JOURNAL OF APPLIED PHYSICS
`
`VOLUME 95, NUMBER 9
`
`1 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)
`Institut fu¨r Niedertemperatur-Plasmaphysik Greifswald, Fr.-L.-Jahn-Str. 19, Greifswald 17489, Germany
`共Received 29 December 2003; accepted 22 February 2004兲
`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 of Physics.
`关DOI: 10.1063/1.1704866兴
`
`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 共VUV兲 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 microcells1,2 or dielectric barrier discharges,3 are ap-
`plied in plasma display panels4–7 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 radiation8–10 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.
`
`a兲Electronic mail: uhrl@inp-greifswald.de
`
`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 1s2
`⫺1s5 共Paschen notation兲 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.
`
`II. EXPERIMENT
`A. Setup
`The experimental arrangement used for the laser absorp-
`tion measurements is shown in Fig. 1. 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 thermoionic emission. Two tungsten probes of 50 ␮m
`
`0021-8979/2004/95(9)/4627/8/$22.00
`4627
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`4628
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`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
`
`Bussiahn etal.
`
`FIG. 1. Experimental setup for the investigation of the positive column plasma by laser atom absorption spectroscopy.
`
`A servoloop inside the laser controller fits the diode injection
`in diameter and 2 mm in length, encapsulated in glass
`sleeves of less than 1 mm in diameter are used to measure
`current to the piezosignal in order to stabilize the adjusted
`the difference of the floating potentials at their positions by
`laser mode.
`means of a statical voltmeter. The probes are positioned
`Because of piezohysteresis effects the laser frequency
`closed to the tube axis in a distance of 10 cm. Considering
`does not exactly follow the control signal. The tuning behav-
`this distance one obtains the axial electric field Ez in the
`ior is monitored by the so-called LASERSCOPE from TUIOP-
`positive column which, in addition, acts as a very sensitive
`TICS Corporation, Martinsried, Germany. Its main component
`indicator of the discharge stability. Already slight variations
`is an etalon with small finesse. Two 90° phase-shifted sinu-
`of Ez point to changes in the gas composition. The tube is
`soidal signals are generated by the LASERSCOPE and can be
`mounted on a translation stage. By moving it perpendicular
`displayed on an analog oscilloscope in XY-mode. Tuning the
`to the optical axis different radial positions of the positive
`laser over a range that equals the free spectral range of the
`column can be probed by the laser beam. The dc discharge is
`etalon causes a circle on the oscilloscope display. Mode-hops
`operated on a regulated power supply with a ballast resistor
`manifest itself in a reduced radius. Backreflections into the
`of 2 k⍀ in series with the tube. The voltage across the dis-
`laser diode occur as little oscillations along the circular arc.
`charge tube and the discharge current are measured by digital
`In order to regulate the laser during a tuning cycle, the LA-
`multimeters.
`SERSCOPE signal can be fed back into a servoloop.
`Before the experiment starts, the discharge tube has been
`At the output of the etalon the laser beam is coupled into
`baked out at temperatures of 380 °C for 8 h under high
`a fiber optical waveguide which is connected to an optical
`vacuum down to 10⫺7 mbar. After this procedure the elec-
`isolator. The laser beam leaves the fiber having a Gaussian
`trodes are processed at heating currents of about 1.5 A. Ad-
`beam profile. Saturation of the observed optical transition is
`ditional cleaning of the 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 100 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 He共99,999%兲 and Xe共99,99%兲. 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 共TUIOPTICS DL100兲 in
`tively, of the discharge tube. An interference filter in front of
`Littrow-configuration 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 of a few megahertz and can be tuned
`is detected by means of a photodiode Soliton UPD 500SP. 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
`共typically triangular
`onto this region. Finally, the photodiode signal is coupled to
`shaped兲 is produced by a laser controller that includes also
`an oscilloscope via the internal 1 M⍀ terminator.
`regulators for diode temperature and diode injection current.
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`

`B. Theoretical background of absorption
`measurements
`The net intensity balance of laser radiation at frequency
`␯ 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
`dI ␯共x兲
`dx
`where ␬␯(x) names the absorption coefficient and ␧ ␯,ind(x),
`␧ ␯,spon(x) denote the coefficients of induced and spontaneous
`emission. Induced emission can be avoided by setting the
`laser power well below the saturation intensity Is(␯) of the
`observed transition12
`2冑2h␯3A21
`c2
`with the transition probability A21 and the speed of light c.
