J. Phys. D: Appl. Phys. 38 (2005) 3417–3421 doi:10.1088/0022-3727/38/18/015
Ion-acoustic solitary waves in a high power pulsed magnetron sputtering discharge
K B Gylfason
1,2, J Alami
3, U. Helmersson
3and J T Gudmundsson
1,21Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
2Department of Electrical and Computer Engineering, University of Iceland, Hjardarhaga 2-6, IS-107 Reykjavik, Iceland
3Department of Physics and Measurement Technology, Link¨oping University, SE-581 83 Link¨oping, Sweden
E-mail:tumi@hi.is (J T Gudmundsson)
Received 5 December 2004, in final form 17 April 2005 Published 2 September 2005
Online atstacks.iop.org/JPhysD/38/3417 Abstract
We report on the creation and propagation of ion-acoustic solitary waves in a high power pulsed magnetron sputtering discharge. A dense localized plasma is created by applying high energy pulses (4–12 J) of length≈70 µs, at a repetition frequency of 50 pulses per second, to a planar magnetron sputtering source. The temporal behaviour of the electron density, measured by a Langmuir probe, shows solitary waves travelling away from the magnetron target. The velocity of the waves depends on the gas pressure but is roughly independent of the pulse energy.
1. Introduction
Korteweg and de Vries derived a model equation (the KdV equation) for shallow water waves, incorporating the effects of dispersion, and showed that their equation has a solitary wave solution [1]. By taking the dispersion of the medium into account, a balance can be reached between the effects of steepening and dispersion, leading to a wave of permanent form. Solitary waves in systems that can be modelled by the KdV equation have become known as KdV solitons.
They have the distinguishing features that their velocity is amplitude dependent and the product of the soliton amplitude and the squared soliton width is constant [1]. Washimi and Taniuti [2] showed that small but finite amplitude one- dimensional ion-acoustic waves, in a two component quasi- neutral plasma consisting of electrons and positive ions, could be modelled by the KdV equation. Ion-acoustic waves are named by their similarity to sound waves in air; both are density waves propagating from one layer to the next. Ion- acoustic waves, however, differ from sound waves in the way momentum is transferred—in sound waves momentum is transferred by collisions but in ion-acoustic waves momentum is transferred through the intermediary of an electric field [3].
More recently, systems of increasing complexity have been
modelled, leading to the derivation of, e.g. the higher dimensional Kadomtsev–Petviashvili equation [4] and the modified KdV equation [5] that describe a quasi-neutral three component plasma consisting of electrons and positive and negative ions.
The first observation of KdV solitons in a two component quasi-neutral plasma was made by Ikezi et al [6] in a double plasma device. Since the initial observation, refinements of the theory have gone hand in hand with extensive experimentation.
This includes multiple soliton production in a double-plasma device [7,8] and excitation of cylindrical [9] and spherical [10] ion-acoustic KdV solitons. The multidipole plasma device [11,12] has served as a testing site for many of the experiments. It provides a more uniform environment than can be achieved in a simple double plasma device. Of special relevance to our work is the study of a compressive ion density perturbation in a multidipole device excited by a potential step [13,14] and more recently by amplitude modulation of a high frequency signal [15].
The terms solitary wave and soliton have been used ambiguously and even interchangeably in the literature. For our work we shall adopt the definition put forward by Arnold [16]. The term solitary wave refers to a non-linear wave that travels with a fixed velocity and exactly preserves its
shape under propagation. A soliton, however, is a solitary wave solution of a specific integrable partial differential equation (PDE) having additional stability and robustness features which are inherited directly from the integrability of the describing PDE. The KdV soliton is the best known example. Lonngren [17] has recently given a good review on solitary waves. Older review papers include more detailed discussions [1,18].
Conventional dc magnetron sputtering is a very successful technique used for plasma assisted deposition of thin films.
Some limitations are however obvious such as low target utilization, low ionization of the sputtered material and risk of arc generation in reactive sputter deposition of dielectric materials. Some of these problems have been alleviated by pulsing the applied voltage [19,20], others by additional ionization by rf [21] or microwave [22] power or by increased magnetic confinement [23].
Two principal methods of pulsing have been proposed:
asymmetric bipolar pulsing [19] and unipolar pulsing [20].
Asymmetric bipolar pulsing in the medium frequency range (10–250 kHz), has become established as one of the main techniques for deposition of oxide and nitride films [19,24].
Unipolar pulsing, which is applied in the experiment described here, utilizes short high power pulses but operates at fairly normal average power levels due to a low duty factor of less than 1%. In this way a substantial increase in the instantaneous plasma density is achieved without increasing the thermal load of the target. Very high electron densities (ne≈ 6 × 1018m−3) have been obtained in the substrate vicinity [25,26]. Furthermore, the target utilization is improved and ionization fractions of sputtered species of up to 70% on average and more than 90% in the peak have been reported [20,27,28]. In earlier work we have reported on the spatial and temporal behaviour of the plasma parameters in the unipolar pulsed magnetron discharge [26].
