ENTE PER LE NUOVE TECNOLOGIE, L’ENERGIA E L’AMBIENTE

Dipartimento Innovazione

EROSION PROCESSES AND MICRO-PARTICLE PRODUCTION IN GAS DISCHARGE LASERS

TOMMASO LETARDI, GUALTIERO GIORDANO ENEA - Dipartimento Innovazione Centro Ricerche Frascati, Roma

CHENGEN ZHENG (ENEA GUEST) EL.EN - Via Baldanzese 17, 50041 Calenzano (Fl)

RT/1NN/99/14 Manuscript received in final form on January 1999

Printed on July 1999

...

This report has been prepared and distributed by: Servizio Edizioni Scientifiche - ENEA Centro Ricerche Frascati, C.P. 65-00044 Frascati, Rome, Italy

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Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. SUMMARY

The erosion processes of the cathode for pulsed excimer gas lasers are explained by comparing the initiation conditions of the pulsed excimer gas laser discharge to that of the vacuum discharge breakdown. The numbers of the micro-particles, generated due to the above cathode-processes, are estimated. Several possible influences of the rnicro-par~icles on performances of the gas discharge iasers are analyzed. Two methods for eliminating the micro-particles or reducing their influences are discussed

(EXCIMER LASERS, ELECTRODE EROSION, PARTICULATE, DISHCARGE MICRO-PARTICLE, MIRROR PROTECTION)

RIASSUNTO

Vlene descritto, comparandolo con la scarica in vuoto, il processo di erosione del catodo di un laser ad eccimeri a scarica. Viene stimato il numero delle micro- particelle generate dal processo di scarica. Vengono analizzate le possibili influenze di tali micro-particelle sulle prestazioni dei laser a scarica. Sono presentati e discussi due possibili metodi per la eliminazione delle micro-particelle generate dalla scarica.

INDEX

1- INTRODUCTION ...... p. 7

2- SIMILARITY OF THE FORMATION FOR CATHODE SPOTS IN GAS DISCHARGE AND

VACUUM BREAKDOWN ...... p. 8

3- DISCHARGE EROSION PROCESS OF THE CATHODE ...... p. 9

4- ESTIMATION FOR GENERATION RATE OF THE MICRO-PARTICLES ...... p. 13

5- INFLUENCE OF THE MICRO-PARTICLES ON PERFORMANCES ON ONE-FILL ...... p. 16

GAS-MIXTURE EXCIMER LASERS

5.1. Gas discharge breakdown ...... p. 17

5.2 Influence of the particles on mirror quality ...... p. 18

5.3 Discussion of the laser scattering by micro.paHicles ...... P. 25

6- PROTECTION OF THE MI~ORS ...... P. 25

7- SUMMARY AND REMARKS ...... P. 29

APPENDIX: Movement of a particles in gas chamber ...... ~...... P. 31

REFERENCES ...... P. 37

7

EROSION PROCESSES AND MICRO-PARTICLE PRODUCTION IN GAS DISCHARGE LASERS

1- INTRODUCTION

The particulate contamination is one of the principal problems which influence the operation life time of the XeCl excimer lasers [1,2]. The particulate, which are composed of many particles with different dimensions, arise primarily from the discharge processes. On one hand, there are always some molten droplets which are emitted from the filament or arcing spots on the electrode surfaces during the discharge either due to large electrostatic forces acting on the electrodes inside the cathode sheath, or due to superheating resulted from joule heat and ion bombardment. On the other hand, some chloride compounds, such as chlorocarbons and so on, can be also generated especially in the discharge or preionizer (for the case using UV-preionization) region, where the reactions of HC1 with metal or dielectric materials are promoted by discharge, and laser beam or UV radiation from the plasma [1].

Both particulate or chloride compounds can deposit or adhere to the interior of the laser window or mirror to form a coating layer, causing degradation of the optics. For the deposition of the chloride compounds, the situation may be more serious, since some of the compounds can be further photo-dissociated to carbon or other compositions by incident laser beam through a single or multi-UV photo effect [1].

Since most of gaseous chloride compounds have liquefying temperatures higher than those for HC1 or other constituents of the laser gas mixture, they can be efficiently removed by a low temperature gas trap, for example, a liquid nitrogen cryogenic purifier. Different from the case for gaseous impurity the solid particles are often eliminated by using some particulate 8

filters. In order to know the requirements for the filters, we need to know something more about these particles, for example, what kind of dimensions they have, where they cc~mefrom, how much their generation rates are, and so on. In this work, we try to discuss these questions.

2- SIMILARITY OF THE FORMATION FOR CATHODE SPOTS :[N GAS DISCHARGE AND VACUUM BREAKDOWN

It is observed both in vacuum breakdown and for high pressure gas discharge experiments that after a short interval of the time delay relative to applying a voltage to an electrode gap, there are some spots appearing on the surface of the cathode, which lead to a final short circuit of the gap. For XeCl gas discharge case, the cathode spots, which are called as hot spots, are observed to have a linear density of 4 /cm under the experimental condition reported in [3]. The main discharge energy deposition in the gas mixture is also found to be dominated by these spots. Suppose that at the beginning, there is a very uniform discharge between two electrodes, then the spots emerge first from the cathode and later at the anode, and each of these spots initiates a single filament being growing with time into the main discharge gap [3]. With the development of these filaments, the glow discharge surrounding the filaments becomes weaker and weaker and finally disappears. The cathode spots which appear are not only observed in XeCl discharge lasers, but also for other types of gas discharge devices, for example, pulsed N2 discharges and so on [4,5]. For vacuum breakdown case, it is known that explosive emission of electrons plays an important role for initiating the discharge and maintaining the cathode spots (for example, see [6-9]). Since vacuum breakdown is a very complicated phenomenon, and only some processes are made clear now, here we only mention some results about formation of the spots, which are important to the description of this work:

