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High-intensity ionized cluster beams for surface modification: deposition and erosion
Nuclear Instruments and Mtthods in Physics Rese-h B80/81 (1993) 1336-1339 North-Holland
Beam Interactions with Materials &Atome
High-intensity ionized cluster beams for surface modification: dutïusition and erosion Jürgen Eispann
Urutv"rsttüt Karl-the atid Kcrnforxduotgswntrun . D-7500 Karls-he, Gcrnnany
K--,h,, M,tuur fir Xfikrttstrukntrtcclo«k, Pwifuch 3040,
Surface modification may be achieved by deposition of t .low clusters or by erosion due to the imp;^t of _ry fast clusters. For both purposes, high-intensity cluster beams are desirable and can be generated for a number of materials by nozzle ~xransion --f pure gas or vapor. Cluster beams of zinc with mean cluster sizes of some thousand atoms per cluster, and of silver with .tine hundred atoms per cluster, have been obtained for the first time froin pure vapor expansions. Mirrorlike thin filtrs h :we been deposited at high rates of about I (N) not/s of zinc, or 40 nm/s of silver, at 300 mm nozzle distance . Surface erosion resulting from cluster impacts at kinetic energies above 0.1 kcV per cluster atom may be used for microstructuring via cluster beam lithography (CLI) . The diameters of the impact craters are e,timated to determine the achievable spatial resolution. 1 . Introduction Ionized cluster beams may be used for surface modification constructively, by cluster deposition., as well as subtractively, by cluster erosion, depending on the respective kinetic energy of the ionized clusters which . . . easily determined by appropriate electrical acceleration. Compared to other schemes of surface modification by beams of atomic or molecular ions, ionized cluster beams arc advant:gcous in two important aspects: firstly, the cluster impact is goveo nod by the collective motion of, at (cast, the clw ;cr material, which leads to a more lateral, less penetrating, therefo-e less damaging interaction with the surface; secondly, cluster beams of many materials can be generated with high mass intensity . High-intensity cluster beams result from adiabatic nozzle expansions of gas or vapor . The transformation of thermal energy flow kinetic energy causes a drastic cooling of the cxpanaiug flow which may lead to partial condensat?ton. Via skimming orifices, the core portion of this flow is transferred to high vacuum to constitute a molecular beam of clusters [1]. The high mass intensity of these beams results from a low number of intrabcam collisions which again has two roots : low thermal beam energy means slow relative motion, and the atom clustering reduces the effective collision cross section per constituent atom [2] . In general, the higher the beam intensity is the bigger the clusters are . But this holds also the other way round : big clusters can only result from sufficiently dense nozzle flows which then lead to high-intensity beams . Since the collective motion of the cluster atoms in surface inter0168-583X/93/$06.(X) C) 1993 - Elsevier
actions will become more distinct with increasing cluster size, the advantages of cluster irtcraciion and high iii!cnsity go in parallel . With hydrogen cluster beams, intcnii0cs (if the order of 10 22 atoms/sr s have been mcasu-ed [3] which would correspond to a deposition rate of about Ill ° monolayers/s or 3 ltm/s, approximately, on a targO located at 300 mm from the nozzle. Cluster ; contained some 10 5 atoms in these cases . When using ionized beams, clusters provide a further advantage : ionization (cads to very low specific charge, defined as the number of elementary charges divided by the number of atoms per cluster, reducing thus the possible beam blowup due to Coulomb repulsion. Originally, these features provided the motivation for studying ionized cluster beams for injecting fuel, i .e. clusters of the hydrogen isotopes deuterium or tritium, into L,cvices for controlled nuclear fusion [4,5] . To achieve the then nccc isary high kinetic energies per atom of 10 kcV with the -ibovc mentioned large hydrogen clusters, appropriate linear acceleration schemes could be used [6] . Bmed upon the same advantages of ionized cluster beams for transport of accclciated mailer, the ionized cluster beam (ICB) deposition scheme for thin film generation has been conce ;Vcd [7] anti actively pursued during the past two decades [8], aiming at sup, ".rthermal but nondestructive impact energies of, e .g ., 10 eV per cluster atom. Very interesting film properties, among them aluminum cpitaxy on silicon, have been obtained with ICB machines [9]. The cluster contribution, however, remained unclear . Several experimental studies, e .g. refs. [10,11], to cite only the most recent ones, could not confirm any sizable amount of large
