Self-organized transient facilitated atomic transport in PtA

a r X i v :0802.0347v 1 [c o n d -m a t .m t r l -s c i ] 4 F e

b 2008

Self-organized transient facilitated atomic transport in Pt/Al(111)

P.S¨u le

Research Institute for Technical Physics and Material Science,

Konkoly Thege u.29-33,Budapest,Hungary,

sule@mfa.kfki.hu,mfa.kfki.hu/～sule,

(Dated:February 5,2008)

During the course of atomic transport in a host material,impurity atoms need to surmount an energy barrier driven by thermodynamic bias or at ultra-low temperatures by quantum tunneling.In the present article we demonstrate using atomistic simulations that at ultra-low temperature transient inter-layer atomic transport is also possible without tunneling when the Pt/Al(111)im-purity/host system self-organizes itself spontaneously into an intermixed con?guration.No such extremely fast athermal concerted process has been reported before at ultra low temperatures.The outlined novel transient atomic exchange mechanism could be of general validity.We ?nd that the source of ultra-low temperature heavy particle barrier crossing is intrinsic and no external bias is necessary for atomic intermixing and surface alloying in Pt/Al although the dynamic barrier height is few eV.The mechanism is driven by the local thermalization of the Al(111)surface in a self-organized manner arranged spontaneously by the system without any external stimulus.The core of the short lived thermalized region reaches the local temperature of ～1000K (including few tens of Al atoms)while the average temperature of the simulation cell is ～3K.The transient facilitated intermixing process also takes place with repulsive impurity-host interaction potential leading to negative atomic mobility hence the atomic injection is largely independent of the strength of the impurity-surface interaction.We predict that similar exotic behaviour is possible in other materials as well.

PACS numbers:66.30.Jt,68.35.Fx,05.45.-a,66.30.-h,81.10.-h

I.INTRODUCTION

The spontaneous formation of self-organized nanoscale structures has attracted much attention in recent years due to its potential application in the fabrication of nanodevices 1,2.The understanding of atomistic pro-cesses which lead to the formation of nanostructures has been one of the main focuses of research in materials science 1,3.

The self-assembly induced atomic movements towards an ordered structure can be understood as thermally acti-vated processes driven by the thermodynamic bias of the system 1,4.Also,concerted atomic transport processes during self-organization such as adatom nucleation via detechment and attachment processes at step edges and thin ?lm growth and processing,however,often lead to abrupt surface alloying and intermixing 5,6,7,8.These pro-cesses proceed via atomic site exchanges within the top-most atomic layer 9,10,11,12.

Ultrafast di?usional dynamics can be studied by clas-sical molecular dynamics (MD)simulations at the atom-istic level 10,12,13,14,15,16.Recently it has been shown by MD studies in accordance with experimental results that under externally forced conditions,transient enhanced intermixing of heavier impurities could occur in bulk materials 17,18.In the absence of considerable external load of perturbation,such as during atomic deposition ultrafast intermixing and surface alloying can also be induced 7,8,19,20,21.Moreover,the most recently it has also been found that the bulk mobility of atomic metal-lic clusters could also be enhanced leading to ballistic

burrowing in Al and in Ti 22.

