- Email: [email protected]
Molecular dynamics simulation of Ga+ ion collision process
Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Molecular dynamics simulation of Ga+ ion collision process S. Satake a,⇑, K. Ono a, M. Shibahara b, J. Taniguchi a a b
Dept. of Applied Electronics, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, JAPAN Dept. of Mech. Eng. Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
a r t i c l e
i n f o
Article history: Received 17 August 2012 Received in revised form 28 November 2012 Accepted 2 December 2012 Available online 9 February 2013 Keywords: Focused ion beam Molecular dynamics Sputtering Deformation
a b s t r a c t Molecular dynamics (MD) simulations of 30 keV accelerated Ga ions has been carried out, colliding with a Si surface. Using this procedure the amorphous structural region of the Si was found to expand with the progression of the interface region, that lie between the amorphous structure and the crystalline structure, as fluence increased in the depth direction. The height of the structure is increased and has a peak value around 1.6 1015 ion/cm2, the height becomes the negative value beyond the peak, that is, the phenomenon changes from a deformation to a remove. The tendency of distribution for height and depth is a good agreement with an experimental data. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Focused ion beams (FIBs) are very useful tools in the processes of lithography, [1] doping, [2] deposition, [3,4] and etching. [5] In particular, the FIB etching and deposition techniques have been widely used for the mask repair [6] and TEM sample preparation. [7] Recently, these techniques have been extended to the fabrication of three-dimensional (3D) nanostructures. The FIB chemical vapor deposition (CVD) is used to fabricate 3D nanostructures [8] and the aerial wiring applied to photonic crystals and nanoscale tweezers. [9] The FIB etching, however, has had very limited use in the fabrication and formation of 3D structures, [10] such as predetermined curved shapes, microlens components, and diffractive optical elements, because of the very limited specifications for etching tasks. P. Schmuki et al. [11] carried out the ion implantation in Ga, As with Si++ doses ranging from 3 1013 to 3 1016 cm2 using a focused ion beam. They found that the protrusions of the ion beam treated areas is of the range of 1–15 nm in heights and shows an increase in surface roughness. Recently, a surface deformation at the nanometer precision on a Si surface was systematically achieved in experiments with a Ga ion beam collision process after an etch pit process created on the Si surface. [12] The height of the deformation was proportional to the ion beam fluence. These experiments demonstrate the requirement for a high-accuracy process technology for the masking at the nanometer precision. On the other hand, a molecular dynamics (MD) simulation can ⇑ Corresponding author. E-mail address: [email protected] (S. Satake). 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.12.066
track such phenomena, because it can track each ion and atom dynamically. Thus, the MD simulation is a powerful and effective tool for analyzing material deformation by ion beam processing. In an earlier work, there has been considerable interest in time development study of the behavior of sputtered silicon atoms after undergoing collision with the Ga ions. In previous our work, we carried out molecular dynamics (MD) simulations of 50 keV accelerated Ar ions collision with a Si surface. The impact of Ar ions on the Si surface gave rise to the formation of hillock structure. [14] They also elucidated the mechanism of sputtering during the progression of the interface region between the amorphous structure and the crystalline structure, the clusters formed during the sputtering are classified by the tracking of atoms that lie within the computational domain. [15] The heights of the hillocks obtained from the simulation were in good agreement with the experimental data. Using this procedure we found that with increased fluence in the direction of the depth, the amorphous structural region of the Si expanded with the progression of the interface region lying between the amorphous structure and the crystalline structure. The present study considers nano-order deformation and remove of a surface when the ion seed of the irradiation for the calculations is set to be Ga ion with a realistic value for an FIB. Estimations of the deformation height from the simulation results will be important information for the crafting of nano masks by ion beam processing. Large-scale MD simulations were performed for acceleration voltages of 30 keV for Ga ions. The objective of the current study is to elucidate the mechanism of sputtering during the progression of the interface region between the amorphous structure and the crystalline structure. After the convex region
236
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
Fig. 3. Effects of fluence on height of hillock structure.
