monte carlo simulation of hyperthermal physical vapor deposition

Acta mater. 49 (2001) 3321–3332www.elsevier.com/locate/actamat

MONTE CARLO SIMULATION OF HYPERTHERMAL PHYSICALVAPOR DEPOSITION

Y. G. YANG, X. W. ZHOU, R. A. JOHNSON and H. N. G. WADLEY†Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22903-2442,

USA

( Received 25 July 2000; received in revised form 19 February 2001; accepted 24 February 2001 )

Abstract—Low-pressure sputtering and ionized vapor deposition processes create atomic fluxes with kineticenergies in the 1.0–20 eV (and above) range. The impact energy of these hyperthermal atoms significantlyeffects the surface morphology and structure of vapor deposited films. Recent molecular dynamics simulationsof metal atom interactions with a metal surface have established the energy and angular dependence of manyof the impact energy induced mechanisms of atomic assembly including biased diffusion, atomic reflection,resputtering, and thermal transient induced “athermal” diffusion. These four effects have been incorporatedinto an earlier two-dimensional kinetic Monte Carlo model that analyzes the thermally driven multipathdiffusional processes active during vapor deposition (Y. G. Yanget al., Acta Mater., 45 (1997) 1445). Thecontributions of the energy-dependent mechanisms to surface morphology were found to grow in importanceas the substrate temperature was reduced and/or as the rate of deposition increased. The simulation method-ology was used to establish functional dependence of surface roughness upon the atom’s kinetic energy andits direction of incidence during the hyperthermal deposition of nickel vapor. The simulations reveal theexistence of a minimum surface roughness at an incident angle which increased with impact atom kineticenergy. Modification of the impact energy is shown to be a viable means for controlling surface morphologyduring physical vapor deposition under high deposition rate, low deposition temperature growth conditions. 2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.

Keywords: Physical vapor deposition (PVD); Monte Carlo simulation; Thin films

1. INTRODUCTION

The growth of materials from the vapor phase iswidely used to create thin films and coatings [1–3].Increasingly stringent levels of film perfection areoften needed. For example, thin film devices basedupon the giant magnetoresistance (GMR) effectrequire the growth of Ni88Fe17/Cu/Ni83Fe17 planarmultilayers in which the interfacial roughness is lessthan a few angstroms and intermixing of the dissimi-lar metal layers is negligible [1–3]. Vapor depositionstrategies that achieve this microstructure exploit kin-etically limited growth mechanisms. However, thedesign of deposition processes that achieve atomicscale perfection by controlling the kinetics of filmgrowth is complicated because of the many mech-anisms that contribute to the atomic assembly process[4, 5]. Interest has therefore developed in the use ofatomistic computer simulation techniques to better

† To whom all correspondence should be addressed. Tel.:+1-804-982-5670; fax:+1-804-982-5677.

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

1359-6454/01/$20.00 2001 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.PII: S1359-6454(01 )00139-2

understand and model the atom-by-atom assembly ofthin films [4–15].

The atomic assembly events that occur in vapordeposition processes are “enabled” by both thermallyactivated atomic diffusion and hyperthermal atomimpact induced mechanisms. To realistically simulatethe growth of films under energetic conditions, amodel must address both conventional thermally acti-vated processes and the energetic impact effectsresponsible for additional atomic rearrangementmechanisms.

The impingement of energetic atoms with a growthsurface can induce numerous physical and chemicalphenomena [4, 5, 16]. Depending upon the energyand the surface condition, an incident atom can betrapped on the surface, implanted beneath it, reflected,and/or undergo long range biased diffusion in theimpact direction on the surface. It can also causelocalized heating which may induce atomic rearrange-ments that would normally not occur (athermaldiffusion). For high-energy impacts, they may evencause resputtering of the already deposited atoms [4,5]. Chemical reactions can occur with other chemi-sorbed species or a gas-phase atom or a physisorbed

3322 YANG et al.: HYPERTHERMAL PHYSICAL VAPOR DEPOSITION

molecule. Electronic scale processes resulting frominelastic scattering are also possible, but are lesslikely to influence the final structure of the film [16].

The complex effects of incident atom energy dur-ing vapor deposition are pervasive for many lowpressure sputter deposition processes. This is becausesputtered atoms are emitted from targets with a broadenergy spectrum extending from a few tenths of anelectron volt up to 20 eV or more [17]. This spansthe energy barriers of many atomic assembly pro-cesses [4, 5, 18]. While experiments indicated thatmany impact phenomena can cause a change of thelocal atomic configurations [17, 18], it is difficult toquantify their individual contributions. It is also dif-ficult to know how these mechanisms are dependentupon the incident energy and angle, deposition rateand substrate temperature.

