Localized heating of electrons in ionization zones: Going beyond the Penning-Thornton

Localized heating of electrons in ionization zones: Going beyond the Penning-Thornton paradigm in magnetron sputtering André Anders Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA Electronic mail: aanders@lbl.gov Abstract The fundamental question of how energy is supplied to a magnetron discharge is commonly answered by the Penning-Thornton paradigm invoking secondary electrons. Recently, Huo and coworkers (C. Huo, D. Lundin, M.A. Raadu, A. Anders, J.T. Gudmundsson, and N. Brenning, Plasma Sources Sci. Technol. 22, 045005 (2013)) used a global discharge model to show that electron heating in the electric field of the magnetic presheath is dominant over heating by secondary electrons. In this contribution, this concept is applied locally taking into account the electric potential structure of ionization zones. Images of ionization zones can and should be interpreted as diagrams of the localization of high electric potential and related electron energy. 1

Since the broad introduction of sputtering magnetrons for the deposition of thin films in the 1970s, a large number of papers were published elucidating many aspects of discharges in crossed electric and magnetic fields, of particle fluxes, and applications. Among the early work, Thornton s description 1 captures our conventional understanding of the principles. We find the importance of classical concepts like the role of charged particle motion in crossed electric and magnetic fields, and the anticipation that collective effects (waves and instabilities) are important as they govern charged particle transport and thereby determine the discharge impedance and overall performance. Thornton wrote Electron drifts perpendicular to the magnetic field develop in the presence of a perpendicular electric field or a density gradient. Such drifts are inherently unstable, since any departure from charge neutrality in the form of charge bunching and separation create electric fields which cause second-order E B drifts that can exacerbate the perturbation. 1 Indeed, publications in recent years have confirmed that discharge plasma in crossed electric and magnetic fields are often structured or self-organized. 2-4 This seems especially relevant for high power impulse magnetron sputtering, 5-7 HiPIMS, where film deposition is based on an intense flux of ions arriving at the substrate. 8 One of the fundamental questions we still wrestle with is how the magnetron discharge is energized, i.e., how energy supplied by the power supply is actually brought to electrons that cause excitation and ionization and thereby enable the very functioning of the discharge. The conventional paradigm, as summarized by Thornton, 1 was originally described by Penning 9 for glow discharges. It postulates that plasma generation is based on the supply of energy via secondary electrons (SEs) from the target. SEs are critically important because they travel through the cathode sheath and pick up kinetic energy equivalent to the sheath voltage: ESE evsheath. The sheath accommodates most (about 80-90%) 2

of the applied voltage; this is usually several 100 V. Using a simple energy conservation argument, each SE has the capability of producing multiple ion-electron pairs, namely up to evsheath E eff, where eff E is the effective energy cost to form an ion-electron pair, a value typically about twice the ionization energy, i.e. about 30 ev for argon. 1 Penning 9 was well aware, in 1936, that this mechanism has some difficulties when the glow discharge is in a magnetic field, namely that the number of available secondary electrons is very small because (a) the SE yield SE from primary ion impact is small to begin with (typically 0.1 or less), and (b) some SEs would be recaptured when the magnetic field vector is approximately parallel to the target surface. The latter point can be seen when considering the equation of motion (neglecting all kinds of collisions for now) dv e dt m e E v B, (1) where the second term of the right hand side, the Lorentz force, causes electrons to gyrate around magnetic field lines. Unless it makes a collision, or the local magnetic field is not parallel to the emitting cathode, a SE is likely to return to the cathode surface and could be recaptured after completing only about ½ of one gyration. The point of this discussion is that SE emission may be insufficient to provide the necessary energy to electrons of the discharge plasma. The relatively large potential drop (e.g. of order 100 V) can exist in the quasineutral plasma of the presheath because a magnetic field is present: it causes gyration of electrons and impedes their motion perpendicular to the magnetic field. In a magnetron, the electric field is perpendicular to the magnetic field lines and causes the well-known E B drift of electrons. 1 The magnetic field arches over the target and the magnetic presheath is most expanded where the 3

