Hyperthermal vapor deposition of copper: reﬂection and ... · 62 X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73 is also the adatom), the resputtered atom, and velocity

Surface Science 431 (1999) 58–73www.elsevier.nl/locate/susc

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 1998; accepted for publication 2 February 1999

Abstract

Three-dimensional molecular dynamics simulations of hyperthermal copper atom impacts with copper surfaceshave been used to investigate the effects of incident atom energy upon atomic reflection and resputtering duringphysical vapor deposition. No reflection or resputtering has been observed for incident energies below 10 eV. However,as the incident energy was increased to 20 eV and above, the likelihood of both adatom reflection and sputtering ofpredeposited atoms rapidly increased. The probability of reflection increased with the angle of incidence and wasgreatest for oblique (glancing) angle impacts. The reflected adatoms were strongly forward scattered and retained alarge fraction of their initial incident energies. The resputtering yield was highest for incident angles around 40° tothe surface normal. The resputtered atoms were typically ejected with significantly smaller energies than those of theincident atoms, and were preferentially ejected in the forward direction with a maximum probability at an angle ofabout 45° to the surface normal. These results have been compared with the published experimental data for lowenergy ion impact. The dependence of the reflection probability, the resputtering yield, as well as the angular andenergy distributions of both reflected and resputtered atoms upon the adatom’s incident energy and angle have beenobtained and fitted to simple relations suitable for incorporation in models of vapor deposition. © 1999 ElsevierScience B.V. All rights reserved.

Keywords: Atom–solid interactions; Copper; Growth; Metallic films; Models of surface kinetics; Molecular dynamics; Sputtering;Sticking

1. Introduction adatom skipping across the growth surface in theimpact direction leading to biased adatom diffu-sion; (iii) adatom reflection; and (iv) adatomThe morphology and microstructure of physicalinduced resputtering [7–17]. A detailed under-vapor deposited (PVD) materials can be signifi-standing of these mechanisms and their depen-cantly modified by changing the incident energydence upon incident energy and angle is aof the depositing atoms [1–7]. The atomistic mech-precursor in unraveling the complex dependenceanisms responsible for these incident energy effectsof film morphology and microstructure upon PVDare thought to include: (i) local transient surfaceprocess conditions. Predictive models that incorpo-heating which induces athermal diffusion; (ii)rate the effects of incident energy and angle uponthe morphology and microstructure of films mighteventually aid the design of improved vapor depos-* Corresponding author. Fax: +1-804-982-5677.

E-mail address: [email protected] (H.N.G. Wadley) ition techniques.

0039-6028/99/$ – see front matter © 1999 Elsevier Science B.V. All rights reserved.PII: S0039-6028 ( 99 ) 00336-2

59X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73

An atom impact model based upon a three- the trench walls. Since these processes only occurfor energetic atom impacts, interest has grown indimensional molecular dynamics (MD) analysis

has recently been developed and used to investigate the use of high incident energy deposition tech-niques such as bias sputter deposition [7–10,20]impact atom induced diffusional processes during

the deposition of hyperthermal atoms [18]. This or thermal evaporation with sputter etching [11].The sputtering of metals by atomic bombard-impact model used an embedded atom method

(EAM) potential to calculate the interaction forces ment of their surface has been widely investigatedusing various experimental approaches [21]. Thebetween metal atoms during impacts. It was used

to analyze the local surface heating responsible for focus of much of the work has been the sputteringof metal targets by high energy (~1–10 keV ) inertathermal diffusion and the momentum effects that

caused biased diffusion of adatoms. The results gas ions in order to investigate the process thatare normally used to create a metal atom flux forindicated that the local transient heating induced

by a hyperthermal adatom impact is often sufficient subsequent deposition [21]. Recently, Doughtyet al. at Oak Ridge National Laboratory haveto activate atomic diffusion and the reconstruction

of locally defective structures. They also revealed measured the angular distribution of copper atomsejected by helium, argon and xenon ions incidentthat long-range adatom biased diffusion readily

occurs. The bias diffusion distances sometimes on copper surface at incident angles of 30, 45, and60° with low incident energies of 40, 160 andexceed 100 A, especially when incident energies are

above ~20 eV and incident angles are above 70°. 600 eV [22]. The sputtering yields of silicon surfaceby low energy (25–200 eV ) argon ion bombard-As a result, increasing the incident energy is

expected to reduce the defect concentrations and ment were calculated by Kubota et al. [23]. Whilethese data are useful for assessing some aspects ofto promote a flatter surface morphology for thin

films deposited under kinetically limited conditions low energy impacts, they are inadequate for aquantitative analysis of the contribution of reflec-(i.e. at low temperatures or high deposition rates).

