S4-2

Molecular Dynamics Simulation of Chemical Sputtering
MD シミュレーションによる化学スパッタリングの物理機構解析
Satoshi Hamaguchi and Hideaki Yamada*
浜口智志
山田英明*

Science and Technology Center for Atoms, Molecules, and Ions Control, Graduate School of Engineering,Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan
大阪大学大学院工学研究科原子分子イオン制御理工学センター，〒565-0871 大阪府吹田市山田丘2-1*

Diamond Research Center, National Institute of Advanced Industrial Science and Technology,
1-8-31 Midorigaoka, Ikeda, Osaka, 563-8577, Japan*
産業技術総合研究所ダイヤモンド研究センター，〒563-8577 大阪府池田市緑丘1-8-31

Surface sputtering processes by plasmas often involve surface chemical reactions. The physicalmechanisms of such chemical sputtering processes, which are also known as reactive ion etching (RIE)
processes, are not yet completely understood. In the present work we shall present the method of molecular
dynamics (MD) simulation to analyze chemical reactions occurring on a material surface which is subject
to simultaneous energetic ion bombardment and the inflow of charge- neutral radical species. Especiallyour recent analyses of carbon-based material etching processes by hydrogen or hydrocarbon plasmas arereviewed.

1. Introduction
Plasma processes such as reactive ion etching(RIE) and plasma enhanced chemical vapor
deposition (PECVD) constitute a large and essential
part of semiconductor manufacturing processes
today [1,2]. For such applications as well as otherindustrial applications of plasmas, controlling
plasma-wall (i.e., plasma-surface) interactions is ofsignificant importance since the quality ofprocessed materials is largely determined by suchinteractions. For magnetic fusion devices, too, studyof plasma-wall interactions has attracted muchattention as the bulk plasma conditions are often
influenced by interactions of the plasma with thefirst wall and divertor materials.
Recently various investigators have examinedsurface reaction mechanisms for materials exposed
to beams or plasmas by using molecular dynamics(MD) simulations. It has been demonstrated thatsuch MD simulations can provide useful, andsometimes quantitatively reliable, information on
plasma-surface interactions.
For classical MD simulations, reliability of theresults is in general largely affected by the choice ofinteratomic potential functions for the particles
constituting the system. To simulate plasma-surface
interaction, one usually needs to handle a large
number of particles (i.e., atoms) and repeat similar
simulation runs of energetic particle injections for
sufficiently many times to reduce statistical noise.
Therefore, the cost of such simulations precludes

the use of more detailed ab initio (i.e., quantummechanical) simulations. In classical MD
simulations, therefore, the employed potential
model needs to be sufficiently representative of thetrue atomic interactions for the system.
In this work, we shall review the method of MD
simulation to analyze chemical sputtering processes,
i.e., chemical reactions occurring on a material
surface which is subject to simultaneous energetic
ion bombardment and the inflow of charge- neutral
radical species, using examples of our recent
analyses of carbon-based material etching processes
by hydrogen or hydrocarbon plasmas.
2. Interatomic potential functions for covalentbondsFirst let us briefly discuss the classicalinteratomic potential functions. If there are N atoms
and the position of the i th atom is given by ri ,then the total potential energy of the system V may
be written in cluster expansion asV ( r1 , r2 ," , rN ) = ∑ vij(2) ( ri , r j ) +i< j∑ v (r , r , r ) +i< j<k(3)ijkijk(1)(N )" + v1,2,3,", N ( r1 , r2 , " , rN )In this way, the force exerted on each atom may beregarded as a multi-body force in the time scale ofatomic motion since electron orbitals are often

shared by multiple atoms. In Eq. (1), vij( ) is called2

thetwo-bodypotential,

( 3)
vijk
thethree-bodypotential, and so on. This expansion can be done
uniquely, regardless of the nature of atomicinteractions. For example, interactions of rare gas
atoms may be well approximated by the first term
only, possibly by the well-known Lennard-Jones
potential. In general, for given atoms, it is nearly
impossible to construct classical interatomic
potential functions with high accuracy in the formof Eq. (1) since it is hardly practical to take into
account all possible multi-body interactions.
Therefore, depending on the purpose of simulations,
we selectively incorporate only the important
effects of atomic interactions and represent them byrelatively simple functional forms, so that we canachieve both computational efficiency classical MD
simulations and reasonable accuracy of atomicdynamics [3].

Fig.1: Surface morphology of PPP after 2.4×1016
atoms/cm2 dose of carbon atom injections. White andblack spheres represent carbon and hydrogen atoms

3. MD simulations
In MD simulations, the equations of motion basedon the interatomic potentials mentioned above aresolved numerically [3-8]. The substrate material isplaced in a simulation cell and periodic boundary
conditions are imposed in the horizontal directions.
Physical quantities such as sputtering yields
generally depend on beam dose and usually aremeasured after the surface conditions reach a steadystate by sufficient beam bombardment. Energeticparticles (e.g., atoms, molecules, radicals, etc.) areinjected from randomly chosen locations to thesurface with a given injection angle. Most transientetching processes such as breaking andre-formation of bonds by particle bombardment
typically occur within a pico second. Therefore
each ion bombardment may be considered as anindependent process. To simulate a series of suchindependent processes efficiently, we usually solve
the motions of all particles under constant-energy
conditions for a certain time interval (typically ofthe order of pico seconds) after each injection andthen apply artificial cooling to the system in a
relatively short period (again typically of the orderof pico seconds). At the end of this cooling process,a new energetic particle is directed to the surface
and the whole simulation cycle is repeated.
Chemical sputtering processes of the surface
often proceed simultaneously with deposition
processes of some specific atomic/molecularspecies. Deposition processes are in general moresensitive to the thermal relaxation processes, so one
needs to incorporate thermal effects in MD
simulations effectively. One possibility for suchprocesses is to use a Monte Carlo algorithm. In thepresentation, we review the recent development ofMD
simulation
methods
tostudy
beam/plasma-surface interactions, using our recent
results of sputtering/deposition processes forcarbon-based materials by hydrogen or hydrocarbon
plasmas [6,7].
References[1] S. Hamaguchi: IBM J. Res. Develop. 43, (1999)
199.
[2] S. Hamaguchi: Thin Films 22, (1996) 81.
[3] S. Hamaguchi, H. Ohta, and H. Yamada: J. Plasmasand Fusion Research, in press.
[4] H. Ohta and S. Hamaguchi: J. Chem. Phys. 115(2001) 6679.
[5] H. Ohta and S. Hamaguchi: J. Vac. Sci. Technol.
A19 (2001) 2373.
[6] H. Yamada and S. Hamaguchi: J. Appl. Phys. 96,(2004) 6147.
[7] H. Yamada and S. Hamaguchi: J. Plasmas andFusion Research, in press.
[8] S. Hamaguchi, Oyo Buturi 70 (2001) 1099 [inJapanese].