B-field is approximately parallel to the target (Fig. 1). This is the region of most ionizing collisions caused by electrons. Positive ions are accelerated toward the negatively biased target, causing sputtering and the formation of the well-known erosion racetrack. A large potential drop in the plasma has been linked with the Hall parameter h ce ve, where ce is the electron cyclotron angular frequency and e is the electron collision frequency. 10 With increasing distance from the target, the magnetic field weakens, the Hall parameter decreases, and less of a voltage drop is accommodated. A gyrating electron periodically reverses direction due to the magnetic mirror effect, as indicated by Thornton 1 in his Fig. 2f, or due to the electric field when reaching the sheath boundary. Averaging over gyration and back-and-forth motion leads to the already-mentioned electron E B drift (and other drifts such as the B B drift). Without collisions and instabilities, the drift is on equipotential surfaces as long as the electric field is perpendicular to the magnetic field. Electrons gain energy as they diffuse to magnetic field lines where the potential is higher. This statement was the basis for a different electron heating mechanism introduced by Huo et al. 11 It greatly reduces the need for SEs. Considering a global model of the magnetron discharge, it was shown that the voltage drop in the magnetic presheath can lead to very significant energy dissipation and electron heating. The voltage drop in the magnetic presheath (a.k.a. ionization region between sheath and bulk plasma) is of the order 100 V, i.e. much smaller than the voltage drop in the sheath (several 100 V), however, the number of electrons experiencing the voltage drop in the presheath is much greater. Following Huo et al., 11 one can write the power that is given to electrons as a sum of the power by the Penning-Thornton mechanism, and the heating power in the presheath, P P P I V I V 2, (2) e e,sheath e,presheath SE sheath discharge presheath 4

where the sheath voltage is Vsheath Vdischarge Vpresheath ; the SE current is I 1 1 1 SE I discharge based on the effective or net SE yield. The factor ½ in the last term of Eq.(2) is due the argument that in the presheath, where ionization occurs, about ½ of the current is carried by electrons (going to the anode), and the other half is carried by the ions going to the target. Equation (2) can be written as 1 V Pe Idischarge 1 Vdischarge Vpresheath 1 2 presheath (3) The ratio of the two terms in the brackets determines the contribution of the Penning-Thornton mechanism (first term) versus presheath heating (second term): P P PenTho presheath 1 V discharge 21 1 1 V presheath (4) For example, picking reasonable values: ~ 0.05, V ~ 500 V discharge, and V ~ 100V presheath we find a ratio of 0.29, i.e. heating by SEs cannot be neglected but is smaller than presheath heating. In this contribution, the idea of presheath heating of electrons 11 is examined on a local level, and it is shown that there is an interdependence between presheath heating of electrons, the formation of ionization zones 5-7 (a.k.a. spokes 12-14 ), and associated potential humps. 15 Fast imaging of ionization zones and measurements of charged particle fluxes have revealed important features: (a) ion and electron fluxes appear in short pulses (jets), 16,17 (b) doubly charged ions have approximately twice the energy of singly charged ions, 15,16 and (c) ions emitted in the E B direction have higher energy than ions leaving the magnetron in the E B direction. 15 All of these features can be explained 15 assuming that an ionization zone is a locations in the presheath with a potential hump of several 10 V. Consistent with Maxwell s 5