a) There are always micro-protrusions with the height in the order of several Km on the cathode surface, and the local fields can be enhanced by these protrusions with a factor of y=(10-102) [8,10,13-15]. A very high electric field, which may be of the order of 5~106 V/cm at least, can also induce some new micro-protrusions on the surface of the cathode [10- 12]. b) On application of a high voltage to an electrode gap, the micro-protrusions on the cathode surface are heated by field emission current. If the field is high enough, the joule h,eating of the protrusion-tips results in transition of the pure field emission to field-assistecl thermo- ionic emission, leading to a further increase in temperature of the tips, and finally the formation of local plasma burst, i.e. the explosion of the micro-protrusions [6,7.,16]. The 9

critical value of the local field near the micro-tips for vacuum electrical breakdown is - measured to be in the range of (5-11)=107 V/cm for a variety of electrode materials, and this value is related to the explosions of the micro-protrusions on the cathode surface [5,7,16-22].

For the case of pulsed discharges at a high gas pressure, the formation of cathode spots is similar to the above described vacuum breakdown case. In fact, after a pulsed high voltage is applied between two electrodes, an electron-depleted layer, which is often called as the cathode fall region or cathode sheath, is left to be close to the cathode surface due to a drift of free electrons towards the anode inside the electrode gap, leading to a very high electric field strength in this layer. Suppose that the electric field across the electrode gap is finally counteracted by the field produced by the space charge in the sheath, we may approximately estimate the field near the cathode surface as [23]

2e. ne-V0 ECat~ = (1) r E() ‘

where e= 1.602”10-19 C is the electron charge, ~. =8-854-10-14 CN the dielectric coefficient in vacuum, V. the voltage drop on the electrode gap, and ne the free electron number density. For example, Ecath is of the order of 106 V/cm when ne=(1013-1015)/cm3 and VO=30 kV. A detailed study for cathode sheath of a discharge-sustained XeCl laser shows that under normal conditions of operation the cathode electric field can have a value of 4“106 V/cm during the plateau part of the discharge voltage [24]. Taking the field enhancement factor y=(10-100), the local field near the micro-protrusions may reach the value of (107-108)) V/cm, which is clearly sufficient to give rise to explosive process of the micro-protrusions [6,7,16]. Experimentally Microscopic craters are really observed in an atmospheric discharge with a voltage pulse duration of 50 ns even for the case of fields down to = 105 V/cm, as reported in [25], and this is to further confirm that the cathode spot explosion is an inevitable process for pulsed discharges of the gas at high pressures.

3- DISCHARGE EROSION PROCESS OF THE CATHODE

As seen in the above, there are inevitable destruction and production of the micro-protrusions on the surface of the cathode for a gas laser during its discharges, and this certainly leads to a continual erosion of the electrode with the increase of the discharge number. Some data show that for a XeCl or KrF laser device with a usual type of electrode materials, after a number in the order of N&&e – 2.108 shots of discharges, the electrode surface is apparently 10

deformed and has to be refurbished or replaced (for example, see [26]) in order homogeneous discharge. We may take a XeCl laser as an example to see h the erosion rate of the cathode is in this case.

Suppose that the pulsed laser output energy is E1a~,having the electrode length and gap, respectively, of ldi~ and h.gapwith a charge vokage of Vch for primary capacita the laser discharge modulator. Since most of electric charge on the prima capacitance will finally go through the electrode gap, we may estimate the elect transported through the gap per pulse as

2Elas Q$:Ise = cc~ . vc~ = ~las “‘ch ‘ where qlas is the laser energy output efficiency. Therefore, before the electrode i: etched, the total electric charge, which passes through the electrode gap, is

Q?! = N%$ge “Q$ke “

Suppose that the spatial distribution of the laser output energy follows an exponen with a usually defined full width Wile of I/e-laser output intensity. In this waj energy density distribution near the output mirror, which is assumed to be close to window of the gas chamber for an external laser cavity case, may be approximately by

where E~ = E~~~(0), the coordinate origin o is taken at the intersecting point bc output mirror surface and optical axis with the o-z axis along the optical axis and o to the electrode sufiaces. Here E~~~(x, y) is assumed to be insensitive to the coordin certain extent, E~~s(x) is proportional to the discharge energy density E(x)-j(x).~ E(x) is the discharge field between the electrodes, j(x) the discharge current densit the discharge duration. Noting that E(x) changes by only a few percent with dimension of the laser spot, i.e. E(x)=EO, we may approximate 11

2 2x j(x) = jo. exp – — [[ ‘he ) where jo=j(0). Suppose that the erosion depth h$~e per pulse of discharge on the cathode surface be proportional to the electric charge which passes through a unit area of the electrode surface x, then we get

(6)

Therefore, the mass of the cathode removed per pulse of discharge is

etch dx , ‘pulse = Pel.de “ldis “J~ ‘jfte(”)” exP – ~ (7) [( 1 and for N~~~~ge pulse of discharges, the total mass removed from the cathode surface is

(8) where ~el.de is the mass density of the cathode, and hetch (0) = N~~$ge . h~~l~e(0).