One approach to the modeling of hyperthermaldeposition utilizes molecular dynamics (MD) tech-niques to simulate energetic impact processes. TheMD method solves for the trajectories of each atom ina crystal by integrating Newton’s equations of motionusing an interatomic force law [4–7, 9–11]. Since thelattice atom vibration is explicitly traced in thisapproach, the forces on atoms must be calculated sev-eral times per lattice vibration period. This leads tointensive computational demands. As the shortest lat-tice vibration periods are about 10�13 s, only 1–10 nsof real time can be simulated. Many thermally acti-vated atomic relaxations take microseconds or longerto complete and are not represented in an MD simul-ation of vapor deposition. However, since the MDmethod evolves atomic configurations by explicitlyanalyzing interatomic forces, it rigorously incorpor-ates the atomic assembly mechanisms initiated by thehigh kinetic energy atom impacts that are frequentlycompleted in less than 5 ps [4–7].

Kinetic Monte Carlo (KMC) methods are beingdeveloped to analyze multipath thermally activateddiffusion [8, 14, 15]. These techniques evolve atomicconfigurations by identifying their thermally activatedatomic jump paths and implementing a probabilisticscheme for their subsequent execution. In KMCanalyses of film growth, the likelihood that an atomjumps from one lattice site to another depends uponits local atomic configuration which can be charac-terized by an activation energy and a jump attemptfrequency [8]. The simulation first deduces the set ofjump probabilities for every allowed jump path usingprecalculated activation energies and then executesjumps according to their relative probabilities. Aftera jump is executed, time is advanced by a compu-tational time step determined by the residence timeof the system, i.e. the reciprocal of the sum of thejump rates for all the allowed jump paths of the sys-tem. This process is then repeated until the timebetween atom arrivals is exhausted. A new atom isadded and the algorithm iterated.

Two- (2D) and three-dimensional (3D) forms ofthe KMC method have been developed to treat dif-

fusion on defective growth surfaces. The 2D methodsenable the surface morphology evolution to be simu-lated, but the out-of-plane constraint upon diffusionrestricts the predictive accuracy. Three-dimensionalapproaches are computationally expensive toimplement, especially if an off-lattice approach isused. Nonetheless, both approaches are beginning toenable an investigation of the effects of substrate tem-perature, deposition rate and incidence angle of theflux upon the surface morphology and void structureof physical vapor deposited thin metal films growneither on flat or featured surfaces (like those used fordual damascene grown integrated circuitinterconnects) [19–21]. While the KMC methodsaddress the numerous thermally activated routes ofatomic assembly, they have not yet incorporated theeffects of adatom energy or possibly important contri-bution from the adatom’s potential energy (i.e. thelatent heat of condensation) which is released duringeach atom’s condensation.

Here, the computationally efficient 2D KMCmethod for the analysis of multipath thermal diffusionduring low energy vapor deposition has been modi-fied to incorporate the effects of atom potential andkinetic energy. The resulting energy-dependent KMCmodel is then used to systematically investigate trendsbetween the surface morphology of vapor depositednickel films and the adatom kinetic energy, substratetemperature and deposition rate.

2. SIMULATION METHODOLOGY

A variety of phenomena can occur following theenergetic impingement of an atom with a surface.They can be broadly classified as either thermallyactivated or energy impact induced. Examples of thelatter are adatom reflection and resputtering of pre-viously deposited material. The phenomena initiatedby energetic interactions are generally completedwithin a few picoseconds [4]. This is usually muchsmaller than the atom residence times at the substratetemperatures of typical interest [22]. As a result, theenergetic reassembly events and thermal diffusion canbe treated sequentially. In other words, followingeach adatom arrival, the impact energy effects canbe treated first using approximations described in thefollowing sections, followed by regular KMC simu-lated thermal diffusion. In order to incorporate theenergy effects, we utilize results from moleculardynamics simulations. These results have been fittedto functional relationship linking atom assembly pro-cesses to the energy and angle of adatom impacts.

2.1. MD analysis of atom–surface interactions

To calculate the nickel adatom–surface interactionan embedded atom method (EAM) determined byFoiles et al. [23] was used as the interatomic poten-tial. The free parameters of the model have been fittedwith experimental material properties such as the lat-tice constant and the sublimation energy. Because the

3323YANG et al.: HYPERTHERMAL PHYSICAL VAPOR DEPOSITION

sublimation energy is exactly reproduced [23], theEAM correctly accounts for the energy transfer dur-ing atom collisions with a surface. On the other hand,high-energy impacts cause atoms to approach eachother closely and short-range interaction dominates.If the impact energy is not too high (say, less than100 eV), the EAM potential should reasonably cap-ture the impact phenomenon and accurately reveal thesubsequent atomic relaxation processes because itsenvironment-dependent potential form realisticallydescribes the energetics of local non-equilibriumatomic configurations.

