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Simulation of deposition and densification in an ion beam environment
Sm~liwcand ('oatin,~s Technolo,~y, 51 I1992132X 332
328
Simulation of deposition and densification in an ion beam environment T. D. A n d r e a d i s , M e r v i n e R o s e n , M . I. H a f t e l a n d J, A. S p r a g u e Napal R~,s~rch Luhormory. lYashin.~lon, DC 20,~75 5000 ~USA
AksCraet We studied the role played by the incident ion beam in ion-beam-assisted deposition by lirxt investigating the morphology of a val~*r-delx~sitednickel film onto an Nil 100lsurface using thr¢-c-dimensionalmoleculardynami..~, Ion-beam-inducedx'oid reduction was then mt~leled for the case of argon ions onto a germanium lilm using MARLOWE, The diffusion of residual ~acancies and interstitials was taken into account, The nickel lilms exhibilLxlcolumnar ribbon-like voids and an average packing fraction of 80'%, Void volumeloss as a function of depth, initial void volumeand beam energy was determin~.'xl,Voidcollapse occurred at depths well beyond the incident beam range: an increa~ in void size at shallow depths and higher beam energieswas seen, The depth ~1"the I~ak void Io~ rate was insensitiveto beam enemy,
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Many of the properties of vapor-deposited films may be improved by bombarding with energetic ions during the deposition process. Films may be produced using this technique that are more resistant to environmental attack and adhere better to the surfaces onto which they were deposited. The improvement in the films produced by ion-beamassisted deposition (IBAD) has been linked to an increa,~ in the density of the films. Ion bombardment brings about the collapse of voids in the film, resulting in the higher density. We investigated, by computer simulation, the ability of beams to bring about the reduction of voids in thin germanium films. Calculations were based on the binary collision (BC.) code MARLOWE. We examined how the ability of the ion beam to reduce voids changes with depth, void size, and beam energy. We also modeled the growth of vapor-deposited nickel films using three-dimensional molecular dynamics (MD) in order to estimate the density of the deposited films, Two-dimensional simulations have been carried out on nickel [ I ] but we were concerned about the influence of the missing direction on the results. The M D modal simulates conditions for low atom mobility deposition. Measurements of films deposited at low temperatures show columnar-like voids with an orientation that is dependent on the directk~n of ineidence of the deposited atoms. This "memory" of the incident direction indicates that the mobility is low, Void density diminishes with increasing temperature, as difl'usion becomes increasingly important.
Simulation results from M A R L O W E [2] were used to examine the rate at which voids in germanium are reduced by argon bombardment. The parameters varied were beam energy, void size, and void depth. We bombarded a germanium film containing a void lan agglomeration of vacancies) with argon and recorded the position of all the interstitials and vacancies produced, An auxiliary computer program, ANNEAL, recombined appropriate interstitials and vacancies including void vacancies - - and determined the remaining void. Voids of various sizes were used to see the dependence of the collapse rate on void size. Spherical voids of radius 1.0, 1.5, 2.0, and 2,5 lattice lengths (LL) (corresponding to 35, 123, 281, and 525 vacancies respectively) were used. The lattice length of germanium is 5,65 A. The void depth was the distance from the surface to the center of the sphere. We obtained a void size distribution from a transmission electron micrograph of a vapor-deposited germanium film [31. The voids generally appear to be spherical in the micrograph but this may be because of the perspective of the photograph. The radii of the voids we selected for M A R L O W E calculations go up to 2.5 LL, which is close to the peak of the void distribution, Films produced using ion bombardment woukt have a void distribution shifted towards smaller voids, Our selection of sizes is representative of voids in such [iims, Since vapor-produced voids are cylinders, our use of spheres permits us to obtain the depth and void size dependence at the expense of some geometrical distortion.
