HTITIL RBSTRHCT * Lll'Il><S
`
`JOURNAL OF APPLIED PHYSICS
`
`VOLUME 95, NUMBER 9
`
`l MAY 2004
`
`Experimental and theoretical investigations of a low-pressure He—Xe
`discharge for lighting purpose
`
`R. Bussiahn, S. Goitchakov, H. Lange, and D. Uhrlandta’
`Inslitzzlfiir Niec/eriemperatz.ir—P/asmap/nzsi/it G/‘eifswva/d, Fr.-L.-Jahn-S11: 19. Greifswa/d 17489. Germany
`
`(Received 29 December 2003; accepted 22 February 2004)
`
`Low-pressure cylindrical dc glow discharges in a mixture of helium and 2% xenon are studied by
`experiment and selficonsistent modeling. They can be used for the design of mercury-free vacuum
`ultraviolet sources and fluorescent lamps for publicity lighting. Experimental diagnostics of the
`column plasma includes measurements ofthe axial electric field strength and ofthe axis densities of
`the four lowest excited states of xenon. The electric field is determined from probe measurements.
`The particle densities are derived from the results of tunable diode laser absorption spectroscopy.
`Experimental
`investigations are assisted by a self—consistent analysis of the dc positive column
`plasma. A comparison between calculated and measured values of the axial electric field strength
`and the densities of excited xenon atoms is presented and discussed. The validated model is used for
`optimization of the discharge conditions by variation ofthe discharge current. gas pressure. and tube
`radius with respect to the radiation power and efficiency ofthe l47 nm resonance line of xenon. The
`discussion includes an analysis of the power budget of the column plasma. © 2004 American
`Institute of Physics.
`[DO]: lO.l063/l.l704866]
`
`l. INTRODUCTION
`I
`_
`h
`h
`I
`d
`d
`Int 9 ast
`“'51 et 6 ummnmema “pat became one
`of the impoitant requirements in the development of light
`sources. From this point of view, weakly ionized plasmas in
`rare—gas mixtures containing xenon are favorite candidates
`for Sources of "écuum umaviolet O/UV) Iiadlafion‘ 1” midi"
`tion, discharges in xenon based mixtures advise a large op-
`eraimg temperature rang? and an Instant “gm Output after
`Switching On‘ By use Of photolumlnesceme of appropriate
`phosphors they Ca“ also be applied as sources of Visible
`light‘ Discharges in pure Xenon or E“ mixtures Operating at
`higher pressures and at relatively Small electrode distances’
`,
`-
`1.2
`.
`-.
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`.~
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`_
`Sllch ‘is mlcrocellé
`0' dlelectgg bamer d1sCh,arge_S‘J ale ap
`plied in plasma display panels
`or for backlighting. Under
`these conditions. the xenon excimer radiation is the signifi-
`
`cant output. Contrary to this the low-pressure discharges pro—
`duce mainly the atomic resonance radiations“) and are pro—
`posed to design tube sources based on a very similar
`OigiliCi:liorisstglfidjllghfi::i::<f:smi:an[:§1:l131::
`°_‘
`_
`‘
`_
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`_
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`However’ more mvestlgatlons are needed to find Optimal ms’
`charge pammetefs a“d_ Operfmllg Cogndftlolls of Such “gm
`Soumes Corfcemmg the” Tadlauon _effi‘?le“Cy am} Output ifs
`well as their stable operation and life—time. Detailed expei'i-
`mental and meOre"C_al mVeSt'_ga“On‘? of the posmve Column
`plasma of a glow discharge in a mixture of 2% xenon and
`_
`.
`g
`.
`98% helium have been performed in the frame of the present
`wO"k'_The glow discharge is dc Operated a't total gas preS'
`sures in the range from 1.5 to 3.5 Torr and discharge currents
`froni l(lto 1.00 mA. The measurements ofthe absolute den-
`Smes Oi excltedvxe metastable
`resonance atoms are 'm'
`portant for testing model predictions of these discharges.
