Hyperthermal vapor deposition of copper: reflection and resputtering effects

Transcription

1 Surface Science 43 (999) Hyperthermal vapor deposition of copper: reflection and resputtering effects X.W. Zhou, H.N.G. Wadley * Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22903, USA Received 23 November 998; accepted for publication 2 February 999 Abstract Three-dimensional molecular dynamics simulations of hyperthermal copper atom impacts with copper surfaces have been used to investigate the effects of incident atom energy upon atomic reflection and resputtering during physical vapor deposition. No reflection or resputtering has been observed for incident energies below 0 ev. However, as the incident energy was increased to 20 ev and above, the likelihood of both adatom reflection and sputtering of predeposited atoms rapidly increased. The probability of reflection increased with the angle of incidence and was greatest for oblique (glancing) angle impacts. The reflected adatoms were strongly forward scattered and retained a large fraction of their initial incident energies. The resputtering yield was highest for incident angles around 40 to the surface normal. The resputtered atoms were typically ejected with significantly smaller energies than those of the incident atoms, and were preferentially ejected in the forward direction with a maximum probability at an angle of about 45 to the surface normal. These results have been compared with the published experimental data for low energy ion impact. The dependence of the reflection probability, the resputtering yield, as well as the angular and energy distributions of both reflected and resputtered atoms upon the adatom s incident energy and angle have been obtained and fitted to simple relations suitable for incorporation in models of vapor deposition. 999 Elsevier Science B.V. All rights reserved. Keywords: Atom solid interactions; Copper; Growth; Metallic films; Models of surface kinetics; Molecular dynamics; Sputtering; Sticking. Introduction adatom skipping across the growth surface in the impact direction leading to biased adatom diffusion; The morphology and microstructure of physical (iii) adatom reflection; and (iv) adatom vapor deposited (PVD) materials can be signifistanding induced resputtering [7 7]. A detailed undercantly modified by changing the incident energy of these mechanisms and their depen- of the depositing atoms [ 7]. The atomistic mechprecursor dence upon incident energy and angle is a anisms responsible for these incident energy effects in unraveling the complex dependence are thought to include: (i) local transient surface of film morphology and microstructure upon PVD heating which induces athermal diffusion; (ii) process conditions. Predictive models that incorpo- rate the effects of incident energy and angle upon the morphology and microstructure of films might * Corresponding author. Fax: eventually aid the design of improved vapor depos- address: haydn@virginia.edu (H.N.G. Wadley) ition techniques /99/$ see front matter 999 Elsevier Science B.V. All rights reserved. PII: S ( 99 )

2 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) An atom impact model based upon a three- the trench walls. Since these processes only occur dimensional molecular dynamics (MD) analysis for energetic atom impacts, interest has grown in has recently been developed and used to investigate the use of high incident energy deposition techniques impact atom induced diffusional processes during such as bias sputter deposition [7 0,20] the deposition of hyperthermal atoms [8]. This or thermal evaporation with sputter etching []. impact model used an embedded atom method The sputtering of metals by atomic bombard- ( EAM) potential to calculate the interaction forces ment of their surface has been widely investigated between metal atoms during impacts. It was used using various experimental approaches [2]. The to analyze the local surface heating responsible for focus of much of the work has been the sputtering athermal diffusion and the momentum effects that of metal targets by high energy (~ 0 kev ) inert caused biased diffusion of adatoms. The results gas ions in order to investigate the process that indicated that the local transient heating induced are normally used to create a metal atom flux for by a hyperthermal adatom impact is often sufficient subsequent deposition [2]. Recently, Doughty to activate atomic diffusion and the reconstruction et al. at Oak Ridge National Laboratory have of locally defective structures. They also revealed measured the angular distribution of copper atoms that long-range adatom biased diffusion readily ejected by helium, argon and xenon ions incident occurs. The bias diffusion distances sometimes on copper surface at incident angles of 30, 45, and exceed 00 Å, especially when incident energies are 60 with low incident energies of 40, 60 and above ~20 ev and incident angles are above ev [22]. The sputtering yields of silicon surface As a result, increasing the incident energy is by low energy ( ev ) argon ion bombardexpected to reduce the defect concentrations and ment were calculated by Kubota et al. [23]. While to promote a flatter surface morphology for thin these data are useful for assessing some aspects of films deposited under kinetically limited conditions low energy impacts, they are inadequate for a (i.e. at low temperatures or high deposition rates). quantitative analysis of the contribution of reflec- Both the impact induced local heating and the tion and resputtering to hyperthermal metal atom biased diffusion results were fitted to empirical (or metal ion) deposition. These processes remain equations, simplifying their incorporation in the poorly characterized and are only superficially various modeling schemes utilized for the simulation understood. of vapor deposition [9]. Atomistic modeling provides an alternative Experimental studies have shown that hyperthermal approach to the study of atom impact processes. adatoms with incident energies of 20 ev or At high incident energies, sputtering has been above can also be reflected and/or induce sputtering reasonably simulated using a Monte Carlo method of predeposited atoms (resputtering) [6]. These based upon a binary atomic collision approxima- reflection and resputtering processes can have tion [ 24]. However, at the lower incident energies important consequences for the manufacture of of interest here, many-body collision effects thin films and the metal interconnects used in become important, and the binary collision large-scale integrated circuits [7]. To increase the approximation fails. Collisions must therefore be device density, narrow conductive lines are used simulated using methods that better account for for interconnecting individual devices. As a result, the many-body nature of the interaction. In a metals must be deposited into deep narrow (i.e. molecular dynamics simulation, the trajectories of high aspect ratio) trenches. However, when the atoms within the interaction field of all the other aspect ratio is high, the deposit often covers the atoms can be traced by solving Newton s equation trench opening before fully filling it. This results of motion using a predefined interatomic potential. in large voids becoming trapped within the If electronic excitation and chemical reaction interconnect, and the premature failure of the effects can be ignored, the MD method provides a device [6,7]. Reflection and resputtering may be tractable approach to the analysis of an adatom able to retard the formation of overhangs at the substrate impact process. MD simulations have trench top and promote more even coverage of been extensively used to investigate the ion sputter-