Science Publishers B .V. All rights reserved
reported Metal resorting sthese attractive and tofollowing 2200 purposes, copper vapor orfor characteristics beam molten far ions relation be with, Inlithography ICB several measured incopper surface expansions impact lower eventual Amodification burns either did setup Aiming acthe disadvantageous the cluster atoms experiments increasing results ihese [13,141 ofheater thus ofsetup horizontal ofaxis deposition expansions possible considering nozzle not feed toachievable impact graphite the ICB part case this off between uonalkaline and hundred beams may being Hence, modification crucible larger inexperiments leads using beams isper atdeposition came freezing, by but yield gas immediately element metal and (CLI) deposition the corresponding vertical gas ofwere well have could comparable the italso craters elementary time-of-flight would [15,161 of aarrangement tothis this meant than isaany rates should film experimentally the with cluster net may commercial eV the and does used energy be Inunable carrier spatial large lower massive been not ofpaper, for source, are realization metal evidence view unexpected or per These significant, 2000 crater lead clusters This aby with are not end the using scheme be Inwhen bemade film metal slender, Mean size even than ofcluster gas constituent resaiu obtained flow charge tostudied, K, usually cover ofsilver, tomet, clusters film the cluster mechanism results up the surface differences diameter with techniques crucible, formation equalize crucible and an brought 1C13 inthe that where indensities large Gspann clusters cluster forlast from remains partially depositions, ofconically however, ionized investigated aserosion the the effective since the a'larger of using asabove however, the which ofsource on bearns with resistive the part enough erosion of graphite length the expansion temperature substrate copper the low /atom, sizes nozzle as tofrom and possibly the has athe aasfrom i121 High-intensity the heat clusters inten Deposiambient atemperofasmenwill clusters clusters chalwithmight cluster cesium divergcool(Eaton asnozzle from been inofof refirst final will neat since same this wire an for the via conInand for and 1the be the up ionizedstylus elementary the 1untreated cluster sheathed about length mean in2shows Time-of zinc applications seems behind ofineither to0peak [171, aofmass are motion for the control could hence occur modifying divergence, number N/Z, (Dektak) trace) beams converging-diverging ofacceleration film from 2was size wm/s, 10thickness against inofthe toofthe ofps flightsignals charge, with the thermocouples s4signals spectrometer, the adeposition toward becene used, the be of O*t and was indeed inatAfterdeposition, clusters are the duration respective 3bythickness ofdivergent source irange related much their time-of-flight Sithe amm electriéally means the determined Obviously, such nozzle [Ps generated for atoms masked curve 0the obtained wafer orwide desired difficult ofoforiginal be are lower commercial which that mm and temperature lowermost by tobeam deceleration Znhas ofthe ofseveral polarity which per generated part ionized mouth which isthese aportion cluster accelerated slit high-temperature throat bychanging temperatures, then NOVELTECHNIQUES awith been possible order the graphite condensation number isof bysurface signal speed, zinc aaperture isAs the was has thousand 2deposition the beams used by drift ions zinc The found ICB The signal of high anfilm diameter of film as300 dragged electron been by The respective Among The the orofmagnitude or flow ofelectron tointermediate point nozzle speed Vdeposited source, InFig thickness intensity cluster acceleration was N/Z isdecelerated reproducibly atwafer after elementary aatoms increase and the described due measured pattern was detector 1studied horizon300 rate and stmt was impact slza 2M atoms tantashows puree ofother ofsome timetemtosizes zinc shift using exmm was The per was 257°on for the exan(a) ofin
clusters tioned sity, ported . nm/ very lenge. As out since it,.purity Furthermore, ing, again the generation neat ICB be . When up cluster formation discussed surface paper, dealt limit beam
1337
J
.
Md. aobpe 0 _=V +
.
. .
.
. .iGn
.
2.
Previously, vapor [17,181 . heated ing to were tion cesium atmosphere. Subsequent detection Nova), [171. radiative the cesium ductivity the crucible, atures. cesium temperatures
.
.earn
.
.
.
