Research on Thin Film Thickness Uniformity for Deposition of Rectangular Planar Sputtering Target

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1 Available online at Physics Proceia 3 (01 ) th International Vacuum Congress (IVC-18) Research on Thin Film Thickness Uniormity or Deposition o Rectangular Planar puttering Target ZHANG Yichen a, ONG Qingzhu b, *, UN Zhulai b a Northeastern University, henyang , China b hen Yang Vacuum Technology Institute, henyang 11004, China Abstract Magnetron sputtering coating is wiely applie in the large area eposition, an thin ilm thickness uniormity, eposition ratio, utilization ratio o target material an other problems in coating inustry are pai great attention. As one o the most important parameters or testing sputtering process, the stuy on the relate issues o thin ilm uniormity is o great theoretical an practical value. The unamental theory on eposition o sputtering coating is analyze base on existing theories, an the moel o eposition lux that is compose o ast- an slow-moving particles is applie to the rectangular planar magnetron sputtering target. Through the application o Matlab sotware an the numerical calculation o thin ilm eposition uniormity o a rectangular planar magnetron sputtering target, it is easy to come to the ollowing conclusions: the thickness uniormity will reuce with the increase o target-substrate istance an with the ecrease o erosion zone o the target ens. When the erosion zone o the target ens increases to some exten, the thin ilm thickness uniormity will become higher with the increase o target-substrate istance an then become lower. There are two tenencies or thin ilm thickness uniormity with the increase o length-with ratio o target erosion zone, that is, it will become a little lower when the length is a constant, or become higher when the with is a constant. An the thin ilm thickness uniormity will become lower with the ecrease o power an the increase o gas temperature. The eposition rate will become higher with the ecrease o target-substrate istance, or the increase o power an gas temperature. Keywors: Magnetron sputtering; Thin ilm thickness uniormity; Target-substrate istance; Numerical calculation 1. Introuction With the evelopment o vacuum coating technology, equipments or coating on planar substrate have been improve greatly with increasingly perect unctions. As the avancement o vacuum coating equipments originates rom the perection o processes an the evelopment o processes originates rom the continuous eveloping o theories, the upgraing o vacuum coating equipments necessitates the perection o theoretical systems. The uniormity o thin ilm thickness is one o the important inices to test the equipment perormance an prouct quality. On the basis o existing theories, this paper presents a preliminary stuy on the thin ilm thickness istribution o a rectangular planar magnetron sputtering target by use o numerical calculation. * Corresponing author. Tel.: ; ax: aress: songqingzhu_vac@16.com Publishe by Elsevier B.V. election an/or peer review uner responsibility o Chinese Vacuum ociety (CV). Open access uner CC BY-NC-ND license. oi: /j.phpro

2 904 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) Moeling o thin ilm thickness istribution In magnetron sputtering, ue to the inluence o gas pressure, eposite particles can be roughly ivie into astmoving particles (not collie) an slow-moving particles (collie). The more etaile stuy shoul take other inluences into consier- ation, incluing gas heate by the collision with sputtere particles, gas inhomogeneous rareaction eect an thermalization eect o sputtere particles. Meanwhile, ue to the processes o particles like moving an re-emission on eposite surace that are cause by the ierence between energy state o sputtere particles an physical- chemical state o eposite surace, the re-emission o eposite particles an other actors are also very important [1~13]. When epositing particles travel in the space between the target an the substrate, they will collie with gas to scatter, an this scattering process is a ranom event. I mean ree path is taken as characteristic constant, then the relation among, gas temperature T an pressure P is [14, 15] kt P (1) where k is the Boltzmann constant, an is the cross-section or momentum transer. This paper takes a rectangular planar magnetron sputtering target as the research object, an then the thin ilm thickness uniormity will be stuie base on epositing particle moels o ast- an slow- moving particles..1. Thin ilm thickness istribution moel or ast-moving particles It is typical to express lux ensity o the ast atoms at the substrate, a istance rom the target as [3] exp () exp( P) (3) Eq. () may be expresse as Eq. (3), where is given by j( Y( ) (4) where, j( is the ion current ensity, Y is the normal target sputtering yiel, () is a unction o the emission [4, 16, position on the target an the cosine istribution actor, Yamamura et al. propose a itting ormula o the orm 17, 18] ( ) cos (1 cos ) (5) where is the ejection angle o the sputtere atoms with respect to the surace normal an is a itting parameter. is epenent on the ree path o the atoms, etermine by the gas-target combination, normal pressure an the applie power ue to gas rareaction eect. Using Eq. (3) an rom Fig. 1(a), the lux ensity o the particles sputtere rom an element area A T o the target onto an element area A o the substrate may be expresse as : exp( C) A / A (6) where C P= 1, A cos/, cosz/. The rectangular target is escribe by circular cylinrical coorinates easily, A T rr. The total lux ensity o the ast moving sputtere particles at the substrate may be obtaine by integrating Eq. (6) over the area o the target etch track as: j( Yz (1 ( z / ) ) exp( C) rr (7) 4 Using the geometry o Fig.1 (a), =(z +r +R - rrcos) 1/. The integral omain is the area o the etch track. Eq. (7) can be integrate numerically or the epositing rate o the ast-moving particles. T