Fig. 1. Computational domain.
Energy[eV]
200x10
Simulation
3
150
100 Fig. 4. Effects of fluence on local order parameter.
50 0.5
1.0
1.5 2
Fluence[ions/cm
2.0
2.5x10
15
[
0.0
Fig. 2. Time history of the system energy.
caused on the Si surface, the clusters formed during the sputtering are classified by the tracking of atoms that lie within the computational domain. 2. Simulation methods
Here i, j, and k label the atoms of the system, rij is the length of the ij bond, and hijk is the bond angle between bounds ij and jk. The parameters in Eq. (1) are referred to our previous study. [14] Russo et al. also succeeded in MD simulation of Ga ion bombardment by using Tersoff potential. [16] 2.2. Ga ion for Ziegler, Biersack, and Littmark (ZBL) potential The Ga ion potential is represented by the Ziegler, Biersack, and Littmark (ZBL) potential: [17] 2
In this work, the large-molecular dynamics simulations were performed by same program code [13,14] for ion collision processing.
/ðrÞ ¼ Z41pZe2reij UðrÞ
UðrÞ ¼
4 X r ck expðdk aiju Þ; k¼1
0 au ¼ Z0:8854a ; 0:23 þZ 0:23 i
2.1. Potential function for Si crystal
Here Z1 and Z2 are atomic numbers.
For the simulation with a Si target, the Tersoff potential function [15] was employed:
2.3. Computational parameters
/¼
1 XX fc ðr ij ÞffR ðr ij Þ þ bij fA ðr ij Þg 2 i j–i
fR ðrÞ ¼ A expðkrÞ
f c ðrÞ ¼
fA ðrÞ ¼ B expðlrÞ
bij ¼ ð1 þ bn fnij Þ1=2n ;
fij ¼
gðhÞ ¼ 1 þ
2
d
c2 2
1;
þ 12 cos pðrRÞ ; SR : 0 1 >2
X fc ðrik Þgðhijk Þ; k–i;j
c2
8 > <
ð1Þ
d þ ðh cos hÞ2
rS
a0 ¼ 0:529
ð4Þ
j
The computational domain for the large-scale calculation is shown in Fig. 1. The target domain is 21.72 nm 21.72 nm 25.9 nm, consisting of 644400 Si atoms. Langevin layers as heating bath boundary conditions in the target material were applied except the surface area. The Langevin layers[18] consist of a fixed layer and a temperature control layer. The target surface boundary was represented by a free boundary condition. The initially surface was (0 0 1) crystalline at 300 K. The irradiation area is defined as 2.0 nm 2.0 nm. At the beginning of each Ga ions impact, the Ga ion was introduced at a random location above the irradiation area on the Si surface. The Ga ion directly impacts to the Si surface without incident angle to the normal direction. The number of radiated Ga atoms in this simulation can be calculated
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
237
Fig. 5. Snapshots at the surface region; (a) 5.0 1014 ions/cm2, (b) 1.0 1015 ions/cm2, (c) 1.5 1015 ions/cm2, (d) 2.0 1015 ions/cm2 and (e) 2.5 1015 ions/cm2.