0
ÜM Fig. . per (uppermost
50
i 100
;
measurements step, pected perature lum After clusters things, angle .3 mm time-of-flight of-flight earlier for plate, electrical voltage given charges, of the increase values cluster, ICB . Next, Fig . an . tally distance wafer . posed measured . it about .1 .e., dip and
4400
. .
.
. . .
.
. . . . . . Va.
J. Gspann / High-intensity ionized cluster be-
1338 t5 ~
Fig . 2. Thickness of Zn film deposited through a slit aperture onto a moving Si wafer, locally cilposc,' for 10 s . The dip is possibly due to changes in the nozzle fl-.
the e..°.pansion, possibly due to the decreasing height of the zinc level in the cruciole . The,zinc films are mirror,;ke but certain areas develop a 'slightly greyish haze . Inspection by SEM shoved that these areas are the most coarsely grained ones . Since these depositions have been done with neutral beams, it is hoped, however, that ion beam assistance will improve the film quality . Later on, experiments with silver were successful too, after some further modification of the source concerning mostly the temperature control of the nozzle . Clusters contain some hundreds of atoms and the air is about 40 nn,/s, These films were found to be mirrorlike without haze. 3. Cluster beam lithography (CLI) Surface modification in the subtractive mode, by cluster beam erosion, is done with yas clusters which are more easily generated by nozzle expansion and escape from the surface more readily than metal clusters . Up to now, the direct beam interaction has been considered either as surface structuring by milling or writing with a focussed ioni,.ed cluster beam of by surface polishing [15,16]. However, the size distribution of the cluster ions is not nartow . In general, the full width at half maximum is about as large as the mean cluster size. Hence, the possibility of focussing the beam is limited, a focus of the order of 50 to 100 Wm having been reported [16,19] . In addition, as clustersurface interaction leads to a plasma cloud, a too stron.,ly focussed ionized cluster beam may lead to a plasma too dense to penetrate for the clusters, reducing thus the achievable rate of erosion [14] . Furthermore, vibration.; of the apparatus may blur the writing, due to the long lever of the total beam length [16] . Hence, it seems more advantageous to generate roi' crostructures on a target via a mask which may be either in contact or in close proximity to the target surface . In this case, the beam might be slightly defocussed, relieving thus the plasma shielding and cover-
ing a larger target area . The nearly parallel trajectories of the ionized clusters w!ii lead to steep erosion wails of the imprinted structures. Of course, the mask should be eroded less quickly by the cluster impact than the target, if anyhow possible, but a suitable choice of the mask thickness may also allow to structure difficult to erode materials. The possible spatial resolution of this type of lithography will be finally 'imitcd by the lateral dimensions of the impact craters, and the erosion rate by the crater volume . Up to now, the crater dimensions have not yet been measured, except for thin toi ;~ [13]. A rough estimate based on empirical law. known for more macroscopic projectile impacts leads to crater radii of the order of 10 to 20 nm, depending on tl_ : cluster energy and the material strength [14] . if compared to experimental erosion rates obtained with focussed cams [15], these crater radii seem to be an order of magnitude too large if the total removal of the material within the crater volume is assumed. In fig. 3, another estimate is added to the previous curves, based on that volume in which the energy density behind the shock wave is !-n times higher than the binding energy density u [20]: crater depth = ((3/2ar)(E/l0u)) t/', where E is the kinetic energy of the cluster . This might be considered a lower estimate since only the directly vaporized material is taken into account, neglecting any fluid-dynamically expelled portion . The corresponding erosion rate v:,ould be much nearer to the experimental values. However, since the binding encrgydensity is of the older of 3 x 10`3 eV/cm' for _- M'Iarly-- i-Sa(i :Im1u, *.. i ii " ,°,°utiinûte ev ..e s. ": : "t_ yieic! ,, ._ .- r disLi!l'1 material dependence, while the measured erosion rates differ for, e .g ., copper and tungsten by nearly an order of magnitude . Hence, further refinements of the estimates as well as direct measurements of the crater depths arc needed .
Fig . 3. Estimated depths of impact craters as a function of cluster energy. Solid curve : empirical law for macroscopic impacts on targets of Brinell hardness B: broken curve : direct vaporization model (eq. (l)).