For a small XeCl laser device, for example, the laser output energy Elas= (100-200) mJ, with LdiS=50 cm, hgaP––2.5 cm, and Wile =1 cm. Suppose the laser efficiency o.f?lIas=(1- 1.5)% with VC~=30 IsV, Eqs. (2-3) give Q$~se = 0.8 mC and QtOt‘is – 1.6-105 C for ElaS=0.15 J and

W.s=l -25%. In Eqs.(6-8), the maximum thickness hetch(o), allowed to be removed from the cathode for normal operations, can be taken to have the value of about (0.4-1)% of the discharge gap distance [27,28], i.e. hetCh(0)~0.007 hgap. From these data, we obtain m ~~ = (3.5 – 8.9) g with pelde=8 g/cm3, which gives rise to an erosion rate of the cathode in the order of

R~h = (22 - 55) #g/c (9) 12

It is interesting to compare the above value of R$ch with some data obtained under vacuum electrical breakdown condition. The experiments for this case show that the erosion rate R~~h of electrode depends on both the electrode materials, electrode geometry, and the discharge parameters, such as the electric current, discharge voltage pulse duration, or the electrical charge transported per pulse, and so on (for example, see [29-32]). If the electric charge per pulse transferred during the vacuum discharge is less than 10 C, it is observed that there are no much difference in the order of magnitude for the erosion rates R~C~.of aluminum, nickel, copper, and chromium, and all of them are in the range of [29,30,32-35]

R;~h = (10–100) yg/C (lo)

It can be known from comparison of the above results that there is quite a good coincidence between two different kinds of the electrode erosion data, obtained, respectively, under the laser gas discharge and vacuum electrical breakdown conditions. Clearly the cathode materials for these two cases are removed not only at the moment of the explosion of the primary micro-protrusions, but also at subsequent times when there is a discharge current. In fact, based on the following considerations, some results, obtained in the vacuum breakdown case, may be applicable to the gas discharge case:

First, it is shown in some works (for example, see [32]) that the gas pressure developed in the emission zone due to ohmic heating, which leads to a formation of micro-crater or explosion, is up to 104 atmospheres, which is much higher than that of the gas pressure, filled inside laser discharge chamber. Secondly, the convective energy exchange between ambient gas and micro-protrusion surface can be neglected compared to the conductive and radiative heat transfer processes. In fact, for a protrusion, there are three sorts of thermal energy losses: the convective loss @onv between its surface and ambient gas, the conductive loss QCOndUC. through its base connected to the cathode surface, and the radiative loss Qradia. through its surface. During the time interval At between the electric field application and protrusion explosion, these energy losses can be, respectively, approximated by

Q...,-‘x-(T-Tw)A9sAt> (11)

(’T- Tcath.) . Abase . At , Q...ctu,. = Kc,th. - Ah (12) 13

Qr.diat.= o “T4“Agas “At (13) - where T, Tga~, and Tcath. are, respectively the temperatures for protrusion, gas, and cathode, Aga~ and A~a~e are, respectively, the areas of the protrusion surfaces which neighbors the gas and connects to the cathode, Ah is the height of the protrusion, L the heat transfer coefficient between the gas and micro-protrusion surface, Kcath. the thermal conductivity of the cathode, 0=4.88x 10-8 kCal/hour m2 deg4 the Stefan-Boltzmann constant. It can be obtained from Eqs (1 1–13) that

Qconv. ~ k.‘h.‘gas <<~ , (14) Qconci. ‘cath. “‘base and

Qconv. ==<<1~ , (15) Qradiat. G ~T

A where we use k= 14 kCal/hour*m2*deg., Kcath-=16 kCal/hour*m.deg., Ah = 5 pm, ~as- <10, ‘base and T@a~–’-TCath=300 deg. K, and T>2,000 deg. K for Cu, W, or Mo electrode materials (for exam~le, see [30,36,37]).

From the above comparison of the data obtained for two different conditions, the cathode spot explosive process appears to play a very important role for the electrode wear. In addition, for halogen gas excimer laser case, the electrode mass loss rate could be a little higher than the data measured in the vacuum breakdown conditions, since there may be chemical reactions for electrode materials participated by HC1 or F2 under the discharge condition.

4- ESTIMATION FOR GENERATION RATE OF THE MICRO-PARTICLES

It is known from some investigations of the vacuum discharge that during the explosions of the micro-protrusions and following arcs originated from the spots on the cathode surface, three different kinds of species other than electrons leave the spot region. The first one is ions of metal vapor, the second is the neutral vapor gas, and the third is the molten metal particles of various sizes [29,31,32,36,38-39]. It is observed in some measurements which use Cu and Mo electrodes for the electrodes that the dominant flows consist of ions and molten micro- 14

particles ranging in size from less than 0.2 ym to several ~m , and the cathode mass flow in - vapor form is considered to be small [38]. The measurements for copper electrodes indicate that only about 10 YOof the cathode mass would be lost in vapor form, and the mass loss in particle form appears to be of the same order as that for ions [38]. According to these results, it may be roughly estimated from Eq. (10) that the copper cathode mass loss rate in micro- particle form is in the order of

RdU~t=(5 - 50) vg/C (16)

Using a current pulse duration in the range of (5-1,500) ms under vacuum discharge breakdown conditions, some measurements for copper, molybdenum, or cadmium electrode cases show that the distributions of the particle numbers ANdu~~per Coulomb against the particle sizes can be approximated in an exponential form [38]

‘dust _ f ~OAQ – coH . No -w@ “Do) , (17) where K is a constant depending on experimental parameters such as cathode material and electrode gap distance, AQ is the average charge transfer, Do is the outer diameter of the particle, No is the extrapolated value when DO=O, and fcoll is a constant depending on the particle collection geometry. IVhen the voltage pulse duration At decreases to the order of 102 ns, the particle size distribution, given in Eq. (17), seems to be good only for the case with their sizes not too small. The detailed studies using copper cathodes and with the voltage pulse duration of At=35,50, 100, or 300 ns under vacuum discharge condition reveal that for every emitted particle diameter distribution curve, there is a peak, whose position is not much sensitive to its pulse duration, and when the discharge pulse duration changes from 35 ns to 300 ns, the positions of the maxima for these curves remain in a small range of the diameters of @=(O.06-O.13) Wm [32].