as 100 from irradiation area (2.0 nm 2.0 nm) and corresponding radiation dose (up to 2.5 1015 ions/cm2). The MD timestep is set to be 0.0230 fs. The MD simulation under the regular interval im-
pact condition was performed for the acceleration voltage of 30 keV for Ga ion. The interval time between ion impacts is defined as 230 fs that is sufficient to simulate the cooling process of the tar-
238
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
get. The interval time was determined from the simulation result for a single damage event. 3. Results and discussion Fig. 2 shows the energy of Si target versus time. The lineally increasing enhancement shows with small peaks. The peak to peak is corresponded to be the interval time between ion impacts. The distribution has many spikes owing to the boundary condition of the Langevin layers except for the target surface. As the results, the energy distribution gradually increased with repeated by the increasing and decreasing of temperature. Although averaged temperature is 0.3 eV which is higher than melting temperature of the Silicon after 2.5 1015 ions/cm2 of radiation, the temperatures of all atoms are not the melting temperature of the Silicon. That is, temperature of atom in an irradiated area is 1.75 eV, and temperature of atom in the side area of computational volume is 0.071 eV. The dominant area is the irradiation area; the energy of the irradiation area makes the melting temperature of the Silicon higher. Fig. 3 shows height and depth against fluence amount. The height of the hillock structure provided from MD simulation is defined to be the highest position in the deformed region beyond the initial surface coordinate, and the region is detected by the tracking distance between Si atoms. Moreover, the height is expressed as the distance from the initial coordinate before the collision. The height ranged from 0 nm to 4 nm, when the fluence amount is larger than 1.0 1014 ions/cm2. The height of the resultant hillock structure is exhibiting an increasing height with increasing fluence amount. The height and depth of the hillock structure provided from the experiment is also shown in Fig. 3 as the triangle closed symbol, showing the height irradiated by Ga ions when the acceleration energy is 30 keV for the fluence from 2.17 1014 to 1 1016 ion/cm2. The experiment result was exposed by FIB drawing system (JEOL JFIB-2300) at the ion beam current of 0.35 pA, acceleration voltage of 30 kV, and where the ion source was Ga+. After the development, FIB irradiated area was removed. The developed pattern depths of resists were measured with surface profilometer (KLA-Tencor a-step 500) and nano-order surface topography was observed with atomic force microscope (SII SPA-400) and scanning electron microscope (SEM). The results of simulation and experiment have a similar tendency; the heights are increased and have a peak value around 1.6 1015 ion/cm2, the heights become the negative value, that is, the transitional phenomenon from a deformation to a remove. The both height values have a good coincidence. To examine the state in the Si target, the local parameter is investigated for the fluence value:
n¼
1 ðkx þ ky þ kz Þ; 3
ð1Þ
With
N 1X 8p kx ¼ cos xi ; N atomi a
ky ¼
N 1X 8p cos yi ; N atomi a
kz ¼
1 8p umNatomi cos zi ; N a
ð2Þ
where xi is the x position of atom i in the lattice and a is the lattice constant. Note that the order parameter switches smoothly from 1 to 0 and shows zero for liquid or amorphous solid and unity for a perfectly crystalline. In Fig. 4 the local value becomes less