3 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) Thin ilm thickness istribution moel or slow-moving particles low-moving particles are the scattere ones which are transporte by iusion. It is typical to apply the istribute source moel to etermine slow-moving ones [19]. Pertrov et al. believe that the sputtere atoms, however, were not thermalize in a single collision event. The average istance L travele by the atoms in the initial irection beore being thermalize. The istance L is proportional to the thermal mean ree path with a actor which is a unction o the ratio o the mass o the gas an the target atom, an the energy o the sputtere atom. From Fig. 1(b), the total particles emitte rom an element area o the target, which has reache a point, P, without scattering is [3] : I pressure were zero, the total particles at P woul be: j( Y( ) rr exp( C) j( Y( ) rr Thus, the number o particles scattere rom the epositing lux is: 0 (9) j( Y( ) rr [1 exp( C)] (10) The ensity in atoms cm -3 s -1 o the particles scattere into an element volume, V=, rom the lux emitte rom the target element is given by ubstrate plane Direction o motion Etch track Target plane Y Y1 Z h O r R AT As R1 X1 ubstrate plane Direction o motion X Etch track Target R plane Y Y1 Z h O V= P R r AT X Diusion path (a) (b) Fig. 1 ystem geometry use in moeling the lux o (a) ast- an (b) slow-moving particles rom a planar target onto a planar substrate. Cj( Y( ) exp( C ) rr (11) V The ensity o the iusing source in an element volume is n: Cj( Y( ) n exp( V C) rr Ekpe et al. transorm Eq. (11) rom the source ensity o a conservation equation an Fick's irst law [4] ( ) ( ) [ ( )] V (1) Cj( Y( ) [ ( )] exp( C) rr (13) In a certain range, when the system, where the research objects (a certain number o particles) are in, keeps its number o particles constant, that is, particles into the system equal particles out o it, it will meet Fick's irst law, as shown in Fig.. The number o molecular passing an element area in an element time is: n ( ) D (14) R1 R X1 (8)

4 906 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) where D is the iusion coeicient. These particles erive rom the etching unit o the whole etching zone, an they iuse in all irections with the soli angle 4 o the point. Thereore, Ekpe et al. gave the equation o the lux iusing in a given irection: zc r j() r Yrr 3 4 r 1 (1 ( z/ ) )exp( C) (15) 1 0 Fig. The iusion moel o Fick s irst law or the lux o slow-moving particles The improper integral o is ivergent at lower limit. A parameter which can escribe the transport process is neee to eine the lower limit. L {(atom s mean ree path ), M(gas mass) /M(atom s mass), E(atom s enery)} may be the parameter given by Pertrov et al. The unction o L can be inuce through experiments. A parameter Q is also neee to eine the upper limit an epens on the ree path o the sputtere atoms, which is etermine by the gas-target combination an energy, an so on. All iusing particles o not reach the substrate by the same path way. Uner the integrability conition o, either L or Q is the unction o. The result o the improper integral shoul be the unction o. From Fig. 1(b), the total iusing lux is irectly euce by Fick's irst law in this paper n Cj( Y( ) ( ) D D C exp Crr (16) 3 It is easy or slow-moving particles to re-emit into the ischarge space ater epositing on the substrate ue to lower energy. The eposition rate is the exclusion o the re-emission part. The total iusing lux at the point P, ue to the emitte lux rom all the target elements, is: q z DCj() r Y(1 ( z/ )) 5 4 ( C )exp( C) rr (17) Where q is the coeicient o eposition eiciency or the slow-moving particles [0, 1]. Generally, the value o q is below 0.5, an the value is 0.1 in this paper. Eq. (17) can be integrate numerically or the total lux o slow-moving particles. The total epositing particles at the substrate is the sum o the ast-moving ones expresse in Eq. (7) an the slow-moving ones expresse in Eq. (17): (18) total The total epositing particles are ivie into the ast- an slow-moving ones approximately. In act, ater collision some o the particles reach the substrate with high energy an o not iuse. Moreover, there is not the only orm o iusion [0, 1]. 3. Moel Application The thin ilm thickness uniormity is uner the inluence o geometric parameters: target- substrate istance, temperature, gas pressure, electromagnetic an other actors. For the target, it is important to eine the geometric parameters o erosion zone (etch track), or they are irectly etermine the overall tren o thin ilm eposition. To simpliy the moel, it is necessary to propose the ollowing hypotheses: the eatures o erosion zone an the