Both the impact induced local heating and the tion and resputtering to hyperthermal metal atom(or metal ion) deposition. These processes remainbiased diffusion results were fitted to empirical

equations, simplifying their incorporation in the poorly characterized and are only superficiallyunderstood.various modeling schemes utilized for the simula-

tion of vapor deposition [19]. Atomistic modeling provides an alternativeapproach to the study of atom impact processes.Experimental studies have shown that hyperth-

ermal adatoms with incident energies of 20 eV or At high incident energies, sputtering has beenreasonably simulated using a Monte Carlo methodabove can also be reflected and/or induce sputter-

ing of predeposited atoms (resputtering) [6 ]. These based upon a binary atomic collision approxima-tion [24]. However, at the lower incident energiesreflection and resputtering processes can have

important consequences for the manufacture of of interest here, many-body collision effectsbecome important, and the binary collisionthin films and the metal interconnects used in

large-scale integrated circuits [7]. To increase the approximation fails. Collisions must therefore besimulated using methods that better account fordevice density, narrow conductive lines are used

for interconnecting individual devices. As a result, the many-body nature of the interaction. In amolecular dynamics simulation, the trajectories ofmetals must be deposited into deep narrow (i.e.

high aspect ratio) trenches. However, when the atoms within the interaction field of all the otheratoms can be traced by solving Newton’s equationaspect ratio is high, the deposit often covers the

trench opening before fully filling it. This results of motion using a predefined interatomic potential.If electronic excitation and chemical reactionin large voids becoming trapped within the

interconnect, and the premature failure of the effects can be ignored, the MD method provides atractable approach to the analysis of an adatom–device [6,7]. Reflection and resputtering may be

able to retard the formation of overhangs at the substrate impact process. MD simulations havebeen extensively used to investigate the ion sputter-trench top and promote more even coverage of

60 X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73

ing of metals [25]. The reflection of a 40 eV silicon surfaces are identical to those reported previously[18]. The geometry of the crystals and the basicatom from a (111) silicon surface at an incident

angle of 12° has been simulated using MD [16,17], directions and angles are schematically shown inFig. 1. As in the previous work, periodic boundarybut no work has sought to establish a detailed

understanding of the adatom reflection and resput- conditions were used along the x- and z-directions.Atoms within d0 of the bottom surface were fixedtering mechanisms that are active during depos-

ition of hyperthermal atoms. at the equilibrium positions of the bulk crystal,the region dT (identified by the darker atoms inHere, a MD vapor atom impact model devel-

oped earlier to analyze impact induced diffusion Fig. 1) was kept at a fixed substrate temperature,while the atoms above the thermostatically con-[18] was extended to investigate atomic reflection

and resputtering as a function of the incident trolled volume were left free.The impact process was simulated by usingenergy and angle of the depositing atoms. The

work concentrates on the reflection and resputter- molecular dynamics to calculate the positions andvelocities of atoms for 2 ps following the arrivaling of copper from a copper surface because of

the importance of copper in integrated circuits of a copper adatom at the cut-off distance of theinteratomic potential above the crystal surface.[26 ], its widespread use in GMR devices [27–30],

and the availability of a highly validated intera- The copper adatom was assigned an initial speedcorresponding to a far-field ‘incident’ kinetictomic potential of copper [31].energy, Ei, and an incident direction. The initialdirection of the impacting copper atom was con-strained to lie in the x–y plane and could therefore2. Computational methodbe defined by a single incident angle, h, Fig. 1. Thetrajectories of the reflected or resputtered atomsAtomic reflection and resputtering during atom

impacts with low index {100}, {110} and {111} are generally not confined to the x–y plane, andhence two angles, h1 and h2, were used to specifycopper surfaces have been studied. The computa-

tional crystals and the MD scheme used for the their directions. 50 MD runs were performed foreach condition to obtain a reliable estimate of thesimulations of single atom impacts with crystal

Fig. 1. Schematic geometry of the computational crystal and definitions of directions and angles.


Fig. 2. Trajectories of reflected and resputtered atoms during a 50.0 eV adatom impact. Adatom, resputtered atom, and other atomsare marked by dark, grey and light balls, respectively: (a) reflection at an incident angle of 70°; (b) resputtering at an incident angleof 45°.

reflection probability and resputtering yield (the 3. Time resolved impactsnumber of resputtered atoms per adatom impact),and to permit analysis of the angular and energy To investigate the basic mechanisms responsible

for hyperthermal atomic reflection and resputter-distributions of the ejected atoms. Incident energiesranging from 0 to 50.0 eV and incident angles ing, time resolved results for a 50.0 eV atom impact

with a {100} copper surface at impact angles (h)ranging from 0 to 90° were investigated. All thesimulations were conducted with a fixed substrate of 70° and 45° are shown in Fig. 2a and b, respec-

tively. In Fig. 2, the adatoms (the reflected atomtemperature of 300 K.


is also the adatom), the resputtered atom, and velocity component normal the surface, reflectionis most significant for oblique angles of incidence.other crystal atoms are marked with black, grey

and lightly shaded balls, respectively. The crystals At oblique angles of incidence, the adatom’s veloc-ity component parallel to the surface remains largeare displayed by atomic positions at the time of

impact, and the trajectories of the incident, with respect to its velocity component normal tothe surface after impact, and as a result, thereflected and resputtered atoms are revealed by

marking their positions at time steps of either reflection angle is large and the atom was oftenseen to be reflected in an almost specular manner.0.05 ps (for reflection) or 0.1 ps (for resputtering).