3 60 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) ing of metals [ 25]. The reflection of a 40 ev silicon atom from a () silicon surface at an incident angle of 2 has been simulated using MD [6,7], but no work has sought to establish a detailed understanding of the adatom reflection and resputtering mechanisms that are active during deposition of hyperthermal atoms. Here, a MD vapor atom impact model developed earlier to analyze impact induced diffusion [8] was extended to investigate atomic reflection and resputtering as a function of the incident energy and angle of the depositing atoms. The work concentrates on the reflection and resputtering of copper from a copper surface because of the importance of copper in integrated circuits [26], its widespread use in GMR devices [27 30], and the availability of a highly validated interatomic potential of copper [ 3]. 2. Computational method Atomic reflection and resputtering during atom impacts with low index {00}, {0} and {} copper surfaces have been studied. The computational crystals and the MD scheme used for the simulations of single atom impacts with crystal surfaces are identical to those reported previously [8]. The geometry of the crystals and the basic directions and angles are schematically shown in Fig.. As in the previous work, periodic boundary conditions were used along the x- and z-directions. Atoms within d of the bottom surface were fixed 0 at the equilibrium positions of the bulk crystal, the region d (identified by the darker atoms in T Fig. ) was kept at a fixed substrate temperature, while the atoms above the thermostatically controlled volume were left free. The impact process was simulated by using molecular dynamics to calculate the positions and velocities of atoms for 2 ps following the arrival of a copper adatom at the cut-off distance of the interatomic potential above the crystal surface. The copper adatom was assigned an initial speed corresponding to a far-field incident kinetic energy, E, and an incident direction. The initial i direction of the impacting copper atom was constrained to lie in the x y plane and could therefore be defined by a single incident angle, h, Fig.. The trajectories of the reflected or resputtered atoms are generally not confined to the x y plane, and hence two angles, h and h, were used to specify 2 their directions. 50 MD runs were performed for each condition to obtain a reliable estimate of the Fig.. Schematic geometry of the computational crystal and definitions of directions and angles.

4 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Fig. 2. Trajectories of reflected and resputtered atoms during a 50.0 ev adatom impact. Adatom, resputtered atom, and other atoms are marked by dark, grey and light balls, respectively: (a) reflection at an incident angle of 70 ; (b) resputtering at an incident angle of 45. To investigate the basic mechanisms responsible for hyperthermal atomic reflection and resputter- ing, time resolved results for a 50.0 ev atom impact with a {00} copper surface at impact angles (h) of 70 and 45 are shown in Fig. 2a and b, respectively. In Fig. 2, the adatoms (the reflected atom reflection probability and resputtering yield (the number of resputtered atoms per adatom impact), and to permit analysis of the angular and energy distributions of the ejected atoms. Incident energies ranging from 0 to 50.0 ev and incident angles ranging from 0 to 90 were investigated. All the simulations were conducted with a fixed substrate temperature of 300 K. 3. Time resolved impacts