These are interesting results beacuse it is widely ac-cepted that enhanced di?usion occurs the mostly on solid surfaces e.g.when the barrier of atomic transport ?E ≤k B T ,where k B and T are the Boltzmann con-stant and the temperature,respectively,superdi?usion occurs,that is the nearly dissipationless atomic trans-port with transient atomic jumps (random walk,Levy ?ight)5,6,14,15,24.In the topmost layer fast atomic ex-change processes with long jumps have also been re-ported which thought to be driven,however,by ther-modynamic forces 10,11,12.In the bulk,non-Arrhenius (athermal)atomic (not necessarily transient)transport has been studied mostly under nonequilibrium condi-tions,such as during ion-implantation 16,in driven-alloys or mechanical alloying 25,26,by mechanical force biased chemical reactions 27or using shock-induced alloying 49.In the bulk athermal rates can only be accom-plished via under barrier atomic jumps called quantum tunneling 4,23.This can be done mostly for light par-ticles at ultra-low temperatures.Quantum di?usion of H has been studied in detail on solid surfaces 30.In the bulk,only few light elements show ultrafast inter-stitial di?usion 4,29,31.However,the quantum tunneling di?usion of heavy adatoms on various substrate surfaces have also been observed recently 32,33.Quantum di?usion (QD)have not been observed yet for heavy elements in the bulk although the de Broglie wavelength could be in the range of tunneling distance which allows QD on the surface 32.The most recently reactive di?usion dynamics has been interpreted as a superdi?usive process during

2

the front propagation of interfaces34which could be the ?rst(though theoretical)?nding that transient di?usive atomic transport takes place in the bulk.

We would like to present classical MD results which suggest that transient rates could also be occurred with-out tunneling at ultra-low temperature via a pecu-liar mechanism during surface alloying.The employed semiempirical approach is validated by ab initio den-sity functional calculations.The explored new transient atomic exchange process is driven in a self-organized manner:the impurity/host system spontaneously reor-ganizes itself in such a way that abrupt surface alloying takes place at an ultra-low temperature.We also?nd that impurity induced local thermalization occurs at～0 K external temperature although no forced condition has been applied.Such a mechanism has not been observed yet although is likely to be of general validity.The local thermalization of the substrate facilitates atomic injec-tion while the overall temperature of the substrate re-mains very low(few K).A surprising consequence is that repulsive intermixing(and negative transient atomic mo-bility)could also occur theroretically,the process is not sensitive to the strength of the Al-Pt interaction.

II.THE SIMULATION APPROACH Classical tight-binding molecular dynamics simulations39were used to simulate soft landing and vapor deposition of Pt atoms on Al(111)substrate at～0K using the PARCAS code40which has been used for the study of various atomic transport phenomena in the last few years18,40.We also employ?rst principles calculations to validate our heteronuclear potential (details will be given later on).

Although we carry out simulations at～0K,we?nd a substantial local heating up in a local surface region of Al,hence the correct dissipation of the emerged heat should be handled via using temperature control.A variable timestep and the Berendsen temperature con-trol is used at the cell border13,42,43.The simulation uses the Gear’s predictor-corrector algorithm to calcu-late atomic trajectories13.The maximum time step of 0.05fs is used during the operation of the multiple time st ep algorithm42.The system couples to a heat bath via the damping constant to maintain constant tempera-ture conditions and the thermal equilibrium of the entire system43.The time constant for temperature control is chosen to beτ=70fs,whereτis a characteristic relax-ation time to be adjusted42,43.The Berendsen temper-ature control has successfully been used for nonequilib-rium systems,such as occur during ion-bombardment of various materials16,17,18,24,40,41.Further details are given in ref.40,41and details speci?c to the current system in recent communications17,18,36.

For simulating deposition it is appropriate to use tem-perature control at the cell borders.This is because it is physically correct that potential energy becomes kinetic energy on impact,i.e.heats the lattice.This heating should be allowed to dissipate naturally,which means temperature control should not be used at the impact point.Periodic boundary conditions are imposed later-arily.The observed anomalous transport processes are also observed without periodic boundary conditions and Berendsen temperature control.Further details are given in41and details speci?c to the current system in recent communications18,36.

The top of the simulation cell is left free(the free sur-face)for the deposition of Pt atoms.The bottom layers are held?xed in order to avoid the rotation of the cell. Since the z direction is open,rotation could start around the z axis.The bottom layer?xation is also required to prevent the translation of the cell.