`—.—{s.._~—.~.;
`“Electronic mail: uhrl@inp-grcii‘swald.dc
`
`Thus one of the objectives of this work is to apply a tech-
`nique based on tunable diode laser absorption measurements,
`which provides data for the four lowest excited states ls;
`_1S5 (paschen notation) of Xenon Over an extended range of
`Current and total gas pressure_ The paper is Organized as
`fouowsv In Sec Hvthe experimental apparatus Ema methods
`of investigations are presented. Section 111 gives an overview
`Of the applied model_ The results of measurements and ca1_
`culations for the electric field strength and the densities of
`excited xenon atoms are compared in Sec. IV. The validated
`model is used for the study of the influence of variations of
`discharge current. gas pressure. and tube radius on the VUV
`radiation power and efficiencywith respect to the electrical
`,
`.
`‘
`input into the column plasma. Results ofthe calculations are
`presented and discussed
`
`H EXPERIMENT
`'
`A- Setup
`The experimental arrangement used for the laser absorp-
`tion measurements is shown in Fig. l. The main components
`are the discharge tube, the electric power supply, the tunable
`diode laser system with the detector. and electronics for sig-
`nal processing. In order to allow the laser beam to pass axi-
`g
`.
`any mmuuh the pogitive Column an U_Shaped discharge tube
`with plane windows on both ends of the horizontal section is
`used. The electrodes are mounted in the vertical sections.
`Thus discharge regions close to the electrodes do not interact
`with the laser beam. An absorption length of 26.7 cm results
`along the part of the positive Column in the horizontal SeC_
`tion? which has an inner diameter of 175 mm. Electmm
`emitting tungsten coiled—coil filaments pasted with a mixture
`of Ba_S1,_Ca Oxide are used as e1€ctmdeS_ The Cathode is
`separately heated with a dc current of 1.5 A to force suffi—
`cient thermoionic emission. Two tungsten probes of 50 ,um
`
`© 2004 American Institute of Physics
`4627
`O021-8979/2004/95(9)/4627/8/$22.00
`ASML 1023
`
`

`
`4628
`
`J. Appl. Phys, Vol. 95. No. 9, 1 May 2004
`
`
`
`Bussiahn at al.
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`lixperirnental setup for the investigation of the positive column plasma by laser atom absorption spectroscopy.
`
`in diameter and 2 mm in length, encapsulated in glass
`sleeves of less than 1 mm in diameter are used to measure
`
`the difference of the floating potentials at their positions by
`means of a statical voltmeter. The probes are positioned
`closed to the tube axis in a distance of 10 cm. Considering
`this distance one obtains the axial electric field
`in the
`
`in addition. acts as a very sensitive
`positive column which,
`indicator of the discharge stability. Already slight variations
`of
`point to changes in the gas composition. The tube is
`mounted on a translation stage. By moving it perpendicular
`to the optical axis different radial positions of the positive
`column can be probed by the laser beam. The dc discharge is
`operated on a regulated power supply with a ballast resistor
`of 2 kt) in series with the tube. The voltage across the dis-
`charge tube and the discharge current are measured by digital
`multimeters.
`
`A servoloop inside the laser controller fits the diode injection
`current to the piezosignal
`in order to stabilize the adjusted
`laser mode.
`
`Because of piezohysteresis effects the laser frequency
`does not exactly follow the control signal. The tuning behav-
`ior is monitored by the so-called l.ASERSCOPl:5 from ’1‘UlOP-
`TICTS Corporation, Martinsried. Germany. Its main component
`is an etalon with small finesse. Two 90° phase-shifted sinu-
`soidal signals are generated by the LASERSCOPE and can be
`displayed on an analog oscilloscope in XY-mode. Tuning the
`laser over a range that equals the free spectral range of the
`etalon causes a circle on the oscilloscope display. Mode-hops
`manifest itself in a reduced radius. Backrefiections into the
`laser diode occur as little oscillations along the circular arc.
`in order to regulate the laser during a tuning cycle, the l..A—
`SERSCOPF. signal can be fed back into a servoloop.
`At the output ofthe etalon the laser beam is coupled into
`a fiber optical waveguide which is connected to an optical
`isolator. The laser beam leaves the fiber having a Gaussian
`
`Before the experiment starts, the discharge tube has been
`baked out at temperatures of 380 °C for 8 h under high
`vacuum down to l0"7 mbar. After this procedure the elec—
`trodes are processed at heating currents of about 1.5 A. Ad-
`beam profile. Saturation of the observed optical transition is
`ditional cleaning ofthe tube walls is achieved by several gas
`avoided by reducing the laser intensity via a neutral density
`fillings with pure He and burn—ins at about lO0 mA. The final
`filter within the optical path.