5 62 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) is also the adatom), the resputtered atom, and velocity component normal the surface, reflection other crystal atoms are marked with black, grey is most significant for oblique angles of incidence. and lightly shaded balls, respectively. The crystals At oblique angles of incidence, the adatom s velocity are displayed by atomic positions at the time of component parallel to the surface remains large impact, and the trajectories of the incident, with respect to its velocity component normal to reflected and resputtered atoms are revealed by the surface after impact, and as a result, the marking their positions at time steps of either reflection angle is large and the atom was often 0.05 ps (for reflection) or 0. ps (for resputtering). seen to be reflected in an almost specular manner. 3.. Reflection 3.2. Resputtering Fig. 2a shows the reflection of a 50.0 ev hyperthermal atom impacting a surface at an oblique angle of incidence (h=70 ). It can be seen that the reflection occurred with only a small penetration of the adatom into the surface. The reflected atom retained about 60% of its incident energy. It was reflected with an angle (h ) of about 73. The reflection angle was therefore close to the incident angle. About 40% of the incident energy was transferred to the lattice. This transferred energy was partitioned amongst the vibration modes of the lattice near the impact site and caused a thermal spike near the impact site similar to that previously observed and analyzed [8]. During an atom impact with a surface, the incident atom is subject to force components normal and parallel to the surface. For a successful atom reflection, the incident atom must reverse its velocity component normal to the surface. For impacts with a low normal velocity component (e.g. h=70 ), recoil forces are able to rapidly reverse this velocity component during the impact and, as indicated above, a moderate fraction of the impact energy was transferred to the crystal. As the velocity component normal to the surface increases (i.e. as h0 ), the incident atom penetrates into the surface more, and velocity reversion is only achieved after multiple collisions. This results in more energy transfer to the crystal. For an atom to completely escape from a surface after impact, its initial energy must be higher than the sum of the surface binding energy E (E b b ranges from 2.5 to 3.5 ev for different crystallographic surfaces of copper [8]), and the energy E dissipated by energy transfer. Since a decrease a of E can be achieved by increasing the adatom s a in-plane velocity component and/or decreasing its Fig. 2b shows a 50.0 ev hyperthermal atom impacting a surface at an incident angle of 45. In this case, the impacting atom fully penetrated the crystal surface and eventually occupied one of the surface lattice sites. This process caused a large transient lattice distortion and energy transfer to neighboring atoms. While the initial momentum of the incident atom pointed into the crystal, some of the nearby surface atoms achieved significant momentum out of the surface due to multiple collisions. Fig. 2b shows that one of these surface atoms was ejected at an angle near 45 to the surface normal, and a resputtering event occurred. In Fig. 2b it can be seen that the spacing between two consecutive snapshots of the resputtered atom is much shorter than that of the incident adatom, indicating that the resputtered atom had a much lower velocity, or energy (about 4.9 ev for the collision shown in the figure) than that of the incident atom. The observations above indicate that a successful resputtering event requires sufficient energy and momentum transfer to a lattice atom for it to overcome the binding force in a direction out of the crystal surface. Energy transfer is more likely for lower incident angles since the impacting atom can then more easily penetrate the crystal. However, as the incident angle falls toward zero, the velocity component of the first knock-on sur- face atoms more directly points into the crystal, which is less favorable for escape and thus resput- tering. The trade-off between energy transfer and momentum vector conversion results in a resput- tering yield peak at an intermediate incident angle. The large difference in both the energies and angles of the reflected and resputtered atoms are likely to result in different effects on film growth.

6 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Reflection and resputtering are therefore separately analyzed and parameterized. 4. Atomic reflection 4.. Reflection probability MD simulations of a copper atom impact with the {00}, {0} and {} surfaces of copper crystal were conducted for incident angles between 0 and 90, and for incident energies between 0.0 and 50.0 ev. Impact results of the type shown in Fig. 2a were analyzed to determine the reflection probability. Results for the three surfaces as a function of incident angle at a fixed (high) incident energy of 50.0 ev are given in Fig. 3. For the reasons discussed above, the reflection probability is seen to be negligible at low incident angles, but becomes much more significant as the incident angle approaches 60. The reflection probability was close to unity between 65 and 80, and then decreased at incident angles above 80. Similar Suppose the adatom arrival rate is uniform across a surface. The local growth rate then scales with the adatom s sticking probability, Y. st Sticking is related to adatom reflection, Y = Y, where Y is the adatom s reflection s rf rf probability. In some cases (e.g. deposition into a trench), the reflected atoms are sometimes depos- ited again. The positions where these reflected atoms redeposit are determined by the reflected angles and the film geometry. Depending on the energy and propagation direction, the redeposition of the reflected atoms may induce athermal and/or biased diffusion [8]. The reflected atoms retain a high energy, and they can also cause a second reflection and/or resputtering event. These processes can significantly affect the evolution of a thin film s surface morphology and microstruc- ture. It is therefore important to characterize the incident energy and incident angle dependence of reflection probability, as well as the angular and energy distributions of the reflected atoms for the range of energies and angles encountered in vapor deposition processes. Fig. 3. Reflection probability as a function of incident angle at a fixed incident energy of 50.0 ev. reflection probability verses incident angle trends were observed at lower incident energies. Since a maximum reflection probability occurred at incident angles between about 65 and 80, a fixed incident angle of 80 was selected to illustrate the dependence of the reflection prob- ability upon incident energy, Fig. 4. Fig. 4 shows that the reflection probability was close to zero for incident energies less than a threshold value, E, ic of about 0 ev. As the incident energy increased from 0 ev, the reflection probability rapidly increased. The results shown in Figs. 3 and 4 indicate that the reflection probability was rela- tively insensitive to the crystallographic type of surface. The reflection was significant for impacts with oblique angles. However, the reflection probability Fig. 4. Reflection probability as a function of incident energy at a fixed incident angle of 80.