The size of the simulation cell is80×80×42?A3in-cluding16128atoms(with a fcc lattice).The simulation uses the Gear’s predictor-corrector algorithm to calcu-late atomic trajectories42.The maximum time step of 0.05fs is used during the operation of the multiple time step algorythm42.15active MLs are supported on3?xed bottom monolayers(MLs).We?nd no dependence of the anomalous atomic transport properties of the deposited atoms on the?nite size of the simulation cell.Finite size e?ects do not play a role in the appearance of the anomalous transport of Pt in Al(the variation of the cell size does not in?uence the intermixing process down to cell sizes including few hundreds of atoms).Deposited atoms were initialized normal to the(111)surface with randomly selected lateral positions4?5?A above the surface with nearly zero velocity.The initial kinetic en-ergy of the deposited particles in the case of ultrasoft landing is nearly zero eV.In order to make a statistics of impact events we generated100events with randomly varied impact positions.The conservation of the total energy is maintained during the simulations.

A.The interaction potential

We use the many-body tight-binding second-moment approximation(TB-SMA)interaction potential to de-scribe interatomic 4ddcfffb941ea76e58fa042ding the Cleri-Rosato (CR)parameterization of the TB-SMA potential we con-sider the interaction between two atoms and the interac-tion with their local environment.

The TB-SMA potential is formally analogous to the embedded atomic method(EAM,45)formalism,e.g.the potential energy of an atom is given as a sum of repulsive pair potentials for the neighboring atoms(usually for the ?rst or second neighbors and a cuto?is imposed out of this region)and an embedding energy that is a function of the local electron density given as follows45,

E tot=

1

3

a function of the interatomic distance(?A)obtained by the a

b initio PBE/DFT method.For comparison the interpolated semiempirical potential(TB-SMA)is also shown calculated for the Al-Pt dimer.

ρi and for the embedding function F[ρi]45.In the code PARCAS40the forces have been calculated using a built-in functional derivative of Eq.(1).We utilize EAM func-tional forms in the code for F[ρi]and for the densityρsimilar to that given in refs.45,53.The EAM routine in the code employs a cubic spline interpolation for the evalua-tion of the EAM potentials and their derivatives(forces) starting from various kind of input potentials given in discrete points as a function of r ij(the number of points per functions is5000in this study).

Within the TB-SMA we use no explicit dependence on ρi.The attractive part of the potential reads,

F i(r ij)=? j,r ij

r0?1

.(3)

The parameters(ξ,q,A,p,r0)are?tted to experimental values of the cohesive energy,the lattice parameter,the bulk modulus and the elastic constants c11,c12and c4439 and which are given in Table1.The summation over j is extended up to?fth neighbors for fcc structures39.The cuto?radius r c is taken as the third neighbor distance for all the interactions.We tested the Al-Al and the Al-Pt potential at cuto?radius with larger neighbor dis-tances and found no considerable change in the results. This type of a potential gives a very good description of lattice vacancies,including migration properties and a reasonable description of solid surfaces and melting39. The CR potential correctly provides the adatom binding and dimerization energies24.

Cleri-Rosato parameters39used in the tight

(TB-SMA)give n in Eqs.(1)-(2)39The

crosspotential have been obtained as follows

scheme52:For the preexponentialsξ

the harmonic mean A AlP t=(A Al×A P t)1/2

to the heat of mixing of the AlPt alloy

in ref.36),for q and p we use the geometrical

=(q Al+q P t)/2.The?rst neighbor distance

is given also as a geometrical mean of

)/2.

ξq A p r0

1.3164.5160.1228.612

2.87

2.6954.0040.29810.6122.78

2.7

3.2580.1919.612 2.83

Recently it has also been shown,that the CR potential remarkably well describes di?usion in liquid Al46,47and energetic deposition of Al clusters on Al48.For the Al-Pt crosspotential of substrate atoms and Pt we employ an interpolation scheme which has widely been used in the literature10,12,18,24,36,37.The Al-Pt potential provides a reasonable melting point and heat of alloying for the AlPt alloy24.