5 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) ynamic characteristics o particles in the epositing process are consistent, that is, the sputtering conition, current ensity, emission an transportation o sputtere particles are consistent; the erosion zone is lat. Generally, the shape o the zone is the unction o time. When target-material is eroe, it will present complicate threeimensional spatial surace macroscopically. As the actual size will be conine to the computing time an mesh scale in calculating, the substrate size is esigne as 00mm40mm an place right to the target surace. For the size o the geometry o the zone, please reer to Fig R =4 1 Fig. 3 The geometry o the erosion zone R =0 The selection o parameters: this paper takes copper Cu as the target-material, an argon Ar as working gas. For the value o [4], when the ion incient energy is 100, 600, 1000 an 5KeV respectively, the corresponing value o is , 0.84, an 1.5; when the value o is 0, the istribution o emitte particles is the usual cosine istribution. Usually the energy o the sputtere copper atoms is lower than 10eV [14]. Thereore, the corresponing momentum collision section is approximately taken as m [, 3], an the mean ree path Cu or copper atoms is kt 4 T Cu m P P The energy o the copper atoms that are away rom the target-surace is approximate to 10eV; the variation range o T is 300~400K. For the variation ranges o P an Cu are 1~5Pa an 1~138mm, respectively. The programming calculation is obtaine by mathematical sotware MATLAB. The stuy on the uniormity o eposition rate is realize through the stuy on the istribution curve o the eposition rate on the substrate, which is an inirect stuy on the thin ilm thickness uniormity Thickness istribution o ast- moving particles Assuming that the change o target substrate will not inluence other actors greatly, incluing pumping spee an ensity istribution o spatial particles, that is, it will not inluence the parameters o the unction expression or the eposition rate. This paper only takes the relative movement o the substrate to the target into consieration. The values o that correspons to the incient ion energy are taken as 0, 0.84, 0.603, the sputtering yiel Y is taken as 1.5 atoms/ion, the current ensity is ma/cm, an Cu is 40mm. Taken the length percent o uniorm eposition zone as longituinal axis, that is, the ratio between the length o uniorm eposition zone on the substrate an the substrate length is taken as an important measurement to juge the thin ilm thickness uniormity uner the conition o ierent target-substrate istance (lateral axis), the uniorm eposition zone mentione in this paper is the zone whose thin ilm thickness non- uniormity is lower than 5%. Following is the veriication o the change o target-substrate istance rom 30mm to 80mm. Through numerical integration calculation, ierent results will be obtaine. From Fig. 4, it is easy to notices that when the substrate moves relatively to the target an the istance changes rom 30mm to 80mm, the length percent ecreases accoringly. The conclusion that thin ilm thickness uniormity will rise with the ecrease o target-substrate istance mae by Gencoa Inc. is consistent with the conclusion o this paper [4], as Fig. 5(a) shows. imilarly, as Fig. 6 shows, when Cu has ierent values, the unctional relationship between target-substrate istance an the length percent is ierent. The general tren presente in Fig. 6 is similar to that o Fig. 4, that is, with the increase o target-substrate istance the length percent will ecrease.