Elsevier ~uuoia
T. D, Andreadis et al, / Simulation of deposition and densiJication
In the MARLOWE calculations, argon ions impinged on the (100) surface of germanium at a slightly offnormal angle of incidence (9°) with energies of 0.065, 0.2, and 0.5 keV. MARLOWE calculations are suspect at 65 eV but the results were consistent with those of the higher energy calculations. For the present calculation, the beam atoms struck random locations on a surface area of about 10×10 A void was placed at various depths on an axis through the center of this surface area. The area struck by the beam ions was large enough so that ions hitting its edges had a negligible effect on the reduction of the void, About 2000 incident atoms were used in each calculation, ANNEAL first carries out athermal recombination of vacancies and interstitials. Vacancies and interstitials recombine immediately when they are within a distance of 2 LL. MD calculations, which we have carried out on f.c.c. [4] metals, indicate that this is a reasonable number. Calculations on silicon [5] give a slightly smaller number, The void decreases in size when interstitials recorabine with void vacancies, Void volume grows when vacancies produced by the collision cascade are near neighbors to other vacancies, Residual interstitials and vacancies remain after this calculation, ANNEAL then approximates the diffusion of the residual interstitials and vacancies, First the interstitials, which are highly mobile in comparison with vacancies, are moved each in a randomly selected direction, If the path of an interstitial comes within a recombination distance of a vacancy, it annihilates, Next, the vacancies are moved in random directions, If the vacancy comes within a nearest neighbor distance to another vacancy (either void vacancy or a residual vacancy) they will be joined and the void volume will inca'case,
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is dramatic for the larger voids and higher energy, and offers another mechanism of surface roughening by energetic ion beams. To ascertain the effect of diffusion, the above results are compared, in Fig. 2, with those obtained when diffusion is neglected. It is apparent that the diffusion is responsible for the negative cross-section. Our results
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indicate that diffusion of residuals tends to reduce the effect d the cascade at shallow depths and increases (more pronounced for small voids) the effect at greater depths. For the 1.0 LL void bombarded with 0.065 keV ions, diffusion increased the cross-section at all depths. Figure 1 shows the maximum cross-section for void loss to occur at about 4 6 L L The depth at which the maximum occurs does not change very much from one case to the next. The projected ranges, however, for argon in a germanium target are 1.4, 2.1, and 3,8 LL for beam energies of 0.065, 0.2, and 0.5 keV respectivdy. These vary by a factor of almost 3 while the crosssection maxima remain fixed. It is important to note that the effective depth for void collapse extends wall beyond the projected range of the ions (by a factor of 3.5 for the 0,065 keV case). Moreover, these deep voids shrink both in the presence and the absence of diffusion, Now the beam straggling is large 1500 of the range) and cascade atoms go deeper yet+ However, the bulk of the residuals lies at a depth near the projected range. For these, deep voids provide a relatively small target and so diffusion has little effect.
Understanding the process of void growth during vapor deposition is crucial to modeling the densification during IBAD. in order to gain some insight into the mechanisms involved we carried out MD simulations of the vapor deposition of nickd using embedded atom meth(~l (EAM) potentials, in these calculations no ion bombardment is taking place, Nickd atoms drop at randomly selected positions onto the 11001 surface of a nickel substrate. The deposited att~ns are normally incident with an energy of 0,1 eV. Five atoms hit the surface at the same time, separated by at least ihe cut-off" distance of the EAM ~tential so that they do not interact. After this cascade has been quenched to a selected temperature (0 K and 300 K in this studyk using Langevin energy extraoion, another tire atoms are deposited, Quenching takes about 2 ps after a deposition: however, we do not deposit other atoms until 4 ps have elapsed - in order to be sure that deposited atoms were fully quenched. This is in keeping with low laboratory deposition rates, which are on the order of a monolayer per second. Quenching time is not important for low mobility conditions since atoms stay dose to their deposited positions. The substrate in the calculation consists of six atomic layers I1200 atoms) covering six layers of frozen atoms. Frozen atoms exert forces on other atoms but are not able to move. The layers on top of the frozen layers bufl~r the surface from possible anomalies produced by the frozen layers. Periodic boundary conditions arc employed in the X-Y surface directions, but not in the Z direction (normal to the surfaceL where free-surface boundary conditions are used.
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Figure 3 shows the packing density of the nickel simulations for the two temperatures studied as a function of the deposited layer. The substrate is just below layer I. The packing density is defined as the fraction filled of the total available lattice locations in the layer. We estimate the average packing density to be 0.80_+0,05, in calculating the average, the outermost layers were not included since continued deposition would increase their density, Crystal structure is maintained except for slight deterioration near large voids and substantial deterioration in the topmost layers where only a small fraction tff a full layer is deposited. Deposited layers maintained the
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periodic interlayer separation of 1.76 A nearly up to the topmost layers, Some buckling of layers was seen of the order of 1%-2% of the interlayer distance near the substrate and 5%-10% for the last few deposited layers. The voids observed in the nickel deposition simulation consisted of ribbon-like shapes, 5-10 vacancies across, This is illustrated in Fig, 4, which shows a cross-section through a void in the deposited layer for the 300 K case.
