A simple, gas‐fed, radio‐frequency‐driven plasma source is described. By use of lower hybrid waves, noble gas plasmas were produced with electron densities up to 10^12 cm -3 over a range of magnetic fields from 400 G to 1.5 kG and rf frequencies from 2–220 MHz

Edrich, D.

McWilliams, R.

Platt, R. C.

Sheehan, D. P.

English

University of San Diego

University of San DiegoDigital USDPhysics and Biophysics: Faculty Publications Department of Physics and Biophysics11-1-1990Simple overdense rf plasma sourceR. McWilliamsUniversity of California, IrvineD. EdrichUniversity of California, IrvineR. C. PlattUniversity of California, IrvineD. P. SheehanUniversity of San Diego, dsheehan@sandiego.eduFollow this and additional works at: http://digital.sandiego.edu/phys-facultyPart of the Physics CommonsThis Article is brought to you for free and open access by the Department of Physics and Biophysics at Digital USD. It has been accepted for inclusionin Physics and Biophysics: Faculty Publications by an authorized administrator of Digital USD. For more information, please contactdigital@sandiego.edu.Digital USD CitationMcWilliams, R.; Edrich, D.; Platt, R. C.; and Sheehan, D. P., "Simple overdense rf plasma source" (1990). Physics and Biophysics:Faculty Publications. 19.http://digital.sandiego.edu/phys-faculty/19Simple overdense rf plasma source R. McWilliams, D. Edrich, R. C. Platt,a) and D. P. Sheehanb) Department of Physics, University of California, Irvine, CA 92717 (Received 21 May 1990; accepted for publication 30 July 1990) A simple, gas-fed, radio-frequency-driven plasma source is described. By use of lower hybrid waves, noble gas plasmas were produced with electron densities up to 1012 em - 3 over a range of magnetic fields from 400 G to 1.5 kG and rf frequencies from 2-220 MHz. I. INTRODUCTION Radio-frequency driven plasma sources have been used for over 15 years. 1- 3 Generally, these sources couple the rf energy into the plasma formation via specific waves launched into low pressure gases or plasma from a coupler. Many of these sources rely upon wave coupling which re-quire detailed tuning of the source to the desired plasma, such as choosing a source frequency which depends on the background magnetic field. The use of lower hybrid waves provides a radio-frequency plasma source, reasonably de-coupled from the magnetic field, generating moderate plasma densities with low temperatures. 2,3 This article de-scribes a lower hybrid wave plasma source which is simple to construct, and flexible in operation, It is easy to insert and remove from vacuum vessel, provide some desirable boundary conditions for plasma experiments, is relatively decoupled from B field consideration. and can be used with a wide variety of gases. Previous lower hybrid plasma sources2,3 have been suc-cessful. The source described here utilizes some of the ben-efits achieved with these sources while avoiding some of their complexities of design and operation. Earlier lower hybrid sources required substantial matching network elec-tronics and differential vacuum pumping2 or were operated in a single-ended "gun" type design, 3 Advances in rf am-plifiers have obviated some of the matching network re-quirements. Differential pumping may not he desirable in all cases and the difficulty of doing so may be avoided here. The use of a "gun" type source produces a unidirectional plasma with a metallic boundary condition across the mag-netic field at the source. Some experiments benefit from having plasma flow along magnetic field lines without en-countering obstacles at the plasma source. A further re-quirement of source simplicity may demand that a source be removable easily and quickly from the experiment chamber, a characteristic of the source described here. II. THEORY The theory of lower hybrid rf plasma sources has been developed previously and compared with experiment. 