In order to check the accuracy of the employed inter-polated crosspotential,the crosspotential energy has also been calculated for the Al-Pt dimer using ab initio lo-cal spin density functional calculations55together with a quadratic convergence self-consistent?eld method.The G03code is well suited for molecular calculations,hence it can be used for checking pair-potentials.The Kohn-Sham equations(based on density functional theory, DFT)56are solved in an atom centered Gaussian basis set and the core electrons are described by e?ective core potentials(using the LANL2DZ basis set)57and we used the Perwed-Burke-Ernzerhof(PBE)gradient corrected exchange-correlation potential58.First principles calcu-lations based on density functional theory(DFT)have been applied in various?elds in the last few years59. The obtained pro?le is plotted in Fig.1together with our interpolated semiempirical many-body TB-SMA po-tential for the Al-Pt dimer.We?nd that our interpolated TB-SMA potential when calculated for the Al-Pt dimer matches reasonably well the ab initio one hence we are convinced that the TB-SMA model accurately describes the heteronuclear interaction in the Al-Pt dimer.We as-sume that this dimer potential is transferable for those cases when the Pt atom is embedded in Al.This can be done because,as we outlined above,the interpolated Al-Pt potential properly reproduces the available exper-imental results for the Al-Pt alloy.

We also calculate the binding energy U i b of the impurity particle i which can be expressed in terms of its potential energy U(r)=(summed over interactions with its neigh-bors cut o?at r c)and its?rst derivative(Newtonian forces).Hence at each time step U i b can be calculated

FIG.2:The snapshots of the ultrafast atomic injection at 0,0.45,0.55,and at2,ps(from left to right)0.8,1.2and at 1.5,ps(from left to right)Pt atom and Al atoms are shown with light and dark(blue)colors,respectively.Only few hun-dreds of atoms of the simulation cell in the”active”region are shown.The deposited particle is in rest at t=0K(no initial kinetic energy is given).Therefore the atomic injection occurs spontaneously.

from the Newtonian forces.

U i b=? j,r ij

?r r=r ij give the total energy of the simulation cell.r can be replaced by the internuclear separation r ij in the pair interaction term U(r ij).

III.RESULTS

Transient inter-layer atomic mixing(TILAM):The simulation of vapor deposition in the Pt/Al(111)system leads to an unexpected result.The deposited atoms,in-dependently of the energy of deposition,intermix sponta-neously with ultrafast atomic exchange entering the top Al(111)layer even at～0K within a ps leading to the ex-tremely large jumping rate ofΓ≈1012Hz.Such a robust rate at～0K has never been reported before in metal system.Moreover we?nd that the deposited Pt atom undergoes an abrupt inter-layer migration spontaneously regardless to the impact energy and to the strength of the Pt-Al interaction potential.Hence we?nd it important to understand the details of this porcess.Although the obtained rate is surprisingly high,the employed simula-tion approach is highly standard and hopefully there is no reason to question the validity of the results.In particu-layers(in a crossectional slab cut the middle of the simula-tion cel l)induced by the deposition of a Pt atom at～0K (the scale is in?A in the axes,the depth position of the surface is at z=0).The trajectory of the Pt is also shown with a black curve.The positions of the atoms are collected up to 2ps during a deposition event.The di?erent colors of the points correspond to the local temperature range(K)of the Al atoms in the thermalized region shown above.Inset on the top:The?uctuating local average temperature(T local(t),K) of the thermalized region(～10×10×5?A3)which includes 30?40hot atoms as a function of the time(ps).

lar,we do not think that the result is the artifact of the employed semiempirical interaction potential.Our DFT dimer calculations support the reliability of our interpo-lated semiempirical potential.We?nd such a peculiar behavior only for few di?usion couples(Pt/Cu,Pt/Al, Au/Al)among those couples for which interpolated CR potential has been available.Many experimental results support indirectly our?nding.Strong exothermic solid state reactions have long been known between various metals and Al8,35,50.

