@Eq. ~7!#. The contributions of the inert gas are limited,

FIG. 6. Axially resolved plasma potentialVpl for an argon rf plasma at 1 PaThe rf electrode is atz50.

FIG. 7. Axially resolved electron temperaturekTe for argon and oxygenplasma, respectively, at 1 Pa. The sheath edge is atz51.9 cm.


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there are no association and chemical reactions at thestrate surface. Only transfer of internal energy has to be csidered.

In order to modelJe andJi the internal plasma parameters obtained by Langmuir-probe measurements havetaken. The quantities are calculated for different substrvoltagesVS . The results are plotted in Fig. 9. It is obviouthat forVS,Vfl , only the positive ions dominate the integrenergy influxQin , while the contribution of electrons becomes important forVS.Vfl . In the rangeVS.0, Je in-creases dramatically due to the flux of electrons whichnow drained by the substrate25 acting as an additional disturbing electrode. Therefore, for positive substrate voltagthe model calculation on the basis of the Langmuir-promeasurements will fail and one should take the electronj e which can be directly obtained from the substrate charteristic ~Fig. 3!:

j e5I S

e0AS. ~15!

The contribution by electrons forVS.0 according to thisexpression is remarkably smaller than the values one obtby assuming an undisturbed plasma and applying

FIG. 8. Electron densityne in dependence on axial positionz.

FIG. 9. Calculated contributions by ions (Ji ,Jrec) and electrons (Je) to thethermal balance of the substrate. The calculations are based onne measuredby the Langmuir-probe and obtained by the substrate characteristics, retively.


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Langmuir-probe measurements. This can be expectedcause a relatively large, positively biased thermal probesignificantly drain the electrons from the plasma. As a csequence,j e andJe are lowered.

The energy influx due to charged particles, if both eletrons and ions are present, can also be estimated fromBohm flux @Eq. ~6!#. Assumingj e5 j i and remembering thain this case the electron energy flux can be neglected, theenergy flux is simply given byJi5 j i(Eion1eVbias). Substi-tuting the electron density and temperature measured uthe probe technique (ne523109 cm23,kTe53.5 eV) yieldsa total ion current to the thermal probe of 0.5 mA, whichin excellent agreement with the measured flux shown in F3. The total energy flux by ions forVs5Vfl to our probe thusis about 1022 J/s, which remarkably agrees well with thextrapolated value for ion heating plotted in Fig. 9.

Finally, the measurements of the total energy influx afunction of the substrate voltage are shown in Fig. 10 fordifferentVS regions. The influxQin measured by the thermaprobe ~solid squares! decreases with increasing substravoltage in the rangeVS,Vfl , reaches its minimum atVS

5Vfl and increases again with the supplied voltage inrangeVS.Vfl . For sufficiently negative substrate voltag~left part of the graph!, the ion saturation currentj i towardsthe substrate is nearly constant and the deposited thepower depends only on the ion energy, which is given bydifference between the plasma and substrate potential. Ifdifference becomes smaller, the contributionJi decreasesThe model, which takes the Bohm criterion and the plasparameter measured by the Langmuir-probe into acco~open circles! reflects the experimentally obtained slopeJin quite well. The constant difference between the two dsets reflects the heating by neutrals. The measurementsright branch that means for positive substrate voltages hbeen modeled with the electron flux derived from the sstrate characteristic shown in Fig. 3. In this region, the ioare not important, while the probe model yields electron ctributions which are much too large.

It can be easily seen that the contribution of neutral scies to the thermal load is about 231022 J/s. In our case, the

FIG. 10. Comparison of measured energy influxQin with several modelassumptions for the different contributions.


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contribution of photons can be neglected. The plasma istically dense for resonant photons, so they cannot reachsubstrate, while photons in the optical region are reflectedthe probe has a metallic surface. The energetic neutralcies in an argon plasma are most likely the argon metaststates. Their density is about 1011cm23.30 Indeed, followingthe estimation given in the theoretical part and assumintotal conversion at the surface, we find the missing thermload.

Thus, in an argon plasma the integral energy influxJin

can be determined by a calorimetric method. It consiststhe kinetic energy of charge carriers and their recombinaenergy and the energy released by relaxation of metastaThe contribution of ions (Jion) and electrons (Je) can bedistinguished by a variation of the substrate potentialVS .