The molecular dynamics results were based onsimulations conducted on (111) nickel surface. A cellof 24(224)×9(111)×14(220) (x, y, z) was used withperiodic boundary conditions applied along x and zaxes and the free surface of (111) normal to y. A fixedsubstrate temperature was applied to a region of twoatomic layers at the bottom while the atoms abovewere left free. To simulate the impact, a nickel atomwith desired incident energy and incident angle wasintroduced at a random location above the surface.The positions and velocities of all the atoms werethen calculated throughout the impact process (about2–5 ps) and were recorded as a function of time. Toreduce statistical variations, the results werepresented as an average of five separate runs usingdifferent random number seeds.

The calculations identified four major assemblymechanisms associated with atom impact: adatomreflection, resputtering of the previously depositedatoms, biased diffusion and thermal spike inducedatom rearrangement (Fig. 1). Briefly, atom reflectionoccurs most frequently for oblique angles of inci-dence when the atom’s energy exceeds a thresholdvalue (Fig. 1a). The threshold for nickel is about15 eV and the reflection is most likely for incidentangles between 65 and 80°. Resputtering is observedmost significantly for angles in the range of 30–45°and at higher energy (Fig. 1b). When an impact doesnot initiate the processes above, the incoming atomcan be trapped by attractive forces near the surfacewhile its lateral momentum enables the adatom toskip along the surface. This is referred to as biaseddiffusion (Fig. 1c). Finally, every atom impact resultsin a temporary increase in local surface temperature(thermal spike). It results from the combined contri-butions of the latent heat of condensation and dissi-pation of the incident kinetic energy. This transientthermal spike can induce local atomic rearrangement(Fig. 1d).

The four mechanisms above have been systemati-cally studied as a function of the atom energy andincidence angle. Details can be found in Refs. [4, 5].Here, relevant results from these analyses have beenfitted to functional relationships summarized inTables 1–3 to facilitate subsequent KMC execution.The function forms were fitted in a way that theylooks physically meaningful. In equation (1), forexample, θc is the minimum and θm the optimal angle

Fig. 1. Schematic illustration of four interaction events follow-ing an energetic atom impingement with a substrate. The darkdisks represent incident atoms at transitional positions and thelight ones represent substrate atoms deposited previously. Thedashed lines point to and connect with all involved atoms and

their eventual locations.

to create an atom reflection. Equation (2) shows thatthe threshold energy in creating a reflection is 15 eV.In quantifying the thermal spike, a continuummedium approximation was made for the crystal. Thespace- and time-dependent surface temperatureT(s,t) (s position relative to impact site and t timeafter impact), equation (12) in Table 3, was a solutionof the standard Fourier equation for conduction heattransfer [24]. The initial effective temperature at theimpact site came from applying equipartition theoremin which the average kinetic energy was obtainedfrom MD calculations.

2.2. The energy-dependent KMC model

During an evaporation process at low depositionrate and/or high substrate temperature, thermally acti-vated atomic jumping allows a thin film to reduce itsoverall energy and defect content. KMC methods cansimulate the overall effect of multipath atomic jumpsduring deposition [8], and hence the structure ofvapor deposited films. Incident atoms are introducedinto the system at random positions above the sub-strate and are assigned an incident angle by randomsampling of a pre-defined distribution. In the intervalbetween atom impacts with the surface, the key stepsof the diffusion simulation include: (1) calculating the


Table 1. Fitted equations for reflection probability, angular and energy distribution of reflected atoms

Equation no. Equations Parameters

(1) Reflection probability as a function of q at Ei = 70.0 eV qc = 22°, qm = 72°, p = 0.55, l = 1.43

Yrf(q) � min�1,p � p sin�90.0 � 180.0� q�qc

qm�qc�l��,

q�qc

(2) Reflection probability as a function of Ei at q = 80°: Eic = 15 eV, p = 31.5, l = 2.03

Yrf(Ei) � 1.0�exp��Ei�Eic

p �l�,

Ei�Eic

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

Yrf(Ei,q) � Yrf(q)Yrf(Ei)

Y(Ei � 70.0 eV)