The injection of a Pt atom leads to the ejection of an Al atom to the surface.The deposition of1ML of Pt leads to the formation of an adlayer rich in Al in agreement with the experimental?ndings8,35.The available room temperature experimental results also report us strong intermixing for Pt/Al8,35.The computer animation of the atomic injection can be seen in a web page54.We ?nd direct injection only in the case of certain transition metal elements around Pt in the periodic table,such as Ir,Au and also for the Pt/Cu couple.

The spontaneous local thermalization of the substrate: In order to get more insight into the details of the atom-istic mechanism of TILAM we follow the atomic trajec-tories of surface Al atoms.The TILAM induced surface disordering of Al(111)is shown in Fig.3where the tra-jectories of the transient vertical jump of few Al atoms to the surface(adlayer)can be seen.We plot the atomic positions of a crossectional slab cut in the middle of the simulation cell(with a slab thickness of15?A)for the

top layer atoms during vapor deposition of Pt(Fig3) at～0K.The mobility of the substrate atoms is large with large amplitudes around their equilibrium positions. This is surprising because the overall temperature of the entire cell does not exceed few K during the simulations. However,we?nd that within a small volume below the surface including few tens of atoms the local temperature can be surprisingly high.

A.Local temperature within a thermalized

subsurface nanoscale zone

An approach will be outlined brie?y which has been used for obtaining continuously distributed local proper-ties from the positions and velocities of constituent atoms obtained by MD simulations.The applied methodology is similar to that obtained for analyzing the results of MD simulations for systems with?nite size and which can not be described by continuum models60,61.Unfortunatelly, when the system size is shrinked to the nanoscale?uc-tuations,such as the spatial oscillation of the tempera-ture will be enhanced61.Therefore speci?c de?nitions are needed for giving time dependent local quantities,such as the local temperature of a nanoscale system. Thermondynamic quantity,such as the temperature T can only be assigned to an atomic ensemble in which the number of particles N is su?ciently high to exclude the e?ect of local?uctuations(statistical ensemble average). Unfortunatelly,a nanosystem,which often includes less than～1000atoms(nanoclusters)can not be described by T in a conservative point of view.In these cases,how-ever,one should introduce the quantity local temperature T local which can be used to explain the thermal properties of nanostructures.We de?ne T local as the time aver-aged temperature of the thermalized sub(nano)region ob-tained during simulations sampling the su?ciently large portion of the phase space42.As a natural consequence, T local →T,when N→∞,or N is su?ciently large to have a statistical meaning of the ensemble.

The total simulation cell of Pt/Al during the inter-mixing of Pt is a highly anisotropic and inhomogeneous system.In this case the thermalized region of the sub-

strate can be taken as a nanosystem including few tens of hyperthermal atoms at the surface,however,which is not isolated from its low-temperature environment.There is a continous thermal exchange between the”hot spot”and the ultra-low temperature environment and with the heat bath.

Much e?ort has been put forward in establishing a relationship between thermodynamic quantities and MD data13,42,61,62,63.The ergoditic theorem ensures in thermodynamics the relation between the observ-able ensemble averages and the simulated time averaged quantities13,42.Under ergodic condition the time average or ensemble average of the velocity distribution of the constituents will closely follow the Maxwell-Boltzmann distribution.MD studies provides microscopic(atomic)thermalized region below the surface(with the volume of～10×10×5?A3)as a function of time(ps)obtained for a typical event.The average temperature of the simulation cell is also shown with a dashed line.Inset:The number of Al atoms in this subsurface nanoscale region as a function of time(ps).Fig4b:The oscillating kinetic energy(eV)of the impinging Pt atom and of the transient Al atoms(summed up for the thermalized ensemble)as a function of the time(ps) shown with a continous and dashed lines,respectively.The Pt atom has been initialized4.6?A above the Al(111)surface with zero velocity.The initial temperature of the Al cell is nearly zero.Fig4c:The average cohesive energy/atom(eV) in the thermalized region of Al as a function of time(ps).