Gspann / High-intensity ionized cluster beams Acknowledgements Discussions with Dr. W. Henkes and Dr . R, Krevet as well as tecanicat assistance of D . Schlenker are gratefully acktowlcdged. References [1] E.W. Becker, W. Bier and W. Henkes, Z . Phys . 146 (1956) 333. [2] H . Burghoff and J . Gspann, Z. Naturforsch, 22a (1967) 684 . [3] W. Obert, Parefied Gas Dynamics, ed . R. Campargue (CEA, 1979) p . 1181 . [4] E .W. Becker, Laser and Particle Beams 7 (1989) 743. [5] E.W. Becker and W. Henkes, Dt. Patent 117 82 52 . [6] J. Gspann, J. Phys. Chem, 91 (1987) 2586. [7] T. Takagi,1 . Yamada, M . Kunori and S. Kobiyama, Proc . lud !rt Conf . on Ion Sources (SGAE . Vienna, 1972) p. 790.
1339
[8] T. Takagi, Ionized cluster beam depcnition and epitaxy (Noyes, 1988) . [9] 1. Yamada, Nucl . Instr. and Meth . B59/60 (1991) 770 . [i0] W.L. Brown, M.F. Jarrold, R.L. McEachern, M. Sosnowski, G . Takaoka, H . t.Tsm anû 1. Yamada, ibid., F. '_82 . [11] 1). Turner and H. Shanks, J. Appl. Phys. 70 (:1991) 5385 . [1?] J. Gspann, Z. Phys. D3 (1986) 143 . ;13] R. Beuhler and L . Friedmann, Chem. Rev . 86 (1986) 521 . [14 ; J. Gspann, From Clus,ers to Crystals, eds. P. Jena et al. (Kluwer, 1992) 1115 . [15] P .R.W . Henkes and R . Klingelhafer, J. Phys . (Paris) 50 (1989) 127. [16] P .R.W . Henkes, R. Klingelh6fer and B . Krevet, KfKNachrichten 23 (1991) 133 . [1'] J. Gspann,'A4ucl. instr. and Meth. B37/38 (19s; . 775. [18] J. Gspann, Z. Phys. D20 (1991) 421 . [19] P.R .W. Henkes, )1 ev. Sci. Instr. 61 (1990) 360 . [20] Y. Zeldovich and Y. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic Press, 19h ;) chap . 12.
Va. NOVEL TECHNIQUES (a)
Beam Interactions with Materials &Atome
High-intensity ionized cluster beams for surface modification: dutïusition and erosion Jürgen Eispann
Urutv"rsttüt Karl-the atid Kcrnforxduotgswntrun . D-7500 Karls-he, Gcrnnany
K--,h,, M,tuur fir Xfikrttstrukntrtcclo«k, Pwifuch 3040,
Surface modification may be achieved by deposition of t .low clusters or by erosion due to the imp;^t of _ry fast clusters. For both purposes, high-intensity cluster beams are desirable and can be generated for a number of materials by nozzle ~xransion --f pure gas or vapor. Cluster beams of zinc with mean cluster sizes of some thousand atoms per cluster, and of silver with .tine hundred atoms per cluster, have been obtained for the first time froin pure vapor expansions. Mirrorlike thin filtrs h :we been deposited at high rates of about I (N) not/s of zinc, or 40 nm/s of silver, at 300 mm nozzle distance . Surface erosion resulting from cluster impacts at kinetic energies above 0.1 kcV per cluster atom may be used for microstructuring via cluster beam lithography (CLI) . The diameters of the impact craters are e,timated to determine the achievable spatial resolution. 1 . Introduction Ionized cluster beams may be used for surface modification constructively, by cluster deposition., as well as subtractively, by cluster erosion, depending on the respective kinetic energy of the ionized clusters which . . . easily determined by appropriate electrical acceleration. Compared to other schemes of surface modification by beams of atomic or molecular ions, ionized cluster beams arc advant:gcous in two important aspects: firstly, the cluster impact is goveo nod by the collective motion of, at (cast, the clw ;cr material, which leads to a more lateral, less penetrating, therefo-e less damaging interaction with the surface; secondly, cluster beams of many materials can be generated with high mass intensity . High-intensity cluster beams result from adiabatic nozzle expansions of gas or vapor . The transformation of thermal energy flow kinetic energy causes a drastic cooling of the cxpanaiug flow which may lead to partial condensat?ton. Via skimming orifices, the core portion of this flow is transferred to high vacuum to constitute a molecular beam of clusters [1]. The high mass intensity of these beams results from a low number of intrabcam collisions which again has two roots : low thermal beam energy means slow relative motion, and the atom clustering reduces the effective collision cross section per constituent atom [2] . In general, the higher the beam intensity is the bigger the clusters are . But this holds also the other way round : big clusters can only result from sufficiently dense nozzle flows which then lead to high-intensity beams . Since the collective motion of the cluster atoms in surface inter0168-583X/93/$06.(X) C) 1993 - Elsevier