It can be known from these particle diameter distribution curves that, starting from the position of the distribution peak, the emitted particle number, respectively, decreases very quickly or slowly with the increase or decrease of the particle diameter. The particle numbers corresponding to the diameter of 0.025 ~m, which is the minimum size discernible in the electron microscope used in this experiment, are only about (10-30)% less than their correspondent maximum values [32]. For the case with the discharge pulse duration of (50-100) ns, the numbers of the micro-particles with diameters of (0.025-0.1) pm and (O.1–0.2) pm are nearly the same, and both of them are about 1/3 of the total numbers of the 15

collected particles. For those with the diameter larger than 0.2 pm, their numbers decrease very quickly with the increase of the diameter. For example, the ratio F(0.5.0.6)Wm of the particle numbers with its diameter between (0.5–0.6) pm to the total ejected particle numbers are only about F(O+5_0-6)Wm=(3-4)%.

Although the fraction of particles with the diameter more than 0.5 pm is very small, they carry most of the total ejected particle mass. For example, for the case of pulse duration of tP=50 ns, the number of the particles having diameter from 0.5 to 1 ~m is only about 10% of the total number, but they carry about 80% of the ejected particle mass [32].

In general, both the dimensions of the particles and its total number for the particles emitted from the cathode per pulse trend to decrease with reducing its discharge pulse duration [31,32]. In fact, for long pulse cases, the emission centers on the cathode may appear and disappear many times, and for the ejection of the micro-particles on each emission center may last only for a short time.

The diameter of the largest particle is generally less than the crater radius. In the vacuum discharge experiments with the current pulse duration in the range of (5-1500) ms, the expelled globules from the cathode have the maximum sizes of the order of 25 pm for copper, 10 ~m for molybdenum, and 30 ~m for cadmium [38]. It is indicated in [31] that there is negligible chance to emit a molten metal particle larger than 1 pm in diameter if the arc duration is shorter than 0.5 US for Au-cathode. A similar result can be also seen from the measured particle diameter distribution curves, where for At=35, 50, 100, or 300 ns, the ratio of the number for the particles of the diameter larger than 1 ~m to the total emitted number appears to be negligible [32].

The vacuum breakdown discharge experiments using copper or gold cathode give the number of micro-particles, emitted from cathode per unit charge, as [31,32]

N;~f”/C =(l–3) .107/C . (18)

The results given in Eqs. (16) and (18) are consistent to each other. In fact, the mass 10SSrates of the cathode, which are calculated by using the measured particle size distributions, reported in [32], and emitted total particle numbers, given in (18), well fall inside the range, indicated by (16).

It should be noticed that a particle ejected from the cathode in the gas discharge laser case experiences much strong resistance-force during its flight, caused by the gas viscosity, compared to that for the vacuum breakdown case, where the gas density is so low that 16

intermolecular collisions are actually infrequent, and so that the viscosity is very small in this case [40]. Since the initial velocity of these molten particles can be in the order of 102 m/s, there may be a very high gas resistance, determined by drag coefficient [41,42]. As seen for raindrop [43], the drops large enough to fall with greater velocity are broken up during their falling, and also experimentally observed that a drop initially spherical is found to be deformed, by the air resistance, to the shape of an inverted cup before it bursts into fragments. Similar to this case, the non uniformly distributed residence on the molten metal-droplet may tear it into many pieces, when the drag is larger than its surface tension which, as is known, decreases with its temperature. Considering this effect, the total number of the particle per Coulomb, emitted from the cathode craters, should be larger by a factor of 17>1 than the value given by (18), i.e. we have

N::; IC=FN;$VC

or (19)

N:::/c= r.(1–3).lo7/c .

5- INFLUENCE OF THE MICRO-PARTICLES ON PERFORMANCES CJF ONE- FILL GAS-MIXTURE 13XCIMER LASERS

Since most of micro-particles generated in the discharge or spark-preionization region have a very small size, they can be suspended in gas for a long time. For example, a spherical particle with a diameter of 0=0.5 pm and density p=8 g/cm3 is put inside the neon gas at the pressure of 5 atm for t=5 hours, it can only fall by a distance of y(t)= 1 cm (see Appendix). In Fig. 1 we show more data of y(t) versus t for three different particle diameters.

Some particles, which have already deposited or adhered to the internal surfaces of the laser gas chamber, are liable to be agitated into the gas again by either discharge or gas flow-caused vortices or eddies because of their small mass.

As long as the particles leave the surface, they can be very quickly to reach the velocity which the gas flow has. For example, if a particle of density of p=8 g/ems with a diameter of cP=2 pm and having an initial velocity of zero is injected into a five-atmosphere neon-gas current flow of the velocity of 10 rds, then due to gas viscosity, it would be accelerated, and in a distance of less than 0.4 mm, it can have 80% of the gas velocity value (see appendix). More data of the acceleration scale for several different particle diameters are shown in Fig. 2. 17

102

101

100

10-1

10-2

10-31 , I I 100 101 102 103 Time (rein)

Fig. 1- Falling distance of a spherical iron-particle with a diameter @ in the gravity field versus time tfor the case with $=0.5 (solid), 1 (dotted), and 2 pm (dashed lines), where the initial speed of the particle is supposed to be zero.

From these data, shown in Fig. 1 and 2, it is known that many micro-particles trend to either follow the gas current or suspend inside the gas mixture during the time when an excimer laser is operated in a repetition rate mode. Since the particles are mainly created by discharges, their densities clearly increase with the number of the pulsed discharges. In some of one-fill gas-mixture excimer laser systems, whose life time can be extended to the order of (4-5).107 shots by using some special technologies (for example, see [44]), the particle number can be accumulated to so high level, that it may cause some problems for laser performances. Here we will discuss some of the effects of these particles in a little more detailed way.