The aim of this work is to explore the temporal behaviour of the dense localized plasma in a unipolar high power pulsed magnetron sputtering discharge (HPPMS). We report on ion- acoustic solitary waves that are generated. The absence of an initial quiescent background plasma differentiates their production significantly from earlier forms of ion-acoustic solitary wave generation reported.
2. Experimental apparatus and method
A standard planar magnetron source was operated with a titanium target of 150 mm diameter. The cathode is located inside a stainless steel sputtering chamber of radius R= 22 cm and height L = 75 cm. Argon of purity 99.9997% and pressure 1, 5 and 20 mTorr was used as the discharge gas. The base vacuum pressure was approximately 1× 10−6Torr. The magnetron cathode is driven by a pulsed power supply that can deliver peak power pulses of up to 2.4 MW (2000 V at 1200 A) at a repetition frequency of 50 pulses per second (20 ms between pulses) and a pulse width in the range of 50–100 µs.
For the measurements presented here the pulse energy was 4–12 J and pulse width was roughly 70 µs. Electron density perturbations were detected using a cylindrical Langmuir probe made from a tungsten wire of radius rpr= 130 µm. The Langmuir probe was biased to detect the electron saturation
current Isatand time curves of the probe current were collected with a digital oscilloscope. The electron density neis taken to be proportional to the probe current at electron saturation Isat. Although we measure the electron density, our data represent ion-motion as well since the assumption of quasi-neutrality, ni≈ ne, is valid on the time scale considered. Measurements made in the same chamber with a similar setup (tantalum target, 20 mTorr Ar pressure and pulse energies in the range 6–17 J) using a flat probe, biased in the ion saturation region, support this assumption [29]. The probe was positioned on the axis of the chamber at distances z between 4 and 15 cm from the target. A detailed description of the setup has been provided elsewhere [26].
3. Results and discussion
Representative temporal behaviour of the probe electron saturation current for pulse energy 6 J and Ar pressure 5 mTorr at 4, 6, 8, 10 and 12 cm below the magnetron target is shown in figure1. The curves are arbitrarily translated, for clarity, but drawn to scale. Examining the curve at 4 cm, we first notice that before the pulse is switched on the probe current is negligible since the plasma from the last pulse has died out completely. The pulse starts at t= 0 and a few microseconds later a strong peak, travelling away from the target, is detected by the probe. A precursor precedes the first peak at all distances. It is most visible at 8 cm as a kink in the leading shoulder of the peak. The existence of such a precursor has been attributed to a group of streaming ions reflected from the wave front [6,17,30]. A dip occurs in the probe current close to time t = 0. At the time resolution of our measurement, the dip appears at the same time at all distances and hence is most likely due to electro-magnetic interference from the target power supply. The temporal behaviour of the probe electron saturation current for pulse energy 8 J, at various locations below the magnetron target, is shown in figure2for discharge pressure of 1, 5 and 20 mTorr. For 1 mTorr, in figure2(a), the electron saturation current peaks at 51 µs after initiating the pulse at 4 cm below the target and 65 µs after initiating the pulse at 12 cm below the target. The peak thus travels away from the cathode target. After the peak, the electron saturation current decays again and reaches a seemingly stable plateau roughly 200 µs after initiating the pulse after which it stays more or less constant for the remaining 500 µs recorded. The plasma eventually decays down to null before the next pulse appears. Note that although the amplitude of the peak decays considerably after it reaches 9 cm, significant dispersion effects are not visible and the form is kept throughout the journey.
The temporal behaviour of the electron saturation current at 5 mTorr is shown in figure2(b). A strong peak appears early in the pulse and decays to a more broad peak after reaching 9 cm. This sharp peak appears 33 µs after initiating the pulse at 4 cm below the target, 79 µs at 12 cm and 97 µs at 15 cm below the target. After the pulse decays, a stable plateau is reached roughly 200–300 µs after initiating the pulse. The temporal behaviour of the electron saturation current at 20 mTorr is shown in figure2(c). The current reaches a peak value 39 µs after initiating the pulse at 4 cm and 115 µs at 11 cm below the target. The amplitude decay starts earlier at 20 mTorr than at the lower values and the peak broadens considerably.
Figure 1. The electron saturation current Isat, measured by a Langmuir probe, as a function of time from pulse initiation at 4, 6, 8, 10 and 12 cm below the target. The curves are arbitrarily translated but drawn to scale. The argon pressure was 5 mTorr, the target was made of titanium, the pulse length was≈70 µs and pulse energy was 6 J.
A second peak is apparent at a later time. It peaks at 545 µs after initiating the pulse at 4 and 12 cm below the target. This second peak does not seem to travel away from the target; it is stationary.
The trajectories of the initial peaks are shown in figure3.
Each peak travels with a fixed velocity through the chamber.