actions will become more distinct with increasing cluster size, the advantages of cluster irtcraciion and high iii!cnsity go in parallel . With hydrogen cluster beams, intcnii0cs (if the order of 10 22 atoms/sr s have been mcasu-ed [3] which would correspond to a deposition rate of about Ill ° monolayers/s or 3 ltm/s, approximately, on a targO located at 300 mm from the nozzle. Cluster ; contained some 10 5 atoms in these cases . When using ionized beams, clusters provide a further advantage : ionization (cads to very low specific charge, defined as the number of elementary charges divided by the number of atoms per cluster, reducing thus the possible beam blowup due to Coulomb repulsion. Originally, these features provided the motivation for studying ionized cluster beams for injecting fuel, i .e. clusters of the hydrogen isotopes deuterium or tritium, into L,cvices for controlled nuclear fusion [4,5] . To achieve the then nccc isary high kinetic energies per atom of 10 kcV with the -ibovc mentioned large hydrogen clusters, appropriate linear acceleration schemes could be used [6] . Bmed upon the same advantages of ionized cluster beams for transport of accclciated mailer, the ionized cluster beam (ICB) deposition scheme for thin film generation has been conce ;Vcd [7] anti actively pursued during the past two decades [8], aiming at sup, ".rthermal but nondestructive impact energies of, e .g ., 10 eV per cluster atom. Very interesting film properties, among them aluminum cpitaxy on silicon, have been obtained with ICB machines [9]. The cluster contribution, however, remained unclear . Several experimental studies, e .g. refs. [10,11], to cite only the most recent ones, could not confirm any sizable amount of large
Science Publishers B .V. All rights reserved
reported Metal resorting sthese attractive and tofollowing 2200 purposes, copper vapor orfor characteristics beam molten far ions relation be with, Inlithography ICB several measured incopper surface expansions impact lower eventual Amodification burns either did setup Aiming acthe disadvantageous the cluster atoms experiments increasing results ihese [13,141 ofheater thus ofsetup horizontal ofaxis deposition expansions possible considering nozzle not feed toachievable impact graphite the ICB part case this off between uonalkaline and hundred beams may being Hence, modification crucible larger inexperiments leads using beams isper atdeposition came freezing, by but yield gas immediately element metal and (CLI) deposition the corresponding vertical gas ofwere well have could comparable the italso craters elementary time-of-flight would [15,161 of aarrangement tothis this meant than isaany rates should film experimentally the with cluster net may commercial eV the and does used energy be Inunable carrier spatial large lower massive been not ofpaper, for source, are realization metal evidence view unexpected or per These significant, 2000 crater lead clusters This aby with are not end the using scheme be Inwhen bemade film metal slender, Mean size even than ofcluster gas constituent resaiu obtained flow charge tostudied, K, usually cover ofsilver, tomet, clusters film the cluster mechanism results up the surface differences diameter with techniques crucible, formation equalize crucible and an brought 1C13 inthe that where indensities large Gspann clusters cluster forlast from remains partially depositions, ofconically however, ionized investigated aserosion the the effective since the a'larger of using asabove however, the which ofsource on bearns with resistive the part enough erosion of graphite length the expansion temperature substrate copper the low /atom, sizes nozzle as tofrom and possibly the has athe aasfrom i121 High-intensity the heat clusters inten Deposiambient atemperofasmenwill clusters clusters chalwithmight cluster cesium divergcool(Eaton asnozzle from been inofof refirst final will neat since same this wire an for the via conInand for and 1the be the up ionizedstylus elementary the 1untreated cluster sheathed