5.1- Gas discharge breakdown

Suppose that there is a spherical metal ball between two electrodes, the field stress on the surface of the ball can be expressed by

E=3Eo”cos(3 r , (20) where r is the radial unit vector of the ball, and (3is the angle between r and the direction of 18

Fig. 2 -. Acceleration scale of a spherical iron-particle with a diameter of @, which is put inside a gas stream of velocity Vg = 10 m/s, versus the ratio of the particle velocity Vx to Vg for ~he case with cP=O.6 (so!id), 1.2 (dotted), and 2.4 pm (dashed lines), where the initial speed of the particle is supposed to be zero.

the uniform field Eo established by two electrodes. On the surface of the ball, the field reaches its maximum value of EmaX–––+3E0 when O=O,X. Clearly, during the pre-discharge period, some micro-streamer or filamentaries may be initiated first from these points, and then they may be prematurely developed into arcs to have the discharge uniformity destroyed (for example, see[45]). In addition, the micro-particles may be overheated or even explclded again by the gas ion bombardments on their surfaces, and release lots of absorbed or adsorbed gas impurities which influence the both discharge kinetic and discharge processes.

5.2- Influence of the particles on mirror quality

The total number NtOt of the micro-particles ejected from the cathode after NPul~e pulses of discharges is

(21) where

(22) ‘f$=(N~$’c)-Npulse”Q$Jse and 19

(23) - are, respectively, the micro-particles generated by main discharges between two electrodes and UV-sparks for the case of UV-preionized gas discharges, N~~ts/ C is the cathode-emitted particle number per Coulomb, as expressed in (19), and Q$se and Q~~ are, respectively, the electric charges (in units of Coulomb) per pulse, transported by main discharge and UV- spark.

For small UV-preionized lasers, so-called automatic UV preionization spark connection is often used in a charge transfer circuit 46-49], and in this case we may write

Q;::: = E“Q;;Ise , (24) with S= 1 for the spark arrays being connected in series with the charging circuit of the capacitor Cch, as is often done in some commercial excimer lasers (for example, see [49]. Here Q$~se can be estimated by Eq. (2).

Sometimes the sparks are connected in parallel with the discharge gap and the discharge capacitance Cch (for example, see [46]) or using other types of connections, and in these cases the values of& depend on several factors, such as the discharge geometry, gas pressure and so on. For an estimation, we may still take S= 1 later.

Usually, the micro-particles do not uniformly deposit on the internal surfaces of the gas chamber, and the nearer to the discharge region, the more particle density there may be. On some parts of interior of the gas chamber, such as the dielectric material surfaces or somewhere with less gas disturbance, there may be a very small chance for a deposited particle to leave again. It is rather difficult to give an accurate quantitative estimation to describe the influence of the quality for the surface on the deposition density of the particles. However, as an order estimation for the total density D~Ot of the particles on the interior surfaces of the optics, it may be assumed that all the particles generated during the discharges be uniformly deposited on all the internal surfaces of the laser gas chamber. In this way, Eqs. (21-24) yield

D:ot = D~iS+ DRPark ~ (25) where 20

@i~ = 2(N:::’c)Np.Ise”Elas 9 (26) ~l,s “‘Vch - ‘;t and

(27) with S~t being the total internal surface area of the laser gas chamber

x@2 Noting that each deposited particle has a projected area of sp~oj(o) “ — to the mirror 4 surface along the direction of optical axis, where @ is the diameter of the particle, we may average the area sproj(0) over al~ the deposited particles on the mirror surface, i.e.

s&j = ~sProj(Q)fzD(@)d@ (28) o and

~J ‘~sProj(@)ft,(@)d@ , (29) o where the superscripts or subscripts ~~ and ~D, respectively, mean the pulse durations of the preionization spark and main discharges, f~D(@)and f~, (Q) are, respectively, the normalized micro-particle diameter distribution functions for main discharge and UV-spark discharge, i.e. with

;f@l)d@=l , 0 and 21

cm

0

We may introduce a quantity: the optical area blocking factor Stotblock, which is defined as the ratio of the sum of the projected areas for all the particles deposited on the mirror to the total mirror surface area, i.e.

(30)

where

(31)

and

(32)

are, respectively, the values contributed from the main discharges and UV-sparks.

From the geometrical point of view, StotblOck is the opaque ratio of the light, which is blocked

by the particles, i.e. 1– S~~~k is the light transmittance of the mirror. Since the sizes of the ( ) particles are comparable to the laser wavelength, the diffraction effect of the particles should be considered. The scattering problem of the light by metal sphere was dealt by some persons many years ago (for example see [50]). The main result is as follows. When the particle diameter $ is much less than the wavelength k, there is a symmetrical distribution in the polar diagram of the light scattering with the intensity maximum in the forward (6=0) and reverse directions (0=180 0 ) and the minimum in the direction of 6=90° ; and as the diameter of the sphere is increased there is a departure from symmetry, more light being scattered in the forward direction than in the opposite direction (Mie effect); as the diameter is increased still further almost all the scattered light appears around the forward direction [50]. In all these cases, the forward scattering lights appear to have quite a large divergence angle compared to hgap the ratio of the discharge gap to the distance of the laser oscillation cavity length, i.e. — L’Osc

, 22

thus when a laser beam is incident on the surfaces of these particles, it would suffer a very - heavy intensity loss. To a great extent, 1– S~~~k is still related to the light transmittance. ( )

Now we give an example to see how much the particle deposition density is for a small UV-preionized XeCl excimer laser device. Suppose that we have a maximum laser output of El,~=300 mJ with an efficiency of about qlM=(l-l .5) % and charging voltage of Vch=35 kV, from (24) and (2) we can obtain

(33)

Suppose that for a one fill laser gas mixture, we have the total discharge pulse number of

NPU1~e=3. 107 pulses, (34) then from (19) and (22-23), we obtain the total numbers of the micro-particles ejected, respectively, from the main discharge cathode and the spark gaps as

N:~: = 1.231012 micro – particles, (35) and

N:::k = E . N:) , (36) where we take N~~~/C = 3. 10’7/C with r=l in (19).