`state is reached after some fillings with a gas mixture of ultra
`The radial resolution of the experiment is determined by
`pure Hei99,999%) and Xe(99,99%). Then the tube is filled
`two pinholes with diameters of 0.6 mm which are arranged
`up to the desired pressure and sealed.
`directly in front of and behind the plane windows, respec-
`An external cavity diode laser (TUIOPTICS DLl00) in
`tively, of the discharge tube. An interference filter in front of
`Littrow—configur'ation is used as a background radiation
`the detector is used to reduce stray light from the discharge.
`source for the absorption measurements. The laser frequency
`The laser radiation which is transmitted through the plasma
`has a typical bandwidth ofa few megahertz and can be tuned
`is detected by means ofa photodiode Soliton UPD SOOSP. To
`over a range of about 40 GHZ without mode—hopping by
`acquire the total transmitted laser intensity on the active di-
`tilting the Littrow—Grating in front of the laser diode via a
`ode area a short-focal—length lens focuses the laser beam
`piezocrystal. The necessary signal
`(typically triangular
`onto this region. Finally, the photodiode signal is coupled to
`shaped) is produced by a laser controller that includes also
`an oscilloscope via the internal
`1 M0 terminator.
`regulators for diode temperature and diode injection current.
`<2’: £2 %<.2a::.>.
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`
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`
`Bussiahn et al.
`
`4629
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`J. Appi. Phys, Vol. 95, No. 9, 1 May 2004
`
`B. Theoretical background of absorption
`measurements
`
`The net intensity balance of laser radiation at frequency
`12 that passes a layer dx of a medium, is influenced by ab-
`sorption and spontaneous as well as induced emission and
`given by the radiation transport equation
`
`d[,(x)
`dx
`
`T‘ Ki/lX)[i:(~Y) + 8 1/.ind(xl[z/(X) + 8 u,spon(X)~
`
`where /<,,(x) names the absorption coefiicient and .e,,_,r,,d(X).
`e,,__(.p(,,,(x) denote the coefiicients of induced and spontaneous
`emission.
`induced emission can be avoided by setting the
`laser power well below the saturation intensity Is.( 12) of the
`observed transition”
`
`2 F272 3A
`'7
`at v) = ~‘-—'”—“
`C
`
`<2)
`
`with the transition probability A2, and the speed of light c.
`Under the given experimental conditions spontaneous emis-
`sion is also negligible” and than the solution of Eq.
`(1)
`yields the Lambert--Beer’s~law
`
`1.< L) 2 /.< Ole *'~"f»‘~’i/<'«\'i'<'»\’.
`
`(3)
`
`which describes the decay oflight intensity due to absorption
`within a medium of the length L. The exponent defines the
`optical depth 7,” hence
`
`7",:
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`I’
`0
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`K,,(.\')d.r 2 - ln
`
`\\
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`/T
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`‘« ]1r(0)
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`(4)
`
`is obtained. The absorption coefficient itselfcan be written as
`
`/<,,(x) =0',,N,,(x).
`
`(5)
`
`Here, /\’,,,(x) is the particle number density of the lower en-
`ergetic level, that is probed by the laser and
`
`82
`
`U“w4a0/nfic
`
`fir/(Pu
`
`is the photoabsorption cross-section, where e denotes the el-
`ementary charge,
`so the permittivity, f,,.
`the oscillator
`strength of the observed transition, and P, the line profile of
`the transition normalized according to f,,P,,dv= 1.
`Using Eq.
`(5) and assuming homogeneous distributed
`absorbing species gives an expression for the particle num-
`ber density
`
`/V’./“
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`(7)
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`l.,aserScope signals; main frame: channels in y(z) mode
`FIG. 2. Typical
`with 90° phase shill, inlay: same signals in xy mode. The laser is tuned over
`0.8><FSR of the etalon.