(4) Angular distribution of reflected atoms as a function of incident angle and b = 1.38, Gi = Ei�39.1 + |Ei�39.1|,energy: pn=normalization factor (integral of r

equals 1)

r(x) � pn(x�ql)a(90.0�x)b

where

a �b(qp�ql)90.0�qp

qp � min�90.0,q �90.0�q

90.0·

18.6Gi

Gi � 2.0�

ql � max�0.0,q�15.1�1.3×104

E2i

�(5) Energy distribution of reflected atoms as a function of incident angle and b = 2.1, c = 1.07, E0 = �13.39,

energy: q0 = 50.8°

r(E) � pnEa(Ei�E)b

where

a �bEp

Ei�Ep

Ep � (cEi � E0)sin�90.0(q�q0)90.0�q0

�

jump rates (pi) for all possible jump paths; (2) sel-ecting and executing a jump according to its relativejump rates; (3) summing up the rates of all possible

jumps (P = �i

pi) and marching the system clock for-

ward by a time interval tn (tn = 1/P). The new atomicconfiguration is then used to compute new jump ratesand the algorithm is repeated until the time betweenatom arrivals is exhausted. This algorithm is able toaccount for the effects of deposition rate, temperatureand incident flux distribution upon thin film growth.

By using the relationships in Tables 1–3, the KMCmodel can be extended to include the effects of inci-dent energy.

2.2.1. Incorporation of reflection and resputtering.Three steps were used to incorporate reflection and

resputtering events. The first step identified the typeof event. Suppose that an atom with a kinetic energyE approaches a surface at an incident angle (definedas the angle between the local surface normal andthe incident direction), its probability for reflection or


Table 2. Fitted equations for resputtering yield, angular and energy distributions of resputtered atoms

Equation no. Equations Parameters

(6) Resputtering yield as a function of q at Ei = 70.0 eV: p = 0.28, l = 1.93, q0 = �40.9°,qm = 40°

Yrs(q) � p � p sin�q0 � (90.0�q0)� qqm�l�

q�qm�270.0�q0

90.0�q0�1/l

(7) Resputtering yield as a function of Ei at q = 40°: p = 0.60, Ef = 44.7 eV, l = 5.93

Yrs(Ei) � p exp��Ef

Ei�l�

(8) Resputtering yield as a function of incident angle andincident energy:

Yrs(Ei,q) � Yrs(q)Yrs(Ei)

Yrs(Ei � 70 eV)

(9) Angular distribution of resputtered atoms: c = 0.031, l = 0.003

r(x) � c exp[�l(x�45.0)2]

(10) Energy distribution of resputtered atoms as a function of Gi = Ei�38.0, a = �0.027, c = 1.9,incident energy: a0 = 2.0, l = 0.124

r(E) � pnEa exp��a

Em

E�where

a � a0 � c exp(�l((Gi � |Gi|)/2))

Em � 3.8 � 6.2[1.0�exp(a((Gi � |Gi|)/2))]

Table 3. Fitted equations for local effective temperature and biased dif-fusion distance

Equation Equations Parametersno.

(11) Biased diffusion distance: z = 1.31×10�7,l = 1.16, n = 3.83

d(q,Ei) � zEli qn�1�12� qqm

�n�where

qm � 81.0�30.0 exp(�0.18Ei)

(12) Local effective temperature due Tsub=substrateto latent heat release and temperature,incident kinetic energy: Ei=incident energy,

t=elapsed time,s=distance from adatomT(t,s) � Tsub � (66.0 � 3.6Ei

�18.8 e�8Ei)(t � 0.05)3/2

×exp� 0.009s2

t � 0.05�

resputtering can be calculated using equation (3) inTable 1 and equation (8) in Table 2, respectively. Arandom number (between 0 and 1) is then generatedand compared with the probability. If the randomnumber is less than the probability, the correspondingreflection or resputtering event is executed. Otherwisethe program proceeds to simulate biased diffusion andeffects of the thermal spike as described below. Casesexist where both reflection and resputtering eventscan occur. In that case, the kinetic energy and emit-ting direction are saved for the resputtered atoms andthe reflection is first executed. Once reflection is com-pleted, the data for the resputtered atom is thenretrieved and the atom is treated as new incidentatom. In step 2, the reflected or the resputtered atomis ballistically moved until it impinges upon new sur-face, or removed from the system when no new sur-face will be encountered. A third step is used to deter-mine the possibility of further reflection and/orresputtering events if a reflected or resputtered atomstill retains sufficient kinetic energy. The same pro-cedure is repeated until no further reflection andresputtering events are possible.


The local incident angle θ needed for the calcu-lations described above depends on the local surfacenormal at the impact site. This can be defined for asmall surface area near the impact. In the case of aflat plane, its value remains the same regardless thesize of the sample area, but for a rough surface, thesample area needs to be large enough to fully coverthe local information, yet small enough to avoid inac-curacy caused by features such as sharp corners andother rough sites. Various test calculations were per-formed to determine an appropriate size for definingthe local normal. It was found that five surface atomsgenerally give rise to reasonable surface normal andwere hence used for all the simulations.