7 64 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) decreased rapidly as the incident angle was atom s reflected angle. However, the average angle increased beyond 80. Examination of simulations of the reflection depends on the incident energy, indicated that incoming atoms that propagated the incident angle of the incoming atom, and the almost parallel to the surface interacted with the surface type. MD data were therefore analyzed to surface weakly, and their velocity component par- deduce normalized probability density distribuallel to the surface could not be converted into a tions for both h and h (see Fig. ) in terms of direction for escape. As a result, adatoms would 2 incident energies, incident angles and types of gradually shed their energy to the crystal and surface. It was found that the surface type had many were eventually captured by the surface. only a minor effect on the angular distribution of To parameterize the incident angle dependence reflected atoms, and so only results obtained for of the reflection probability shown in Fig. 3, two the {00} surface are shown. angles, h and h, are introduced. h represents the c m c Examples of the h distribution for reflected threshold incident angle at which the reflection atoms following impact at an energy of 50.0 ev probability starts to rise. h is the incident angle m and different incident angles of 65 and 75 are at which the reflection probability is a maximum. shown in Fig. 5a. Examples of the h reflection The probability of reflection from a general flat distribution at an incident angle of 80 and surface as a function of incident angle h at an different energies of 30.0 and 50.0 ev are shown incident energy of 50.0 ev was then fitted by an in Fig. 5b. The h distribution and its dependence appropriate equation and the result is listed as Eq. 2 on the incident angle are shown in Fig. 6. Figs. 5 () in Table. The curve of Eq. () is also shown and 6 clearly indicate that the h distribution in Fig. 3. peaked at a reflected angle approximately equal to Based on the observation that the reflection the incident angle h, while the h distribution fell probability approached unity at large incident 2 within a fairly narrow range between ±40, with energies, the reflection probability for a flat surface a sharp peak at about 0. These results indicate as a function of incident energy, E, at a constant i that reflection often occurred in a near specular incident angle of 80 was fitted and the result is manner. The reflected atoms were strongly forward listed as Eq. (2) in Table. In order for Eq. (2) directed with small lateral spreading (no backward to be consistent with Eq. ( ), the relation scattering), consistent with a usually modest inelas- Y (h=80 )=Y (E =50 ev ) was used to determine rf rf i the parameters. The line corresponding to Eq. (2) tic interaction with the substrate. is included in Fig. 4. Examination of Fig. 5b indicates that increasing The similar shape of the reflection probability the incident energy at a fixed incident angle shifted vs. incident angle curves for various incident enerenergy of the adatom was increased, its velocity the h distribution to higher angles. As the incident gies enables the incident angle and energy depencomponents both normal and parallel to the surdent reflection probability, Y (h, E ), to be rf i approximated by multiplying Y (h), defined by face increased. Because a larger fraction of the rf Eq. (), with Y (E ), given by Eq. (2), and normalnent was transformed during the reflection, energy associated with the normal velocity comporf i izing the result at E =50 ev. Y (h, E ) defined in i rf i this way is listed as Eq. (3) in Table. Since the increasing the incident energy increased the relation Y (h=80 )=Y (E =50 ev ) has been concated that in general, h could be described as reflected angle. Careful analysis of the data indi- rf rf i sidered in fitting Eqs. () and (2), Eq. (3) returns to Eq. () at E =50 ev and to Eq. (2) at h=80. distributed in a range between h and 90, with a i L peak at an angle h. Both h and h depend on p L P 4.2. Angular distribution of reflected atoms the incident energy and the incident angle. An incident angle and energy dependent h probability Variations in the exact impact point within a density function for reflected atoms was conunit cell and the stochastic nature of lattice vibration result in statistical variation of the incident fitted function is listed as Eq. (4) in Table. structed based on the values of h and h. The L p The

