J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)399–401
000–000

Effects of Van der Waals Interactions on SiO2 Etchingby CFx Plasmas
OHTA Hiroaki and HAMAGUCHI Satoshi
Department of Fundamental Energy Science, Kyoto University, Uji 611-0011, Japan(Received: 9 December 2003 / Accepted: 24 February 2004)

Abstract
We have performed Molecular Dynamics (MD) simulations of silicon dioxide etching processes by fluorocarbon
plasmas. It is known that both etching and deposition caused by carbon atoms can take place simultaneously in suchprocesses. In order to understand the atomic scale mechanisms of such processes, we have developed empiricalinteratomic potential models for MD simulations, which include covalent bonds and Van der Waals (VW) interactions
among Si, O, C, F atoms. Especially, to clarify the effect of VW interactions, we have performed two different
simulations with and without VW interactions. Deposition of fluorocarbon films is observed only in the case with
VW forces. In the early stage of carbon deposition, small carbon clusters are formed sparsely without being boundwith the substrate atoms through covalent bonds. Therefore such carbon clusters can easily depart from the surface
without VW interactions. Although VW interactions are order-of-magnitude smaller than covalent bonds in terms ofbond energy, we found it is VW interactions that keep such deposition precursors near the substrate surface to assist
the growth of fluorocarbon films.
Keywords:
plasma processing, plasma-surface interaction, deposition, molecular dynamics, interatomic potential

1. Introduction

mechanisms. [1,2,3,4]
In order to perform MD simulations of SiO2 etching byfluorocarbon plasmas, we have developed a phenomenologicalmodel of the covalent bonds and Van der Waals (VW)
interactions for Si/O/C/F systems. Details of this interatomic
potential model will be published elsewhere.

The atomic-scale understanding of plasma-surface
interaction during plasma etching processes is of significant
importance in the development of advanced dry etching
technologies for microelectronics applications. Etchingprocesses of silicon dioxide (SiO2), which is widely used as
insulator material for interconnect in microchips, are typicallydone with fluorocarbon plasmas (CFx). One of the problems
that are difficult to understand in such processes is thecoexistence of both etching and deposition processes caused
by carbon atoms. Surface reactions during the etching process,i.e., “plasma-surface interactions”, may be understood in its
simplistic form as a “beam-surface interaction,” without
taking into account effects of background neutral species. Theenergy range of ions accelerated in the plasma sheath (thebeam energy) is typically 10–1000 eV.
Recently numerical simulations by classical molecular
dynamics (MD) methods have attracted a great deal ofattention as a means to analyze plasma-surface interactions.
Various such simulations have demonstrated that this classicalapproach, as opposed to ab initio quantum mechanicalsimulations, provides sufficiently good descriptions of surface
reaction dynamics. Numerical studies based on classical MD
simulations can often compensate shortage of experimental
data and give physical insight into the atomic-scale reaction

2. Model and MD procedure
For MD simulations, our model consists of two types ofinteractions: the covalent bond and VW interaction. Theformer is strong (several eV) and of short range, effective only
among neighboring atoms. By contrast, the latter is weak
(10-2 eV) and of longer range, which can reach more than
third neighboring atoms (several Å). The total VW interactionenergy per atom is typically about 10-1 eV as about a dozenof atoms may exist in the interaction range.
Let us briefly outline our interatomic potential model for
Si/O/C/F systems. During plasma etching, energetic ions hit
the material surface and interact with it chemically andphysically. Chemical reactions often involve breaking andreconnection of covalent bonds. To represent chemical
reactions correctly in MD simulations, it is important tomodel interatomic potentials associated with covalent bonds
with good accuracy. To construct our phenomenological

Corresponding author’s e-mail: hamaguch@ppl.eng.osaka-u.ac.jp1399©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

OHTA H. et al., Effects of Van der Waals Interactions on SiO2 Etching by CFx Plasmas

way that no atom will pass through the bottom layer during
the simulation. The typical number of atoms employed torepresent the substrate in our simulations is about twothousand. The pseudo β-cristobalite is used as the initiallattice of our SiO 2 substrate, where O atoms are inserted
between Si atoms located at the diamond lattice sites.
Energetic atoms or clusters are directed normally to thesubstrate surface and the trajectory of each atom is traced
numerically based on Newton’s equation of motion. Each
impact by energetic atom or a cluster is considered as anindependent event. In a single event of impact, atomic
motions are calculated under the constant energy conditions
for 0.4 ps. Almost all reactions such as breaking andreformation of bonds by energetic impact take place during
this period. After then an artificial temperature control(Berendsen thermostat [5]) is imposed on atoms constituting
the surface (except for atoms bound with the surface weakly
through VW interactions) during the next 0.1 ps, which
represent energy dissipation from the surface. At the end of
the cycle, the surface temperature is set to the initial surface
temperature, i.e., 300 K. Atoms that leave the substrate surface
with a momentum in the upward direction are automaticallydetected and removed from the simulation cell.