3.1. Reflection 3.2. Resputtering

Fig. 2b shows a 50.0 eV hyperthermal atomFig. 2a shows the reflection of a 50.0 eV hyper-thermal atom impacting a surface at an oblique impacting a surface at an incident angle of 45°. In

this case, the impacting atom fully penetrated theangle of incidence (h=70°). It can be seen that thereflection occurred with only a small penetration crystal surface and eventually occupied one of the

surface lattice sites. This process caused a largeof the adatom into the surface. The reflected atomretained about 60% of its incident energy. It was transient lattice distortion and energy transfer to

neighboring atoms. While the initial momentumreflected with an angle (h1) of about 73°. Thereflection angle was therefore close to the incident of the incident atom pointed into the crystal, some

of the nearby surface atoms achieved significantangle. About 40% of the incident energy wastransferred to the lattice. This transferred energy momentum out of the surface due to multiple

collisions. Fig. 2b shows that one of these surfacewas partitioned amongst the vibration modes ofthe lattice near the impact site and caused a atoms was ejected at an angle near 45° to the

surface normal, and a resputtering event occurred.thermal spike near the impact site similar to thatpreviously observed and analyzed [18]. In Fig. 2b it can be seen that the spacing between

two ‘consecutive’ snapshots of the resputteredDuring an atom impact with a surface, theincident atom is subject to force components atom is much shorter than that of the incident

adatom, indicating that the resputtered atom hadnormal and parallel to the surface. For a successfulatom reflection, the incident atom must reverse its a much lower velocity, or energy (about 4.9 eV for

the collision shown in the figure) than that of thevelocity component normal to the surface. Forimpacts with a low normal velocity component incident atom.

The observations above indicate that a success-(e.g. h=70°), recoil forces are able to rapidlyreverse this velocity component during the impact ful resputtering event requires sufficient energy and

momentum transfer to a lattice atom for it toand, as indicated above, a moderate fraction ofthe impact energy was transferred to the crystal. overcome the binding force in a direction out of

the crystal surface. Energy transfer is more likelyAs the velocity component normal to the surfaceincreases (i.e. as h�0°), the incident atom penet- for lower incident angles since the impacting atom

can then more easily penetrate the crystal.rates into the surface more, and velocity reversionis only achieved after multiple collisions. This However, as the incident angle falls toward zero,

the velocity component of the first knock-on sur-results in more energy transfer to the crystal.For an atom to completely escape from a surface face atoms more directly points into the crystal,

which is less favorable for escape and thus resput-after impact, its initial energy must be higher thanthe sum of the surface binding energy Eb (Eb tering. The trade-off between energy transfer and

momentum vector conversion results in a resput-ranges from 2.5 to 3.5 eV for different crystallo-graphic surfaces of copper [18]), and the energy tering yield peak at an intermediate incident angle.

The large difference in both the energies andEa dissipated by energy transfer. Since a decreaseof Ea can be achieved by increasing the adatom’s angles of the reflected and resputtered atoms are

likely to result in different effects on film growth.in-plane velocity component and/or decreasing its


Reflection and resputtering are therefore separatelyanalyzed and parameterized.

4. Atomic reflection

Suppose the adatom arrival rate is uniformacross a surface. The local growth rate then scaleswith the adatom’s sticking probability, Yst.Sticking is related to adatom reflection,Ys=1−Yrf, where Yrf is the adatom’s reflectionprobability. In some cases (e.g. deposition into a

Fig. 3. Reflection probability as a function of incident angle attrench), the reflected atoms are sometimes depos-a fixed incident energy of 50.0 eV.ited again. The positions where these reflected

atoms redeposit are determined by the reflectedreflection probability verses incident angle trendsangles and the film geometry. Depending on thewere observed at lower incident energies.energy and propagation direction, the redeposition

Since a maximum reflection probabilityof the ‘reflected’ atoms may induce athermaloccurred at incident angles between about 65 andand/or biased diffusion [18]. The ‘reflected’ atoms80°, a fixed incident angle of 80° was selected toretain a high energy, and they can also cause aillustrate the dependence of the reflection prob-second reflection and/or resputtering event. Theseability upon incident energy, Fig. 4. Fig. 4 showsprocesses can significantly affect the evolution ofthat the reflection probability was close to zero fora thin film’s surface morphology and microstruc-incident energies less than a threshold value, Eic,ture. It is therefore important to characterize theof about 10 eV. As the incident energy increasedincident energy and incident angle dependence offrom 10 eV, the reflection probability rapidlyreflection probability, as well as the angular andincreased. The results shown in Figs. 3 and 4energy distributions of the reflected atoms for theindicate that the reflection probability was rela-range of energies and angles encountered in vaportively insensitive to the crystallographic type ofdeposition processes.surface.

