APPLIED PHYSICS LETTERS
`
`VOLUME 78, NUMBER 22
`
`28 MAY 2001
`
`Evolution of the electron energy distribution and plasma parameters
`in a pulsed magnetron discharge
`J. T. Gudmundssona)
`Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavı´k, Iceland
`J. Alami and U. Helmersson
`Department of Physics, Linko¨ping University, SE-581 83 Linko¨ping, Sweden
`共Received 27 February 2001; accepted for publication 2 April 2001兲
`We demonstrate the creation of high-density plasma in a pulsed magnetron discharge. A 2.4 MW
`pulse, 100 ␮s wide, with a repetition frequency of 50 Hz is applied to a planar magnetron discharge
`to study the temporal behavior of the plasma parameters: the electron energy distribution function,
`the electron density, and the average electron energy. The electron density in the vicinity of the
`substrate, 20 cm below the cathode target, peaks at 8⫻1017 m⫺3, 127 ␮s after initiating the pulse.
`Towards the end of the pulse two energy groups of electrons are present with a corresponding peak
`in average electron energy. With the disapperance of the high-energy electron group, the electron
`density peaks, and the electron energy distribution appears to be Maxwellian like. Following the
`electron density peak, the plasma becomes more Druyvesteyn like with a higher average electron
`energy. © 2001 American Institute of Physics.
`关DOI: 10.1063/1.1376150兴
`
`The dc magnetron sputtering discharge has found wide-
`spread use in coating processes, particularly in the deposition
`of thin metallic films. In magnetron sputter deposition, atoms
`are sputtered from the cathode target by ions drawn from
`a magnetically
`confined
`plasma. A dense
`plasma
`(⬃1018 m⫺3) is generally trapped close to the cathode-target
`surface. However, the plasma densities close to the sample to
`be deposited 共⬃5 – 10 cm below the target兲 are several orders
`of magnitude lower (1015– 1016 m⫺3). Furthermore, the ion-
`ized fraction of the sputtered species is small 共⬃1%–10%兲
`and the majority of the species extracted on the negatively
`biased substrates are ions of the discharge gas.
`Recently, pulsing the magnetron has been shown to in-
`crease the ion density significantly.1,2 By pulsing the magne-
`tron, very high plasma densities (⬃1018 m⫺3) have been ob-
`tained 6–10 cm away from the target with a degree of
`ionization of 30%–70%.2,3 Furthermore, the target utilization
`is improved.1 The pulsed magnetron has been demostrated
`for use in high-aspect-ratio filling applications and improved
`thickness homogenity of deposited films compared to con-
`ventional dc magnetrons.1 However, the energetics of the
`discharge, the composition of the plasma, and the reactions
`among the species remain to be investigated. The fundamen-
`tal plasma characteristic for better understanding of the
`plasma chemistry is the electron energy distribution function.
`Measurements in a conventional dc magnetron indicate that
`the electron energy distribution on axis is strongly assym-
`metric, representing a net electron drift from the cathode to
`the anode.4 A non-Maxwellian electron energy distribution is
`to be expected since the source is localized to the magnetic
`trap region, and at this low neutral pressure 共1–5 mTorr兲 the
`electron mean-free path is relatively long. The electron en-
`ergy distribution in a dc argon discharge in the vicinity of the
`substrate has been measured by Ivanov et al.5 They report
`
`a兲Electronic mail: tumi@hi.is
`
`the presence of two energy groups of electrons in the plasma.
`For sputter deposition of thin films, knowledge of the elec-
`tron energy distribution and plasma parameters in the near-
`substrate vicinity are of great importance for determining the
`process parameters. The aim of this work is to investigate the
`temporal evolution of the electron energy distribution func-
`tion 共EEDF兲 and the plasma parameter electron density ne ,
`average electron energy 具E典, and plasma potential Vpl for a
`pulsed high-density plasma in a magnetron sputtering dis-
`charge in the substrate vicinity.