Typically, the total internal area and volume for the laser gas chamber in this case are, respectively, in the order of

S~t =(6–10).103 cm2 , (37) and

vi”~a, =(4-8).104 cm3 , (38) 23

Therefore, Eqs.(35-37) give

dis D~is = ‘totSin – I .54.108 particles/ cm2 , (39) tot

and

D&rk = ~. D~is = &-1.54.108 particles/ cm2. (40)

Since the particle diameter distribution is dependent on the discharge pulse width, the value of

the average area for the particles S~roj (see Eqs.(28-29)) will depend on the pulse duration.

For three different discharge widths S~roj are calculatedto have the values as follows [32]:

l~m s50ns .. f50ns(@)d@ =5.3310 -10 cm2 , (41) proj = J sproJ o

lym 1Oons= s s (42) proJ J proj . floons(@)d@” = 7.88.10-10 cm2 , 0 and

_. .._ l~m S300ns = s (43) proJ J proj ~f300ns(@)@ = 8.93.10-10 cm2 , o where f.50nS(@), f 10onS(@), and f300nS(@) are the micro-particle diameter distribution functions, which, respectively, correspond to the discharge pulse duration of z=50, 100, and 300 ns. Here we take the upper limit of the integration to be 1 ~m as the pulse duration is very short. For the above mentioned UV-preionized XeCl laser, the typical main discharge and electric transfer times are respectively, in the order of 50 and 300 ns.

Finally Eqs. (30-32), (39-41), and (43) give 24

It is reported in [1] that for a XeCl excimer laser, the reflectivity of the mirror after 3.: pulse discharges is reduced by about ( 1O-25)9ZOdue to something deposited on the m surface, which is of the same order as that, given by our estimation in Eq. (44). From result, it seems that the deposition of the micro-particles, emitted during the discharges, o mirror surface is one of the important causes for the mirror contamination.

For X-ray preionized discharge lasers, there is no contribution of the UV-sparks tf generation of the particles. Let’s consider Hercules laser system. In this case we LC-inversion circuit for the discharge excitation, with DC charging capacitance

C% = 2CCh = 960 nF .

and DC charge voltage

Vch =35 kV .

We obtain

Q~$l,e = C% . V,h = 33.6 mC .

Suppose that we have the total pulse number

NPUl~e=3*106pulses,

and then the total particle number generated in the main discharges is

~dis ’01‘(N~:f’c)”Np.lse”Q:Jlse=3024”’0*2‘aticles-

The total internal area of the Hercules is estimated to have the value of

S$t =(2–4)”104 cm’ ,

and we get

, 25

dis Dais = ~‘tot – 3.37.107 particles/cm2 s tot

If we take the discharge pulse duration of 300 ns, we can have the optical blocking area ratio

$:yk = sdi~blOck= 9.0% .

5.3 -Discussion of the laser scattering by micro-particles

The micro-particles which are suspended in the laser optical path cause the laser light scattering. If the density of the particles is too high, the laser output characteristics, such as the coherence, output energy and so on, maybe deteriorated very much.

From the geometrical point of view, the light transmittance T would be reduced in this case, since a part of beam which falls on the particles would be stopped. It is not difficult to express the light blocking percentage Sblock=1-T as a function of the suspended particle density N~U~~ and optical length LOPtas

Sblock Susp N dust = cw (45)

As an example, we still use the data given for the above-described XeCl laser system and suppose LOpt=80 cm. In this case, if the number density N~u~~ of the particle inside the optical cavity is in the order of 106 cm-3, the optical area blocking percentage is about 4%.

6- PROTECTION OF THE MIRRORS

For a longitudinal gas flow laser, the interior surface of one of the optical windows or mirrors, which is facing to the coming direction of the gas flow, is often found more dirty after a period of discharge experiments than the other window or mirror. The calculation shows that the maximum flying range of a spherical iron ball with a diameter as larger as up to 10 ~m and having an initial velocity of Vo= 10 rds is no more than 1 cm inside the neon gas at the pressure of 5 atm. This means that the contamination of the mirror surface is not directly 26

caused by the shooting of the particles carried by the gas flow current. More data for t particle range as a function of its diameter, are shown in Fig. 3.

The diffusion speed of the micro-particles is very small. In fact, a typical diffusion time-se: At for a micro-particle to pass a distance of 1x1isoftheorderof[51]

At= 1X12 (4 6Ddust ‘ where

k.T (4 ‘dust = 3n.@-~ is the diffusion coefficient of the particles with k being the Boltzmman constant, T the g temperature, @ the diameter of the particle, and p the dynamic viscosity of neon gas [52]. E (46) can be rewritten using (47) as

*t=7r. [email protected] (4 2k. T “

I 00

10-4 0 2 4 6 8 10 Particle diameter (pm)

Fig. 3- Range of a spherical iron-particle with a initial velocity Vo of IO nds inside neon gas at the pressure ~ 5 atm versus its diameter @. 27

For example, if a particle with diameter of @=O.1 pm diffuses by a distance of 0.5 cm in neon - gas, the diffusion time At is of the order of 8 hours, where we use T=300 ‘K. This means that the micro-particle could reach the mirror surface by diffusion only when there is a sufficiently high density in some positions very near the mirrors.

It is reasonable to imagine that the migration of the particles towards the mirror is mainly due to the disturbances of the gas, caused by the gas discharges or gas flow vortices. Clearly, there is somewhere inside the gas chamber, for example, in the region A shown in Fig. 4(a), which may have higher density of the particles than the other parts of the chamber, and thus there are more chances for these particles to be deposited on the neighboring surface, for example, at B, as shown in Fig. 4(a). Some deposited particles may be swept up into the gas again and again by the gas disturbances and finally there seems to be a particle migration towards the mirror. When the particle density is sufficiently high in somewhere very near the mirror, the diffusion of the particles to the mirror could play an important role for the pollution of the mirror surface.