The reflection was significant for impacts with4.1. Reflection probability oblique angles. However, the reflection probability

MD simulations of a copper atom impact withthe {100}, {110} and {111} surfaces of coppercrystal were conducted for incident angles between0 and 90°, and for incident energies between 0.0and 50.0 eV. Impact results of the type shown inFig. 2a were analyzed to determine the reflectionprobability. Results for the three surfaces as afunction of incident angle at a fixed (high) incidentenergy of 50.0 eV are given in Fig. 3. For thereasons discussed above, the reflection probabilityis seen to be negligible at low incident angles, butbecomes much more significant as the incidentangle approaches 60°. The reflection probabilitywas close to unity between 65 and 80°, and then Fig. 4. Reflection probability as a function of incident energy

at a fixed incident angle of 80°.decreased at incident angles above 80°. Similar


decreased rapidly as the incident angle was atom’s reflected angle. However, the average angleincreased 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 thealmost parallel to the surface interacted with the surface type. MD data were therefore analyzed tosurface weakly, and their velocity component par- deduce normalized probability density distribu-allel to the surface could not be converted into a tions for both h1 and h2 (see Fig. 1) in terms ofdirection for escape. As a result, adatoms would incident energies, incident angles and types ofgradually shed their energy to the crystal and surface. It was found that the surface type hadmany 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 forof the reflection probability shown in Fig. 3, two the {100} surface are shown.angles, hc and hm, are introduced. hc represents the Examples of the h1 distribution for reflectedthreshold incident angle at which the reflection atoms following impact at an energy of 50.0 eVprobability starts to rise. hm is the incident angle and different incident angles of 65 and 75° areat which the reflection probability is a maximum. shown in Fig. 5a. Examples of the h1 reflectionThe probability of reflection from a general flat distribution at an incident angle of 80° andsurface as a function of incident angle h at an different energies of 30.0 and 50.0 eV are shownincident energy of 50.0 eV was then fitted by an in Fig. 5b. The h2 distribution and its dependenceappropriate equation and the result is listed as Eq. on the incident angle are shown in Fig. 6. Figs. 5(1) in Table 1. The curve of Eq. (1) is also shown and 6 clearly indicate that the h1 distributionin Fig. 3. peaked at a reflected angle approximately equal to

Based on the observation that the reflection the incident angle h, while the h2 distribution fellprobability approached unity at large incident within a fairly narrow range between ±40°, withenergies, the reflection probability for a flat surface a sharp peak at about 0°. These results indicateas a function of incident energy, Ei, at a constant

that reflection often occurred in a near specularincident angle of 80° was fitted and the result is

manner. The reflected atoms were strongly forwardlisted as Eq. (2) in Table 1. In order for Eq. (2)directed with small lateral spreading (no backwardto be consistent with Eq. (1), the relationscattering), consistent with a usually modest inelas-Yrf(h=80°)=Yrf(Ei=50 eV ) was used to determinetic interaction with the substrate.the parameters. The line corresponding to Eq. (2)

Examination of Fig. 5b indicates that increasingis included in Fig. 4.the incident energy at a fixed incident angle shiftedThe similar shape of the reflection probabilitythe h1 distribution to higher angles. As the incidentvs. incident angle curves for various incident ener-energy of the adatom was increased, its velocitygies enables the incident angle and energy depen-components both normal and parallel to the sur-dent reflection probability, Yrf(h, Ei), to beface increased. Because a larger fraction of theapproximated by multiplying Yrf(h), defined byenergy associated with the normal velocity compo-Eq. (1), with Yrf(Ei), given by Eq. (2), and normal-nent was transformed during the reflection,izing the result at Ei=50 eV. Yrf(h, Ei) defined inincreasing the incident energy increased thethis way is listed as Eq. (3) in Table 1. Since thereflected angle. Careful analysis of the data indi-relation Yrf(h=80°)=Yrf(Ei=50 eV ) has been con-cated that in general, h1 could be described assidered in fitting Eqs. (1) and (2), Eq. (3) returnsdistributed in a range between h1L and 90°, with ato Eq. (1) at Ei=50 eV and to Eq. (2) at h=80°.peak at an angle h1p. Both h1L and h1P depend onthe incident energy and the incident angle. An4.2. Angular distribution of reflected atomsincident angle and energy dependent h1 probabilitydensity function for reflected atoms was con-Variations in the exact impact point within astructed based on the values of h1L and h1p. Theunit cell and the stochastic nature of lattice vibra-

tion result in statistical variation of the incident fitted function is listed as Eq. (4) in Table 1. The


Table 1Best fit equations for reflection probability, and angular and energy distribution of reflected atoms

Equations Parameters

(1) Reflection probability as a function of h at Ei=50.0 eV: hc=22.0°, hm=72.0°, p=0.59, and l=1.70