potential energy (eV)interatomic potential functions, we fit model functions toenergy data obtained from ab initio quantum mechanicalcalculations. In this process, special attention was paid toensure that the model potentials are designed to correctly
reproduce stable molecules in thermal equilibrium. In otherwords, the bond energy, bond length, and frequency of
harmonic oscillation of each covalent bond were carefully fit
to ab initio data. In addition, our model includes an algorithm
to select the bond order of each covalent bond appropriately,
so that the model can represent the dependence of the π-bondenergy for C-C, C-O, O-O atoms on the configuration ofsurrounding atoms. The de-localized double bond, thecoordinate bond in CO molecule, and the +Iπ effect by a F
atom (an effect that F atoms weaken neighboring π-bonds)
are also taken into account. In the model, all isolated atoms
and atomic clusters are assumed to be charge neutral.
Van der Waals (VW) interactions are also included in
the potential model. The VW interaction is typically given by
a two-body potential function of Lennard-Jones type. In thepresent model, for the sake of simplicity, we use the same
VW attractive potential function for all atomic pairs and its
potential depth is about 10-2 eV. The repulsive part of the VW
potential is not included since it is already in the covalentbond potential. The VW potential function is shown together
with the C-C pair potential function in Fig. 1, where the VW
potential energy is magnified by a factor of 10, so that theshapes of both covalent bond potential and VW potential canbe seen in the figure.
To emulate surface reactions caused by energetic ion(atomic) impact, atomic-scale MD simulations are performed
in a cell with a fixed boundary at the bottom of the cell andperiodic boundaries in the horizontal directions. The substrateconsists of atoms arranged in a specific manner and is brought
to thermodynamical equilibrium with a given (usually theroom) temperature. In our simulations presented here, thesubstrate surface area is about 2.1 × 2.1 nm2 and its depth is
kept sufficiently deep as the code automatically adds extra
atomic monolayers to the substrate from the bottom in such a

3. Simulation results
First we performed MD simulation by using the potential
model of covalent bonds only. As shown in Fig. 2 (a), nostable deposition was observed without VW interactions. In
these simulations, atomic clusters, especially those containing
many carbon atoms, are created and most of them end up
leaving the surface even with extremely small upward
momenta if they are not bound with the substrate through

10Van der Waals force (×10)-1-2-3Covalent bond-4024

6810(a)bond length (Å)
Fig. 1Fig. 2

Potential energy curve for the C-C bond including VWinteraction. The VW potential energy is magnified by afactor of 10, so that it can be seen in this figure.

2400(b)

Typical surface conditions during 100 eV CF beam
impact: (a) without and (b) with VW interactions. Large
white, small white, gray, and black spheres represent
Si, O, F, and C atoms, respectively.

OHTA H. et al., Effects of Van der Waals Interactions on SiO2 Etching by CFx Plasmas

covalent bonds. As a result, carbon atoms remain in thesubstrate only sparsely. Under these conditions, etching
reactions take place, which does not agree with experimental
observations of beam etching performed under similar
conditions. [6]Second we introduced VW interactions in oursimulations in addition to the covalent bonds. With VWinteractions, deposition was observed, as shown in Fig. 2 (b).
This agrees with observations in beam experiments [6]. For
an atom located near or in the substrate, its total VW
interaction energy is of order of 10-1 eV due to its relatively
long interaction range (in which there are dozens ofinteracting atoms) although the pair-wise VW potential energy
is only about 10-2 eV. The VW potential energy per atoms is,however, still lower by a factor of 10 than the corresponding
covalent-bond potential energy.
Nevertheless VW interactions significantly increase thechance to trap unbound atoms and clusters. In order toconfirm that the long-range nature of the VW interaction,rather than the potential depth of it, causes deposition, we
also performed simulations using 10 % stronger covalent
forces without VW interactions. We have found no deposition
takes place under such conditions.

Under the conditions given in Fig. 2 (b) (i.e., CF 100eV), a relatively rich carbon layer is formed. Carbon atoms
accumulate gradually as the ions bombard the surface. Under
these conditions, sputtering also occurs and the C deposition
rate measured in simulations is about 0.7. The main etchproducts are F and C atoms. When deposition occurs, we haveobserved that the distribution of F atoms has a peak near theinterface between the carbon layer and SiO2 substrate, which
seems consistent with experimental observations [7]. On theother hand, for the 300 eV CF2 beam, as shown in Fig. 3, acarbon layer is not formed and C atoms remain in thesubstrate only sparsely. In this case, steady etching wasobserved. The number of deposited C atoms is saturated atabout 3 × 1015 (atoms/cm2). The main etching products inthis case are F, CO, C, O, CF, SiF2, SiF3, and SiF4. This isalso in agreement with experimental results [6].
In summary, our new potential model for Si/O/F/C
systems enables us to perform MD simulations of surface
reactions under energetic bombardment by atoms and clusters.
In particular, we have observed that deposition processes canbe caused by VW interactions. Our simulation results areoverall consistent with experimental observations.

Acknowledgements
This work is supported by the Semiconductor
Technology Academic Research Center (STARC) and theAssociation of Super-Advanced Electronics Technologies(ASET).

References

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Typical surface during 300 eV CF2 beam impact. Big
white, small white, gray, and black spheres are Si, O, F,and C atoms, respectively.

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