2.2.2. Biased diffusion. To execute biased dif-fusion, the incident atom’s skipping distance d(q,E)is first calculated using equation (11) in Table 3. Theexecution of biased diffusion on a smooth surfacesimply moves the incident atom in the direction of itsmomentum by the skipping distance. To move anatom on a rough surface, the skipping distance wasfirst compared with the unit move distance (takingto be the nearest neighbor distance). If the skippingdistance is greater, the atom is moved by the unit dis-tance. Then the remaining skipping distance isreduced by a predetermined value to account for fric-tion of a rough surface. The procedure continues untilthe skipping distance is completely consumed. Math-ematically, this can be described by:

Si � 1 � Si�Cia (1)

where Si is the remaining skipping distance at the ithjump, a the unit distance, Ci is a coefficient andSi + 1 the remaining skipping distance at (i+1)th jump.As long as Si + 1 is positive and greater than a, wecontinue to move the atom.

The parameter Ci was obtained based on the stat-istic analysis of MD results for skipping on roughsurfaces. The values of Ci are usually different at eachjump site i. For example, Ci = 1 for a perfect smoothsurface, Ci is larger when the atom moves down oragainst a ledge, and Ci = Si/a (i.e. stop after the jump)when the atom encounters a sharp valley or a higherledge and so on.

2.2.3. Transient thermal diffusion. When anenergetic atom impinges upon a growing film,rearrangement among atoms in the thermal spike zonenear the impact site takes place. The extent of thislocal rearrangement depends upon both the energy (orequivalently the temporary rise of temperature)acquired by the atoms near the impact site and theirneighborhood restraint. The atom with highest energyyet least neighborhood restraint has the highest prob-ability to jump to a lower energy site. The criterionfor a jump to occur then can be expressed by

Pi�P, Pi � �EQi�n

(2)

where E is the energy of an atom in the thermal spikezone (obtained using equation (12) in Table 3), Qi

the neighborhood restraint taking to be the activationenergy for ith jump pathway, and n and P are adjust-ment parameters. Suppose that an atom has a pathwaymeeting the condition of equation (2), it is then saidto have a probability to jump to a new place throughthat path. When many atoms have the probability tojump in different paths, the jump simulation is con-ducted in such a way so that probability for the jumpin the ith pathway scales with Pi. Once the jump ismade, Pi is updated for all the paths. This procedurewas repeated until no atoms have probability to move.

The parameters n (energy sensitivity index) and P(a cut-off number) were determined by matching theconfigurations obtained using MD simulations atshort time/length scale to those obtained from KMCcalculations at the same conditions. Using the valuesof P and n determined this way, MD and KMC simul-ations give similar configurations at various atom kin-etic energies ranging from 0.1 to 2.0 eV under normalincidence condition.

3. RESULTS AND DISCUSSION

The KMC model described above was used toexplore the importance of various kinetic energymechanisms. Based on a 2D approximation of nickeldeposition [8], the substrates were constructed to con-tain eight rows of 200 close-packed nickel atoms. Per-iodic boundary conditions were employed laterally tominimize the effect of small system size. Eight thou-sand atoms were deposited for each condition. Toquantify the surface morphology, a surface roughnessparameter was calculated as the ratio of the surfacearea of a simulated configuration to that of the smoothsubstrate [22, 25] (for a flat surface, the roughnessratio=1.0; while for a rough surface, the roughnessratio �1.0). To minimize statistic variation of theresults, 10 separate simulations (each with a differentrandom number seed) were conducted and the aver-age used for a roughness data point. Since this is a2D model, the actual temperatures used for depositionare not directly related to those of a 3D system. Tocompensate, we note that the 2D vacancy formationenergy is about 2/3 of the corresponding 3D value[26]. Thus, a homologous temperature is also given,based on a melting temperature, Tm, of 1150 K, whichis 2/3 of the 3D nickel melting temperature of1726 K.

3.1. Relative contributions of mechanisms

Simulations of vapor deposition at an incidentenergy of 40 eV, a deposition rate of 0.1 µm/min, anda normal cosine angular distribution for the incidentflux and two different temperatures were carried outto examine the contribution of each atomic assemblymechanism (Fig. 2). The use of a high energy of40 eV can more clearly reveal the energy effects (thiswould mimic the conditions when a metal flux was


Fig. 2. Contributions of various growth mechanisms in hyperthermal physical vapor deposition. The substratetemperatures (T/Tm) were 0.17 and 0.43, respectively. The deposition rate was 0.1 µm/min, and the kineticenergy was 40 eV. The incident flux had a cosine distribution. The deposition of 8000 nickel atoms wassimulated. The configurations in (a) result from ballistic deposition with only nearest neighbor relaxation afteratoms’ impingement. The configurations from (b) to (g) result from combined mechanisms sequentially added

one at a time to show the difference that each additional one makes.