2,3 Some essential elements of this theory are repeated here. Lower hybrid waves (LHW) arc free to propagate from the source into the plasma at angles oblique to the plasma confining magnetic field. When a plasma is present such that the density satisfies wpe> W, where wpe and ware the plasma and wave frequencies, respectively, then typi-cally densities of order 106_108 cm -- 3 are required to sat-isfy this condition for source frequencies in the tens of MHz. The wave and source near fields provide the ionizing electric field for background gas. Thus LHW propagate into the plasma while creating additional plasma, accord-ing to the dispersion relation w2=wi[{( 1 + kOm/k2m e), where kit is the component of k, the wavenumber, which is parallel to the confining magnetic field. For rf source fre-quencies below the geometric mean of the ion and electron gyrofrequencies, this process may continue until the plasma density rises sufficiently to make (1) where wpi is the ion plasma frequency and wee is the elec-tron gyrofrequency. At a density high enough to satisfy Eq. ( 1 ), the rf field is prevented from propagating to higher densities. Similarly, for waves with w above the mean gyrofre-quency, the rf fields will propagate into the plasma until the density rises enough to violate I 2 2 W;i< w2 [ ,;'ilW -,{I + NiI(-~ - 1) 1 ' \jwcewcj V wcewcl I (2) where Nil = kliC/w is the component of the normalized wavenumber parallel to the magnetic field. Hence, there are two possible density limitations and plasma may be created by the rf source until the limit of Eqs. (1) or (2) is encountered. It should be noted that there are relatively few restrictions on the source frequency used. There is also a general trend that higher wave frequencies have higher maximum attainable plasma densities. Equations (1) and (2) are applied to specific examples in Fig. 1. In Fig. 1 (a) a rf source frequency of 10 MHz is applied to argon gas and the resulting maximum density achievable is plotted versus confining magnetic field, For the range of magnetic field examined, only Eq. (2) applies and that prediction is plotted for three different values of Nn excited by the rf source. In Fig. 1 (b) four different-source wave frequencies are examined, for helium plasmas, all with Nit = 10 assumed, and in this case both equations ")Science Applications International Corporation, Alhuquerque, NM 87106. b;Dcpartment of Physics, University of San Diego, Alcala Park, San Diego, CA 92110. 3460 Rev. Sci. Instrum. 61 (11), November 1990 0034-6748/90/113460-04$02.00 (e) 1990 American Institute of Physics 3460 ~ ,., \ E u "--" c (ill ~ ,., i E () '-../ C (b) 13 10 ,2 10 t Ar + [" 1 0 MHz 11 10 I ldo~I ____ b-__ ~ __ ~~ __ ~ __ ~ f 10 11 ~ 10 10 0,2 0.4 0.6 O.B 1.0 8 (kG) 10 MHz 0.2 0.4 0.6 0.8 1,0 B (kG) FIG. 1. (a) Theoretical argon plasma density limit vs magnetic field at 10 MHz with N" of 10--40. (b) Theoretical helium plasma density limit vs magnetic field for rf frequencies 10-100 MHz with '\)I O~ 10. must be applied to find the maximum aehievable densities for the range of magnetic field examined. As an example, at 10 MHz, maximum helium plasma densities in the mid lOll em' -3 can be achieved at 300 G, yet the same source could achieve only 1010 em - 3 at 1 kG. On the other hand, at 50 MHz a density of 3 X 1012 em -- 3 could be reached at 1 kG. Graphs similar to Fig. 1 can be generated for other gases from Eqs. (1) and (2). In order to sustain a plasma, the ion creation rate must overcome ion loss mechanisms. In our experiment, ion dif-3461 Rev. Sci. Instrum., Vol. 61, No. 11, November 1990 fusion across the confining magnetic field is believed to be the dominant loss mechanism. Earlier work" has estab-lished (3) as the diffusion coefficient due to density fluctuations driven by lower hybrid waves, An upper-limit confinement time Tp of about 0.4 ms is calculated for cross-field diffusion for this experiment and was found to agree with experi-ment. The ion creation rate per unit volume is njl,,(uv)iz where no and flo are the neutral and electron densities and «(Tv) iz is the ionization rate. The loss and creation rates can be equated when steady state is reached. A significant frac-tion of free electrons in the oscillating electric field will acquire enough energy to ionize neutrals through colli-sions. In a singly ionized plasma, a minimum