`Under the given experimental conditions spontaneous emis-
`sion is also negligible13 and than the solution of Eq. 共1兲
`yields the Lambert–Beer’s-law
`L␬␯共x兲dx,
`I ␯共L兲⫽I ␯共0兲e ⫺兰0
`共3兲
`which describes the decay of light intensity due to absorption
`within a medium of the length L. The exponent defines the
`optical depth ␶␯, hence
`L
`
`0
`is obtained. The absorption coefficient itself can be written as
`␬␯共x兲⫽␴␯N ␯共x 兲.
`共5兲
`Here, N ␯(x) is the particle number density of the lower en-
`ergetic level, that is probed by the laser and
`e2
`4␧0mec f ikP ␯
`is the photoabsorption cross-section, where e denotes the el-
`f ik
`the permittivity,
`the oscillator
`ementary charge, ␧0
`strength of the observed transition, and P ␯ the line profile of
`the transition normalized according to 兰 ␯P ␯d␯⫽1.
`Using Eq. 共5兲 and assuming homogeneous distributed
`absorbing species gives an expression for the particle num-
`ber density
`4␧0mec2
`4␧0mec
`␶␯
`P ␯L
`e2f ikP ␭L
`e2f ik
`where P ␭⫽P ␯c/␭2, i(␭)⬅I ␯(L) and i0(␭)⬅I ␯(0).
`
`␴␯⫽
`
`N ␯⫽
`
`⬅⫺
`
`
`
`ln冉 i共␭兲i0共␭兲冊 ,
`
`共6兲
`
`共7兲
`
`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
`
`Bussiahn etal.
`
`4629
`
`⫽⫺␬␯共x 兲I ␯共x 兲⫹␧ ␯,ind共x 兲I ␯共x 兲⫹␧ ␯,spon共x 兲,
`
`共1兲
`
`Is共␯兲⫽
`
`共2兲
`
`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
`0.8⫻FSR of the etalon.
`
`␶␯⫽冕
`
`
`
`␬␯共x 兲dx⫽⫺ln冉 I ␯共L兲I ␯共0兲冊
`
`共4兲
`
`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 共plasma switched off兲. 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 共Bur-
`leigh WA-4500, see Fig. 1兲 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 共FSR兲 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
`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 LABVIEW™ program,14 that fits an analytic function
`to the measured circle. Finally the program assigns the cal-
`culated ⌬␭ scale to the measured photodetector signals in
`C. Measurement of particle number densities
`every point in time 共see Fig. 3兲.
`Typically two tuning cycles of the laser are recorded for
`In the frame of the experimental work the four lowest
`exited states 1s2⫺1s5 of xenon are probed by laser radia-
`one absorption measurement. This allows an averaging over
`four absorption profiles in the following data analysis. At
`tion. Therefore, the laser is tuned to the optical transitions
`1s2↔2p2 共826 nm兲, 1s3↔2p4 共820 nm兲, 1s4↔2p5 共828
`first the optical depth in dependence on the wavelength is
`nm兲, and 1s5↔2p6 共823 nm兲.
`calculated. By area normalization of this curve a line profile
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`4630
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`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
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`Bussiahn etal.
`
`FIG. 3. Wavelength scaling of absorption signals; relative wavelength shift
`⌬␭ from the LaserScope signal in the upper frame and photodetector signals
`of the laser intensity with 共solid line兲 and without plasma 共dashed line兲 in
`the lower frame in dependence on time t during laser tuning.
`
`function P(␭) as shown in Fig. 4 is obtained. The shape of a
`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.
`
`FIG. 5. Xenon energy level scheme and processes considered in the model:
`excitation and deexcitation in electron collisions 共solid arrows兲, ionization in
`electron collisions 共dashed arrows兲, radiative transitions 共dashed double line
`arrows兲, and quenching processes 共double line arrows兲 with xenon and he-
`lium ground state atoms.