than unity with the irradiation progressing, that is, the amorphous region is progressed with increasing of the fluence. The small local parameter value already have achieved at the central computational region (150 angstrom) on the fluence amount of 2.5 1013, shown in Fig. 4. At the beginning of the irradiation, the Si substrate immediately became the amorphous by the Ga ion collisions. Therefore, the suddenly energy transfer from Ga ion to Si substrate can be seen at there. The amorphous region is developed from the surface; the surface location is larger than the initial coordinate from the bottom boundary (270 angstrom). Therefore, the surface deformation is caused by the expanding of amorphous region. Fig. 5 is a visualization of hillock structures at five fluence values of 5.0 1014 ions/cm2, 1.0 1015 ions/cm2, 1.5 1015 ions/ cm2, 2.0 1015 ions/cm2, and 2.5 1015 ions/cm2 where the energy of Si substrate is plotted as a function of fluence. These figures are the sections crossed at a perpendicular plane to an irradiation side. The figure shows that at 5.0 1014 the concavity of the structure is very small, at 1.0 1015 ions/cm2, after a hillock structure is formed in the upper region at the surface, a few sputtered atoms are observed, and at 2.5 1015 ions/cm2 the cluster atoms such as monomer and trimer atoms become observable. The progressing amorphous domain can be seen at these figures with increasing an amount dose. Furthermore, the same thing can be seen at time progress distribution of the local order parameter of Fig. 4. The cluster atoms under an irradiation area moving upper direction cause a blank space to make, and their quantities are mostly seen at a dose amount of 2.5 1015 ions/cm2. 4. Conclusions Large-scale MD simulations were carried out to understand the effect of fluence and acceleration energy of the ions on Si surface deformation during ion collision. A hillock structure was observed and the sputtering clusters were analyzed and studied in terms of the time development of the energy distribution of Si substrate. The results of simulation and experiment have a similar tendency; the heights are increased and have a peak value around 1.6 1015 ion/cm2, the heights become the negative value, that is, the phenomenon changes from a deformation to a remove. The both height values have a good coincidence. Acknowledgments This work is partially supported by ‘‘Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures’’ in Japan. References [1] J. Taniguchi, K. Koga, Y. Kogo, I. Miyamoto, Microelectron. Eng. 83 (2006) 940. [2] J. Brugger, G. Beljakovic, M. Despont, N.F. de Rooij, P. Vettiger, Microelectron. Eng. 35 (1997) 401. [3] K. Murakami, T. Matsuo, F. Wakaya, M. Takai, J. Vac. Sci. Technol. B 28 (2010) C2A9. [4] S. Nagamachi, M. Ueda, J. Ishikawa, J. Vac. Sci. Technol. B 16 (1998) 2515. [5] J. Taniguchi, J. Yokoyama, M. Komuro, H. Hiroshima, I. Miyamoto, Microelectron. Eng. 53 (2000) 415. [6] Zheng Cui, Philip D. Prewett, John G. Watson, Microelectron. Eng. 30 (1996) 575. [7] T.S. Yeoh, N.A. Ives, N. Presser, G.W. Stupian, M.S. Leung, J.L. McCollum, F.W. Hawley, J. Vac. Sci. Technol. B 25 (2007) 922. [8] S. Matsui, T. Kaito, J. Fujita, M. Komuro, K. Kanda, Y. Haruyama, J. Vac. Sci. Technol. B 18 (2000) 3181. [9] T. Morita, R. Kometani, K. Watanabe, K. Kanda, Y. Haruyama, T. Hoshino, K. Kondo, T. Kaito, T. Ichihashi, J. Fujita, M. Ishida, Y. Ochiai, T. Tajima, S. Matsui, J. Vac. Sci. Technol. B 21 (2003) 2737. [10] P.M. Nellen, V. Callegari, R. Bronnimann, Microelectron. Eng. 83 (2006) 1805. [11] P. Schmuki, L.E. Erickson, G. Champion, B.F. Mason, J. Fraser, C. Moessner, Appl. Phys. Lett. 70 (10) (1997) 1305.
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239 [12] N. Kawasegi, N. Morita, S. Yamada, N. Takano, T. Oyama, K. Ashida, J. Taniguchi, I. Miyamoto, Trans. J. Soc. Mech. Eng. C 71 (705) (2005) 1754. [13] S. Satake, S. Momota, S. Yamashina, M. Shibahara, J. Taniguchi, J. Appl. Phys. 106 (2009) 044910. [14] Shin-ichi, Satake, Sadao Momota, Akinori Fukushige, Shun Yamashina, Masahiko, Shibahara, Jun, Taniguchi, Nucl. Instr. Meth. Phys. Res. B 272 (2012) 5.