331
Voids were observed for both of the temperatures studied, Recent M D deposition calculations on the (I I I) surface of a silver substrate at 300 K did not show a similar void network [71; the deposition formed a fully packed crystal except for a large crater at the surface. In that calculation therlnagy activated diffusion of atoms was significant owing to the low migration energy on the (11 I) surface and the generally higher mobility of silver atoms; the melting temperature of silver is 491 K below that of nickel, Silver atoms on the (! ! 1) surface of silver have a 0,06 eV [8] migration energy in comparison with nickel atoms oct the (100) surface of nickel, which we calculate to have a migration energy of 0.65 eV, Figure 5 shows the depth distribution of deposited atoms, grouped 400 atoms (! layer equivalent) at a time. In this figure the substrate ends with layer 5 and the first deposited layer is layer 6. This figure illustrates that further deposition has a small effect on the initially deposited layers and these can therefore he used to estimate the packing fraction.
6. Smmwry For the IBAD process the deposited film may he separated into two regions: the transition region and the bulk or deep region, The transition region lies within the effective range of the ion beam, The deep region extends from the edge of this region through the deposited film to the substrate below, In the transition region the void size distribution changes gradually with increasing depth until it reaches that of the deep region, Our calculations for an argon beam on germanium indicate
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Fig. 5, The depth d i s U i k t i o n of (lelx~ited atoms, grouped 400 atoms (I layer equivalent) at a time, for the 300 K case, The substrate ends with layer 5 and the first deposited layer is layer 6,
332
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Sim~dalion 0fd~'posilion and den.~(licalion
that in the transition region the beam brings about a reduction of void volume. To produce a fully densitied bulk film it is necessary to select ion-beam-to-delx~sit~atom arrival ratios so that complete densifieation can take place within the transition region. Our calculations indicate that this transition region is about 12 14 lattice lengths for germanium and that it extends beyond the projected range of the beam. Increasing the beam energy increases its etTectiveness in collapsing voids. In addition. larger voids are more easily depleted. Our results also indicate that diffusion of residual interstitiais and vacancies is important in the densitication process. In the MD simulations of nickel deposition, ribbonshaped voids were produced 5 10 vacancies wide. The average packing density for low mobility surfaces of nickel was found to he 0.80+0.05. The density of the deposited layers at a given temperature depends on the mobility ot" the atoms.
.~,¢kaowledga~a4 The transmission electron micrograph was supplied courtesy of J. E. Yehoda. Pennsylvania State University. Referemces I K.-lt. Muller. Pity.x, Re~', B, 35 {l~Tb 7q(16. 2 M.T. Robinson and I. M, "l'~rren,'.. I~hys. R~'r. B, ~ 11~741 51X1~, 3 J. I!. Ychoda. B. Yung. K. Vcdam aud R, Me.~sicr. ,I. I'a~'. S~'i. l't'~'llllol. 4 . 6 119X~I 163 I. 4 T, I), Andrcadis. M. Rosen. J. M. I~ridon and I)..1. Ronen..~lawr. R~,s. So~'. Syrup. I~ro~'., 12~' (1~)~91 175. 5 M. l. Baskes. Personal communication, Sandia Nuti~nal i.abL~rat~tics. Livermore. M, I. Baskcs. Ph.vs. R~'~'. Lerl., 59 11~),~71 2666, (~ I".,H. Hirsch and I. K. Vargu. Thi. Solid Films, 52 I 1'981~1~1',). 7 (', Gilmore and J.A. ~-~rague. Sl~rl~ ('oat. /~.ch~u~l., 51 11~,~121 324 327. W, K. Rilling. ('. M, Gilmore. T. I). Andreadix :lnd .I.A. Spragt, e. ('a~. ,I. Ph.vx., 6,',' 11911(11 1035.