`
`III. 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 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
`
`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-term approximation10,16 of the 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.17
`The basic equations and details of the solution method
`have been already described in previous papers,15,16 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(1p0), nine individual excited states, i.e., the metastable
`levels Xe(1s5) and Xe(1s3), the resonant levels Xe(1s4)
`and Xe(1s2), five lowest p-levels Xe(2p10), Xe(2p9),
`Xe(2p8), Xe(2p7), Xe(2p6),
`two lumped states Xe(2p5
`⫹3d⫹3s,...,9s)
`关denoted further for brevity reasons as
`Xe(2p5)] and Xe(2p4,...,1), 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
`FIG. 4. Line profile function of the 2p4↔1s3 transition in Xe obtained at
`used. It includes the ground state, a lumped excited state
`He*, and the ion He⫹ in the ground state. Figure 5 presents
`p0⫽2.5 Torr, Iz⫽60 mA.
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`

`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
`
`Bussiahn etal.
`
`4631
`
`FIG. 6. Radial variation of the densities Nk of excited xenon and helium
`atoms for Iz⫽60 mA, p0⫽2.5 Torr, and rw⫽0.87 cm.
`
`FIG. 7. Experimental data 共crosses兲 and data predicted by the model
`共circles兲 for the axial electric field strength Ez as a function of the discharge
`for three different gas pressures p0 and a tube radius rw
`current Iz
`⫽0.87 cm 共a兲 and for three different tube radii in the case of p0⫽2.5 Torr
`共b兲.
`
`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(1s5) 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(1s5) 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.
`
`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.
`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(1s5) and Xe(1s4) 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(1s3) and Xe(1s2) states are important for the establish-
`IV. RESULTS AND DISCUSSION
`ment of the densities in the triplet system.18
`A. Experimental results and validation of the model
`the individual
`Additional data for
`the treatment of
`p-levels have been taken also from the sources given in Ref.
`A detailed comparison between the model calculations
`18, i.e., cross sections of Nakazaki19 are used to describe the
`and the measurements has been performed for the axial elec-
`excitation of the p-levels from the ground state in electron
`tric field strength and for the axis densities of xenon atoms in
`four lowest excited states 共i.e., 1s5 , 1s4 , 1s3 , and 1s2) in
`collisions, stepwise excitation cross sections are calculated
`Smeets,20 Deutsch–Ma¨rk
`the column plasma.
`according
`to Vriens
`and
`formalism21 is used to determine stepwise ionization cross
`Figure 7 presents measured and calculated values of the
`axial electric field strength at different pressures and tube
`sections.
`radii for varying discharge currents 共data for the radius 1.12
`Figure 6 shows an example for the radial variation of the
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`4632
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`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
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`Bussiahn etal.
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`cm are taken from Ref. 18兲. 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 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.
`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 共e.g., moving striations兲 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 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(1s5) and Xe(1s3) states show a slight decrease with
`growing discharge current. The axis densities of both reso-
`nance states increase with the discharge current. The depen-
`B. Global power balance of the discharge plasma
`dence of the densities on the gas pressure is only weak. Cal-
`culated axis densities of the Xe(1s5) state and of both
`To evaluate the efficiency of the column plasma with
`resonance states reproduce the dependencies found experi-
`respect to its use as a radiation source, the global power
`mentally, and show a good quantitative agreement with the
`budget of the plasma must be analyzed in detail. To derive
`measured values.
`the global power balance equation the spatially resolved
`Predicted axis densities and the dependence on the dis-
`power balance of heavy particles has to be considered to-
`charge current of the Xe(1s3) state do not coincide with the
`gether with the electron power balance.22 Finally, the global
`experimental results. Calculated values increase with the cur-
`power balance equation becomes the form
`rent, saturation occurs not until a discharge current of 80
`fl 典⫹具Lel典⫹具Lh典具LVUV典⫹具LIR␯ 典⫹具Lmetdiff典⫹具Lio典⫹具Le⫺
`
`
`␯
`
`
`mA. Reasons for this discrepancy could be that coupling
`processes between Xe(1s3) and other excited xenon levels
`⫽EzIz .
`共8兲
`are not described well or are not included in the model be-
`␯
`␯ 典 denote the losses due to the VUV
`
`Here, 具LVUV典 and 具LIR
`cause of the absence or the inaccuracy of corresponding
`and infrared 共IR兲 radiation processes, respectively. 具Lio典 de-
`atomic data. However, the maximum discrepancy between
`calculated and measured data for Xe(1s3) does not exceed
`scribes the ionization losses, the action of the radial electric
`TIB Hannover licenced customer copy, supplied and printed for Clients of FIZ Karlsruhe, 2/6/15 at 11:52 AM
`
`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(1s5), Xe(1s4), and
`Xe(1s2) 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.