neutral den-sity of (4) is necessary for electron collisions with neutrals to sustain the plasma. There are several avenues for energy loss available to the plasma. The most significant losses are through charge exchange and particle diffusion. The energy loss must be replaced by the rf source in order to maintain the plasma. The rf source must provide a power density P> noni(av)cxEil'll + (ll/':iTH -+ lleteIH)/'ip + none(av)iztiz, (5) where till! and Ee'lll are the ion and electron thermal en-ergies, Eiz the ionization energy, and (av)cx the charge ex-change rate between ions and neutral atoms. A balance between the fraction of input power chan-neled into heating the ions and the power lost through the ions determines the ion temperature, Ti . Calculations based on collisional cross sections from BrownS show charge ex-change may be the dominant ion energy loss mechanism and the loss rate increases with increasing T,. The mecha-nism for heating the ions is not understood at present. Measurements of Ti were presented in Ref. 2, which spec-ulated that pump-driven low-frequency waves caused the ion heating. III. APPARATUS The rf plasma source consists of the rf coupler and the driving cireuit. The rf coupler is shown in Fig. 2. It consists of a conducting electrode (such as copper) in the shape of a ring (although the shape need not be so restricted) which is fed by both the gas to be ionized and the rf signal. The ring may be oriented at any angle with respect to the back-ground magnetic field. If the ring is oriented so that the magnetic flux through the ring is maximized, then the plasma formed at radii inside the ring will flow along field lines which do not intersect the rf coupler. Gas is injected into the chamber through a slot in the inside of the ring and, hence, directly into the rf excitation region. This aids in maintaining high neutral gas pressures at the source Plasma source 3461 LANGMUIR PROBE ---.: " ________________ -.::~:-I----------------------1--~------I ------1---___ <-,-/./'-' --\ - - -- ........ '-'-',,..-----1 FIG. 2. (a) Diagram of rf plasma source. (b) Source installed in test bed. MAGNET PLASMA Jj.&c::::::~IIt1J==*-· , , ". , ...... --------""'"' - -- ---- --- -- -~-- --- -- ------ - ----- -- ~---(b) relative to the surrounding vacuum chamber and allows vacuum pumping considerations to be fairly sensitive to design considerations other than those of the rf source. The input rf signal was fed to the ring through a vacuum-rated coax line which passes into the vacuum and terminated the center conductor on the ring coupler. It was found that solid coax line of length greater than 20 cm could be run directly into thc vacuum and still allow base pressures below 1 X 10- b Torr in the rf source test stand. If the solid coax and gas feed lines were introduced to the vacuum through Wilson seals, then the rf source could be translated without breaking vacuum. The r1' may be fed to the source in either steady-state or pulsed mode of operation. The VSWR of the device de-pends upon the plasma density and hence varies during operation. The choice of amplifier is important for han-dling the necessarily variable VSWR. An Amplifier Re-search Model toOOL, capable of handling any VSWR. pro-vided up to 4 kW pulsed power over 10 kHz-220 MHz for the experiment described here. Directional couplers pro-vided the forward and reflected power data for the rf cou-pler. The chamber in which the rf plasma source was tested had an approximately linear magnetic field variable from 0.4-1.5 kG. Base pressure of the chamber was < 1>< 10 .. 6 T before introduction of the neutral gas. Movable Lang-muir probes were used to diagnose the plasma. 3462 Rev. Sei.lnstrum., Vol. 61, No.11, November 1990 IV. EXPERIMENTAL RESULTS Figure 1(b) may be used to determine the magnetic field and source frequency for producing helium plasmas. For example, selecting a magnetic field of 0.5 kG, theoret-ically the plasma produced cannot exceed ~ 1010 cm - 3 for frequencies below 10 MHz. Figure 3 shows the helium plasma density produced by constant forward rf power 5, .t .., I E 3 u '" ~o 2 c o 1 • 10 f (MHz) • .. • .. 