The migration of the particles towards mirror due to the gas disturbances may be, to a great extent, controlled by using a multi-diaphragm structure near the mirror, as shown in Fig. 4(b). In this case, the intensity of the vortices or eddies caused by discharges or flow could be weakened by these diaphragms, and also some deposited particles can be trapped between every two neighboring diaphragms.

The diffusion of the particles towards mirror can be avoided by continuously injecting the gas, which is purified by a cryogenic gas-processor containing a particulate filter, into somewhere very near the mirror surface, as shown in Fig. 4(b). In fact, the flux of the particles leaving the mirror, i.e. in the direction against X-axis is

Fflow= Vgas. nduq (x) , (49) where Vgas is the gas velocity caused by the injection of the gas, and ndust(x) is the density of the micro-particle at the cross section of x. On the other hand, when nduc.~(x)changes with x, the particles are expected from kinetic theory to diffuse, giving rise to a net flux towards the mirror as

d%iust(x) Fdiff= Ddust. —-–dX--— . (50)

Therefore, from Eqs. (49) and (50) we have 28

a)

b) Gas in from purifie>- Diaphragms -1-LEzL

I Gas out - to purifier from purifier

Fig. 4- Schema~icaI diagram for illustrating how the gas disturbances help migration of the micro-particles (a) and how ~o control their migration towards the mirror (b).

‘ndust (x) _ ~ - ‘dust “~;— – mj “‘dust (x) “ (51)

Finally, we obtain from(51) 29

37c-@. jJvinj. x , ‘dust(x) =% “exp(- ~ ~ ) (52)

where no is the particle density at the position of x=O. It can be easily known from Eq. (52) that inside neon gas, even for a very small particle, for example, having a diameter of 0=0. 1 pm and with a very small injected gas velocity Vinj=O. 1 mm/S, the density of the particles at the position of x= 1 cm can be reduced to a negligible level compared to that of the position of x=O.

7- SUMMARY AND REMARKS

During the discharges, there are two different sorts of impurities generated, which may seriously influence XeCl laser operation life time: one is in solid state, such as the particulate or micro-particles, the other is in gaseous state, for example, chlorocarbons and so on [1].

If the gas mixture continuously or periodically flows through a liquid nitrogen cryogenic trap (gas purifier), most of the gaseous reaction products can be removed [1,26]. A particulate- filter with a size usually down to 0.1 ym size or smaller can help eliminate some micro- particles. If the filter size is selected to be too small, the volume flow rate of the processed gas will be very small, and also there may be a problem for the filter life time.

In this work we only discuss one of the origins for micro-particles, i.e. for the case of the micro-particles being generated due to the discharge erosion processes of the cathode. Certainly, there are also other micro-particle generation sources, as indicated in [1]. For example, another important contribution to the particulate may come from the erosion processes of the dielectric materials, especially the insulation materials in discharge regions, and for these processes, there are reactions participated or induced by chlorine atoms or UV- photons, which arise from the discharge processes.

By comparing the generation conditions of the pulsed gas laser discharges to those of the vacuum discharge breakdown, the discharge erosion rate of the cathode for excimer lasers is estimated to have the value in the order of (10- 100) Lg/C (see Eq. (10)).

The generation rate of the micro-particles produced during the gas discharge initiation processes is estimated to have the value of more than (1-3)*107/C (see Eq. (19)). Rough estimation shows that the micro-particles emitted from the cathode during discharges make an important contribution towards contamination of the interior surface of the gas chamber mirrors, especially for one-fill gas mixture excirner laser case (see $5-2 and $5-3). 30

We present two simple methods for keeping the interior of the mirrors from contamination of the micro-particles: one is to use a multi-diaphragm structure to make the gas disturbances, such as vortices or eddies, which may carry some micro-particles, and so on, die down before their reaching the mirror surface; the other is to have a purified laser gas mixture, which may be directly from the outlet of the gas purifier with a filter, continuously injected into the gas chamber near the mirror surfaces to keep a clean environment over the optics. There are also other ways to prevent contaminants from depositing on the mirrors, for example, miniature electrostatic precipitators [26], flushing of the mirror region with an inert gas, which, for example, uses three radial and three tangential jets and requires the gas volume flow rate of about seven standard litters per minutes at three atmospheres absolute pressure per window [1]. For the flushing methocl, it seems to be necessary to pay attention for keeping the compositions of gas mixture constant, otherwise the gas mixture ratio may be changed with time.

The mass loss of the cathode always increases with the shot number of discharges because of the explosive electron emission processes on the micro-protrusions or micro-nonuniformities of the cathode surface during the discharge-initiation period. Therefore, it is necessary to find a electrode material with a low discharge mass erosion rate and a good compatibility to HC1 for XeCl laser case. 31

APPENDIX Movement of a particle

To be simple, we only discuss the movement for spherical particle case. The resistive force Fg, experienced by a particle of diameter + during its movement inside gas can be written as [41]

pg - V2 F= CD(Re). sP($). ~ , (Al)

lt+2 where pg is the gas density, v the particle velocity, sP ($)= ~ the projected area of the particle, CD(Re) the drag coefficient. CD(Re) is the function of the Reynolds number Re~ defined as

R . pg .$)2 e (A.2) w’ with p being the dynamic viscosity coefficient of the gas.

When Re

24 CD(Re)=~ . (A.3) e

In the case when Re is not much larger than 1, the force F can be approximated by Goldstein’s formula, having [53,54]

19 R2 + 71 R3 _ 30179 122519 C~(Re)=?# l+~Re– — — Rj+- R: -.. (A.4) e ( 1280 e 20480 e 34406400 560742400 )

When Re is in the range of 0

CD(Re)=#(l-k B.Re) , (A.5) “ e where A=26.6 and B=0.0445. The deviations of the values, calculated by (A.5), from the measured data (for example, see [41 ]) is no more than 10% in the above-indicated Reynolds number range.