fully ionized and a bias voltage of about 40 V usedto accelerate the metal atoms towards the substrate).First, a ballistic deposition model was used to showthe configuration of deposited film with very limitedatomic relaxation. This was done by simply placingthe depositing atom at the lattice site nearest to thelocation of impingement and then freezing it. Thesimulated configurations are shown in Fig. 2a. Obvi-ously, these configurations are independent of tem-perature. The very rough and highly porous structureresults from self shadowing. This is likely to representthe porous configuration under extremely low tem-perature conditions. The traditional KMC model wasthen used to simulate the effects of thermal diffusionand the results are shown in Fig. 2b. It representsthermal deposition excluding only latent heat. By suc-

cessively turning on the mechanisms of athermal dif-fusion due to latent heat release (i.e. thermal spikeat zero incident energy), atom reflection, resputtering,biased diffusion, and athermal diffusion due to impactenergy (i.e. thermal spike at non-zero incidentenergy), the KMC simulations described earlier werecarried out to reveal the effects of individual mech-anisms. The results are shown as Fig. 2c–g.

Low-temperature (T/Tm = 0.17) configurationsshown in the left column of Fig. 2 were first exam-ined. Comparison between Fig. 2a and b shows thatthermal diffusion significantly increases the columnsize. Fig. 2c indicates that the latent heat release cancause considerable atomic rearrangements that lead toeven larger column sizes and less inter-column voids.High-energy reflection and resputtering are not seen


to have noticeable effects on the film structures (Fig.2d and e). This is because relatively fewer reflectionand resputtering events occur under the simulatedconditions. More importantly a reflection or a resput-tering event only results in redeposition of atoms atdifferent locations and does not cause a local atomicrearrangement. Fig. 2f shows that the inclusion ofbiased diffusion resulted in fully densified structureand much smaller surface roughness. This occursbecause the biased diffusion enables atoms to moveby either a short or a long distance in the directionof incidence, promoting their attachment at latticeledges. However, the biased diffusion only affects theadatoms, not the other atoms adjacent to theimpinging site. By incorporating thermal spike(including latent heat and kinetic energycontributions) induced rearrangement from neighbor-ing atoms, a fully dense and rather flat configurationwas obtained (Fig. 2g).

At higher temperature of T/Tm = 0.43, effects asso-ciated with various energy mechanisms becamesmaller. The effects of intensive thermal diffusionoverwhelm the energy induced atomic rearrangement.

3.2. Effect of kinetic energy on surface morphology

It has been shown that the contributions of energymechanisms to the atomic assembly process dependon temperature and is especially significant whenthermal diffusion is low. To systematically explorethe energy effects, the full hyperthermal KMC modelwas used to simulate vapor deposition at various inci-dent energies from 0 to 20 eV at a fixed low substratetemperature of T/Tm = 0.17, a deposition rate of0.1 µm/min, and a standard cosine flux angular distri-bution. Four representative configurations are shownin Fig. 3.

It is clear that increasing incident energy helpsdecrease surface roughness and promote a denserfilm. At zero incident energy (thermal energy only),Fig. 3a, the configuration is a porous columnar struc-ture with a rough surface (the roughness ratio wasfound to be 3.22). It results from limited atomicmobilities and self-shadowing. Because there are nobiased diffusion, reflection and resputtering at lowincident energies, only the latent heat release enablesthe local reconstruction of atoms. However, the effectis limited. The microstructure is typical of zone Istructure observed in experiments [18]. At 5 eV, Fig.3b, the porosity significantly decreases and the rough-ness ratio was found to reduce to 1.67. Since reflec-tion and resputtering were not activated at this energy,the observed change was a result of a stronger thermalspike induced athermal diffusion and biased dif-fusion. This trend continued as the incident energywas increased to 10 eV, Fig. 3c, where the roughnessratio was reduced to 1.55 and voids were completelyeliminated. Finally, at 20 eV, Fig. 3d, the surfacebecame much smoother and the roughness ratio wasfurther reduced to 1.29. When the kinetic energy isat 20 eV or higher, several new mechanisms were

Fig. 3. Effect of kinetic energy on surface morphology at asubstrate temperature of 200 K (T/Tm = 0.17). The depositionrate was 0.1 µm/min and the incident flux angle had a cosineprobability distribution. The deposition of 8000 nickel atoms

was simulated.

activated. First, reflection became possible. Areflected atom generally tends to move in the forwarddirection and is less likely to attach to an existingmound. When it jumps onto the edge of the mound,it enables the mound to grow in the horizontal ratherthan in the thickness direction. Secondly, resputteringcan occur at 20 eV. Resputtering is mostly significantat surface asperities as these places are exposed tomore incoming flux. The preferential etching of thesesites also promoted smoothness.