Yrf(h)=minG1, p+p sinC−90.0+180.0A h−hchm−hc

BlDH, h≥hc

(2) Reflection probability as a function of Ei at h=80°: Eic=10.0 eV, p=25.4, and l=2.42

Yrf(Ei)=1.0−expC−AEi−Eicp BlD, Ei≥Eic

(3) Reflection probability as a function of incident angle andincident energy:

Yrf(Ei , h)=Yrf(h)Yrf(Ei)

Yrf(Ei=50 eV)

(4) h1 distribution of reflected atoms as a function pn=normalization (integral of r equals 1) factor,of incident angle and energy: and b=1.62

r(h1)=pn(h

1−h1L)a(90.0−h

1)b, h

1≥h1L

where:

a=b(h1p−h1L)

90.0−h1p

h1L=maxA0.0, h+5.0−6.0×104

E2iB

h1p=minA90.0, h+3.2(Ei−40.0+|Ei−40.0|)

Ei−40.0+|Ei−40.0|+2.0B(5) h2 distribution of reflected atoms as a function of incident angle: c=−1.9×10−10r(h

2)=pn exp(−ch4h2

2)

(6) Energy distribution of reflected atoms as a function of incident c=1.10, E0=−13.06, h0=47.0, b=1.65 for the {100} andangle and energy: {111} surfaces; and c=1.04, E0=−12.76,

h0=47.5, b=1.5 for the {110} surfacer(E )=pnEa(Ei−E)b

where:

a=bEp

Ei−Ep

Ep=maxG5, (cEi+E0) sinC90.0(h−h

0)

90.0−h0DH


curves calculated using Eq. (4) are also includedin Fig. 5a and b.

Because the change of the velocity componentparallel to the surface is small, the reflected atomsare expected to be strongly forward directed witha h2 distribution peaking sharply at 0°. Decreasingthe incident angle led to a broader h2 distribution,Fig. 6. The calculations revealed that the breadthof the h2 distribution was insensitive to the incidentenergy. With incident energy and surface typeeffects ignored, the h2 distribution and its incidentangle dependence can be well described by anexponential expression listed as Eq. (5) in Table 1.The curves corresponding to Eq. (5) are includedin Fig. 6.

4.3. Energy distribution of reflected atoms

The effects of incident angle and incident energyon the energy distribution of the atoms reflectedfrom a {100} surface are shown in Fig. 7a and b.The energy spectra in Fig. 7a were obtained usinga single incident energy of 50.0 eV and differentincident angles of 65 and 85°. Fig. 7a also showsthe energy loss. It indicates that the most probableenergy loss was about 10 eV at 85°, but it rose toabout 25 eV near 65°. This rise occurred becauseat lower incident angles, the adatoms had highernormal velocity components and so they pene-Fig. 5. h1 probability density of reflected atoms: (a) incident

angle effect; (b) incident energy effect. trated into the surface more. This induced moremultiple collisions and energy transfer. The energyspectra in Fig. 7b were obtained at a single incidentangle of 80° and different incident energies of 30.0,40.0 and 50.0 eV. In this case the energy loss wasabout 10 eV for all three different incident energies.Because the most probable energy loss decreasedwith incident angle, Fig.7 indicates that thereflected energy increased with both incidentenergy and incident angle. Similar energy distribu-tion spectra were observed for the atoms reflectedfrom the {111} and {110} surfaces.

The energy spectrum of reflected atoms exhib-ited a peak at an incident angle and incident energydependent energy, Ep, between 0 and Ei. Theenergy distribution of the reflected atoms was fittedto an equation and the result is listed as Eq. (6)in Table 1. The corresponding curves calculated

Fig. 6. h2 probability density of reflected atoms. from Eq. (6) are also given in Fig. 7.


energy and angle of the resputtered atoms at thesite of redeposition determine the extent of impactinduced (athermal and biased) diffusion [18]. Tobetter understand the effects of resputtering onthin film morphology and microstructure, it isnecessary to characterize the conditions underwhich resputtering occurs, and to establish theresputtering yield, the angular and the energyprobability density distribution of the resputteredatoms, all as a function of the angle and energyof the incident atom.

5.1. Resputtering yield

Fig. 2b shows a resputtering event that resultedin the emission of one atom (i.e. a resputteringyield of unity). The resputtering yields from flat{100}, {110} and {111} copper surfaces were calcu-lated, and are shown in Fig. 8 as a function ofincident angle for a fixed incident energy of50.0 eV. As discussed above, resputtering was mostsignificant when the incident angle was in the rangeof about 30–45°. This is consistent with experimen-tal measurements and observations of sputteretched facets on metal surfaces which are oftenabout 45° to the incident direction [22]. Theresputtering yields for the {100} and {110} typesurfaces were found to be similar, but that for the{111} surface was always lower. Fig. 8 indicatesthat the peak yield from a {111} surface was about

Fig. 7. Energy probability density of reflected atoms from thehalf that of either the {100} or {110} surface.{100} surface: (a) incident angle effect; (b) incident energy

Fig. 9 shows the calculated resputtering yield aseffect.