6 908 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) Fig. 4 The length percent at ierent target-substrate istance (a) Fig. 5 The relationships between the eposition uniormity an the target-substrate istance (a) or the ratio o the length an with o the erosion zone rom Gencoa Inc. (b) (a) Fig. 6 The variation o the uniorm eposition length with ierent target-substrate istance at ierent conitions (a) an (b) It is generally believe that the thin ilm thickness uniormity o the circle planar magnetron target will rise with the increase o target-substrate istance, while its eposition rate will ecrease accoringly. However, or the (b)

7 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) rectangular planar magnetron target, it is not easy to copy the conclusion o the circle planar magnetron target, which can be prove by the conclusions o this paper an other publishe papers. When incient ion energy an Cu are ixe values, the inluence o the en erosion zone on thin ilm thickness uniormity will be observe, where is 0.84, an Cu is 60mm, as Fig. 7 shows. Through calculation it is known that the proper ecrease o the en erosion zone will make thickness uniormity ecrease as well. As this geometric structure o erosion zone is easy to cause the inhomogeneous etching at en erosion zone, it shoul be avoie. Conversely, the appropriate increase o en erosion zone will cause the uniormity to increase. Meanwhile, when it reaches to certain value (accoring to the geometric parameter o this paper, the oset is -14mm), shown as Fig. 7(b), the uniormity will increase irst an then ecrease with the increase o target-substrate istance. Decreasing the zone Oset (a) Fig. 7 The variation on uniorm eposition length at ierent osets o the erosion zone (a) an the relative value o the uniorm eposition length (b) The urther research nees to consier how to esign the geometric moel parametrically so that the erosion zone can be simpliie as the ollowing stanar moel. This moel can be set by three parameters, shown as Fig. 8, those are R 1, R an L, which can be corresponingly escribe as R 1, mr 1, nr 1, m>1, an 0. When n0, the erosion zone are concentric rings. The ratio between the total length an with is (1+n/m). (b) Fig. 8 The geometry use in the parameterization o the erosion zone The size o the geometric structure, namely, R 1 is 4mmm is 5, n is 0, is 3. Given is 0.84, Cu is 60mm, an R 1 is 4mm, when n is 0, m is 3 or 4when m is 5, n is, 4 an 30. In these two situations, the value o will increase. The research is that how the increase value o has inluence on the thin ilm uniormity. The size o the substrate will change accoringly, such aswhen m is 3, the size is 184mm4mm. It is easy to conclue that when the value o n is not change an the value o m is ecrease, the uniormity will ecrease as well; when the value o m is not change an the value o n is increase, the uniormity will increase clearly. However, their relation is not a simple linear one, please reer to Fig. 6(a) an Fig. 9. The results above inicate that as the way o the increase o length or with is ierent, the change o thin ilm thickness uniormity is ierent. As Fig. 5(b) shows, the conclusion that the uniormity will rise with the increase o length-with ratio o erosion zone mae by Gencoa Inc. is consistent with the conclusion o this paper, yet it oes not point out the way.

8 910 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) (a) Fig. 9 The variation on uniormity with the ratio o length / with o the erosion zone on constant n (a) an constant m (b) conitions (b) 3.. Thickness istribution o slow- moving particles The slow-moving particles or eposition are moving by iusing. Generally, the uniormity o slow-moving particles is better than that o ast-moving ones. This paper only consiers the eatures o slow-moving particles when is 0.84, an Cu is 60mm. As Fig. 10 shows, through the calculation results, it is easy to come to the conclusion that in the same conition the uniormity o slow-moving is better. It is also shows that the length percent in the uniorm eposition zone will ecease with the increase o target-substrate istance, which is the same with the eposition eatures o ast-moving ones, an accors with the actual situation [3, 4] 3.3. Thickness istribution o the total particles Fig. 10 The eposition uniormity o the lux o slow-moving particles The total thickness istribution nees to calculate both ast- an slow- moving particles, as Fig. 11 shows. The ast ones may ominate at low pressure an will ecrease with the increase o pressure, while the slow ones will ominate in the high-pressure regime. With the urther increase o pressure, their proportions will ten to change gently. Assuming the current is constant, when the value o is reuce rom to 0.84 or 0, the power will reuce accoringly, which conorms with the act that the eposition rate will reuce with the ecrease o power.