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[15] J. Tersoff, Phys. Rev. B 39 (1989) 5566. [16] M.F. Russo, M. Maazouz, L.A. Giannuzzi, C. Chandler, M. Utlaut, B.J. Garrison, Microsc. Microanal. 14 (4) (2008) 315. [17] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon, NewYork, 1985. [18] Takaaki Aoki, Jiro Matsuo, Nucl. Instr. Meth. Phys. Res. B 261 (2007) 639.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Molecular dynamics simulation of Ga+ ion collision process S. Satake a,⇑, K. Ono a, M. Shibahara b, J. Taniguchi a a b
Dept. of Applied Electronics, Tokyo University of Science, 6-3-1 Niijuku, Katsushika-ku, Tokyo 125-8585, JAPAN Dept. of Mech. Eng. Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
a r t i c l e
i n f o
Article history: Received 17 August 2012 Received in revised form 28 November 2012 Accepted 2 December 2012 Available online 9 February 2013 Keywords: Focused ion beam Molecular dynamics Sputtering Deformation
a b s t r a c t Molecular dynamics (MD) simulations of 30 keV accelerated Ga ions has been carried out, colliding with a Si surface. Using this procedure the amorphous structural region of the Si was found to expand with the progression of the interface region, that lie between the amorphous structure and the crystalline structure, as fluence increased in the depth direction. The height of the structure is increased and has a peak value around 1.6 1015 ion/cm2, the height becomes the negative value beyond the peak, that is, the phenomenon changes from a deformation to a remove. The tendency of distribution for height and depth is a good agreement with an experimental data. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Focused ion beams (FIBs) are very useful tools in the processes of lithography, [1] doping, [2] deposition, [3,4] and etching. [5] In particular, the FIB etching and deposition techniques have been widely used for the mask repair [6] and TEM sample preparation. [7] Recently, these techniques have been extended to the fabrication of three-dimensional (3D) nanostructures. The FIB chemical vapor deposition (CVD) is used to fabricate 3D nanostructures [8] and the aerial wiring applied to photonic crystals and nanoscale tweezers. [9] The FIB etching, however, has had very limited use in the fabrication and formation of 3D structures, [10] such as predetermined curved shapes, microlens components, and diffractive optical elements, because of the very limited specifications for etching tasks. P. Schmuki et al. [11] carried out the ion implantation in Ga, As with Si++ doses ranging from 3 1013 to 3 1016 cm2 using a focused ion beam. They found that the protrusions of the ion beam treated areas is of the range of 1–15 nm in heights and shows an increase in surface roughness. Recently, a surface deformation at the nanometer precision on a Si surface was systematically achieved in experiments with a Ga ion beam collision process after an etch pit process created on the Si surface. [12] The height of the deformation was proportional to the ion beam fluence. These experiments demonstrate the requirement for a high-accuracy process technology for the masking at the nanometer precision. On the other hand, a molecular dynamics (MD) simulation can ⇑ Corresponding author. E-mail address: [email protected] (S. Satake). 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.12.066
track such phenomena, because it can track each ion and atom dynamically. Thus, the MD simulation is a powerful and effective tool for analyzing material deformation by ion beam processing. In an earlier work, there has been considerable interest in time development study of the behavior of sputtered silicon atoms after undergoing collision with the Ga ions. In previous our work, we carried out molecular dynamics (MD) simulations of 50 keV accelerated Ar ions collision with a Si surface. The impact of Ar ions on the Si surface gave rise to the formation of hillock structure. [14] They also elucidated the mechanism of sputtering during the progression of the interface region between the amorphous structure and the crystalline structure, the clusters formed during the sputtering are classified by the tracking of atoms that lie within the computational domain. [15] The heights of the hillocks obtained from the simulation were in good agreement with the experimental data. Using this procedure we found that with increased fluence in the direction of the depth, the amorphous structural region of the Si expanded with the progression of the interface region lying between the amorphous structure and the crystalline structure. The present study considers nano-order deformation and remove of a surface when the ion seed of the irradiation for the calculations is set to be Ga ion with a realistic value for an FIB. Estimations of the deformation height from the simulation results will be important information for the crafting of nano masks by ion beam processing. Large-scale MD simulations were performed for acceleration voltages of 30 keV for Ga ions. The objective of the current study is to elucidate the mechanism of sputtering during the progression of the interface region between the amorphous structure and the crystalline structure. After the convex region
236
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
Fig. 3. Effects of fluence on height of hillock structure.