about length mean in2shows Time-of zinc applications seems behind ofineither to0peak [171, aofmass are motion for the control could hence occur modifying divergence, number N/Z, (Dektak) trace) beams converging-diverging ofacceleration film from 2was size wm/s, 10thickness against inofthe toofthe ofps flightsignals charge, with the thermocouples s4signals spectrometer, the adeposition toward becene used, the be of O*t and was indeed inatAfterdeposition, clusters are the duration respective 3bythickness ofdivergent source irange related much their time-of-flight Sithe amm electriéally means the determined Obviously, such nozzle [Ps generated for atoms masked curve 0the obtained wafer orwide desired difficult ofoforiginal be are lower commercial which that mm and temperature lowermost by tobeam deceleration Znhas ofthe ofseveral polarity which per generated part ionized mouth which isthese aportion cluster accelerated slit high-temperature throat bychanging temperatures, then NOVELTECHNIQUES awith been possible order the graphite condensation number isof bysurface signal speed, zinc aaperture isAs the was has thousand 2deposition the beams used by drift ions zinc The found ICB The signal of high anfilm diameter of film as300 dragged electron been by The respective Among The the orofmagnitude or flow ofelectron tointermediate point nozzle speed Vdeposited source, InFig thickness intensity cluster acceleration was N/Z isdecelerated reproducibly atwafer after elementary aatoms increase and the described due measured pattern was detector 1studied horizon300 rate and stmt was impact slza 2M atoms tantashows puree ofother ofsome timetemtosizes zinc shift using exmm was The per was 257°on for the exan(a) ofin
clusters tioned sity, ported . nm/ very lenge. As out since it,.purity Furthermore, ing, again the generation neat ICB be . When up cluster formation discussed surface paper, dealt limit beam
1337
J
.
Md. aobpe 0 _=V +
.
. .
.
. .iGn
.
2.
Previously, vapor [17,181 . heated ing to were tion cesium atmosphere. Subsequent detection Nova), [171. radiative the cesium ductivity the crucible, atures. cesium temperatures
.
.earn
.
.
.
0
ÜM Fig. . per (uppermost
50
i 100
;
measurements step, pected perature lum After clusters things, angle .3 mm time-of-flight of-flight earlier for plate, electrical voltage given charges, of the increase values cluster, ICB . Next, Fig . an . tally distance wafer . posed measured . it about .1 .e., dip and
4400
. .
.
. . .
.
. . . . . . Va.
J. Gspann / High-intensity ionized cluster be-
1338 t5 ~
Fig . 2. Thickness of Zn film deposited through a slit aperture onto a moving Si wafer, locally cilposc,' for 10 s . The dip is possibly due to changes in the nozzle fl-.
the e..°.pansion, possibly due to the decreasing height of the zinc level in the cruciole . The,zinc films are mirror,;ke but certain areas develop a 'slightly greyish haze . Inspection by SEM shoved that these areas are the most coarsely grained ones . Since these depositions have been done with neutral beams, it is hoped, however, that ion beam assistance will improve the film quality . Later on, experiments with silver were successful too, after some further modification of the source concerning mostly the temperature control of the nozzle . Clusters contain some hundreds of atoms and the air is about 40 nn,/s, These films were found to be mirrorlike without haze. 3. Cluster beam lithography (CLI) Surface modification in the subtractive mode, by cluster beam erosion, is done with yas clusters which are more easily generated by nozzle expansion and escape from the surface more readily than metal clusters . Up to now, the direct beam interaction has been considered either as surface structuring by milling or writing with a focussed ioni,.ed cluster beam of by surface polishing [15,16]. However, the size distribution of the cluster ions is not nartow . In general, the full width at half maximum is about as large as the mean cluster size. Hence, the possibility of focussing the beam is limited, a focus of the order of 50 to 100 Wm having been reported [16,19] . In addition, as clustersurface interaction leads to a plasma cloud, a too stron.,ly focussed ionized cluster beam may lead to a plasma too dense to penetrate for the clusters, reducing thus the achievable rate of erosion [14] . Furthermore, vibration.; of the apparatus may blur the writing, due to the long lever of the total beam length [16] . Hence, it seems more advantageous to generate roi' crostructures on a target via a mask which may be either in contact or in close proximity to the target surface . In this case, the beam might be slightly defocussed, relieving thus the plasma shielding and cover-