`
`The determination of particle number densities of ex-
`cited xenon states by laser absorption spectroscopy requires
`two series of measurements. The first one is done in order to
`
`analyze /,,(O) in dependence on the laser frequency in ab-
`sence of absorbing species (plasma switched off). Herewith
`transmission properties of every optical component within
`the laser beam path are registered and the power modulation
`of the laser during scanning is considered. In the following
`the plasma is switched on and the actual absorption measure-
`ment is performed. Simultaneously with the laser intensity
`the LASERSCOPE signals are recorded in both series of mea-
`surements. The latter are used to realize a time correlation
`
`between the course ofthe laser intensity and the current laser
`frequency or its wavelength, respectively. The procedure is
`pointed out in the following.
`The exact determination ofthe actual laser wavelength is
`fundamental in the scope of absorption experiments. A coin-
`mercially available tool for this task is a Wavemeter (Bur-
`leigh WA-4500. see Fig.
`l) yielding absolute values with a
`limited temporal resolution of 0.1 s. Therefore. this device is
`used only for calibration. However. the i_.ASF:1RS('.‘OPF. can be
`applied for measuring relative laser frequency changes with
`the required temporal resolution of 0.2 ms during laser tun-
`ing. The free spectral range (FSR) of the IASERSCOPE etalon
`is determined once with the help of the Wavemeter. An ex-
`ample of typical LASERSCOPE signals is given in Fig. 2. The
`transfer function of the etalon is sinusoidal shaped. Display-
`ing both LASERSCOPE channels on an oscilloscope in xy
`mode results in a full circle if the laser is tuned over the FSR
`
`where P}\=ID,,C.-"'}\2, rot);/,,(/.) and z'0(x)s/,(0).
`
`C. Measurement of particle number densities
`
`in the frame of the experimental work the four lowest
`exited states ls2— lss of xenon are probed by laser radia-
`tion. Therefore. the laser is tuned to the optical transitions
`ls2<—--+2p2 (826 nm),
`ls3<—>2p4 (820 nm),
`ls4<—»2p5 (828
`nm), and ls5<—+2p6 (823 nm).
`
`
`
`of the etalon. The value of the phase angle on this circle is a
`measure for the relative frequency shift.
`in practice,
`this
`measurement is done by analyzing the phase angle with the
`help ofa LABVIEWTM program,” that fits an analytic function
`to the measured circle. Finally the program assigns the cal-
`culated Alt scale to the measured photodetector signals in
`every point in time (see Fig. 3).
`Typically two tuning cycles of the laser are recorded for
`one absorption measurement. This allows an averaging over
`four absorption profiles in the following data analysis. At
`first the optical depth in dependence on the wavelength is
`calculated. By area normalization of this curve a line profile
`
`
`

`
`4630
`
`J. Appl. Phys, Vol. 95, No. 9, 1 May 2004
`
`Bussiahn el al.
`
`12
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`FIG. 3, Wavelength scaling of absorption signals; relative wavelength shitt
`A/\ from the l.aserScope signal in the upper frame and photodetector signals
`of the laser intensity with (solid line) and without plasma (dashed line) in
`the lower frame in dependence on time I during laser tuning.
`
`function [’(7\) as shown in Fig. 4 is obtained. The shape ofa
`line profile function is mainly determined by the gas pressure
`of the tube filling. Hence for determining particle number
`densities at different discharge currents a reference line pro-
`file function is used. which has to be measured at a fixed
`
`discharge current whensoever a new gas pressure is to be
`investigated.
`
`lll. DESCRIPTION OF THE MODEL
`
`A detailed self—consistent model of the cylindrical posi-
`tive column of the xenon-helium dc discharge is used to
`assist
`in understanding the processes taking place in the
`plasma and in optimization of the VUV radiation output. The
`positive column is assumed to be axially symmetric and free
`of striations or other inhomogeneities. so that the plasma
`quantities can supposed to be invariant to translations along
`the discharge axis and time independent. The model includes
`a self-consistent treatment of the space—charge field, the ex-
`cited atom balances and the electron kinetics resolved in the
`
`radial space dimension. The cylindrical dc column plasma is
`described by a stationary hybrid method” which comprises
`the coupled solution of the space-dependent kinetic equation
`of electrons. the fluid equations of electrons,
`ions, and ex-
`cited atoms, the Poisson equation for the radial space-charge
`
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`FIG. 4 Line profile unction oi’ the 2p4+- ls‘-, transition in Xe obtained at
`[70:25 Torr, l:=60 mA.