`
`FIG. 8. Experimental data 共crosses兲 and data predicted by the model
`共circles兲 for the axis densities of the excited xenon levels Xe(1s5),
`Xe(1s4), Xe(1s3), and Xe(1s2) as a function of the discharge current Iz for
`a pressure p0⫽2.5 Torr 共a兲 and as a function of p0 in case of Iz⫽60 mA 共b兲.
`
`

`

`J. Appl. Phys., Vol. 95, No. 9, 1 May 2004
`
`Bussiahn etal.
`
`4633
`
`FIG. 9. Important terms of the global power budget of the plasma in depen-
`dence on the gas pressure p0 at Iz⫽60 mA; radially averaged power loss
`rates Lk with respect to the power input EzIz .
`
`FIG. 10. Efficiency ␩VUV 共triangles兲 and output power PVUV 共circles兲 of the
`VUV radiation generation from the levels Xe(1s4) and Xe(1s2) as a func-
`tion of the discharge current Iz for p0⫽2.5 Torr and rw⫽0.87 cm.
`
`field 共radial cooling of the electrons兲 corresponds to the term
`fl 典. 具Lel典 includes the power losses due to the elastic
`具Le⫺
`collisions of electrons with helium and xenon atoms. The
`losses due to the diffusion of the metastable xenon atoms
`diff典. The term 具Lh典
`onto the wall are described by the term 具Lmet
`represents the losses due to the chemoionization.
`Figure 9 presents the important terms of the power bal-
`ance for the discharge current Iz⫽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 具LVUV典/EzIz 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 of VUV radiation
`losses and a growth of elastic losses. All other contributions
`remain nearly independent from the discharge current.
`
`lindrical column, ␩VUV is the ratio of PVUV to the electrical
`input EzIz 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(1s4) and Xe(1s2) 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 of the Xe(1s4) atoms
`is by about a factor of 50 higher than that of the Xe(1s2)
`atoms. Therefore,
`the corresponding contributions to the
`VUV radiation efficiency and power due to the radiation
`from the Xe(1s2) level with the wavelength of 130 nm
`reaches only about 3% of the contributions due to the
`Xe(1s4) radiation 共147 nm兲. Therefore, the VUV radiation
`from the considered discharge is mainly due to the resonance
`radiation of the Xe(1s4) state, and further analysis will be
`performed for this transition only.
`Figure 11 presents the dependencies of the efficiency and
`power of the 147 nm radiation on the discharge current den-
`2 , the gas pressure and the tube radius. The effi-
`sity Iz /rw
`ciency decreases with increasing current and pressure be-
`cause the density of resonance atoms is nearly pressure
`independent and the axial electric field grows in consequence
`of increasing elastic losses 共gas heating兲. An efficiency of
`about 30% has been predicted at a pressure of 1.5 Torr and a
`discharge current of about 10 mA/cm2. The VUV radiation
`power increases with the discharge current and decreases
`with the pressure. A VUV radiation power of about 8.5 W/m
`is reached at a gas pressure of 1.5 Torr and a discharge cur-
`rent density of about 130 mA/cm2, where the efficiency is
`about 20%. An increase of the tube radius causes a decrease
`of the efficiency and a growth of the output power.
`C. Optimization of discharge conditions
`Main results of the optimization study are summarized in
`The validated model has been applied to analyze the
`Fig. 12 presenting the VUV radiation efficiency as a function
`VUV radiation of the positive column of the xenon discharge
`of the radiation power. Hence, every point in the graph of
`in the dc operation regime for varying discharge conditions.
`Fig. 12 represents specific discharge conditions, i.e., dis-
`Particularly, the dependencies of its efficiency ␩VUV and ra-
`charge current, gas pressure, and tube radius. Each line has
`diation power PVUV on the discharge current, gas pressure,
`been obtained by varying one of these conditions and fixing
`and tube radius have been predicted by the model. Here,
`the two other. As it becomes obvious from Fig. 12, discharge
`PVUV denotes the radiation power per unit length of the cy-
`operation at low pressure and high cu