328
Simulation of deposition and densification in an ion beam environment T. D. A n d r e a d i s , M e r v i n e R o s e n , M . I. H a f t e l a n d J, A. S p r a g u e Napal R~,s~rch Luhormory. lYashin.~lon, DC 20,~75 5000 ~USA
AksCraet We studied the role played by the incident ion beam in ion-beam-assisted deposition by lirxt investigating the morphology of a val~*r-delx~sitednickel film onto an Nil 100lsurface using thr¢-c-dimensionalmoleculardynami..~, Ion-beam-inducedx'oid reduction was then mt~leled for the case of argon ions onto a germanium lilm using MARLOWE, The diffusion of residual ~acancies and interstitials was taken into account, The nickel lilms exhibilLxlcolumnar ribbon-like voids and an average packing fraction of 80'%, Void volumeloss as a function of depth, initial void volumeand beam energy was determin~.'xl,Voidcollapse occurred at depths well beyond the incident beam range: an increa~ in void size at shallow depths and higher beam energieswas seen, The depth ~1"the I~ak void Io~ rate was insensitiveto beam enemy,
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Many of the properties of vapor-deposited films may be improved by bombarding with energetic ions during the deposition process. Films may be produced using this technique that are more resistant to environmental attack and adhere better to the surfaces onto which they were deposited. The improvement in the films produced by ion-beamassisted deposition (IBAD) has been linked to an increa,~ in the density of the films. Ion bombardment brings about the collapse of voids in the film, resulting in the higher density. We investigated, by computer simulation, the ability of beams to bring about the reduction of voids in thin germanium films. Calculations were based on the binary collision (BC.) code MARLOWE. We examined how the ability of the ion beam to reduce voids changes with depth, void size, and beam energy. We also modeled the growth of vapor-deposited nickel films using three-dimensional molecular dynamics (MD) in order to estimate the density of the deposited films, Two-dimensional simulations have been carried out on nickel [ I ] but we were concerned about the influence of the missing direction on the results. The M D modal simulates conditions for low atom mobility deposition. Measurements of films deposited at low temperatures show columnar-like voids with an orientation that is dependent on the directk~n of ineidence of the deposited atoms. This "memory" of the incident direction indicates that the mobility is low, Void density diminishes with increasing temperature, as difl'usion becomes increasingly important.
Simulation results from M A R L O W E [2] were used to examine the rate at which voids in germanium are reduced by argon bombardment. The parameters varied were beam energy, void size, and void depth. We bombarded a germanium film containing a void lan agglomeration of vacancies) with argon and recorded the position of all the interstitials and vacancies produced, An auxiliary computer program, ANNEAL, recombined appropriate interstitials and vacancies including void vacancies - - and determined the remaining void. Voids of various sizes were used to see the dependence of the collapse rate on void size. Spherical voids of radius 1.0, 1.5, 2.0, and 2,5 lattice lengths (LL) (corresponding to 35, 123, 281, and 525 vacancies respectively) were used. The lattice length of germanium is 5,65 A. The void depth was the distance from the surface to the center of the sphere. We obtained a void size distribution from a transmission electron micrograph of a vapor-deposited germanium film [31. The voids generally appear to be spherical in the micrograph but this may be because of the perspective of the photograph. The radii of the voids we selected for M A R L O W E calculations go up to 2.5 LL, which is close to the peak of the void distribution, Films produced using ion bombardment woukt have a void distribution shifted towards smaller voids, Our selection of sizes is representative of voids in such [iims, Since vapor-produced voids are cylinders, our use of spheres permits us to obtain the depth and void size dependence at the expense of some geometrical distortion.
Elsevier ~uuoia
T. D, Andreadis et al, / Simulation of deposition and densiJication
In the MARLOWE calculations, argon ions impinged on the (100) surface of germanium at a slightly offnormal angle of incidence (9°) with energies of 0.065, 0.2, and 0.5 keV. MARLOWE calculations are suspect at 65 eV but the results were consistent with those of the higher energy calculations. For the present calculation, the beam atoms struck random locations on a surface area of about 10×10 A void was placed at various depths on an axis through the center of this surface area. The area struck by the beam ions was large enough so that ions hitting its edges had a negligible effect on the reduction of the void, About 2000 incident atoms were used in each calculation, ANNEAL first carries out athermal recombination of vacancies and interstitials. Vacancies and interstitials recombine immediately when they are within a distance of 2 LL. MD calculations, which we have carried out on f.c.c. [4] metals, indicate that this is a reasonable number. Calculations on silicon [5] give a slightly smaller number, The void decreases in size when interstitials recorabine with void vacancies, Void volume grows when vacancies produced by the collision cascade are near neighbors to other vacancies, Residual interstitials and vacancies remain after this calculation, ANNEAL then approximates the diffusion of the residual interstitials and vacancies, First the interstitials, which are highly mobile in comparison with vacancies, are moved each in a randomly selected direction, If the path of an interstitial comes within a recombination distance of a vacancy, it annihilates, Next, the vacancies are moved in random directions, If the vacancy comes within a nearest neighbor distance to another vacancy (either void vacancy or a residual vacancy) they will be joined and the void volume will inca'case,