`
`
`
`
`
` "t'zi'7'fiiii"
`
`HO. 5. Xenon energy level scheme and processes considered in the model:
`excitation and deexcitation in electron collisions (solid arrows). ionization in
`electron collisions (dashed arrows), radiative transitions (dashed double line
`arrows), and quenching processes (double line arrows) with xenon and he-
`lium ground state atoms.
`
`potential. and the balance equation of the electron surface
`charge density at the tube wall. in particular, the radial space-
`charge potential as well as the electron production due to the
`ionization of ground—state and excited atoms are taken into
`account in the electron kinetic equation, which is solved ap-
`plying the two-tenn approxiniationmu’ ofthe velocity distri-
`bution function. The electron kinetic treatment yields radially
`dependent transport coefficients and mean frequencies of the
`ionization and excitation in electron collisions which are
`
`used to solve the fluid equations. The iterative coupling of
`the electron kinetic treatment and the solution of the fluid-
`
`Poisson equation system leads to a sufficiently accurate de-
`scription of the space—charge confinement
`in the column
`plasma. The axial electric field is finally determined by a
`coupled treatment of the charge-carrier budget in the plasma
`volume and the plasma-wall interactions.”
`The basic equations and details of the solution method
`have been already described in previous papers,”‘'(’ where
`the positive column plasma of a neon dc discharge has been
`studied. Specific aspects of the model to describe the colli-
`sion and radiation processes and to treat the balances of the
`excited species in the considered helium-xenon mixture are
`given in Ref. 18.
`However, an extension of the reaction kinetic model,
`which detemiines the densities of the most populated excited
`states in the heliuin—xenon column plasma and which is de-
`scribed in detail
`in Ref.
`l8 has been applied. The present
`model distinguishes 13 states of xenon:
`the ground state
`Xe(1p0), nine individual excited states, ie, the metastable
`levels Xe(1s5) and Xe(1s3),
`the resonant
`levels Xe(ls4)
`and Xe(ls2),
`five lowest p-levels Xe(2p,0). Xe(2p9),
`Xe(2p8), Xe(3;77), X€(2p6),
`two lumped states Xe(2p5
`+3d+3s,...,9s) [denoted further for brevity reasons as
`Xe(2p5)] and Xe(2p4»___‘,), and the ion Xe'*'
`in the ground
`state. Because of the high values of excitation thresholds of
`helium atoms a simplified level model of helium has been
`used.
`lt
`includes the ground state. a lumped excited state
`He*, and the ion He" in the ground state. Figure 5 presents
`
`
`
`

`
`J. Appl. Phys. Vol. 95. No. 9, 1 May 2004
`
`iT“1I1Ii"1"1iI'li"1|'iiIi
`
`Bussiahn el al.
`
`4631
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`FIG. 7. Experimental data (crosses) and data predicted by the model
`(circles) for the axial electric field strength E: as a function ofthe discharge
`current
`I,
`for
`three different gas pressures [70 and a tube radius r,,.
`=0.87 cm la) and for three different tube radii in the case ot‘p(,=2.5 Torr
`tb).
`
`densities of excited xenon atoms for the case of a gas pres-
`sure of 2.5 Torr, a tube radius of 0.87 cm. and a discharge
`current of 60 inA. The metastable Xe( l s 5) state is by far the
`most occupied excited level.
`lts density in the axis is by a
`factor of l()5 smaller than the helium buffer gas density and,
`hence, by a factor of 103 smaller than the xenon ground state
`density under the considered conditions. Because ofthe pro-
`nounced radial space charge confinement of the plasma all
`excited atom densities decrease from their axis value by
`more than one order of magnitude over the column cross
`section.” The density of helium metastable atoms is by
`about six orders of magnitude smaller than the )(e( l S5) den-
`sity. Hence, processes of excited helium atoms are of negli-
`gible importance in the reaction kinetics as well as in the
`charge carrier budget under the considered conditions.