`The standard balanced planar magnetron source is oper-
`ated with a tantalum target of 150 mm diam. The cathode is
`located inside a stainless-steel sputtering chamber of radius
`R⫽60 cm and height L⫽75 cm. Argon of 99.9997% purity
`is used as the discharge gas. The magnetron cathode was
`driven by a pulsed power supply that can deliver peak power
`pulses of up to 2.4 MW 共2000 V and 1200 A兲 at a repetition
`frequency of 50 Hz and a pulse width in the range of 50–100
`␮s. For the measurents presented here, the average power
`was 300 W, pulse width 100 ␮s, and repitition frequency 50
`Hz. The peak voltage was roughly 800 V, and the peak cur-
`rent about 100 A. The argon pressure was 2 mTorr. A cylin-
`drical Langmuir probe, which is a cylindrical tungsten rod of
`length lpr⫽5.5 mm and radius rpr⫽50 ␮m, was applied for
`the measurements. The probe holder is an alumina tube with
`outer radius rprh⫽0.5 mm and 1.9 cm long. The probe is
`designed to fulfill the basic requirements for Langmuir-probe
`as discussed by Godyak,6
`rprhⰆlpr
`and
`diagnostics
`rpr ,rprh ,␭DeⰆ␭e⬃1 cm. Here, ␭De⬃14– 100 ␮m is the De-
`bye length and ␭e⬃1 cm is the electron mean-free path. The
`probe is positioned perpendicluar to the discharge axis, and
`thus to the electric- and magnetic-field lines 20 cm below the
`target. The magnetic field at this position is ⬍0.2 mT, which
`leads to a gyroradius of ag⫽(␲mekTe/2)1/2/eB⬇ 140 ␮m,
`and thus rpr/ag⬇0.4. Therefore, we can neglect the error in
`the measured electron density caused by the magnetic field.7
`The time-resolved probe current was recorded for 500 ␮s
`
`0003-6951/2001/78(22)/3427/3/$18.00
`
`3427
`
`© 2001 American Institute of Physics
`
`Downloaded 02 Oct 2013 to 216.185.156.28. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
`
`GILLETTE 1110
`
`

`
`3428
`
`Appl. Phys. Lett., Vol. 78, No. 22, 28 May 2001
`
`Gudmundsson, Alami, and Helmersson
`
`after initiating the pulse at 1 ␮s intervals for a fixed voltage.
`This was repeated in the voltage range from ⫺30 to 20 V at
`0.1 V intervals. For each time value, the I – V curve was
`reconstructed. The measured I – V curve was smoothed by
`convoluting a Blackman window to the measured data.8 The
`second derivative of the I – V curve was calculated and the
`electron energy distribution function ge(E) found. The EEDF
`is given by the Druyvesteyn formula as9,10
`冉 2eV
`冊 1/2 d2Ie
`2m
`ge共V 兲⫽
`共1兲
`dV2 ,
`e2A pr
`m
`where E is the electron energy in equivalent voltage units.
`The plasma potential Vpl is the voltage where the second
`derivative of the electron current Ie is zero, and the floating
`potential Vfl is where the probe draws equal ion and electron
`currents. The electron density ne is determined as
`ne⫽冕
`ge共E兲dE,
`⬁
`and the average electron energy 具E典 is determined as
`冕
`具E典⫽
`⬁Ege共E兲dE.
`
`共2兲
`
`共3兲
`
`0
`
`1n
`
`0
`e
`Figure 1 shows the evolution of the electron energy dis-
`tribution function with time from initiating the pulse. Ini-
`tially, the distribution can be described by a single peaked
`distribution 关Fig. 1共a兲兴. At around 95 ␮s, a second group of
`high-energy electrons appears. This high-energy group re-
`mains until roughly 115 ␮s after initiating the pulse. This
`presence of two energy groups can be seen at 96 ␮s in Fig.
`1共a兲 and at 105 and 110 ␮s in Fig. 1共b兲. At roughly 120 ␮s
`after initiating the pulse the electron energy distribution
`shows a single group of electrons. At roughly 250 ␮s after
`initiating the pulse the electron energy distribution reaches
`the shape that remains for the following 250 ␮s, as seen in
`Fig. 1共c兲. Higher-energy peaks are seen at 350 and 450 ␮s
`关Fig. 1共c兲兴. The evolution of the electron density with time
`from the initiation of the pulse is shown in Fig. 2共a兲. The
`electron density peaks at 8⫻1017 m⫺3 127 ␮s after initiating
`the pulse. The electron density decreases again and falls to
`8⫻1016 m⫺3 at 500 ␮s after initiating the pulse. The mea-
`sured electron energy distribution function can be fitted to
`the function
`g f共E兲⫽a冑E exp共⫺bE x兲,
`共4兲
`where a, b, and x are constants. For x⫽1, we have a Max-
`wellian electron energy distribution, and for x⫽2 a
`Druyvesteyn distribution. The value of x was determined by
`performing a least-squares analysis of ln关gf(E)/冑E兴 vs E x for
`various x to find the best fit. During the pulse, 50–90 ␮s
`somewhat overestimated. To correct for this smoothing error,
`after initiating the pulse, the parameter x is ⬃2, indicating a
`Eq. 共4兲 is fitted to the measured electron energy distribution
`function from the electron energy where the electron energy
`Druyvesteyn-like energy distribution. The fitting parameter
`is x⬇1 in the range of 115 ␮s, until 150 ␮s after initiating
`distribution function has a maximum value until it has fallen
`roughly one order of magnitude.8 The best fit to Eq. 共4兲 is
`the pulse, indicating a Maxwellian-like electron energy dis-
`then interpolated to zero electron energy. The interpolated
`tribution. Thus, when the electron density is the most dense,
`3 – 8⫻1017 m⫺3, the electron energy distribution is Maxwell-
`electron energy distribution function is used to extend the
`ian like. From roughly 200 ␮s until 500 ␮s we find x
`measured electron energy distribution function to low en-
`ergy. The electron density and the averaged electron energy
`⬇2.5– 3. The smoothing method introduces distortion to the
`are then calculated using the extended electron energy distri-
`electron energy distribution function around the plasma po-
`bution function in Eqs. 共2兲 and 共3兲, respectively. The average
`tential. Due to this distortion, the average electron energy is
`Downloaded 02 Oct 2013 to 216.185.156.28. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
`
`FIG. 1. Normalized EEDF measured 共a兲 during pulses 60, 80, and 100 ␮s
`after initiating the pulse; 共b兲 around the electron density maximum 105, 110,
`and 130 ␮s after initiating the pulse; and 共c兲 250, 350, and 450 ␮s after
`initiating the pulse. Pulse length, 100 ␮s; average power, 300 W; and pres-
`sure 2 mTorr.