For practical purposes, a more simple description ofmeasured curve can be useful by taking

Qin5Qin~Vfl!1I SVS , ~16!

in which Qin(Vfl) denotes the experimentally determined eergy influx at floating potential. By this ‘‘model’’~opensquares in Fig. 10!, one can clearly recognize that the whoelectric power at the substrate is transferred into therpower resulting in a certain thermal balance of the substrEspecially for the ions, this excellent agreement meansthe energy accomodation of Ar1 ions at a metallic surface isclose to unity. Recent investigations by Toyoda and Sug31

show that ion survival at the surface is less than 5%.The results indicate that a description of the energy

flux by charge carriers, which are characterized by plasdiagnostics~probe, substrate!, is an appropriate method fothe treatment of plasma-substrate interaction. Vice versameasuring the energy influx with a thermal probe and unthe assumption of valid models for the differentVS regions,one can also get some information on the plasma data.

C. Oxygen plasma

The discussion ofJin in case of an oxygen plasma can bgiven, in principle, in a quite similar manner as it has bedone for argon. In an oxygen discharge, there are three mcharge carriers, the electrons, the O1 ion, and the O2 ion.Furthermore, there are several minority species like O2

1 ,O2

2 , and O32 , which can be ignored in the energy flu

balance.21 Negative ions also cannot reach the substrate,less VS@0, and even in that case their energy is limiteTherefore, they can be ignored in the flux equations. Nevtheless, the presence of negative ions does alter thecharge. In most cases, the negative ion density will excthe electron density thusne!n1 . Moreover, the transporproperties and sheath structure are different in an electrogative plasma.32 Thus, appropriate changes have to be mato Eqs.~5!–~9!.15 This also makes the interpretation of thprobe measurements of the plasma parameters more cocated.

Nevertheless, treatment of the charged species enflux is relatively straightforward. An accurate estimate of tneutral species contribution to the energy flux is more coplex because of the molecular nature of oxygen. Like arg


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oxygen can be electronically excited. In addition, the oxygmolecules in general will have rovibrational energy. Assciation reactions of oxygen atoms forming oxygen molecuhave also to be taken into account. However, the reacprobabilities for rovibrational deexcitation and associaton a surface exposed to a discharge are poorly known. Nthe final state of the reaction products known. In a previostudy, these reactions were shown to have a major impacthe plasma characteristics.21 Under our conditions, oxidationof the copper probe surface is expected only in the inistage of probe usage, resulting in the formation of a pavating layer. Thus, this term can be neglected, but in genereactions with the probe surface have also to be consideThe principles of both mechanisms are illustrated by scmatic reaction graphs in Fig. 11.

As a complete treatment of an oxygen discharge isyond the scope of this article, in Fig. 12, we only compathermal probe measurements of the energy influx to the sstrate in an O2 and an argon plasma under the same macscopic conditions~1 Pa, 15 W, same geometry!. It is obviousthat the total energy influx for oxygen is higher than fargon. The decreased slope forVS,0 with respect to argonindicates that in contrast to argon, in the oxygen plasmamain contribution to the energy flux is caused by neuspecies.

FIG. 11. Reaction graph for oxygen molecule formation~association! andsubstrate oxidation.

FIG. 12. Measured integral energy influx (Qin) for argon and oxygen, re-spectively, for the same macroscopic discharge conditions.


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V. CONCLUSION

The total energy influx (Jin5Qin /AS) from a low powerargon rf plasma~1 Pa, 15 W! towards a metal substrate habeen determined by a thermal probe to be in the order o31023– 331023 J/cm2 s for negative substrate voltagesthe range of2100–0 V where the ions are the dominaspecies for surface heating. For positiveVS , the flux is in theorder of 331023– 831023 J/cm2 s and the kinetic energy othe electrons is the main source for surface heating.complete kinetic energy of the charge carriers is transferinto substrate heating. In case of an oxygen rf plasma unthe same experimental conditions, the energy influxJin forVS52110– 0 V is in the order of 931023– 531023

J/cm2 s which is about 50% higher than for argon at the sasubstrate voltages. In contrast to argon, in oxygen, the mcontribution to the energy influx is by neutral species andby charge carriers. In both cases, the deposited therpower is rather low in comparison to other plasma procesas sputtering or surface cleaning,18 but probably comparableto the thermal load of macroscopic particles suspended indischarge.11 The results underline the sensitivity of the themal probe method and its capability to separate several ctributions to the total thermal influx.

ACKNOWLEDGMENTS

The work has been supported by the Deutsche Fschungsgemeinschaft~DFG! under SFB198/A14. The authors wish to express their thanks to A. Knuth. E.S., aW.W.S. wish to acknowledge the support of the Royal DuAcademy of Science~KNAW !.

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Documents

Energy influx from an rf plasma to a substrate during plasma processing