23P007-O
Model Analysis of Nanoscale Surface Roughness and Rippling during Plasma
Etching of Si under Oblique Ion Incidence
プラズマエッチング時における表面ラフネス形成メカニズムとイオン入射角度依存性
Hirotaka Tsuda, Yoshinori Takao, Koji Eriguchi and Kouichi Ono
津田博隆，鷹尾祥典，江利口浩二，斧 高一
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University,
Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
京都大学大学院工学研究科 航空宇宙工学専攻 〒606-8501 京都市左京区吉田本町
Three-dimensional atomic-scale cellular model has been developed to reproduce the formation ofnanoscale or atomic-scale surface ripples during Si etching in chlorine-based plasmas under oblique ionincidence. Numerical results implied that ion incident angle and energy, and neutral-to-ion flux ratios
play an important role in the formation of surface rippling or groove-like surface roughness.

1. Introduction
Three-dimensional
measurement
andprediction of atomic-scale surface roughness on
etched features become increasingly important for
the analysis of line edge roughness (LER) andline width roughness (LWR) on feature sidewalls
during etching; however, the feature profiles are
too small and/or too complex to measure thesurface roughness on bottom surfaces andsidewalls of the etched features. To predict thesurface roughness on atomic/nanometer scale, wehave developed our own three-dimensional
atomic-scale cellular model (ASCeM-3D) [1] andfeature profile simulation.
In this study,emphasis is placed on a better understanding of
the formation mechanisms of atomic-scalesurface roughness during Si etching inchlorine-based plasmas and the relationshipbetween plasma parameters (ion incident angle,ion incident energy, and neutral-to-ion flux ratio)
and etched feature profiles, with further attention
being given to the formation of ripple structureson etched surfaces.

Fig. 1 Schematic of the ASCeM-3D model.

2. ModelingIn the ASCeM-3D model shown in Fig. 1, thesimulation domain including substrates is divided

into a number of small cubic cells of L = Si−1/3 =2.7 Å, where Si = 5.0  1022 cm−3 is the atomic
density of Si substrates. Ions and neutrals are
injected from the top of the simulation domain witha given incident angle i and an isotropic
distribution, respectively, and etch and/or sputter
products are taken to be desorbed from etchingsurfaces into microstructural features thermally or
isotropically with a cosine distribution.
The
particle transport is analyzed using thethree-dimensional Monte Carlo (MC) algorithm,
and the local surface normal or local angle  ofincidence is calculated by using the four-point
technique for 5  5  5 neighboring cells (125 cellsin total) at around the substrate surface cell that theion reaches from the plasma. Two-body elastic
collision processes between incident ions andsubstrate atoms are also taken into account toanalyze the ion reflection on etched feature surfaces
and penetration into substrates. The ASCeM-3D
takes into account surface chemistries based on theMC algorithm [2-4], including adsorption andreemission of neutrals, chemical etching,ion-enhanced etching, physical sputtering, andredeposition of etch and/or sputter products on
feature surfaces.
3. Results and Discussion
Figure 2 shows etch rates or ERs and roughness
parameters (RMS) as a function of ion incident
angle θi, simulated for different incident ion
energies of Ei = 20, 50, 100, and 200 eV with an ion
flux i0 = 1.0  1016 cm−2s−1 and a neutral-to-ion
flux ratio n0/i0 = 100, which are typical ofhigh-density plasma etching environments.
Numerical results indicated that ERs increase withincreasing Ei and surface roughness becomes larger

400

200 eV300

100 eV

200

50 eV1000Etch ｒate (nm/min)

Etch ｒate (nm/min)

300

20 eV

i0/n0 = 50200

i0/n0 = 10
100

0030

60

09030

1290

81050 eV

86RMS (nm)

RMS (nm)

60Angle (deg)Angle (deg)200 eV100 eV

420 eV030

i0/n0 = 10064

i0/n0 = 50220

i0/n0 = 100

6090Angle (deg)Fig. 2 Etch rates and roughness parameters (RMS) asa function of ion incident angle θi, simulated for
different ion incident energies of Ei = 20, 50, 100,and 200 eV with a neutral-to-ion flux ratio n0/i0 =100. Here, RMS is the root mean square roughness.

Fig. 4 Surface features of Si at t = 20 s after the startof etching in Cl2 plasma, simulated for different ion
incident angles of θi = (a) 0°, (b) 45°, (c) 75°, and (d)80° with an ion energy Ei = 100 eV and neutral-to-ion
flux ratios n0/i0 = 100.

at higher Ei for θi = 0° or normal incidence of ions.
In addition, for increased θi or oblique ion incidence,
surface roughness at Ei = 50 and 100 eV tends tobecome larger than that at higher Ei (= 200 eV).
In contrast, Fig. 4 shows ERs and the values ofRMS as a function of ion incident angle θi,simulated for different neutral-to-ion flux ratios ofn0/i0 = 10, 50, and 100 with Ei = 100. The
comparison between the results in Fig. 3 and 4
indicates that there are different formation
mechanisms between normal and oblique ion
incidences, and ion incidence angle θi, ion incident
energy Ei, and neutral-to-ion flux ratio n0/i0 play0030

i0/n0 = 106090Angle (deg)Fig. 3 Etch rates and roughness parameters (RMS) asa function of ion incident angle θi, simulated fordifferent neutral-to-ion flux ratios of n0/i0 = 10, 50,and 100 with an ion incident energy Ei = 100. Here,RMS is the root mean square roughness.

an important role in the roughness formation.
Figure 4 shows the surface features of Si at t = 20s after the start of etching in Cl2 plasma for different
ion incident angles of θi = 0°, 45°, 75°, and 80°,
simulated with Ei = 100 eV and n0/i0 = 100.
Numerical results indicated that as the angle θi isincreased, nanoscale convex features drasticallychange and the ripple structures of etched surfaces
occur. For θi = 0° or normal incidence of ions, thesurfaces are randomly roughened. For increased θi= 45°, the ripples are formed perpendicular to thedirection of ion incidence, while parallel to that ofion incidence for further increased θi = 75° and 80°.
The
ASCeM-3D
model
impliedthatneutral-to-ion flux ratio or the neutral particle
supply to etched surfaces plays a role in theformation of surface rippling or groove-like surface
roughness as important as ion incident angle andenergy.
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Ono: Jpn. J. Appl. Phys. 50 (2011) 08JE06.
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[3] H. Tsuda, M. Mori, Y. Takao, K. Eriguchi, and K.
Ono: Thin Solid Films 518 (2010) 3475.
[4] H. Tsuda, M. Mori, Y. Takao, K. Eriguchi, and K.
Ono: Jpn. J. Appl. Phys. 49 (2010) 08JE01.