`
`

`
`Appl. Phys. Lett., Vol. 78, No. 22, 28 May 2001
`
`Gudmundsson, Alami, and Helmersson
`
`3429
`
`again with time. The average electron energy peaks at 3.5 eV
`roughly 100 ␮s after initiating the pulse. This peak in the
`average energy coincides with the presence of the high-
`energy group of electrons appearent in the electron energy
`distribution. At 127 ␮s, when the electron density peaks, the
`average electron energy has decreased to ⬃2 eV. The aver-
`age electron energy reaches a minimum of about 1.5 eV at
`240 ␮s. It increases again until it reaches a plateau of 2.4 eV
`at roughly 290 ␮s, which remains for the following 210 ␮s.
`The average electron energy we report
`in the pulsed
`magntron is comparable to what is observed by Sheridan,
`Goeckner, and Goree.11 The time evolution of the plasma
`potential and the floating potential from initiating the pulse is
`shown in Fig. 2共c兲. As the energy of ions bombarding a
`substrate at the floating potential is determined by the differ-
`ence between the floating potential and the plasma potential
`(Vpl⫺Vfl), this value is plotted in Fig. 2共c兲 as well.
`In conclusion, we have measured the temporal behavior
`of the electron energy distribution function in a pulsed mag-
`netron. Towards the end of the pulse, two energy groups of
`electrons are present with a corresponding peak in average
`electron energy. With the disapperance of the high-energy
`electron group, the electron density peaks, and the electron
`energy distribution appears to be Maxwellian like. Eventu-
`ally, the plasma becomes more Druyvesteyn like with lower
`electron density and higher average electron energy.
`
`This work was partially supported by the Swedish Foun-
`dation for Strategic Research and the University of Iceland
`Research Fund. The company Chemfilt R & D is acknowl-
`edged for the use of the power supply.
`
`1V. Kouznetzov, K. Maca´k, J. M. Schnider, U. Helmersson, and I. Petrov,
`Surf. Coat. Technol. 122, 290 共1999兲.
`2K. Maca´k, V. Kouznetzov, J. M. Schnider, U. Helmersson, and I. Petrov,
`J. Vac. Sci. Technol. A 18, 1533 共2000兲.
`3U. Helmersson, Z. S. Kahn, and J. Alami, in The Third International
`Euroconference on Advanced Semiconductor Devices and Microsystems,
`Somolenice Castle Slovakia 共2000兲, p. 191, IEEE Catalog No. 00EX386.
`4T. E. Sheridan, M. J. Goeckner, and J. Goree, Jpn. J. Appl. Phys., Part 1
`34, 4977 共1995兲.
`5I. Ivanov, S. Statev, V. Orlinov, and R. Shkevov, Vacuum 43, 837 共1992兲.
`6V. A. Godyak, in Plasma–Surface Interactions and Processing of Mate-
`rials, edited by O. Auciello 共Kluwer Academic, Dordrecht, 1990兲, pp.
`95–134.
`7E. Passoth, P. Kudrna, C. Csambal, J. F. Behnke, M. Tichu´, and V.
`Helbig, J. Phys. D 30, 1763 共1997兲.
`8J. T. Gudmundsson, Memorandum No. UCB/ERL M97/38, Electron
`Research Laboratory, University of California, Berkeley 共1997兲.
`9M. J. Druyvesteyn, Z. Phys. 64, 781 共1930兲.
`10M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges
`and Materials Processing 共Wiley, New York, 1994兲.
`11T. E. Sheridan, M. J. Goeckner, and J. Goree, J. Vac. Sci. Technol. A 34,
`2173 共1998兲.
`
`共b兲 average electron energy, and 共c兲
`共a兲 Electron density,
`FIG. 2.
`⫹ floating potential Vfl , ⫻ plasma potential Vpl , and * potential difference
`共Vpl⫺Vfl兲 as a function of time from initiation of the pulse. Target current
`pulse length, 100 ␮s; average power, 300 W; and pressure, 2 mTorr.
`electron energy 具E典 is shown versus time from initiating the
`pulse in Fig. 2共b兲. The average electron energy decreases
`during the pulse, down to 2.5 eV at 92 ␮s, where it increases
`
`Downloaded 02 Oct 2013 to 216.185.156.28. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions