HTITIL HE'STFlFlCT * Lll'll-(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. Gortchakov, H. Lange, and D. Uhrlandta)
`Instirulflir Niederlemperatur—Plasmaphysik Grei/{iwa/d, Fr—L.—Jahn—Sfr. 19, Greijfm’a/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 self—consistent 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 of the axial electric field strength and of the 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 of the discharge current, gas pressure, and tube
`radius with respect to the radiation power and efficiency of the 147 nm resonance line of xenon. The
`discussion includes an analysis of the power budget of the column plasma. © 2004 American
`Institute QfP/tysics.
`[DOIz 10.1063/l.l704866]
`
`I. INTRODUCTION
`
`In the last decade the environmental aspect became one
`of the important 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 vacuum ultraviolet (VUV) radiation. In addi—
`
`tion, discharges in xenon based mixtures advise a large op-
`erating temperature range and an instant light output after
`switching on. By use of photoluminescence of appropriate
`phosphors they can also be applied as sources of visible
`light. Discharges in pure xenon or in mixtures operating at
`higher pressures and at relatively small electrode distances,
`such as microcellsL2 or dielectric barrier discharges,3 are ap—
`plied in plasma display panels4"7 or for backlighting. Under
`these conditions, the xenon excimcr radiation is the signifi—
`cant output. Contrary to this the low—pressure discharges pro—
`duce mainly the atomic resonance radiationg‘m and are pro—
`posed to design tube sources based on a very similar
`technology as for standard fluorescent lamps. One of the pos—
`sible applications of such sources is publicity lighting.11
`However, more investigations are needed to find optimal dis—
`charge parameters and operating conditions of such light
`sources concerning their radiation efficiency and output as
`well as their stable operation and life—time. Detailed experi—
`mental and theoretical investigations of the positive column
`plasma of a glow discharge in a mixture of 2% xenon and
`98% helium have been performed in the frame of the present
`work. The glow discharge is dc operated at total gas pres-
`sures in the range from 1.5 to 3.5 Torr and discharge currents
`from 10 to 100 mA. The measurements of the absolute den—
`sities of excited Xe metastable and resonance atoms are im—
`portant for testing model predictions of these discharges.
`
`“Electronic mail: uhrl@inp—grcifswald.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 152
`_ 155 (Paschen notation) of xenon over an extended range of
`current and total gas pressure. The paper is organized as
`follows. In Sec. II the experimental apparatus and methods
`of investigations are presented. Section III gives an overview
`of the applied model. The results of measurements and cal—
`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 efficiency with respect to the electrical
`input into the column plasma. Results of the calculations are
`presented and discussed.
`
`ll. EXPERlMENT
`
`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—
`ally through the positive 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 17.5 mm. Electron—
`emitting tungsten coiled—coil filaments pasted with a mixture
`of Ba—-Sr-~Ca oxide are used as electrodes. The cathode is
`separately heated with a dc current of 1.5 A to force suffi—
`cient therrnoionic emission. Two tungsten probes of 50 ,u.m
`
`0021—8979/2004/95(9)/4627/8/$22.00
`
`4627
`
`
`
`© 2004 American Institute of Physics
`
`
`
`ASML 1025
`
`ASML 1025
`
`

`

`4628
`
`J. Appl. Phys, Vol. 95, No. 9, 1 May 2004
`
`Bussiahn et al.
`
`1GHz
`
`
`SGs/s
`
`
`Digitizing Oscilloscope
`
`
`
`
`
`
`neutral density filter
`pinhole G 0.6 mm
`interference filter
`focussing lens
`photo diode
`el. stat. voltmeter
`
`0701-wa4
`
`
`Power Supply
`
`
`optical
`
`isolator
`
`
`
`Laser—
`
`
`
`
`Laserhead i—n Scope
`
`
`
`l
`
`(Controller and Display)
`Diode Laser Supply Rack
`scilloscope
`
`
`
`_ O
`
`HG. 3. Experimental 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 E: in the
`
`positive column which, in addition, acts as a very sensitive
`indicator of the discharge stability. Already slight variations
`of E 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 k0 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 LASERSCOPE from TUIOP—
`TICS Corporation, Martinsried, Germany. Its main component
`is an etalon with small finesse. Two 90° phaseashiftcd 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. Backreflections into the
`laser diode occur as little oscillations along the circular are.
`
`In order to regulate the laser during a tuning cycle. the LA—
`SERSCOPE signal can be fed back into a servoloop.
`At the output of the 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 10” 7 mbar. After this procedure the elec—
`trodes are processed at heating currents of about 1.5 A. Ad—
`ditional cleaning of the tube walls is achieved by several gas
`fillings with pure He and burn~ins at about 100 mA. The final
`state is reached after some fillings with a gas mixture of ultra
`pure He(99,999%) and Xe(99,99%). Then the tube is filled
`up to the desired pressure and sealed.
`in
`An external cavity diode laser (TUIOPTICS DLlOO)
`Littrow-configuration is used as a background radiation
`source for the absorption measurements. The laser frequency
`has a typical bandwidth of a few megahertz and can be tuned
`over a range of about 40 GHz without mode—hopping by
`tilting the Littrow—Grating in front of the laser diode via a
`piezocrystal. The necessary signal
`(typically triangular
`shaped) is produced by a laser controller that includes also
`regulators for diode temperature and diode injection current.
`
`
`beam profile. Saturation of the observed optical transition is
`avoided by reducing the laser intensity via a neutral density
`filter within the optical path.
`The radial resolution of the experiment is determined by
`two pinholes with diameters of 0.6 mm which are arranged
`directly in front of and behind the plane windows, respec—
`tively, of the discharge tube. An interference filter in front of
`the detector is used to reduce stray light from the discharge.
`The laser radiation which is transmitted through the plasma
`
`is detected by means ofa photodiodc Soliton UPD SOOSP. To
`acquire the total transmitted laser intensity on the active di—
`ode area a short—focal-length lens focuses the laser beam
`onto this region. Finally, the photodiode signal is coupled to
`an oscilloscope via the internal 1 M0 terminator.
`
`

`

`Bussiahn et al.
`
`4629
`
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`FIG. 2. Typical LaserScope signals; main frame: channels in y(t) mode
`with 90° phase shift, inlay: same signals in xy mode. The laser is tuned over
`0.8XFSR 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 I ”(0) 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 of the laser intensity and the current laser
`frequency or its wavelength, respectively. The procedure is
`pointed out in the following.
`The exact determination of the actual laser wavelength is
`fundamental in the scope of absorption experiments. A com—
`mercially available tool for this task is a Wavemeter (Bur-
`leigh WA-4500, see Fig. 1) yielding absolute values with a
`limited temporal resolution of 0.1 s. Therefore, this device is
`used only for calibration. However, the LASERSCOPE 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 LASERSCOPE 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
`
`J. Appl. Phys, Vol. 95, N0. 9, 1 May 2004
`
`B. Theoretical background of absorption
`measurements
`
`The net intensity balance of laser radiation at frequency
`V 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
`
`61],,(x)
`dX : W K1,(X>]V(X) +811,ind(x)1v(x)+ 81/.spori(x),
`
`(1)
`
`where KV(X) names the absorption coefficient and 8,,‘md(x).
`e V'sp0n(x) denote the coefficients of induced and spontaneous
`emission. Induced emission can be avoided by setting the
`laser power well below the saturation intensity [5(12) of the
`observed transition12
`
`2 {277 113,421
`2
`.
`C
`
`15(11):
`
`(2)
`
`with the transition probability A21 and the speed of light 0.
`Under the given experimental conditions spontaneous emis—
`sion is also negligible13 and than the solution of Eq.
`(1)
`yields the Lambert Beer’s—law
`
`ML):I.(0>ei'fW-W-n
`
`(3)
`
`which describes the decay of light intensity due to absorption
`within a medium of the length L. The exponent defines the
`optical depth 7,, hence
`
`'-_ MI»)
`L
`um J1) KV(x)dX~ ~1n(1u(0)
`
`
`
`(4)
`
`is obtained. The absorption coefficient itself can be written as
`
`K,(x):: UVNV(x).
`
`(5)
`
`Here, N,,(x) is the particle number density of the lower en—
`ergetic level, that is probed by the laser and
`62
`(Twig—Somecfi/‘PV
`
`(6)
`
`is the photoabsorption cross—section, where 6 denotes the el—
`ementary charge, 80 the permittivity, fik the oscillator
`strength of the observed transition, and P, the line profile of
`the transition normalized according to f,P,,d1/:: 1.
`Using Eq. (5) and assuming homogeneous distributed
`absorbing species gives an expression for the particle num—
`ber density
`
`V
`
`N
`
`
`
`480mec
`TV
`
`480171862114, 1'00)
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`(i0(7\)/
`
`ezfik
`
`(7)
`
`Where PfiPuc/AZ, i(7\)EI,,(L) and i0()\)=“=-[,,(0),
`
`C. Measurement of particle number densities
`
`
`
`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 of a LABVIEWTM program,14 that fits an analytic function
`to the measured circlc. Finally the program assigns the cal—
`culatcd AA scale to the measured photodetector signals in
`every point in time (see Fig. 3).
`Typically two tuning cycles of the laser are recorded for
`In the frame of the experimental work the four lowest
`one absorption measurement. This allows an averaging over
`exited states lsz~ 1.95 of xenon are probed by laser radia—
`four absorption profiles in the following data analysis, At
`tion. Therefore, the laser is tuned to the optical transitions
`first the optical depth in dependence on the wavelength is
`lsz<—>2p2 (826 nm), ls3H2p4 (820 nm),
`ls4<—>2p5 (828
`calculated. By area normalization of this curve a line profile
`nm), and 15592106 (823 nm).
`
`é
`3.
`
`
`

`

`4630
`
`1 May 2004
`J. Appl. Phys, Vol. 95, No, 9,
`
`
`
`3 E
`9|
`2‘
`12m
`
`Busslahn er al.
`
`
`
`
`1(5)
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`
`FIG. 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—tcnn approximationm’l6 of the velocity distri-
`bution function. The electron kinetic treatment yiclds 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—
`
`FIG. 3, Wavelength scaling of absorption signals; relative wavelength shift
`AA from the LaserScope signal in the upper frame and photodeteetor 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 P()\) 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.
`
`Ill. DESCRIPTION OF THE MODEL
`
`A detailed self-consistent model of the cylindrical posi-
`tive column of thc 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 method15 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
`
`(J
`
`
`
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`
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`l
`
`
`
`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.17
`The basic equations and details of the solution method
`have been already described in previous papers,”'16 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 determines the densities of the most populated excited
`states in the helium—xenon column plasma and which is de—
`scribed in detail
`in Ref. 18 has been applied, The present
`model distinguishes 13 states of xenon:
`the ground state
`Xe(lp0), nine individual excited states, i.e., the metastable
`levels Xe(ls5) and Xe(ls3),
`the resonant
`levels Xe(ls4)
`and Xe(lsz),
`five lowest p—levels Xe(2pm), Xe(2p9),
`Xe(2p8), Xe(2p7), Xe(2p6),
`two lumped statcs Xe(2p5
`+3d+3s,...,9s) [denoted further for brevity reasons as
`Xe(2p5)] and Xe(2p4‘‘‘‘‘ l), 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.
`It
`includes the ground state, a lumped excited state
`FIG. 4. Line profile ‘unetion of the 2p4<»—> ls} transition in Xe obtained at
`He*, and the ion He+ in the ground state. Figure 5 presents
`170: 2.5 Torr,
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`

`

`J. Appl. Phys, Vol. 95, No. 9,
`
`1 May 2004
`
`Bussiahn et al.
`
`4631
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`FlG. 6. Radial variation of the densities M. of excited xenon and helium
`atoms for 1:: 60 mA, p.,=: 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, decxciting, 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.
`
`The reaction kinetic model given in Ref. 18 has been
`extended
`by
`the
`individual
`treatment of
`the
`levels
`Xe(2p9),...,Xe(2p5) to improve the accuracy of the de—
`scription of the s-levels. This has been done because the
`’Xe(ls5) and Xe(ls4) states are closely coupled with these
`p—levels due to excitation processes in electron collisions and
`spontaneous emission processes in the singlet system. In ad—
`dition, quenching processes between these p—levels and the
`Xe( 153) and Xe( 132) states are important for the establish—
`ment of the densities in the triplet system.‘8
`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 Nakazakilg 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 Vriens
`and
`Smects,20 DeutschiMark
`formalismZI
`is used to determine stepwise ionization cross
`sections.
`
`FIG. 7, Experimental data (crosses) and data predicted by the model
`(circles) for the axial electric field strength E; as a function of the discharge
`current
`I,
`for
`three different gas pressures p“ and a tube radius r“.
`=0.87 cm (a) and for three different tube radii in the case of p[,=2.5 Torr
`(b).
`
`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 mA. The metastable Xe( 135) state is by far the
`most occupied excited level. Its density in the axis is by a
`factor of 105 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 of the 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.18 The density of helium metastable atoms is by
`about six orders of magnitude smaller than the Xe( 155) den-
`sity. Hence, processes of excited helium atoms are of neg1i~
`gible importance in the reaction kinetics as well as in the
`charge carrier budget under the considered conditions.
`
`IV. RESULTS AND DISCUSSION
`
`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.c., 135, 1S4, 1S3, and 153) 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
`
`Figure 6 shows an example for the radial variation of the
`
`
`

`

`Bussiahn et al.
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`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.
`18. The hybrid model is based on less approximations like
`the two—term approximation of the electron velocity distribu—
`tion but includes a strict description of the nonlocal electron
`kinetics and the spatial stmcture 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.
`An important assumption of the model is that the posi-
`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 (c.g., moving striations) has been studied
`by analyzing the time~resolved signal from an optical probe.
`This signal shows fluctuations with an amplitude of about
`5% at a dischaigec :.11rent 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-
`
`pottant 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(lss) and Xe(153) states show a slight decrease with
`growing discharge current. The axis densities of both resom
`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(lss) 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(1s3) 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(ls3) 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(ls3) does not exceed
`
`FIG. 8. Experimental data (crosses) and data predicted by the model
`(circles)
`for
`the axis densities of the excited xenon levels Xe( 135),
`Xe(134), Xe(ls3), and Xe( 153) as a function ofthe discharge cunent I: for
`a pressure 170: 2.5'1‘01‘r(a) and as a function ol‘pn in case oflz=60 111A (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 12%.
`The differences in the axis values of Xe( 155), Xe( ls4), and
`Xe(lsz) densities do not exceed a factor of about 1.2. 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. 22 Finally, the global
`power balance equation becomes the form
`mct
`<L$UV>+<LFR)+<LM>+<L‘°>+<Liw>+<1«°‘>+(Lb)
`
`: 15.1..
`
`(8)
`
`Here, <Lvuv> and (le> denote the losses due to the VUV
`and infrared (IR) radiation processes respectively. (1.”) de—
`scribes the ionization losses, the action of the radial electric
`
`
`
`

`

`Bussiahn et al.
`
`4633
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`FIG. 9. Important terms of the global power budget of the plasma in depen—
`denee on the gas pressure p“ at [3:60 mA; radially averaged power loss
`rates L). with respect to the power input EZIZ.
`
`FIG. 10. Efficiency 77vuv (triangles) and output power Pvuv (circles) of the
`VUV radiation generation from the levels Xe(154) and Xe(ls3) as a func«
`tion of the discharge current II for p0=2.5 Torr and r“.=0.87 cm.
`
`field (radial coolingof the electrons) corresponds to the term
`(L2) (1.“) includes the power losses due to the elastic
`collisions of electrons with helium and xenon atoms. The
`losses due to the diffusion of the metastable xenon atoms
`onto the wall are described by the temi (L33). The term (Lh)
`represents the losses due to the chemoionization.
`Figure 9 presents the important terms of the power bal—
`ance for the discharge current [3: 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 E513.
`Thus, the ratio (Li/UVWEJz 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 of the gas
`
`pressure causes large variations of the loss proportions. A
`decrease of the 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 1 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
`
`lindrical column, 77vuv is the ratio of Pvuv to the electrical
`input E3]: into the column plasma per unit length.
`Because of the very low density of excited helium atoms
`in the plasma, only the transitions from the resonance levels
`Xe(ls4) and Xe(1.93) 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 25 Torr and
`varying discharge current. The density of the Xe(ls4) atoms
`is by about a factor of 50 higher than that of the Xe(lsz)
`atoms. Therefore,
`the corresponding contributions to the
`VUV radiation efficiency and power due to the radiation
`from the Xe(lsz) level with the wavelength of 130 nm
`reaches only about 3% of the contributions due to the
`Xe(ls4) radiation (147 nm). Therefore, the VUV radiation
`from the considered discharge is mainly du