`
`IV. RESULTS AND DlSCUSSl0N
`
`A. Experimental results and validation of the model
`
`A detailed comparison between the model calculations
`and the measurements has been performed for the axial elec-
`tric field strength and for the axis densities of xenon atoms in
`four lowest excited states (i.e., ls5. 1.94,
`ls;,, and 1.92)
`in
`the column plasma.
`Figure 7 presents measured and calculated values of the
`axial electric field strength at different pressures and tube
`radii for varying discharge currents (data for the radius 1.12
`:52 /7*.iv“;
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`
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`
`0.2
`
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`0.8
`
`Flt}. 6. Radial variation of the densities ,«’\/'4. of excited xenon and helium
`atoms for [:=6() mA. pi,=2.5 Torr. and r,,.=0.87 cm.
`
`the xenon level scheme and the manifold of the processes
`included in the model. The reaction kinetic model takes into
`
`account over 190 plasma-chemical processes, including ex-
`citing, deexciting. and ionizing electron-heavy particle colli-
`sions, chemoionization, radiation, quenching, and formation
`of excimer molecules. The choice and the sources of the
`atomic data. rate constants. radiation life-times, as well as the
`description of the equation systems for the determination of
`densities of heavy particles and their radial variation are pre-
`sented in Ref. 18.
`
`l8 has been
`The reaction kinetic model given in Ref.
`the
`levels
`extended
`by
`the
`individual
`treatment of
`Xe(_2p9),...,Xe(2p5) to improve the accuracy of the de-
`scription of the S-l€V€lS.
`This has been done because the
`Xe(ls5) and Xe(l.t4) states are closely coupled with these
`p-levels due to excitation processes in electron collisions and
`spontaneous emission processes in the singlet system, ln ad-
`dition. quenching processes between these p-levels and the
`Xe( ls3) and Xe(ls2) states are important for the establish-
`ment of the densities in the triplet system.”
`Additional data for
`the treatment of the individual
`
`p-levels have been taken also from the sources given in Ref.
`18, i.e., cross sections of Nakazakiw are used to describe the
`excitation of the p-levels from the ground state in electron
`collisions. stepwise excitation cross sections are calculated
`according
`to Vtjiens
`and
`Smeetsfo Deutsch-~Mark
`formalism“ is used to determine stepwise ionization cross
`sections.
`.
`
`Figure 6 shows an example for the radial variation ofthe
`
`
`
`

`
`Bussiahn at al.
`
`101:
`
`"
`via 10“
`2.
`%'
`244
`I010
`
`'
`l
`X6035)
`
`"V
`
`l
`fr
`4
`(h) 15:00 mA _
`
`Xetlsp
`«-9—————N
`::_— —--~'~-"::§::'—'~-1:‘-:::”»
`*
`as)
`
`Q
`
`I
`‘
`t
`3
`7
`
`__
`
`4632
`
`J. Appl. Phys, Vol. 95, No. 9, 1 May 2004
`
`cm are taken from Ref. 18). The axial field shows a pro-
`
`nounced pressure dependence. An increase of the pressure
`leads to higher elastic losses in the plasma and. consequently.
`to a higher axial electric field strength. The dependence on
`the discharge current is less pronounced. The growth of the
`discharge current is accompanied by a decrease of the elec-
`tric field. Such a behavior is typical for a subnormal dis-
`charge, where the total ionization of the gas is dominated by
`stepwise ionization processes. An increase of the tube radius
`causes also an increase of the axial electric field.
`As can be seen in Fig. 7, measured and calculated values
`of the axial field sufficiently well agree in the range of
`smaller discharge current densities, but discrepancies occur
`at currents larger than 60 mA. A detailed discussion of the
`accuracy of the applied model has been already given in Ref.
`l8. The hybrid model
`is based on less approximations like
`the two-terrn approximation of the electron velocity distribu-
`tion but includes a strict description of the nonlocal electron
`kinetics and the spatial structure of the column plasma in
`radial direction. It has been shown, that main sources of er-
`rors are the inaccuracy of the used atomic data and devia-
`tions from the model assumptions.
`is that the posi-
`An important assumption of the model
`tive column plasma is in steady-state and homogeneous in
`axial direction. However. experimental investigations show,
`that this assumption is not fulfilled in the whole range of the
`discharge parameters considered here. The occurrence of dis-
`charge instabilities (:e.g., moving striations) has been studied
`by analyzing the time-resolved signal from an optical probe.