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Figure ! shows the resuks of the calculations described above for the vacancy loss per incident ion per square lattice length of surface area as a function of depth for three beam energies and four void sizes. The vacancy loss per incident atom per unit area is a "cross-section" for vacancy loss by a void due to the ion beam. These figures show that the maximum clfectivc-depth of the beam is about 12-14 LL for the energies considered with higher energy beams having larger crosssections. Larger voids are also more likdy to lose vacancies than smaller voids. The results follow the measurements of Hirsch and Varga [6] in showing that higher energy ions are more effective in void reduction. Higher energy ions, according to our calculations, also increa~ void size at shallow depths - - the cross-section is negative there. This effect
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is dramatic for the larger voids and higher energy, and offers another mechanism of surface roughening by energetic ion beams. To ascertain the effect of diffusion, the above results are compared, in Fig. 2, with those obtained when diffusion is neglected. It is apparent that the diffusion is responsible for the negative cross-section. Our results
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indicate that diffusion of residuals tends to reduce the effect d the cascade at shallow depths and increases (more pronounced for small voids) the effect at greater depths. For the 1.0 LL void bombarded with 0.065 keV ions, diffusion increased the cross-section at all depths. Figure 1 shows the maximum cross-section for void loss to occur at about 4 6 L L The depth at which the maximum occurs does not change very much from one case to the next. The projected ranges, however, for argon in a germanium target are 1.4, 2.1, and 3,8 LL for beam energies of 0.065, 0.2, and 0.5 keV respectivdy. These vary by a factor of almost 3 while the crosssection maxima remain fixed. It is important to note that the effective depth for void collapse extends wall beyond the projected range of the ions (by a factor of 3.5 for the 0,065 keV case). Moreover, these deep voids shrink both in the presence and the absence of diffusion, Now the beam straggling is large 1500 of the range) and cascade atoms go deeper yet+ However, the bulk of the residuals lies at a depth near the projected range. For these, deep voids provide a relatively small target and so diffusion has little effect.
Understanding the process of void growth during vapor deposition is crucial to modeling the densification during IBAD. in order to gain some insight into the mechanisms involved we carried out MD simulations of the vapor deposition of nickd using embedded atom meth(~l (EAM) potentials, in these calculations no ion bombardment is taking place, Nickd atoms drop at randomly selected positions onto the 11001 surface of a nickel substrate. The deposited att~ns are normally incident with an energy of 0,1 eV. Five atoms hit the surface at the same time, separated by at least ihe cut-off" distance of the EAM ~tential so that they do not interact. After this cascade has been quenched to a selected temperature (0 K and 300 K in this studyk using Langevin energy extraoion, another tire atoms are deposited, Quenching takes about 2 ps after a deposition: however, we do not deposit other atoms until 4 ps have elapsed - in order to be sure that deposited atoms were fully quenched. This is in keeping with low laboratory deposition rates, which are on the order of a monolayer per second. Quenching time is not important for low mobility conditions since atoms stay dose to their deposited positions. The substrate in the calculation consists of six atomic layers I1200 atoms) covering six layers of frozen atoms. Frozen atoms exert forces on other atoms but are not able to move. The layers on top of the frozen layers bufl~r the surface from possible anomalies produced by the frozen layers. Periodic boundary conditions arc employed in the X-Y surface directions, but not in the Z direction (normal to the surfaceL where free-surface boundary conditions are used.
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Figure 3 shows the packing density of the nickel simulations for the two temperatures studied as a function of the deposited layer. The substrate is just below layer I. The packing density is defined as the fraction filled of the total available lattice locations in the layer. We estimate the average packing density to be 0.80_+0,05, in calculating the average, the outermost layers were not included since continued deposition would increase their density, Crystal structure is maintained except for slight deterioration near large voids and substantial deterioration in the topmost layers where only a small fraction tff a full layer is deposited. Deposited layers maintained the
T, D, Andreadis et al. / Simulation of deposition and densiflca~ion 0EPOSIT,~\ C; ,I eV Ni 0'4 Ni ('CO) SURFACE
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Fig, 3, Packing density as a function of deposited layer for 0,1 eV nickel deposition onto the (100) face of nickel for substrate temperatures of 0 K and 300 K, The results for two separate runs at 0 K are shown to indicate statistical spread,
periodic interlayer separation of 1.76 A nearly up to the topmost layers, Some buckling of layers was seen of the order of 1%-2% of the interlayer distance near the substrate and 5%-10% for the last few deposited layers. The voids observed in the nickel deposition simulation consisted of ribbon-like shapes, 5-10 vacancies across, This is illustrated in Fig, 4, which shows a cross-section through a void in the deposited layer for the 300 K case.