equations, each potential hump is surrounded by an electric double layer 12,15 as illustrated in Figures 2(a)-(d) in azimuthal, axial, and radial directions. The exact momentary electric potential distribution in the presheath and especially around the ionization zones is difficult to determine as probe measurements very close to the target excessively disturb the discharge. Fortunately, at least time-averaged plasma potential data are available 18-20 measured at some distance from the target. They can be extrapolated to the relevant region up to the presheathsheath boundary (Fig. 1). The data suggest that a drop of the order 100 V occurs from the sheath edge (at about z = 0.5 mm from the target surface) to the plasma outside the magnetic presheath (at about z = 25 mm; those distances may vary depending on the specifics of the magnetron and discharge parameters). The most detailed data 19 were obtained by averaging over 100 times for each location, i.e. they cannot give information on the electric potential structure for an individual, moving ionization zone. Time-averaged, the potential distribution in a plane perpendicular to the direction of the racetrack,, looks like a funnel (cf. Fig. 7 of ref. 19, and Fig. 1 here). The derivative E V gives an electric field that accelerates ions and gives rise to the E B drift of electrons. As shown in Fig. 1, the arched magnetic field lines intersect the electric field approximately perpendicularly, making the magnetic field lines approximate equipotential lines. Electrons drift in a surface of equal potential because the E B drift is by definition perpendicular to the fields. The local electric field can be significantly changed by the space charge of the double layer enclosing the hump, while the magnetic field is only slightly altered by the currents in the plasma. 21 According to the changes of the local electric field, the local E B drift of electrons arriving at the ionization zone is re-directed toward the target as shown in Fig. 2(a). Without interactions, electrons would drift under the hump to emerge on the other side 6

and continue drifting along the racetrack. However, as the ionization zone is a region of enhanced plasma density, and the density is much higher close to the target than far from it, electrons experience an enhanced rate of collisions, leading to enhanced excitation, ionization, and cross-field diffusion as indicated by the dashed lines in Fig. 2(a). Cross-field diffusion is facilitated by collisions (classical mechanism) and microinstabilities (collective effects leading to Bohm and faster-than-bohm diffusion). 22,23 Electrons entering the potential hump are energized beyond the excitation and ionization energy as the potential maximum is estimated to be at least several 10 V above its surroundings. 16 This mechanism explains enhanced light emission from the hump region. It can also explain another peculiar feature, a visible cut of light intensity on the E B side of the ionization zone (Fig. 3): this side is the only region where electrons are directed toward the target and do not leave the near-target region. Up to now, the presence of a potential hump in an ionization zone was a priori assumed. One needs to show that (a) a potential hump can grow from a fluctuation, and (b) the proposed mechanism of electron heating would sustain the potential hump. As already mentioned at the beginning, the importance of fluctuations, feedback and instabilities was already pointed out by Thornton. 1 Recent particle-in-cell Monte-Carlo simulations of low current dc magnetron sputtering showed spontaneous bunching of plasma when starting from a homogenous, low density plasma. 24 A large fluctuation can provide the conditions for a positive feedback: the greater the density the higher is the chance that drifting electrons interact there. The underlying reason for the formation of a potential hump is the difference in inertia of electrons and ions. Electrons and ions behave differently: electrons are magnetized and therefore subject to drift, whereas ion motion is dictated by the local electric field. Due to their small 7

inertia, electrons leave the location of higher density faster than ions, thereby leaving ions behind and creating positive space charge: the condition for the potential hump. While this mechanism amplifies the hump, its growth is limited because electrons need to be able to escape from the hump from an energy point of view. An electron can escape from the potential hump only if its kinetic energy is greater than the smallest difference of potential at its location and a location surrounding the hump, which we designate as V2, E e V (5) e Secondary electrons having gained high energy from the sheath are energetic enough to enter and leave the hump. It is more interesting to consider the majority of electrons entering the hump with energy less than the energy of SEs. This point is amplified by the fact that the Hall current 2 of electrons exceeds the discharge current by a factor 3 or more. 25 According to the localized energizing model, electrons have already some energy ev 0 and gain additional energy e V1 when entering the hump, where V1 can reach several 10 V and thus readily exceeding the ionization energies of the neutrals present. Electrons sufficiently energized can make inelastic collisions and lose the energy E, e loss through collisions with particles of type. One Ee can then write the condition for escape of electrons from the hump as e V E ev. (6) 1 e 2 Localized ionization and electron escape can occur because the potential hump is asymmetric, i.e. V1 V2, due to shape of the hump in z-direction, see Fig. 2(b). Electrons about to leave the hump drift around it (Fig. 2(a)), and have the highest likelihood of escaping at the greatest distance from the target because the magnetic field is weakest at this point. This is consistent 8