8 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Table Best fit equations for reflection probability, and angular and energy distribution of reflected atoms Equations Parameters () Reflection probability as a function of h at E i =50.0 ev: h c =22.0, h m =72.0, p=0.59, and l=.70 Y rf (h)=min G, p+p sin C A h h c h m h c B l DH, h h c (2) Reflection probability as a function of E i at h=80 : E ic =0.0 ev, p=25.4, and l=2.42 Y rf (E i )=.0 exp C A E i E ic p B l D, E i E ic (3) Reflection probability as a function of incident angle and incident energy: Y (E ) Y (E, h)=y (h) rf i rf i rf Y (E =50 ev) rf i (4) h distribution of reflected atoms as a function p =normalization (integral of r equals ) factor, n of incident angle and energy: and b=.62 r(h )=p n (h h L )a(90.0 h )b, where: a= b(h p h L ) 90.0 h p h h L h =max h+5.0 L A0.0, E2 i B h p =min A90.0, h+ 3.2(E i E i 40.0 ) E i E i B (5) h distribution of reflected atoms as a function of incident angle: c= r(h )=p exp( ch4h2) 2 n 2 (6) Energy distribution of reflected atoms as a function of incident c=.0, E = 3.06, h =47.0, b=.65 for the {00} and 0 0 angle and energy: {} surfaces; and c=.04, E = 2.76, 0 h =47.5, b=.5 for the {0} surface r(e)=p Ea(E E)b 0 n i where: a= be p E i E p E p =max G5, (ce i +E 0 ) sin C 90.0(h h 0 ) 90.0 h 0 DH

9 66 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Fig. 5. h probability density of reflected atoms: (a) incident angle effect; (b) incident energy effect. curves calculated using Eq. (4) are also included in Fig. 5a and b. Because the change of the velocity component parallel to the surface is small, the reflected atoms are expected to be strongly forward directed with a h 2 distribution peaking sharply at 0. Decreasing the incident angle led to a broader h 2 distribution, Fig. 6. The calculations revealed that the breadth of the h 2 distribution was insensitive to the incident energy. With incident energy and surface type effects ignored, the h 2 distribution and its incident angle dependence can be well described by an exponential expression listed as Eq. (5) in Table. The curves corresponding to Eq. (5) are included in Fig Energy distribution of reflected atoms The effects of incident angle and incident energy on the energy distribution of the atoms reflected from a {00} surface are shown in Fig. 7a and b. The energy spectra in Fig. 7a were obtained using a single incident energy of 50.0 ev and different incident angles of 65 and 85. Fig. 7a also shows the energy loss. It indicates that the most probable energy loss was about 0 ev at 85, but it rose to about 25 ev near 65. This rise occurred because at lower incident angles, the adatoms had higher normal velocity components and so they pene- trated into the surface more. This induced more multiple collisions and energy transfer. The energy spectra in Fig. 7b were obtained at a single incident angle of 80 and different incident energies of 30.0, 40.0 and 50.0 ev. In this case the energy loss was about 0 ev for all three different incident energies. Because the most probable energy loss decreased with incident angle, Fig.7 indicates that the reflected energy increased with both incident energy and incident angle. Similar energy distribution spectra were observed for the atoms reflected from the {} and {0} surfaces. The energy spectrum of reflected atoms exhibited a peak at an incident angle and incident energy dependent energy, E p, between 0 and E i. The energy distribution of the reflected atoms was fitted to an equation and the result is listed as Eq. (6) in Table. The corresponding curves calculated Fig. 6. h 2 probability density of reflected atoms. from Eq. (6) are also given in Fig. 7.

10 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) energy and angle of the resputtered atoms at the site of redeposition determine the extent of impact induced (athermal and biased) diffusion [8]. To better understand the effects of resputtering on thin film morphology and microstructure, it is necessary to characterize the conditions under which resputtering occurs, and to establish the resputtering yield, the angular and the energy probability density distribution of the resputtered atoms, all as a function of the angle and energy of the incident atom. 5.. Resputtering yield Fig. 7. Energy probability density of reflected atoms from the {00} surface: (a) incident angle effect; (b) incident energy effect. Fig. 2b shows a resputtering event that resulted in the emission of one atom (i.e. a resputtering yield of unity). The resputtering yields from flat {00}, {0} and {} copper surfaces were calculated, and are shown in Fig. 8 as a function of incident angle for a fixed incident energy of 50.0 ev. As discussed above, resputtering was most significant when the incident angle was in the range of about This is consistent with experimental measurements and observations of sputter etched facets on metal surfaces which are often about 45 to the incident direction [22]. The resputtering yields for the {00} and {0} type surfaces were found to be similar, but that for the {} surface was always lower. Fig. 8 indicates that the peak yield from a {} surface was about half that of either the {00} or {0} surface. Fig. 9 shows the calculated resputtering yield as 5. Atomic resputtering Energetic vapor deposition processes such as bias sputter and ion beam deposition all involve atomic impacts with sufficient energy to cause significant sputtering of already deposited materials. In contrast to atomic reflection, resputtering events often occur after multiple collisions of the adatom with the crystal and extensive energy transfer. As a result, the resputtered atoms are likely to possess lower energies and a broader range of ejection angles than those of the reflected atoms. The ejection angles determine where the resputtered atoms are redeposited. The incident Fig. 8. Resputtering yield as a function of incident angle at a fixed incident energy of 50.0 ev.