Fig. 1. Computational domain.
Energy[eV]
200x10
Simulation
3
150
100 Fig. 4. Effects of fluence on local order parameter.
50 0.5
1.0
1.5 2
Fluence[ions/cm
2.0
2.5x10
15
[
0.0
Fig. 2. Time history of the system energy.
caused on the Si surface, the clusters formed during the sputtering are classified by the tracking of atoms that lie within the computational domain. 2. Simulation methods
Here i, j, and k label the atoms of the system, rij is the length of the ij bond, and hijk is the bond angle between bounds ij and jk. The parameters in Eq. (1) are referred to our previous study. [14] Russo et al. also succeeded in MD simulation of Ga ion bombardment by using Tersoff potential. [16] 2.2. Ga ion for Ziegler, Biersack, and Littmark (ZBL) potential The Ga ion potential is represented by the Ziegler, Biersack, and Littmark (ZBL) potential: [17] 2
In this work, the large-molecular dynamics simulations were performed by same program code [13,14] for ion collision processing.
/ðrÞ ¼ Z41pZe2reij UðrÞ
UðrÞ ¼
4 X r ck expðdk aiju Þ; k¼1
0 au ¼ Z0:8854a ; 0:23 þZ 0:23 i
2.1. Potential function for Si crystal
Here Z1 and Z2 are atomic numbers.
For the simulation with a Si target, the Tersoff potential function [15] was employed:
2.3. Computational parameters
/¼
1 XX fc ðr ij ÞffR ðr ij Þ þ bij fA ðr ij Þg 2 i j–i
fR ðrÞ ¼ A expðkrÞ
f c ðrÞ ¼
fA ðrÞ ¼ B expðlrÞ
bij ¼ ð1 þ bn fnij Þ1=2n ;
fij ¼
gðhÞ ¼ 1 þ
2
d
c2 2
1;
þ 12 cos pðrRÞ ; SR : 0 1 >2
X fc ðrik Þgðhijk Þ; k–i;j
c2
8 > <
ð1Þ
d þ ðh cos hÞ2
r
a0 ¼ 0:529
ð4Þ
j
The computational domain for the large-scale calculation is shown in Fig. 1. The target domain is 21.72 nm 21.72 nm 25.9 nm, consisting of 644400 Si atoms. Langevin layers as heating bath boundary conditions in the target material were applied except the surface area. The Langevin layers[18] consist of a fixed layer and a temperature control layer. The target surface boundary was represented by a free boundary condition. The initially surface was (0 0 1) crystalline at 300 K. The irradiation area is defined as 2.0 nm 2.0 nm. At the beginning of each Ga ions impact, the Ga ion was introduced at a random location above the irradiation area on the Si surface. The Ga ion directly impacts to the Si surface without incident angle to the normal direction. The number of radiated Ga atoms in this simulation can be calculated
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
237
Fig. 5. Snapshots at the surface region; (a) 5.0 1014 ions/cm2, (b) 1.0 1015 ions/cm2, (c) 1.5 1015 ions/cm2, (d) 2.0 1015 ions/cm2 and (e) 2.5 1015 ions/cm2.