A least squares fit shows that at 8 J the peaks travel with a velocity of 5.3× 103m s−1 at 1 mTorr, 1.7× 103m s−1 at 5 mTorr and 9.8× 102m s−1 at 20 mTorr. The electron temperature of the plasma after the pulse has been turned off has been measured 1 eV at 5 mTorr and 0.5 eV at 20 mTorr [26].
This corresponds to ion-acoustic velocity of 1.6× 103m s−1 and 1.1×103m s−1at 5 mTorr and 20 mTorr, respectively. The velocity of the peaks versus pulse energy at the three discharge pressures is shown in figure 4. The velocity of the peaks decreases with increasing pressure but is roughly constant with varying pulse energy. Figure5shows the relative changes in the peak density npeakand the average background density n0
with pulse energy at 6 cm below the cathode target. Since our system lacks an initial background plasma we take n0 to be proportional to the seemingly stable probe current remaining after the solitary wave has passed. We see that both the peak plasma density and the background plasma density increase with increasing pulse energy.
The fact that even though the velocity of the solitary wave is independent of pulse power the amplitude of the wave clearly increases with increasing power indicates that the peaks are not KdV solitons. In fact the KdV model [2] assumes a quiescent background plasma with a well-defined electron temperature.
This is not the case in our system where the solitary ion wave expands into vacuum. Despite this deviation we observe that the relation between soliton amplitude and soliton width holds for the waves observed. We plot the maximum density npeak
of the first peak, as it travels away from the magnetron target, in figure6. Intuitively one would expect a spherical symmetry of expanding waves in our system, since the diameter of the target (15 cm) is only one-third of that of the chamber
Figure 2. The electron saturation current, measured by a Langmuir probe as a function of time from pulse initiation and position below the target. The argon pressure is (a) 1 mTorr, (b) 5 mTorr and (c) 20 mTorr. The target is titanium, the pulse length is≈70 µs and the pulse energy is 8 J.
(44 cm). Waves originating at the target can thus expand unrestricted into the half-sphere below. In fact, observations of spherical KdV solitons, excited by a small circular plate, have been reported [31]. In such a non-planar configuration, the amplitude of expanding solitons will decay, just due to the spherical geometry, as
npeak∝ z−4/3, (1) where z is the radius of the soliton [1]. The slope of the solid line in figure6represents the predictions of equation (1). At
Figure 3. The position of the initial density peaks versus the time from pulse initiation. The argon pressure was 5 mTorr, the target was made of titanium and the pulse energy was 8 J. The peaks travel with a velocity of 5.3× 103m s−1at 1 mTorr, 1.7× 103m s−1at 5 mTorr and 9.8× 102m s−1at 20 mTorr.
Figure 4. The velocity of the solitary wave peaks versus the pulse energy for gas pressures 1, 5 and 20 mTorr. The velocity decreases with increasing pressure but is roughly constant with varying pulse energy.
distances between 6 and 11 cm below the target, the peaks follow the polynomial decay model reasonably well. The slopes obtained by a least squares fit in this range are indicated in the legend. For the highest energies data were not available for all the distances; thus the fit is between 9 and 11 cm for 10 J and between 10 and 12 cm for 12 J. Nearest the target the decay is slower and may be due to the fact that ionization is still active. In addition equation (1) assumes a point source and such an assumption is only valid in the far field of a source of finite size. Far from the target the decay is faster since there the amplitude has become so small that the balance between non-linearity and dispersion is lost and dispersion takes over.
Similar behaviour has been observed for spherical KdV solitons [10].
Figure 5. The relative changes in average background density n0/n0(4 J) and amplitude of the leading peak npeak/npeak(4 J) at 6 cm below the target versus pulse energy. The process gas was argon at 5 mTorr and the target was made of titanium.
Figure 6. The maximum density npeakof the leading peak measured at various distances z from the magnetron target for pulse energies of 4–7 J. The process gas was argon at 5 mTorr and the target was made of titanium. The solid line is proportional to z−4/3.
4. Conclusion
We have observed ion-acoustic solitary waves, without the presence of an initial quiescent background plasma, in a pulsed magnetron sputtering discharge. We have investigated how the velocity of the wave depends on pulse energy and gas pressure.
The velocity decreases with increasing pressure and is almost independent of the pulse energy. The amplitude of the wave increases with increasing pulse energy. This fact shows that the waves are not KdV solitons. However, the amplitude decay of the solitary waves at 5 mTorr fits reasonably with a model of spherically expanding KdV solitons. These findings indicate that the simple KdV model is not sufficient to explain the solitary waves observed in our system.
Acknowledgments
This work was partially supported by the Swedish Science Council, the Swedish Foundation for Strategic Research, the Icelandic Research Fund for Graduate Students, the University of Iceland Research Fund and the Icelandic Research Council.
The company Chemfilt R & D is acknowledged for the use of the power supply. JTG is grateful for discussions with Professors A J Lichtenberg and M A Lieberman on the subject of solitary waves and solitons.
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