11 68 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Fig. 9. Resputtering yield as a function of incident energy at a fixed incident angle of 40. angle, h, a sinusoidal function was used to fit the m resputtering yield data. The fitted result for a fixed incident energy of 50.0 ev is listed as Eq. (7) in Table 2. Since Fig. 8 shows virtually no resputtering at high incident angles, a higher bound on h is defined in Eq. (7). The calculated curves with Eq. (7) are also displayed in Fig. 8. Fig. 2b indicates that the bombarding atom penetrated into the surface during a sputtering event. The value of the resputtering yield at very high incident energy is therefore likely to be bounded because when the impacting atom deeply penetrates into the solid, it transfers its energy to the bulk atoms rather than a greater number of near surface atoms that could then be rejected. To a good approximation, the resputtering yield as a function of incident energy can be represented by a function with a near zero slope at large incident energies. In view of this constraint, the resputtering yield was fitted as a function of incident energy at a fixed incident angle of 40, and the result of this fitting is shown as Eq. (8) in Table 2. In order for Eq. (8) to be consistent with Eq. (7), the relation Y (h=40 )=Y (E =50 ev ) was used for deter- rs rs i mining the parameters. The curves defined by Eq. (8) are also given in Fig. 9. Following the same procedure described above, an approximate equa- a function of incident energy for an incident angle of 40 (close to the maximum probability for resputtering). A threshold energy was required for resputtering. This threshold energy is about 7 ev for the {00} and {0} surfaces and near 20 ev for the {} surface. It can be seen from Fig. 9 that resputtering yield rapidly increased with incident energy above the threshold value. These findings are generally consistent with the experimental results for low energy inert ion sputtering [2]. The existence of a high threshold energy for tion for the resputtering yield as a function of resputtering is consistent with the need to transfer both incident angle and incident energy is listed as sufficient energy to a surface atom for it to escape Eq. (9) in Table 2. the surface. The energy transferred to the atom to be resputtered must therefore be sufficient to over Angular distribution of resputtered atoms come its binding energy (i.e. the latent heat of vaporization) to the surface. Molecular statics The locations where the resputtered atoms calculations were carried out and the results indicated that the binding energies of copper atoms to lar probability density functions for the resputtered eventually redeposit can be determined from angu- a flat {00}, {0} and {} copper surface are atoms. The MD data were therefore analyzed to 4.2, 3.79, and 4.24 ev, respectively. The higher determine the (h and h ) distributions for the 2 threshold energy and lower resputtering yield of resputtered atoms for various incident energies, the {} surface is therefore consistent with its incident angles and surface types. To illustrate, higher binding energy. It should be noted that in the h and h probability density functions are 2 addition to the binding energy of the surface, the plotted in Figs. 0 and for the atoms resputtered energy threshold and sputtering yield are also from the {00} surface at an incident energy of dependent on the efficiency with which a single 50.0 ev and an incident angle of 30. surface atom can acquire sufficient momentum Fig. 0 shows that the h angular probability pointing out of the surface. density for resputtered atoms peaked at a value of Since the resputtering yield as a function of ~45. The probability density was near zero at 0 incident angle exhibited a maximum at an incident and 90. This type of distribution can be approxi-