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information and an e?ective temperature can be derived from the inpidual atomic velocities 13,61.Another use-ful quantity,the kinetic temperature of a nanosystem is de?ned as an averaged kinetic energy per an inpidual spatial degree of freedom 62,63.The time averaged tem-perature of the nanosystem with N number of atoms can be given as

T local

N

=lim

t →∞

1

t

∞

t =0

2E kin (t )

M

13k B

j

,(5)

where M is the number of visited con?gurations in the simulations.The instanteneous value of T local (t )will ?uc-tuate around the mean value T local N unless an in?nite number of particles haven been considered.Indeed,un-der the assumption of ergodicity,this mean value exists and is independent of the initial data with identical en-ergy.In nanosystems ergodicity looses its validity and we can not give any macroscopic observable which is related to T local .Nevertheless,the time evolution of T local (t )could be a useful quantity to monitor system changes dur-ing transient phase evolutions such as e.g.local melting transition 36.

The calculation of T local (t )within an arbitrarily small volume including N particles can also be calculated for-mally,however,from the kinetic energy of the inpidual particles obtained from simulations in each time step.The equipartition theorem (ET)allows in principle to re-late the temperature of a system with its average energy.If the mobility of atoms is su?ciently high within the thermalized nanoregion,e.g.the number of hyperther-mal atoms is large,we are close to the limit of classical ideal gas.In this case each of the mobile particles has an average kinetic energy of (3/2)k B T in thermal equilib-rium,where k B is the Boltzmann constant and T is the temperature.However,our system should not be strictly an ideal gas.ET requires only that k T local ?hν,where νis the phonon frequency of an oscillator in the thermal-ized zone,hence in highly excited states quantum e?ects should become negligible 64.

Although our system is not in a thermal equilibrium,we can expect that the ET works also nearly correctly for those cases which are not very far from equilib-rium.It is also known that the spatial-temporal vari-ation of T local (t,r )can be calculated for even highly inhomogeneous systems such as e.g.a plasma,shock loaded systems 60or for ion-bombardment induced ther-mal spikes 36.The thermalized region if assumed as an overheated liquid state of matter,and is close to an ideal gas and than ET can be applied.In an ideal gas atoms can move few ?A /ps (that is a nearly ballistic atomic mo-bility).In our system we ?nd a similar rate of mobility within the thermalized region during simulations when

a Pt impurity atom has been injected.The thermal-ized state of the local subregion in Al persists up to few ps which is a very short lifetime in the thermody-namic sense.The quench rate of the liquid-like phase is extremely fast.Nevertheless,the local temperature T i,local (t )can be formally assigned to each particles dur-ing the molten phase at time t using the ET,

1

2

k B T i,local (t ),

(6)

where v i (t )and m i are the atomic velocity and mass of i th particle.Note that we do not follow the spatial vari-ation of T i,local (t )as it has been calculated e.g.in ref.60.T i,local (t )is always assigned to the velocity v i (t )of par-ticle i at time t .We are interested in the time evolution of T i,local (t )in a particle trajectory.T i,local (t )has no physical meaning in a strict thermodynamic sense since ergodic theory relates only the time averaged T local to the ensemble average (observable temperature).How-ever,summing up for each particles within the thermal-ized volume and calculating the average T local (t )of an ensemble of particles in a local volume could provide a time dependent ensemble averaged local temperature with physical meaning.The averaged local temperature T local (t )within a region of the substrate is given than at time t for N number of hyperthermal atoms

T local (t )=

1

N

N i

m i v 2i

(t )

2kT melt ,where T melt is the bulk melting point of e.g.Al,

E Al kin ≈0.07eV/atom in this case).This thresh-

old value is rationalized by our experience reported in recent publications 36in which we found that local melt-ing transition can be described by the occurrence of suf-?ciently large number of ”liquid”particles which possess E kin ≥3

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