with the energy argument (6) and the observation of plasma flares originate from ionization zones. 17 For a deeper analysis of this situation one needs to develop considerably more complicated models and simulation. Spectroscopic imaging of ionization zones 26 revealed that the higher the excitation level, the sharper and more spatially limited the visible emission are, which can be interpreted as the shape of the potential hump (Fig. 3). This suggests that spectrally integrated 5-7,14 and spectrally selected 26 images show not just regions of enhanced excitation and ionization but regions of elevated electric potential. Images of ionization zones can and should be interpreted as approximate distributions of electric potential and related electron energy. Electrons reaching the center of the ionization zone at greater distances from the target are most energetic as judged by the upper excitation level of the emitted spectral lines, which is consistent with images this time seen from the side. As a side note, one can see that the proposed potential structure has the highest surface electric field at the edges of the racetrack (Fig. 2(c)), which may explain observations 27,28 that arcing preferentially occurs at the edges of the racetrack rather than inside. In conclusion, taking the hypothesis that each ionization zone is associated with a potential hump enclosed by an electric double layer, one finds that drifting electrons are deflected toward the target when they arrive at an ionization zone. In the relatively dense plasma close to the target they are likely to reach greater heights above the target through collisions and microinstabilities. They are energized as they enter a region of higher potential. This enables a feedback mechanism for maintaining and amplifying the ionization zone, namely the potential hump results from the inertia of ions that are left behind as a fraction of electrons escapes from 9

the ionization zone. Since inelastic collisions of energized electrons are the cause for the light emitted from the ionization zones, such zones are closely related to the local electron energy. This suggests interpreting images of ionization zones as approximate images of plasma potential and electron energy. Local energizing of electrons in the magnetic presheath, the appearance of ionization zones, plasma flares, the low-light cut at the E B side of an ionization zone, and the formation of potential humps are all related phenomena. A. Rauch, M. Panjan, P. Ni, J. Andersson, Y. Yang and J. Liu are gratefully acknowledged for their role in producing many images of ionization zones and discussing the underlying physics. Work at LBNL is supported by the U.S. Department of Energy, under Contract No. DE-AC02-05CH11231. 10

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Figure Captions Fig. 1 Composite image showing magnetic field (left) and electric field (right) of a 3 magnetron; r = 0 represents the center of the target. While the magnetic field, produced by permanent magnets and measured with a movable Hall probe, is almost independent of the discharge, the electric field varies with discharge conditions. The E-field distribution shown here was measured with an emissive probe, where the value at each location was obtained by averaging over 100 HiPIMS pulses; for more details see ref. 19 Fig. 2 Schematic presentation of the proposed potential distribution, where is the coordinate along the racetrack, r is the radial coordinate perpendicular to the racetrack, and z is the distance from the target surface; in (a) the E B drift of electrons is indicated by arrows; electrons entering the hump are energized (dashed arrows); (b) shows the potential as a function of distance inside and outside the potential hump; (c) indicates the potential hump over the racetrack across the racetrack, i.e. as seen in radial direction, and (d) the same view but outside the hump. Fig. 3 Fast camera images of ionization zones in the emitted light of Al neutrals (left column) and Al ions (right column) in side-on and end-on view (upper and lower row, respectively). The regions of an electric double layer and high potential are indicated. Since the fast camera can only take one image at a time, the images shown are from different HiPIMS pulses. However, from the large number of images those were selected that represent similar conditions. For experimental details see ref. 26 13

Fig. 1 14

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Fig. 3 16