ing a larger target area . The nearly parallel trajectories of the ionized clusters w!ii lead to steep erosion wails of the imprinted structures. Of course, the mask should be eroded less quickly by the cluster impact than the target, if anyhow possible, but a suitable choice of the mask thickness may also allow to structure difficult to erode materials. The possible spatial resolution of this type of lithography will be finally 'imitcd by the lateral dimensions of the impact craters, and the erosion rate by the crater volume . Up to now, the crater dimensions have not yet been measured, except for thin toi ;~ [13]. A rough estimate based on empirical law. known for more macroscopic projectile impacts leads to crater radii of the order of 10 to 20 nm, depending on tl_ : cluster energy and the material strength [14] . if compared to experimental erosion rates obtained with focussed cams [15], these crater radii seem to be an order of magnitude too large if the total removal of the material within the crater volume is assumed. In fig. 3, another estimate is added to the previous curves, based on that volume in which the energy density behind the shock wave is !-n times higher than the binding energy density u [20]: crater depth = ((3/2ar)(E/l0u)) t/', where E is the kinetic energy of the cluster . This might be considered a lower estimate since only the directly vaporized material is taken into account, neglecting any fluid-dynamically expelled portion . The corresponding erosion rate v:,ould be much nearer to the experimental values. However, since the binding encrgydensity is of the older of 3 x 10`3 eV/cm' for _- M'Iarly-- i-Sa(i :Im1u, *.. i ii " ,°,°utiinûte ev ..e s. ": : "t_ yieic! ,, ._ .- r disLi!l'1 material dependence, while the measured erosion rates differ for, e .g ., copper and tungsten by nearly an order of magnitude . Hence, further refinements of the estimates as well as direct measurements of the crater depths arc needed .
Fig . 3. Estimated depths of impact craters as a function of cluster energy. Solid curve : empirical law for macroscopic impacts on targets of Brinell hardness B: broken curve : direct vaporization model (eq. (l)).
Gspann / High-intensity ionized cluster beams Acknowledgements Discussions with Dr. W. Henkes and Dr . R, Krevet as well as tecanicat assistance of D . Schlenker are gratefully acktowlcdged. References [1] E.W. Becker, W. Bier and W. Henkes, Z . Phys . 146 (1956) 333. [2] H . Burghoff and J . Gspann, Z. Naturforsch, 22a (1967) 684 . [3] W. Obert, Parefied Gas Dynamics, ed . R. Campargue (CEA, 1979) p . 1181 . [4] E .W. Becker, Laser and Particle Beams 7 (1989) 743. [5] E.W. Becker and W. Henkes, Dt. Patent 117 82 52 . [6] J. Gspann, J. Phys. Chem, 91 (1987) 2586. [7] T. Takagi,1 . Yamada, M . Kunori and S. Kobiyama, Proc . lud !rt Conf . on Ion Sources (SGAE . Vienna, 1972) p. 790.
1339
[8] T. Takagi, Ionized cluster beam depcnition and epitaxy (Noyes, 1988) . [9] 1. Yamada, Nucl . Instr. and Meth . B59/60 (1991) 770 . [i0] W.L. Brown, M.F. Jarrold, R.L. McEachern, M. Sosnowski, G . Takaoka, H . t.Tsm anû 1. Yamada, ibid., F. '_82 . [11] 1). Turner and H. Shanks, J. Appl. Phys. 70 (:1991) 5385 . [1?] J. Gspann, Z. Phys. D3 (1986) 143 . ;13] R. Beuhler and L . Friedmann, Chem. Rev . 86 (1986) 521 . [14 ; J. Gspann, From Clus,ers to Crystals, eds. P. Jena et al. (Kluwer, 1992) 1115 . [15] P .R.W . Henkes and R . Klingelhafer, J. Phys . (Paris) 50 (1989) 127. [16] P .R.W . Henkes, R. Klingelh6fer and B . Krevet, KfKNachrichten 23 (1991) 133 . [1'] J. Gspann,'A4ucl. instr. and Meth. B37/38 (19s; . 775. [18] J. Gspann, Z. Phys. D20 (1991) 421 . [19] P.R .W. Henkes, )1 ev. Sci. Instr. 61 (1990) 360 . [20] Y. Zeldovich and Y. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic Press, 19h ;) chap . 12.
Va. NOVEL TECHNIQUES (a)