5. Atomic resputtering

Energetic vapor deposition processes such asbias sputter and ion beam deposition all involveatomic impacts with sufficient energy to causesignificant sputtering of already deposited materi-als. In contrast to atomic reflection, resputteringevents often occur after multiple collisions of theadatom with the crystal and extensive energytransfer. As a result, the resputtered atoms arelikely to possess lower energies and a broaderrange of ejection angles than those of the reflectedatoms. The ejection angles determine where the Fig. 8. Resputtering yield as a function of incident angle at a

fixed incident energy of 50.0 eV.resputtered atoms are redeposited. The incident


angle, hm, a sinusoidal function was used to fit theresputtering yield data. The fitted result for a fixedincident energy of 50.0 eV is listed as Eq. (7) inTable 2. Since Fig. 8 shows virtually no resputter-ing at high incident angles, a higher bound on his defined in Eq. (7). The calculated curves withEq. (7) are also displayed in Fig. 8.

Fig. 2b indicates that the bombarding atompenetrated into the surface during a sputteringevent. The value of the resputtering yield at veryhigh incident energy is therefore likely to bebounded because when the impacting atom deeplypenetrates into the solid, it transfers its energy tothe bulk atoms rather than a greater number ofFig. 9. Resputtering yield as a function of incident energy at anear surface atoms that could then be rejected. Tofixed incident angle of 40°.a good approximation, the resputtering yield as afunction of incident energy can be represented bya function with a near zero slope at large incidenta function of incident energy for an incident angle

of 40° (close to the maximum probability for energies. In view of this constraint, the resputteringyield was fitted as a function of incident energy atresputtering). A threshold energy was required for

resputtering. This threshold energy is about 17 eV a fixed incident angle of 40°, and the result of thisfitting is shown as Eq. (8) in Table 2. In order forfor the {100} and {110} surfaces and near 20 eV for

the {111} surface. It can be seen from Fig. 9 that Eq. (8) to be consistent with Eq. (7), the relationYrs(h=40°)=Yrs(Ei=50 eV ) was used for deter-resputtering yield rapidly increased with incident

energy above the threshold value. These findings mining the parameters. The curves defined by Eq.(8) are also given in Fig. 9. Following the sameare generally consistent with the experimental

results for low energy inert ion sputtering [21]. procedure described above, an approximate equa-tion for the resputtering yield as a function ofThe existence of a high threshold energy for

resputtering is consistent with the need to transfer both incident angle and incident energy is listed asEq. (9) in Table 2.sufficient energy to a surface atom for it to escape

the surface. The energy transferred to the atom tobe resputtered must therefore be sufficient to over- 5.2. Angular distribution of resputtered atomscome its binding energy (i.e. the latent heat ofvaporization) to the surface. Molecular statics The locations where the resputtered atoms

eventually redeposit can be determined from angu-calculations were carried out and the results indi-cated that the binding energies of copper atoms to lar probability density functions for the resputtered

atoms. The MD data were therefore analyzed toa flat {100}, {110} and {111} copper surface are4.12, 3.79, and 4.24 eV, respectively. The higher determine the (h1 and h2) distributions for the

resputtered atoms for various incident energies,threshold energy and lower resputtering yield ofthe {111} surface is therefore consistent with its incident angles and surface types. To illustrate,

the h1 and h2 probability density functions arehigher binding energy. It should be noted that inaddition to the binding energy of the surface, the plotted in Figs. 10 and 11 for the atoms resputtered

from the {100} surface at an incident energy ofenergy threshold and sputtering yield are alsodependent on the efficiency with which a single 50.0 eV and an incident angle of 30°.

Fig. 10 shows that the h1 angular probabilitysurface atom can acquire sufficient momentumpointing out of the surface. density for resputtered atoms peaked at a value of

~45°. The probability density was near zero at 0°Since the resputtering yield as a function ofincident angle exhibited a maximum at an incident and 90°. This type of distribution can be approxi-


Table 2Best fit equations for resputtering yield, and angular and energy distribution of resputtered atoms

Equations Parameters

(7) Resputtering yield as a function of h at Ei=50.0 eV: hm=40.0°, h0=−57.5°, p=0.31, and l=1.61 for the {100} and{110} surfaces; and hm=35.0°, h0=−54.1°, p=0.17,and l=1.18 for the {111} surfaceYrs(h)=p+p sinCh

0+(90.0−h

0)A h

hmBlD,

h≤hmA270.0−h0

90.0−h0B1/l

(8) Resputtering yield as a function of Ei at h=40°: p=1.02, Ef=36.0 and l=2.08 for the {100} and {110} surfaces;and p=0.58, Ef=39.86 and l=2.35 for the {111} surface

Yrs(Ei)=p expC−AEfEiBlD

(9) Resputtering yield as a function ofincident angle and incident energy:

Yrs(Ei , h)=Yrs(h)Yrs(Ei)

Yrs(Ei=50 eV)