`This signal shows fiuctuations with an amplitude of about
`5% at a discharge current of 40 mA and a tube radius of 0.87
`cm. The amplitude increases with the current and reaches
`about 12% at 60 mA. The observed instabilities are less im-
`
`portant at lower currents but may be the reason for the de-
`viations of the model results from the measurements of the
`
`‘
`axial field at currents larger than 60 mA.
`The axis densities of the four lowest excited states of
`
`xenon in the positive column has been studied in a tube with
`a radius of 0.87 cm at different discharge currents and gas
`
`pressures. The experimental and theoretical results are com-
`pared in Fig. 8. The measured densities of the metastable
`Xe(l.s'5) and Xe(l..s'_~,) states show a slight decrease with
`growing discharge current. The axis densities of both reso-
`nance states increase with the discharge current. The depen-
`dence of the densities on the gas pressure is only weak. Cal-
`culated axis densities of the Xe(ls5) state and of both
`resonance states reproduce the dependencies found experi-
`mentally. and show a good quantitative agreement with the
`measured values.
`
`Predicted axis densities and the dependence on the dis-
`charge current of the Xe( 1 S3) state do not coincide with the
`experimental results. Calculated values increase with the cur-
`rent, saturation occurs not until a discharge current of 80
`mA. Reasons for this discrepancy could be that coupling
`processes between Xe(l.s'3) and other excited xenon levels
`are not described well or are not included in the model be-
`cause of the absence or the inaccuracy of corresponding
`atomic data. However, the maximum discrepancy between
`calculated and measured data for Xe( 153) does not exceed
`
` I
`
`109
`
`I
`
`u
`
`T
`
`:
`0-0 model
`>e—x experiment '
`3
`4
`2
`.
`l
`»
`I
`p0 (Torr)
`
`HQ. 8. Flxperimental data (crosses) and data predicted by the model
`(circles)
`for
`the axis densities ol‘
`the excited xenon levels Xe( lS_-1),
`Xe( ls4), Xe( 133). and Xe( 1.32) as a function of the discharge current I_. for
`a pressure [70: 2.5 Torr ta) and as a function ofpi, in case of /3:60 mA (b).
`
`factor 2.5, which is quite satisfactory for the description of
`this level.
`
`Generally a good agreement between the results of
`model and the experiments has been reached. The maximum
`discrepancy in the axial electric field strength is below l2%.
`The differences in the axis values of Xe(ls5), Xe(ls4). and
`Xe(1s3) densities do not exceed a factor of about l.2. Cal-
`culations reproduce well the experimental tendencies when
`the discharge conditions are varied. Therefore. the model can
`be used for reliable quantitative predictions and the study of
`larger ranges of the discharge conditions.
`
`B. Global power balance of the discharge plasma
`
`To evaluate the efficiency of the column plasma with
`respect
`to its use as a radiation source.
`the global power
`budget of the plasma must be analyzed in detail. To derive
`the global power balance equation the spatially resolved
`power balance of heavy particles has to be considered to-
`gether with the electron power balance}? Finally, the global
`power balance equation becomes the form
`
`<z.:m»>~+<LrR>+<L:::§£>+<L*°>+<L:?->+<v‘>+<L**>
`
`=EZIz.
`
`(8)
`
`(LQCUV) and (LIVR) denote the losses due to the VUV
`Here,
`and infrared (IR) radiation processes, respectively. (L‘‘’) de-
`scribes the ionization losses, the action of the radial electric
`
`
`
`

`
`J. Appl. Phys, Vol. 95, No. 9, 1 May 2004
`
`Bussiahn er al.
`
`4633
`
`\_
`
`-
`
`.
`
`»
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`I'=~6Q;mA:.
`_
`_
`,
`
`
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`
`10
`
`
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`
`Q:
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`'3
`::
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`Z
`[
`"
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`p
`,
`Xet_Is,; O
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`O ..
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`O
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`A;
`A .
`A—A efficiency ‘
`6-0 POWCY
`'
`»
`.
`l
`.
`1
`80
`I00 0'01
`
`._z_\.,.