100 FIG. 3. Plasma density versus rf frequency. Helium neutral pressure .= 2.9 X 10· J Torr, rf power ~~ 400 W, B ,= 0.5 kG. Plasma source 3462 <4 .. .. .. '" .. I .3 .. E .. 0 " 2 .. ~o " ~ C 0 -3 -2- -1 0 2 .3 Position (em) FIG. 4. Plasma density vs radial position. Argon neutral pressure c= 2)< 10 4 Torr, rf power = 200 W at 70 MHz, B =,0.5 kG. delivered to the coupler versus rf frequency. For frequen-cies below 10 MHz, the maximum density achieved was 8 >< 109 cm - 3. As the wave frequency was raised to 20 MHz, the plasma density rose by more than a factor of 2 and continued to rise as the frequency was increased further. For fixed wave frequency, the density versus magnetic field was examined previously in Ref. 3 and was found to be consistent with the above predictions of Egs. (1) and (2). Reference (2) calculates that the electron temperature in such a rf generated plasma will be a function only of the gas pressure and the ratio of T/Ti. As shown in Ref. 2,this leads to a strong inverse dependence of electron tempera-ture versus gas pressure and a pressure beiow which no equilibrium is possible. This threshold pressure drops with increasing gas atomic weight, approximately. From Ref. 2 helium plasma has a calculated threshold pressure of about 3>< 10 - 4 Torr. With the present rf plasma source it was found that no plasma could be created at pressures below 1.5 X 10 - 3 Torr, read at a gauge 50 cm from the source. The plasma density profile across the magnetic field is determined partially by geometry of the rf coupler. With a coupler of circular cross section with inner diameter of approximately 5 em, the radial density profile was mea-sured and is displayed in Fig. 4. Generally, the density was reasonably flat or peaked near the center. When the gas pressure is raised significantly hollow profiles may be pro-duced.2 Figure 5 shows plasma density versus rf power at fixed pressure and frequency. For the rf coupler described above, 3 kW of power saturates the argon plasma at a density 30% higher than that achieved with helium. Argon densi-ties up to 8>< lOti cm - 3 were achieved at B = 0.5 kG, f = 70 MHz. These results are consistent with the maxi-3463 Rev. Sci.lnstrum., Vol. 61, No. 11, November 1990 10!2 or» 0 0 C .-0 • '" I 10'1 E ..::., c 0 • • • 1 • 10101 ....... , ., •• " , "...1 0.01 0.1 10 POWIII" (kW) FIG. 5 Maximum attained density as it function of input rf power at 70 MHz. Closed circles represent helium plasma with neutral pressure of 2.9 X 10 J Torr. Open circles represent argon plasma with neutral pressure of 7>< 10- 4 Torr. mum achievable density predicted in Fig. 1 (a) for Nil = 10. ,I The helium plasma density is consistent with the predic-tions in Fig. i (b). The rf power provided more than sat-isfies the power balance of Eq. (5). With a particle loss rate of 0.4 ms and the densities of Fig. 5 a significant fraction of the forward input power must go into reflected power, ion and electron heating, and other waves in the vacuum ves-sel. V. DISCUSSION A simple rf plasma source that utilizes lower hybrid waves has been developed. It does not require differential pumping or a rf matching network. The rf coupler consists of a single conducting loop coaxial with the plasma. It operates over a wide range of frequencies and magnetic fields. Maximum achievable density is consistent with the-oretical predictions. Plasma densities up to Wi2 cm - 3 have been created with argon and helium. I C. Roberson, K.W. Gentle, and P. Nidson, Phys. Rev. Lett. 26. 226 (l97! ). lR. W. Motley, S. Bernabei, W. M. Hooke, and D. L Jassby. J. Apr!. Phys. 46, 3286 (1975). 3R, W. Motley, S. Bernabei, and W. M. Hooke, Rev. Sci. lustrum. 50, 1586 (1979). ·~R. McWilliams, M. Okubo, and N. Wolf, Phys. Fluids B 2,523 (1990). 5S. C. Brown, Basic Data (~l Plasma Physics, J966, (The MIT Press, Cambridge, MA, 1967). Plasma source 3463 

Simple overdense rf plasma source

R. McWilliams

D. Edrich

R. C. Platt

D. P. Sheehan

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Simple overdense rf plasma source

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