331
Voids were observed for both of the temperatures studied, Recent M D deposition calculations on the (I I I) surface of a silver substrate at 300 K did not show a similar void network [71; the deposition formed a fully packed crystal except for a large crater at the surface. In that calculation therlnagy activated diffusion of atoms was significant owing to the low migration energy on the (11 I) surface and the generally higher mobility of silver atoms; the melting temperature of silver is 491 K below that of nickel, Silver atoms on the (! ! 1) surface of silver have a 0,06 eV [8] migration energy in comparison with nickel atoms oct the (100) surface of nickel, which we calculate to have a migration energy of 0.65 eV, Figure 5 shows the depth distribution of deposited atoms, grouped 400 atoms (! layer equivalent) at a time. In this figure the substrate ends with layer 5 and the first deposited layer is layer 6. This figure illustrates that further deposition has a small effect on the initially deposited layers and these can therefore he used to estimate the packing fraction.
6. Smmwry For the IBAD process the deposited film may he separated into two regions: the transition region and the bulk or deep region, The transition region lies within the effective range of the ion beam, The deep region extends from the edge of this region through the deposited film to the substrate below, In the transition region the void size distribution changes gradually with increasing depth until it reaches that of the deep region, Our calculations for an argon beam on germanium indicate
DEPTH DISTRIBUTION OF DEPOSITED ATOMS IgO0 Ni ATOMSDEPOSITEDAT300" K 200
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Fig, 4, A vertical cross-section through the deposited layers for the 300 K case, showing a ribbon-like void, The substrate lies at the right side of the figure,
Fig. 5, The depth d i s U i k t i o n of (lelx~ited atoms, grouped 400 atoms (I layer equivalent) at a time, for the 300 K case, The substrate ends with layer 5 and the first deposited layer is layer 6,
332
T.D. ,.Indreadi,x t'l al,
Sim~dalion 0fd~'posilion and den.~(licalion
that in the transition region the beam brings about a reduction of void volume. To produce a fully densitied bulk film it is necessary to select ion-beam-to-delx~sit~atom arrival ratios so that complete densifieation can take place within the transition region. Our calculations indicate that this transition region is about 12 14 lattice lengths for germanium and that it extends beyond the projected range of the beam. Increasing the beam energy increases its etTectiveness in collapsing voids. In addition. larger voids are more easily depleted. Our results also indicate that diffusion of residual interstitiais and vacancies is important in the densitication process. In the MD simulations of nickel deposition, ribbonshaped voids were produced 5 10 vacancies wide. The average packing density for low mobility surfaces of nickel was found to he 0.80+0.05. The density of the deposited layers at a given temperature depends on the mobility ot" the atoms.
.~,¢kaowledga~a4 The transmission electron micrograph was supplied courtesy of J. E. Yehoda. Pennsylvania State University. Referemces I K.-lt. Muller. Pity.x, Re~', B, 35 {l~Tb 7q(16. 2 M.T. Robinson and I. M, "l'~rren,'.. I~hys. R~'r. B, ~ 11~741 51X1~, 3 J. I!. Ychoda. B. Yung. K. Vcdam aud R, Me.~sicr. ,I. I'a~'. S~'i. l't'~'llllol. 4 . 6 119X~I 163 I. 4 T, I), Andrcadis. M. Rosen. J. M. I~ridon and I)..1. Ronen..~lawr. R~,s. So~'. Syrup. I~ro~'., 12~' (1~)~91 175. 5 M. l. Baskes. Personal communication, Sandia Nuti~nal i.abL~rat~tics. Livermore. M, I. Baskcs. Ph.vs. R~'~'. Lerl., 59 11~),~71 2666, (~ I".,H. Hirsch and I. K. Vargu. Thi. Solid Films, 52 I 1'981~1~1',). 7 (', Gilmore and J.A. ~-~rague. Sl~rl~ ('oat. /~.ch~u~l., 51 11~,~121 324 327. W, K. Rilling. ('. M, Gilmore. T. I). Andreadix :lnd .I.A. Spragt, e. ('a~. ,I. Ph.vx., 6,',' 11911(11 1035.