Detailed simulations on the effect of incidentenergy have also been conducted at various substratetemperatures. The roughness obtained from thesesimulations is plotted in Fig. 4 as a function of inci-dent energy at different fixed substrate temperatures.It can be seen that at a low temperature ofT/Tm = 0.17, the surface roughness initially decreasesvery rapidly as the incident kinetic energy increasesup to 15 eV. Further increases of energy then causeonly a small change in the roughness. Increasing thesubstrate temperature causes a roughness decreaseover the whole energy range. In addition, the effectsof incident energy on surface roughness became less


Fig. 4. Effect of incident energy on surface roughness of nickelfilms under different substrate temperatures (T/Tm), (a) 0.17;(b) 0.22; (c) 0.26; and (d) 0.30. The deposition rate was0.1 µm/min and the incident angle had a cosine distribution.

significant as temperature was increased. For tem-perature above T/Tm = 0.26, the effect of energybecomes negligible. As a result, energy modificationis more effective at low temperatures.

The functional dependence between surface rough-ness and incident energy at different deposition rateswas also calculated at a fixed T/Tm of 0.22 and acosine angular deposition flux. The results of this cal-culation are shown in Fig. 5. It shows that at the high-est simulated deposition rate of 10 µm/min, increas-ing the incident energy from 0 to 15 eV significantly

Fig. 5. Effect of incident energy on the surface roughness ofnickel films deposited with different deposition rates: (a) 10;(b) 1; (c) 0.1; and (d) 0.01 µm/min. The substrate temperature(T/Tm) was 0.22 and the incident angle had a cosine distri-

bution.

reduced the surface roughness. The roughnessappeared to be saturated when the energy wasincreased above 15 eV. Similar to increasing tempera-ture, it can be seen that decreasing the deposition ratereduced both the roughness and its energy depen-dence over the whole energy range simulated.Especially, the roughness becomes almost inde-pendent of incident energy when the deposition ratewas decreased below 0.01 µm/min at T/Tm = 0.22.

The simulations demonstrate the interplay betweenthermal diffusion and various energy related mech-anisms on surface roughness. At either low substratetemperatures or high deposition rates, thermal dif-fusion is not significant and the flattening of the sur-face is then mainly achieved by energy related mech-anisms such as athermal diffusion, biased diffusion,reflection and resputtering. At high temperatures orlow deposition rates, thermally activated diffusion isoften sufficient to enable the formation of a flat densestructure and the effects of energy mechanisms areoverwhelmed.

Extensive experimental results have shown that theuse of energetic atoms during thin films depositioncan promote layer-by-layer growth and that energeticatoms can activate various surface assembly pro-cesses [27–33]. Almost all experimental analysesattributed the formation of dense and flat structuresduring hyperthermal energy deposition to the dis-sociation of surface asperities by energetic bombard-ment induced atomic reconstruction. The dissociatedatoms preferentially reach step edges, resulting in alayer-by-layer epitaxial growth. However, these desir-able results are often compromised by deleteriouseffects of energetic impacts. For instance, whenenergy increases above a threshold, permanent dam-age to the lattice increases more rapidly than theannealing processes are capable of healing, resultingin a sharp increase on the number of defects [30, 33].Thus there is an optimum energy for achieving alayer-by-layer epitaxial growth while maintaininghigh crystalline quality films which are relativelydefect free [30].

3.3. Effect of incidence angle on surface morphology

Thin films grown under low substratetemperature/low impact energy conditions are gener-ally known for their characteristic (and oftendetrimental) columnar structure caused by self-shadowing. Self-shadowing is particularly strongwhen incident atoms are away from the substrate nor-mal. To more clearly show the interplay of incidentenergy and incident angle, the energy-dependentKMC model has been used to simulate depositionswhere all atoms have the same incident energy andincident direction.

A series of calculations were carried out at differ-ent incident angles, but at a fixed temperature ofT/Tm = 0.26, a fixed deposition rate of 0.1 µm/min,and a fixed incident energy of 20 eV. Representativeconfigurations are shown in Fig. 6. At normal inci-


Fig. 6. Effect of incident angle on surface morphology of nickelfilms at a substrate temperature of 300 K (T/Tm = 0.26). Thedeposition rate was 0.1 µm/min and the kinetic energy was20 eV. The deposition of 8000 nickel atoms was simulated.

dence of q = 0°, mounds on a rough surface can beclearly identified. The mounds grow broader and thenumber of the mounds decreased as the incident anglewas increased to 20°. The surface became consider-ably smooth at q = 40° and the mounds can barely beidentified. Further increases in the incidence angle to60° reversed the trend and caused the surface tobecome rougher.