(10) h1 distribution of resputtered atoms: c=3.0×10−2 and l=3.0×10−3r(h

1)=c exp[−l(h

1−45.0)2 ]

(11) h2 distribution of resputtered atoms: r0=7.0×10−4, c=4.3×10−3 and l=1.0×10−4r(h

2)=r

0+c exp(−lh2

2)

(12) Energy distribution of resputtered atoms Em=4.92 eV, a0=1.68, c=207.7, l=1.236×10−1 foras a function of incident energy: the {100} surface; Em=6.88 eV, a0=2.05, c=68.5,

l=9.03×10−2 for the {110} surface; and Em=4.28 eV,a0=1.41, c=8.83, l=4.06×10−2 for the {111} surfacer(E )=pnEa expA− a

EmEB

where:

a=a0+c exp(−lEi)

mately represented by a cosine distribution of the during the low energy impacts analyzed here, thesputtered atoms retain some ‘memory’ of the initialsolid angle H, which is consistent with the sputter-

ing experiments [27]. The data for the h1 angular direction of the bombarding particle and the distri-bution becomes tilted in the forward direction. Indistribution were fitted to a normal distribution

function, listed as Eq. (10) in Table 2. The fitted a three-dimensional situation, the forward tiltingis characterized by the h2 distribution. It can becurve is included in Fig. 10.

During high energy bombardment, the angular seen from Fig. 11 that for a 50.0 eV impact at anincident angle of 30°, h2 distributed between −180distribution of sputtered atoms is always symmet-

ric about the surface normal because the collision and 180°, with a probability density peak at 0°.While the majority of the resputtered atoms werecascade is so large that many knock-on atoms are

involved and hence the ‘memory’ of the initial preferentially ejected in the forward direction,integration of the distribution curve over |h|>90°impingement direction is lost [32]. However,


5.3. Energy distribution of resputtered atoms

Representative energy distribution curves forincident energies of 40.0 eV and 50.0 eV and anormal angle of incidence are shown in Fig. 12a–c for the {100}, {110} and {111} surfaces. Theeffect of incident energy on the average resputteredenergy is illustrated in Fig. 13 for the normalimpact on the {100} surface. It can be seen thatthe energy of resputtered atoms peaked sharply ata value, Em, between 4 and 7 eV. Few atoms hadenergies of 20 eV or above. This result is similarto the experimental measurements of inert gas ioninduced sputtering [32]. Increasing the impact

Fig. 10. h1 probability density of resputtered atoms.

Fig. 11. h2 probability density of resputtered atoms.

indicated that about 25% were emitted back alongthe direction of impact. These results are generallyin agreement with the experimental observations[22].

For the incident energy range of significantresputtering (i.e. 20.0–50.0 eV ), calculations indi-cated that the h1 and h2 distributions were notsensitive to the surface type, the incident angle,and the incident energy. The data in Fig. 11 werebest fitted by a normal distribution function, listedas Eq. (11) in Table 2. The curve represented by Fig. 12. Energy probability density of resputtered atoms: (a)

{100} surface; (b) {110} surface; (c) {111} surface.Eq. (11) is also shown in Fig. 11.


significant for some of these deposition processes.Under some conditions, reflection and resputteringcould significantly modify thin film microstructuresand surface morphology. The reflection andresputtering results obtained above, together withthose for adatom induced diffusion [18], providea starting point for an understanding of theseenergetic vapor deposition processes. For example,the microstructures of DC diode sputter depositedfilms of various metals have been reported byThornton as a function of substrate temperatureand background argon pressure [1]. These resultsindicate that at a fixed relatively low depositiontemperature T~0.5Tm (where Tm is the absolute

Fig. 13. Average resputtered energy as a function of incident melting temperature), and background argon pres-energy for the normal impact on the {100} surface. sure above 30 mTorr, the film microstructure is

porous, containing voids trapped between taperedcrystallites. However, the films become denselyenergy slightly increased the average energy of

resputtered atoms, but the position of the peak packed fibrous grains as the argon pressure isdecreased from 30 to 3 mTorr. These fibrous grainswas almost unaffected. While the resputtered

energy in general increased as more energy was develop into column grains as the argon pressureis further decreased to below 3 mTorr.deposited on the surface, it did not directly scale

with the incident energy because the ‘memory’ of In Thornton’s copper deposition experiments,adatoms collided with the lower energy back-the initial impact energy was increasingly attenu-

ated by ensuing multiple collisions. Fig. 12 also ground argon gas atoms during transportationfrom target to substrate. Their energy thereforeindicates that the energy of resputtered atoms was

lowest for the {111} surface, consistent with the decreased as the argon pressure increased. For atarget–substrate distance of 50 mm, direct simula-highest binding energy on {111} surface. The

energy distribution of resputtered atoms was found tion Monte Carlo calculations [34] indicated thatas the argon pressure is increased from 1 to 10to be insensitive to the incident angle.