`
`.. A ..
`
`X
`
`.
`
`1
`20
`
`I
`40
`
`I
`
`l
`60
`1: (mA)
`
`l
`
`0.3
`
`I
`\\
`‘Q
`\§ \_.'\_‘
`-1
`\\-ii
`d'fl“,
`g
`mu
`L ‘\
`
`_.
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`._
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`\
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`_
`§“\\\‘;§\
`‘
`,
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`._ .-~‘ 1.
`A
`ii
`_
`6-
`.
`L
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`LID
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`1’
`
`Lt?
`
`3:; 0.5-3
`[s
`'
`Z
`
`\ /
`
`14/ V vuv
`
`IR
`
`01
`
`1.5
`
`2.5
`2
`[30 (Torr)
`
`3
`
`3.5
`
`FIG. 9. Important terms of the global power budget of the plasma in depen-
`dence on the gas pressure pr, at 15:60 mA; radially averaged power loss
`rates
`with respect to the power input F:l..
`
`FIG. I0. Iifficiency 7/we (triangles) and output power INW (circles) ofthe
`VUV radiation generation from the levels Xe( Is.,) and Xe( l 32) as a func-
`tion of the discharge current I: for p(,=2.5 Torr and r._, =O.87 cm.
`
`field (radial cooling of the electrons) corresponds to the term
`(Lit).
`(Lei)
`includes the power losses due to the elastic
`collisions of electrons with helium and xenon atoms. The
`losses due to the cliffusion of the metastable xenon atoms
`onto the wall are described by the term
`. The term (UT)
`represents the losses due to the chemoionization.
`Figure 9 presents the important terms of the power bal-
`ance for the discharge current 1,= 60 mA at varying gas pres-
`sure. The areas between the curves denote the proportions of
`the different
`losses with respect to the power input EZIZ.
`Thus. the ratio (1. {i,W)/E31, determines the efficiency of the
`VUV radiation. The dominant power loss in the helium-
`xenon plasma arises in the elastic collisions which consume
`up to 70% of the input power at a gas pressure above 2.5
`Torr. The next important contribution is the loss due to the
`VUV radiation. Comparable contributions to the power bal-
`ance result from IR radiation, ionization, and cooling of the
`electrons in the radial electric field. The variation ofthe gas
`pressure causes large variations of the loss proportions. A
`decrease ofthe gas pressure leads to a diminishing of elastic
`losses and a growth of all other contributions. The elastic
`collision losses decreases down to 30% at
`1 Torr, while the
`
`efficiency of VUV radiation increases from 16% at 3.5 Torr
`to about 31% at
`1 Torr. The proportional
`loss due to the
`diffusion of the metastable xenon atoms onto the wall be-
`
`comes important at a gas pressure below 2 Torr and reaches
`about 5% at l Torr.
`
`The global power balance has also been analyzed for
`varying discharge currents. An increase of the discharge cur-
`rent leads to a decrease of the contribution ofVUV radiation
`
`losses and a growth of elastic losses. All other contributions
`remain nearly independent from the discharge current.
`
`C. Optimization of discharge conditions
`
`The validated model has been applied to analyze the
`VUV radiation of the positive column of the xenon discharge
`in the dc operation regime for varying discharge conditions.
`Particularly, the dependencies of its efficiency 77W_;V and ra-
`diation power IJVW on the discharge current, gas pressure,
`and tube radius have been predicted by the model. Here,
`
`lindrical column, 77pm,’ is the ratio of /km.» to the electrical
`input E3], into the column plasma per unit length.
`Because ofthe very low density ofexcited helium atoms
`in the plasma, only the transitions from the resonance levels
`Xe(ls.;) and Xetlsz) to the ground state contribute to the
`VUV radiation. Figure 10 shows the efficiency and the out-
`put power of these two radiation channels at 2.5 Torr and
`varying discharge current. The density ofthe Xe( 154) atoms
`is by about a factor of 50 higher than that of the Xe( T32)
`atoms. Therefore,
`the corresponding contributions to the
`VUV radiation efficiency and power due to the radiation
`from the Xe(ls3) level with the wavelength of 130 nm
`reaches only about 3% of the contributions due to the
`Xe(ls4) radiation (14