12 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Table 2 Best fit equations for resputtering yield, and angular and energy distribution of resputtered atoms Equations Parameters (7) Resputtering yield as a function of h at E =50.0 ev: h =40.0, h = 57.5, p=0.3, and l=.6 for the {00} and i m 0 {0} surfaces; and h =35.0, h = 54., p=0.7, m 0 and l=.8 for the {} surface Y rs (h)=p+p sin Ch 0 +(90.0 h 0 ) A h h m B l D, h h ma h h 0 B /l (8) Resputtering yield as a function of E i at h=40 : p=.02, E f =36.0 and l=2.08 for the {00} and {0} surfaces; and p=0.58, E f =39.86 and l=2.35 for the {} surface Y rs (E i )=p exp C A E f E i B l D (9) Resputtering yield as a function of incident angle and incident energy: Y (E ) Y (E, h)=y (h) rs i rs i rs Y (E =50 ev) rs i (0) h distribution of resputtered atoms: c= and l= r(h )=c exp[ l(h 45.0)2] () h distribution of resputtered atoms: r = , c= and l= r(h )=r +c exp( lh2) (2) Energy distribution of resputtered atoms E =4.92 ev, a =.68, c=207.7, l= for m 0 as a function of incident energy: the {00} surface; E =6.88 ev, a =2.05, c=68.5, m 0 l= for the {0} surface; and E =4.28 ev, m r(e)=p Ea exp a a =.4, c=8.83, l= for the {} surface n A E B E 0 m where: a=a +c exp( le ) 0 i mately represented by a cosine distribution of the during the low energy impacts analyzed here, the solid angle H, which is consistent with the sputtering sputtered atoms retain some memory of the initial experiments [27]. The data for the h angular direction of the bombarding particle and the distri- distribution were fitted to a normal distribution bution becomes tilted in the forward direction. In function, listed as Eq. (0) in Table 2. The fitted a three-dimensional situation, the forward tilting curve is included in Fig. 0. is characterized by the h distribution. It can be 2 During high energy bombardment, the angular seen from Fig. that for a 50.0 ev impact at an distribution of sputtered atoms is always symmetric about the surface normal because the collision and 80, with a probability density peak at 0. incident angle of 30, h distributed between 80 2 cascade is so large that many knock-on atoms are While the majority of the resputtered atoms were involved and hence the memory of the initial preferentially ejected in the forward direction, impingement direction is lost [32]. However, integration of the distribution curve over h >90

13 70 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Energy distribution of resputtered atoms Representative energy distribution curves for incident energies of 40.0 ev and 50.0 ev and a normal angle of incidence are shown in Fig. 2a c for the {00}, {0} and {} surfaces. The effect of incident energy on the average resputtered energy is illustrated in Fig. 3 for the normal impact on the {00} surface. It can be seen that the energy of resputtered atoms peaked sharply at a value, E m, between 4 and 7 ev. Few atoms had energies of 20 ev or above. This result is similar to the experimental measurements of inert gas ion induced sputtering [32]. Increasing the impact Fig. 0. h probability density of resputtered atoms. Fig.. h 2 probability density of resputtered atoms. indicated that about 25% were emitted back along the direction of impact. These results are generally in agreement with the experimental observations [22]. For the incident energy range of significant resputtering (i.e ev ), calculations indicated that the h and h distributions were not 2 sensitive to the surface type, the incident angle, and the incident energy. The data in Fig. were best fitted by a normal distribution function, listed as Eq. () in Table 2. The curve represented by Eq. () is also shown in Fig.. Fig. 2. Energy probability density of resputtered atoms: (a) {00} surface; (b) {0} surface; (c) {} surface.

14 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) Fig. 3. Average resputtered energy as a function of incident energy for the normal impact on the {00} surface. energy slightly increased the average energy of resputtered atoms, but the position of the peak was almost unaffected. While the resputtered energy in general increased as more energy was deposited on the surface, it did not directly scale with the incident energy because the memory of the initial impact energy was increasingly attenuated by ensuing multiple collisions. Fig. 2 also indicates that the energy of resputtered atoms was lowest for the {} surface, consistent with the highest binding energy on {} surface. The energy distribution of resputtered atoms was found to be insensitive to the incident angle. The energy distribution data of resputtered atoms was fitted to an expression that gives the correct value of E and the skewed response shown m in Fig. 2. The fitted equation is listed as Eq. (2) in Table 2. The curves calculated by Eq. (2) are also plotted in Fig Incident energy effects on thin film morphology and microstructure Vapor deposition techniques such as RF diode sputtering, bias sputtering and ion beam assisted deposition are being developed for the physical vapor deposition of materials. These methods provide a metal flux whose energy can be distributed from about 0. ev to 00 ev [33]. The reflection probability and resputtering yield can therefore be significant for some of these deposition processes. Under some conditions, reflection and resputtering could significantly modify thin film microstructures and surface morphology. The reflection and resputtering results obtained above, together with those for adatom induced diffusion [8], provide a starting point for an understanding of these energetic vapor deposition processes. For example, the microstructures of DC diode sputter deposited films of various metals have been reported by Thornton as a function of substrate temperature and background argon pressure []. These results indicate that at a fixed relatively low deposition temperature T~0.5T (where T is the absolute m m melting temperature), and background argon pres- sure above 30 mtorr, the film microstructure is porous, containing voids trapped between tapered crystallites. However, the films become densely packed fibrous grains as the argon pressure is decreased from 30 to 3 mtorr. These fibrous grains develop into column grains as the argon pressure is further decreased to below 3 mtorr. In Thornton s copper deposition experiments, adatoms collided with the lower energy back- ground argon gas atoms during transportation from target to substrate. Their energy therefore decreased as the argon pressure increased. For a target substrate distance of 50 mm, direct simula- tion Monte Carlo calculations [34] indicated that as the argon pressure is increased from to 0 and then to 30 mtorr, the average incident energies of deposited atoms at the substrate drop from about 00% to 5% and then to 3% of their energies at the target. Taking the average kinetic energy of the atoms emitted at the target to be about 20 ev (some atoms may have energies sig- nificantly higher) [35], the average incident energies of adatoms at the substrate are therefore about 20, 3, and 0.6 ev for argon pressures of, 0 and 30 mtorr. The incident angles also become more isotropically distributed as the pressure increases [34]. At an incident energy of 0.6 ev, effects such as biased diffusion, reflection and resputtering are all negligible. However, the latent heat release and the additional 0.6 ev of incident energy are likely to cause a local temperature rise to more than 000 K for about 0.5 ps [8]. This can result in