9 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) a b c e Fig. 11 The variation o the uniorm eposition length percent (a), (b), (c) an the eposition rate (), (e), () with ierent conitions or the total eposition lux

10 91 ZHANG Yichen et al. / Physics Proceia 3 ( 01 ) When Cu is change rom 80mm to 40mm, the pressure will increase or the temperature will ecrease accoringly, which conorms with the conclusion that the eposition rate will ecrease with the increase o pressure corresponingly [3, 4]. As the rise o gas temperature that is cause by the collision o sputtere particles in the ischarge space is inhomogeneous [5], an the process like inhomogeneous gas rareaction ensity cannot be escribe irectly an accurately by existing mathematical moel, the numerical calculation is usually obtaine by the basic physical moel like the collision moel. Thereore, the spatial istribution unction o gas temperature an ensity can be obtaine, which are the immeiate results or urther calculation. This paper oes not take the process into consieration, hence there exists eviation between moel an actual situation to some exten. From the calculation results iscusse above, we can conclue that the istribution o eposition rate is greatly inluence by the size o the erosion zone, while the power o magnetron target, target-material an pressure will not inluence the general istribution tren or the istribution. Unlike the circle planar magnetron sputtering target, although the thin ilm eposition uniormity o the rectangular planar magnetron sputtering target will not rise with the increase o target istance, its eposition rate will ecrease with the increase o target istance. The calculation result conorms to the actual situation. 4. Conclusion Through the iscussion o thin ilm thickness istribution theory, this paper presents the calculation results or the thin ilm thickness uniormity o rectangular planar target with etaile comparison o the inluence o geometric parameters, target-substrate istance, incient ion energy an other parameters. The calculation results are teste inirectly an consistent with the actual situation: the thickness uniormity will reuce with the increase o targetsubstrate istance an with the ecrease o erosion zone o the target ens. When the erosion zone o the target ens increases to some exten, the uniormity will become higher with the increase o target-substrate istance an then become lower. There are two tenencies or thin ilm thickness uniormity with the increase o length-with ratio o target erosion zone, that is, it will become a little lower when the length is a constant, or become higher when the with is a constant. An the thin ilm thickness uniormity will become lower with the ecrease o power an the increase o gas temperature. The eposition rate will become higher with the ecrease o target-substrate istance, or the increase o power an gas temperature. Reerences [1] K. Meyer, I. K. chuller, C. M. Falco. Thermalization o sputtere atoms [J], J. Appl. Phys., 1981, 5(9): [] T. Motohiro. Applications o Monte Carlo simulation in the analysis o a sputter-eposition process [J], J. Vac. ci. Technol. A, 1986, 4(): [3] I. Petrov, I. Ivanov, V. Orlinov, etc. Comparison o magnetron sputter eposition conitions in neon, argon, krypton, an xenon ischarges [J], J. Vac. ci. Technol. A, 1993, 11(5): [4]. D. Ekpe, L. W. Bezuienhout,. K. Dew. Deposition rate moel o magnetron sputtere particles [J], Thin oli Films, 005, 474(1-): [5] T. Yagisawa, T. Makabe. Moeling o c magnetron plasma or sputtering: Transport o sputtere copper atoms [J], J. Vac. ci. Technol. A, 006, 4(4): [6]. M. Rossnagel. Gas ensity reuction eects in magnetrons [J], J. Vac. ci. Technol. A, 1988, 6(1): [7] D. W. Homan. A sputtering win [J], J. Vac. ci. Technol. A, 1985, 3(3): [8] G. M. Turner. Monte Carlo calculations o gas rareaction in a magnetron sputtering ischarge [J], J. Vac. ci. Technol. A, 1995, 13(4): [9] F. Jimenez,. D. Ekpe,. K. Dew. Inhomogeneous rareaction o the process gas in a irect current magnetron sputtering system [J], J. Vac. ci. Technol. A, 006, 4(4): [10] A. Belkin, F. Jansen. Anoe eects in magnetron sputtering [J], urace an Coatings Technology, 1998, 99(1-): [11] K.. Fancey. A coating thickness uniormity moel or physical vapour eposition systems: overview [J], urace an Coatings Technology, 1995, 71(1): 16-9.

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