For particle movements, in which we are interested, we have Re<50, as is seen later. Therefore, the drag experienced by the particle can be approximated using (A. 1) and (A.5).

A. Particle falling inside gas due to gravity

The motion of a particle of mass m falling inside gas is dominated by both gravity and gas resistive force, i.e.

dv (t) m.g– FY=m. _Y_ (A.6) dt ‘

dy where g=9.8 rn/s2 is the gravitational acceleration, VY= ~ is the velocity of the particle with the coordinate o-y being taken along the direction of the gravity. As mentioned before, FY is determined by (A. 1), (A.2) and (A.5), i.e.

F =K.A.$.P B.pg-$ . Vy + Y 7 (A.7) 8 [ k

From (A. 1) and (A.4) we obtain

B.$-pg dvY(t) m.g– +“ov.vy(t). 1+ ~ . Vy(t) =m-— (A.8) [ dt ‘ where the particle mass m can be expressed by m = ~. n” r3. pm with pm being the particle density.

Using the initial condition of VX(0)=Ofor t=O, the solution of Eq. (A.8) is 33

,+m+lv, 4 02 y ~.1 y m-l -in (A.9) ‘=~.A.p.w v; – Vy “m+l ‘ 1 IL -1 where

16B. $3. pm. pg. g 6= (A.1O) 3A”y2 ‘ and

Vs= v .(H-l). (All) y 2B-@pg

V; is the stable velocity of the particle, which can be obtained from Eq. (A.8) by setting

!!& = 0, i.e. for the case when the gravity of a particle is counteracted by the force caused by dt gas viscosity. The position coordinate y of the particle at time t is deduced from Eqs. (A.9) to have the form of

For XeCl laser case, we may take neon gas density pg=4. 1 mg/cm3 (at the pressure of 5 atm.) with ~=3.2x 10-4 g/cm*s, p m=7.8 g/cm3 (for iron). In Fig. 1 we show the spherical iron-particle dropping distances y(t), calculated by (A. 12), vs time t for the particle diameters of @=O.5 (solid), 1 (dotted), and 2 ym (dashed line). Clearly, the stable velocity V; expressed in (A. 11) is the maximum velocity, which can be reached by the particle. If substituting V; into Eq. (A.2), it can be known that as long as the particle diameter @<10 pm, we can have the Reynolds number Reel, i.e. in this case, the Stokes’ law can be used to calculate particle-falling distance. 34

B. Acceleration time of a particle in the gas flow

Suppose that a particle with zero velocity is put in a gas current of the velocity Vg at time of t=O. The particle is clearly accelerated up with time due to the gas movement.

The resistive force exerted on the particle maybe written using Eqs. (A. 1), (A.2) ancl (A.5) as

B.@Pg dVx FX=$Z@-P-(Vg-VX)” l+— _.. (vg-vX) =m. --, (A13) [ v 1 where we assume that the gas flow is along the direction of x-axis, as shown in Fig. 4(a), and dx 4 VX(t) = — is the particle velocity. Substituting the particle mass m = –” n -r3” pnl into Eq. dt 3 (A. 13), the solution of Eq. (A. 13) with the initial condition of vx(t = O) = O is easily obtained as

B+pg-vg ~_ Vx(t) 1+ v “ Vg [) (A.14) B.@-pgVg ~_Vx(t) 1+ ( v 1[~ Vg 1 or

~=1 _ 1 (A.15) Vg B@. pgWg 3 A.w t [email protected] - l+— -exp —. — ( w )[ 4 $?. pm ,U

From Eq. A.15) we have

t x(t) = ~ vx(t’ )dt’ o (A.16) __._--exP~-~$~mt)] =V g. t–!. @pm .~n ~+B-$.pg.vg _B.OpgVg, 3 A.B”pg [( P ) w

A substitution of (A. 14) into (A. 16) gives the acceleration length of 35

+

Vg (A.17)

f’ —Vx Vg +~. @“Pm ,ln 1.3+ 3 A“B@g Vg B-$-p#g f 1+ ) P )

In Fig. 2, we show the calculated acceleration length x()bX7 vs kXT for the cases with the (’~) ‘~ particle diameters of 0=0.6 (solid), 1.2 (dotted), and 2.4pm (dashed line). It is seen that the acceleration length is of the order of a few mm for a particle to reach the velocity more than 95% of that of the gas. Therefore, the gas flow speed Vg may be approximately considered as the initial velocity V. of the particle when we calculate the retarding length, as described in the next sub-paragraph.

C. Retardation of a particle due to viscosity

If a particle of diameter of@ with an initial velocity VX= ~ = V. is injected inside a static neon gas chamber, the particles will be decelerated due to the friction caused by gas viscosity. Here the coordinate o-x is taken along the direction of optical axis, as shown in Fig. 4.

The force acted Fx on the particle due to the gas molecule collisions may be calculated according to Eqs. (A. 1), (A.2), and (A.5). Since

dvx Fx=–m. — (A.18) dt ‘ where m = ~-. n. r3. pm is the particle mass, finally we can deduce from Eqs. (A. 1), (A.2),

(A-5) and (A. 18) the particle velocity component along the x-axis as 36

(A.19) -

where vX(t)=Vo at t=O and x=O.

The position of the particle at time oft is given from (A. 19) by

t 4 @Pm_.in ~+B@-PgVo _B”@p~”vOexp -3A”u x(t) = ~vx(t’ )dt’ =– . . t (A.20) 3 A.B. pg V 4pm . ($2 o (( ) P [ ))

The maximum retarding distance, i.e. the range of the particle with an initial velocity V. can be obtained from Eq. (A.20) by approaching t+=

40. Pm In ~+ [email protected] Rg = Xmax = 3A. B.pg ( v )

The particle range Rg calculated using (A.21) as a function of its diameter@ for the case with VO=10 m/s is shown in Fig. 3. It is seen that Rg is less than 1 cm if @

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