The energy distribution data of resputtered and then to 30 mTorr, the average incident energiesof deposited atoms at the substrate drop fromatoms was fitted to an expression that gives the

correct value of Em and the skewed response shown about 100% to 15% and then to 3% of theirenergies at the target. Taking the average kineticin Fig. 12. The fitted equation is listed as Eq. (12)

in Table 2. The curves calculated by Eq. (12) are energy of the atoms emitted at the target to beabout 20 eV (some atoms may have energies sig-also plotted in Fig. 12.nificantly higher) [35], the average incident ener-gies of adatoms at the substrate are thereforeabout 20, 3, and 0.6 eV for argon pressures of 1,6. Incident energy effects on thin film morphology

and microstructure 10 and 30 mTorr. The incident angles also becomemore isotropically distributed as the pressureincreases [34].Vapor deposition techniques such as RF diode

sputtering, bias sputtering and ion beam assisted At an incident energy of 0.6 eV, effects such asbiased diffusion, reflection and resputtering are alldeposition are being developed for the physical

vapor deposition of materials. These methods pro- negligible. However, the latent heat release andthe additional 0.6 eV of incident energy are likelyvide a metal flux whose energy can be distributed

from about 0.1 eV to 100 eV [33]. The reflection to cause a local temperature rise to more than1000 K for about 0.5 ps [18]. This can result inprobability and resputtering yield can therefore be


additional surface diffusion, but is not sufficient to tion of surface morphology during trench depos-ition depends on the degree of reflection andreconstruct bulk vacancy defects or eliminate voidsresputtering, where the redeposition of the reflectedcreated during earlier deposition [18]. As a result,or resputtered atoms occurs, and the local surfacefilms deposited at 30 mTorr remained porous andgeometry, etc. Clearly, this is a complicated processcontain voids.to predict, but the results obtained above enableWhen the incident energy is increased to 3 eV,a quantitative kinetic Monte Carlo simulation ofthe local temperature reaches 2000 K or abovethe effects of athermal and biased diffusion, the[18]. This leads to significant athermal diffusionreflection and resputtering upon thin film micro-and a much higher probability for atoms to fill instructure and surface morphology. The kineticvacant lattice sites. This is generally consistentMonte Carlo study of the energy effects duringwith two-dimensional molecular dynamics simula-deposition on flat and featured surfaces will betions of nickel deposition which indicated that thepublished in subsequent papers [19].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

7. Conclusionsby reducing the argon pressure to 10 mTorr.At incident energies of 20 eV and above, biased

Molecular dynamics simulations of adatomdiffusion, adatom reflection and resputtering allimpacts during copper deposition have been usedbegin to become significant. During oblique angleto explore reflection and resputtering during hyper-impact, adatoms can skip on the surface for athermal vapor deposition. Empirical equationsdistance in excess of 0.01 mm [18]. This is likely tohave been obtained to describe the reflection prob-promote a more equilibrium structure because theability, the angular and energy distribution of theprobability for the adatoms to find more stablereflected atoms, the resputtering yield, and thesites (e.g. the sites along the edge of a ledge) isangular and energy distribution of the resputteredincreased by skipping. In addition, the probabilityatoms as functions of incident angle, incidentfor adatom reflection is about 10% at an incidentenergy and surface type. The results indicate the

energy of 20 eV and an incident angle of 80°, while following.the resputtering yield is about 3% at the same 1. Reflection only occurs when the incident energyenergy but an incident angle of 40°. The resulting is above about 10 eV. Above this threshold, thereflection and resputtering can eliminate surface reflection probability increases with incidentasperities and promote flatter surface growth. As energy and incident angle (up to 80°).a result, dense column structures were seen at the 2. Reflected atoms are strongly forward directed,lowest argon pressures or under biased deposition and retain a majority of their initial incidentconditions. energy.

Reflection and resputtering can cause significant 3. Resputtering occurs for incident energies abovesurface morphology effects during deposition of about 15 eV. The resputtering yield increasesmetals into trenches [6,7]. The results above indi- with incident energy and exhibits a peak forcate that reflection and resputtering are likely to intermediate angles of impact.retard the formation of overhangs at trench tops 4. Resputtered atoms are slightly forward directedor to etch them away once they are formed. The with an energy distribution that peaks betweenstrongly forward directed beam reflected from the 4 and 7 eV. The average energy of resputteredsidewalls of the trench helps the depositing atoms atoms has a weak dependence upon incidentreach the bottom of the trench and hence improve energy.the filling. On the other hand, the slightly forwarddirected beam resputtered from the trench top is Acknowledgementslikely to be redeposited in nearby areas, promotingthe pinch-off of the overhangs and consequent We are grateful to the Defence Advanced

Research Projects Agency (A. Tsao, Programvoid formation inside the trench. The exact evolu-


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Hyperthermal vapor deposition of copper: reﬂection and ... · 62 X.W. Zhou, H.N.G. Wadley / Surface Science 431 (1999) 58–73 is also the adatom), the resputtered atom, and velocity