as 100 from irradiation area (2.0 nm 2.0 nm) and corresponding radiation dose (up to 2.5 1015 ions/cm2). The MD timestep is set to be 0.0230 fs. The MD simulation under the regular interval im-
pact condition was performed for the acceleration voltage of 30 keV for Ga ion. The interval time between ion impacts is defined as 230 fs that is sufficient to simulate the cooling process of the tar-
238
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239
get. The interval time was determined from the simulation result for a single damage event. 3. Results and discussion Fig. 2 shows the energy of Si target versus time. The lineally increasing enhancement shows with small peaks. The peak to peak is corresponded to be the interval time between ion impacts. The distribution has many spikes owing to the boundary condition of the Langevin layers except for the target surface. As the results, the energy distribution gradually increased with repeated by the increasing and decreasing of temperature. Although averaged temperature is 0.3 eV which is higher than melting temperature of the Silicon after 2.5 1015 ions/cm2 of radiation, the temperatures of all atoms are not the melting temperature of the Silicon. That is, temperature of atom in an irradiated area is 1.75 eV, and temperature of atom in the side area of computational volume is 0.071 eV. The dominant area is the irradiation area; the energy of the irradiation area makes the melting temperature of the Silicon higher. Fig. 3 shows height and depth against fluence amount. The height of the hillock structure provided from MD simulation is defined to be the highest position in the deformed region beyond the initial surface coordinate, and the region is detected by the tracking distance between Si atoms. Moreover, the height is expressed as the distance from the initial coordinate before the collision. The height ranged from 0 nm to 4 nm, when the fluence amount is larger than 1.0 1014 ions/cm2. The height of the resultant hillock structure is exhibiting an increasing height with increasing fluence amount. The height and depth of the hillock structure provided from the experiment is also shown in Fig. 3 as the triangle closed symbol, showing the height irradiated by Ga ions when the acceleration energy is 30 keV for the fluence from 2.17 1014 to 1 1016 ion/cm2. The experiment result was exposed by FIB drawing system (JEOL JFIB-2300) at the ion beam current of 0.35 pA, acceleration voltage of 30 kV, and where the ion source was Ga+. After the development, FIB irradiated area was removed. The developed pattern depths of resists were measured with surface profilometer (KLA-Tencor a-step 500) and nano-order surface topography was observed with atomic force microscope (SII SPA-400) and scanning electron microscope (SEM). The results of simulation and experiment have a similar tendency; the heights are increased and have a peak value around 1.6 1015 ion/cm2, the heights become the negative value, that is, the transitional phenomenon from a deformation to a remove. The both height values have a good coincidence. To examine the state in the Si target, the local parameter is investigated for the fluence value:
n¼
1 ðkx þ ky þ kz Þ; 3
ð1Þ
With
N 1X 8p kx ¼ cos xi ; N atomi a
ky ¼
N 1X 8p cos yi ; N atomi a
kz ¼
1 8p umNatomi cos zi ; N a
ð2Þ
where xi is the x position of atom i in the lattice and a is the lattice constant. Note that the order parameter switches smoothly from 1 to 0 and shows zero for liquid or amorphous solid and unity for a perfectly crystalline. In Fig. 4 the local value becomes less