15 72 X.W. Zhou, H.N.G. Wadley / Surface Science 43 (999) tion of surface morphology during trench deposition depends on the degree of reflection and resputtering, where the redeposition of the reflected or resputtered atoms occurs, and the local surface geometry, etc. Clearly, this is a complicated process to predict, but the results obtained above enable a quantitative kinetic Monte Carlo simulation of the effects of athermal and biased diffusion, the reflection and resputtering upon thin film micro- structure and surface morphology. The kinetic Monte Carlo study of the energy effects during deposition on flat and featured surfaces will be published in subsequent papers [9]. additional surface diffusion, but is not sufficient to reconstruct bulk vacancy defects or eliminate voids created during earlier deposition [8]. As a result, films deposited at 30 mtorr remained porous and contain voids. When the incident energy is increased to 3 ev, the local temperature reaches 2000 K or above [8]. This leads to significant athermal diffusion and a much higher probability for atoms to fill in vacant lattice sites. This is generally consistent with two-dimensional molecular dynamics simula- tions of nickel deposition which indicated that the vacancy concentration was greatly reduced when the incident energy was increased to about 2.0 ev [2]. As a result, vacancies and voids were reduced by reducing the argon pressure to 0 mtorr. At incident energies of 20 ev and above, biased diffusion, adatom reflection and resputtering all begin to become significant. During oblique angle impact, adatoms can skip on the surface for a distance in excess of 0.0 mm [8]. This is likely to promote a more equilibrium structure because the probability for the adatoms to find more stable sites (e.g. the sites along the edge of a ledge) is increased by skipping. In addition, the probability for adatom reflection is about 0% at an incident energy of 20 ev and an incident angle of 80, while the resputtering yield is about 3% at the same energy but an incident angle of 40. The resulting reflection and resputtering can eliminate surface asperities and promote flatter surface growth. As a result, dense column structures were seen at the lowest argon pressures or under biased deposition conditions. Reflection and resputtering can cause significant surface morphology effects during deposition of metals into trenches [6,7]. The results above indicate that reflection and resputtering are likely to retard the formation of overhangs at trench tops or to etch them away once they are formed. The strongly forward directed beam reflected from the sidewalls of the trench helps the depositing atoms reach the bottom of the trench and hence improve the filling. On the other hand, the slightly forward directed beam resputtered from the trench top is likely to be redeposited in nearby areas, promoting the pinch-off of the overhangs and consequent void formation inside the trench. The exact evolu- 7. Conclusions Molecular dynamics simulations of adatom impacts during copper deposition have been used to explore reflection and resputtering during hyper- thermal vapor deposition. Empirical equations have been obtained to describe the reflection prob- ability, the angular and energy distribution of the reflected atoms, the resputtering yield, and the angular and energy distribution of the resputtered atoms as functions of incident angle, incident energy and surface type. The results indicate the following.. Reflection only occurs when the incident energy is above about 0 ev. Above this threshold, the reflection probability increases with incident energy and incident angle (up to 80 ). 2. Reflected atoms are strongly forward directed, and retain a majority of their initial incident energy. 3. Resputtering occurs for incident energies above about 5 ev. The resputtering yield increases with incident energy and exhibits a peak for intermediate angles of impact. 4. Resputtered atoms are slightly forward directed with an energy distribution that peaks between 4 and 7 ev. The average energy of resputtered atoms has a weak dependence upon incident energy. Acknowledgements We are grateful to the Defence Advanced Research Projects Agency (A. Tsao, Program

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