More simulations on the effects of incident anglewere carried out and the data for surface roughnessas a function of incident angle are summarized in Figs7 and 8. Fig. 7 compares the results for four incidentenergies at fixed T/Tm = 0.22 and deposition rate of0.1 µm/min. Fig. 8 compares the results for four sub-strate temperatures at the same deposition rate and a10 eV energy. Fig. 7 shows that at zero incidentenergy, the surface roughness initially increasesslowly with increasing incident angle up to 40°, thenrapidly increases when the incident angle is beyondabout 40°. This implies that a strong self-shadowinginduced defective structure can not be healed by lat-ent heat induced atomic relaxation alone. The rapidincrease of roughness at 40° results from the forma-tion of voided columnar structure. With the incidentenergy increased to 5 eV, a dramatic change isobserved on the surface roughness versus the incidentangle relationship. The surface roughness initially

Fig. 7. Effect of incident angle on surface roughness of nickelfilms deposited with different kinetic energies: (a) 0; (b) 5; (c)10; and (d) 20 eV. The substrate temperature (T/Tm) was 0.22

and the deposition rate 0.1 µm/min.

Fig. 8. Effect of incident angle on the surface roughness ofnickel films with different substrate temperatures (T/Tm), (a)0.17; (b) 0.22; (c) 0.26; and (d) 0.30. The deposition rate was

0.1 µm/min and the incident energy was 10 eV.

decreases as incident angle is increased to about 30°,then starts to increase as the incident angle is furtherincreased. A roughness minimum is seen around 30–40°. The surface roughness also becomes very sig-nificant at incident angle up to 60°. Compared withthe low energy curve, the overall roughness has beengreatly reduced. With an increase in energy to 10 eVand then to 20 eV, roughness is continuously reduced.This reduction is more significant at high incidentangles. Nevertheless, the roughness versus incident


angle trend remains similar. Interestingly, the incidentangle at which the minimum roughness is obtainedincreases with increasing energy. This occurs becausehigh energy activates more surface processes whichcauses surface asperity flattening and a consequentreduction of self-shadowing. Fig. 7 also shows thatan increase of energy from 0 to 5 eV causes moreflattening than an increase of energy from 10 to20 eV. This indicates that the effects of athermal andshort-range biased diffusion on smoothing the surfaceare significant.

The effect of substrate temperature on the rough-ness–incident angle curves is similar to that of inci-dent energy as seen in Fig. 8. Increasing the tempera-ture generally reduces the roughness, especially athigh incident angles. For an incident energy of 10 eV,the angle for the minimum roughness increases fromabout 35 to about 42° as the temperature increasesfrom T/Tm = 0.17 to 0.30. This arises because thermaldiffusion promotes surface reconstruction that flattensa rough surface and eliminates voided columnar struc-ture.

At the energy levels treated above, reflection andresputtering were not significant. The observed micro-structures were mainly caused by the thermal spikeinduced athermal diffusion and biased diffusion.Biased diffusion had a significant effect duringoblique angle deposition. When all atoms had thesame incident angle, the unidirectional biased dif-fusion on the surface promote local layer-by-layergrowth and resulted in a smooth surface. This effectincreases with increasing the incident angle. How-ever, large incident angles can cause self-shadowing,resulting in rough surfaces. There is a compromisebetween these two mechanisms. The optimal anglefor minimum roughness depends on many processconditions including the incident energy.

4. CONCLUSIONS

An energy-dependent kinetic Monte Carlo methodhas been developed to simulate sputter deposition ona flat substrate. The method allows a realistic studyof incident energy effects during deposition and theirinterplay with other conditions, such as substrate tem-perature, deposition rate, and incident angle. Appli-cation of the method to the deposition of nickel filmsreveals that:

1. In addition to thermal diffusion, the primaryenergy induced contributions to the thin film’sdensification and smoothing come from short-range atomic rearrangement mechanisms includingbiased and thermal spike induced athermal dif-fusion, while those from reflection and resputter-ing are secondary and cause only redeposition.

2. Surface roughness decreases with increasing kin-etic energy. The effect becomes stronger as thesubstrate temperature is lowered and/or the rate ofdeposition is increased.

3. For directional hyperthermal deposition, a mini-mum surface roughness at a nonzero angle of inci-dence is observed. The angle corresponding to theminimum roughness increases with increasing kin-etic energy, substrate temperature and withdecreasing deposition rate.

Acknowledgements—We are grateful for the support of thiswork by the Advanced Research Projects Agency (A. Tsao andS. Wolf, Program Managers) and the National Aeronautics andSpace Administration (D. Brewer, Program Monitor) throughgrant NAGW1692.

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monte carlo simulation of hyperthermal physical vapor deposition

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