than unity with the irradiation progressing, that is, the amorphous region is progressed with increasing of the fluence. The small local parameter value already have achieved at the central computational region (150 angstrom) on the fluence amount of 2.5 1013, shown in Fig. 4. At the beginning of the irradiation, the Si substrate immediately became the amorphous by the Ga ion collisions. Therefore, the suddenly energy transfer from Ga ion to Si substrate can be seen at there. The amorphous region is developed from the surface; the surface location is larger than the initial coordinate from the bottom boundary (270 angstrom). Therefore, the surface deformation is caused by the expanding of amorphous region. Fig. 5 is a visualization of hillock structures at five fluence values of 5.0 1014 ions/cm2, 1.0 1015 ions/cm2, 1.5 1015 ions/ cm2, 2.0 1015 ions/cm2, and 2.5 1015 ions/cm2 where the energy of Si substrate is plotted as a function of fluence. These figures are the sections crossed at a perpendicular plane to an irradiation side. The figure shows that at 5.0 1014 the concavity of the structure is very small, at 1.0 1015 ions/cm2, after a hillock structure is formed in the upper region at the surface, a few sputtered atoms are observed, and at 2.5 1015 ions/cm2 the cluster atoms such as monomer and trimer atoms become observable. The progressing amorphous domain can be seen at these figures with increasing an amount dose. Furthermore, the same thing can be seen at time progress distribution of the local order parameter of Fig. 4. The cluster atoms under an irradiation area moving upper direction cause a blank space to make, and their quantities are mostly seen at a dose amount of 2.5 1015 ions/cm2. 4. Conclusions Large-scale MD simulations were carried out to understand the effect of fluence and acceleration energy of the ions on Si surface deformation during ion collision. A hillock structure was observed and the sputtering clusters were analyzed and studied in terms of the time development of the energy distribution of Si substrate. The results of simulation and experiment have a similar tendency; the heights are increased and have a peak value around 1.6 1015 ion/cm2, the heights become the negative value, that is, the phenomenon changes from a deformation to a remove. The both height values have a good coincidence. Acknowledgments This work is partially supported by ‘‘Joint Usage/Research Center for Interdisciplinary Large-scale Information Infrastructures’’ in Japan. References [1] J. Taniguchi, K. Koga, Y. Kogo, I. Miyamoto, Microelectron. Eng. 83 (2006) 940. [2] J. Brugger, G. Beljakovic, M. Despont, N.F. de Rooij, P. Vettiger, Microelectron. Eng. 35 (1997) 401. [3] K. Murakami, T. Matsuo, F. Wakaya, M. Takai, J. Vac. Sci. Technol. B 28 (2010) C2A9. [4] S. Nagamachi, M. Ueda, J. Ishikawa, J. Vac. Sci. Technol. B 16 (1998) 2515. [5] J. Taniguchi, J. Yokoyama, M. Komuro, H. Hiroshima, I. Miyamoto, Microelectron. Eng. 53 (2000) 415. [6] Zheng Cui, Philip D. Prewett, John G. Watson, Microelectron. Eng. 30 (1996) 575. [7] T.S. Yeoh, N.A. Ives, N. Presser, G.W. Stupian, M.S. Leung, J.L. McCollum, F.W. Hawley, J. Vac. Sci. Technol. B 25 (2007) 922. [8] S. Matsui, T. Kaito, J. Fujita, M. Komuro, K. Kanda, Y. Haruyama, J. Vac. Sci. Technol. B 18 (2000) 3181. [9] T. Morita, R. Kometani, K. Watanabe, K. Kanda, Y. Haruyama, T. Hoshino, K. Kondo, T. Kaito, T. Ichihashi, J. Fujita, M. Ishida, Y. Ochiai, T. Tajima, S. Matsui, J. Vac. Sci. Technol. B 21 (2003) 2737. [10] P.M. Nellen, V. Callegari, R. Bronnimann, Microelectron. Eng. 83 (2006) 1805. [11] P. Schmuki, L.E. Erickson, G. Champion, B.F. Mason, J. Fraser, C. Moessner, Appl. Phys. Lett. 70 (10) (1997) 1305.
S. Satake et al. / Nuclear Instruments and Methods in Physics Research B 307 (2013) 235–239 [12] N. Kawasegi, N. Morita, S. Yamada, N. Takano, T. Oyama, K. Ashida, J. Taniguchi, I. Miyamoto, Trans. J. Soc. Mech. Eng. C 71 (705) (2005) 1754. [13] S. Satake, S. Momota, S. Yamashina, M. Shibahara, J. Taniguchi, J. Appl. Phys. 106 (2009) 044910. [14] Shin-ichi, Satake, Sadao Momota, Akinori Fukushige, Shun Yamashina, Masahiko, Shibahara, Jun, Taniguchi, Nucl. Instr. Meth. Phys. Res. B 272 (2012) 5.
239
[15] J. Tersoff, Phys. Rev. B 39 (1989) 5566. [16] M.F. Russo, M. Maazouz, L.A. Giannuzzi, C. Chandler, M. Utlaut, B.J. Garrison, Microsc. Microanal. 14 (4) (2008) 315. [17] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon, NewYork, 1985. [18] Takaaki Aoki, Jiro Matsuo, Nucl. Instr. Meth. Phys. Res. B 261 (2007) 639.