Application of the Level Set Method in Three-Dimensional Simulation of the Roughening and Smoothing of Substrates in Nanotechnologies

Branislav Radjenović, Marija Radmilović-Radjenović

Institute of Physics, University of Belgrade, Zemun, Serbia.

DOI: 10.4236/wjnse.2014.42011                

Abstract

This paper contains results of the comprehensive studies of the effect of the isotropic etching mode on roughening of the nanocomposite materials and on smoothing of the roughed nanostructure made of homogeneous materials. Three-dimensional simulation results obtained illustrate the influence of the isotropic etch process on dynamics of the roughening and smoothing of the surfaces, indicating the opposite effects of the same etch process on the surfaces made of different materials. It was shown that root mean square roughness obeys simple scaling laws during both roughening and smoothing processes. The exponential time dependences of the rms roughness have been determined.

Keywords

Nanocomposite, Roughness, Smoothing, Isotropic Etching

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bianconi, G. and Barabási, A.-L. (2001) Competition and Multiscaling in Evolving Networks. Europhysics Letters, 54, 436-442. http://dx.doi.org/10.1209/epl/i2001-00260-6
[2]	Frost, F., Fechner, R., Ziberi, B., Flamm, D. and Schinler, A. (2004) Large Area Smoothing of Optical Surfaces by Low-Energy Ion Beams. Thin Solid Films, 459, 100-105. http://dx.doi.org/10.1016/j.tsf.2003.12.107
[3]	Roy, A., Bhattacharjee, K., Lenka, H.P., Mahapatra, D.P. and Dev, B.N. (2008) Surface Roughness of Ion-Bombarded Si(100) Surfaces: Roughening and Smoothing with the Same Roughness Exponent. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 266, 1276-1280. http://dx.doi.org/10.1016/j.nimb.2007.10.045
[4]	Bhattacharjee, K., Bera, S., Goswami, D.K. and Dev, B.N. (2005) Nanoscale Self-Affine Surface Smoothing: Dependence on Ion Fluence and Initial Surface Roughness. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 230, 524-532. http://dx.doi.org/10.1016/j.nimb.2004.12.095
[5]	Yarin, A.L., Megairids, C.M., Mattia, D. and Gogotsi, Y. (2008) Smoothing of Nanoscale Roughness Based on the Kelvin Effect. Nanotechnology, 19, Article ID: 365702. http://dx.doi.org/10.1088/0957-4484/19/36/365702
[6]	Guo, W. and Sawin, H.H. (2009) Review of Profile and Roughening Simulation in Microelectronics Plasma Etching. Journal of Physics D: Applied Physics, 42, Article ID: 194014 http://dx.doi.org/10.1088/0022-3727/42/19/194014
[7]	Radmilovic-Radjenovic, M., Radjenovic, B. and Petrovic, Z.L.J. (2009) Application of Level Set Method in Simulation of Surface Roughness in Nanotechnologies. Thin Solid Films, 517, 3954-3957. http://dx.doi.org/10.1016/j.tsf.2009.01.123
[8]	Twardowski, T.E. (2007) Introduction to Nanocomposite Materials: Processing Characterization. DesTech Publications, Lancaster.
[9]	Makabe, T. and Petrovic, Z.L.J. (2006) Plasma Electronics. Taylor and Francis, New York.
[10]	Chason, E., Mayer, T.M., Kellerman, B.K., McIlroy, D.T. and Howard, A.J. (1994) Roughening Instability and Evolution of the Ge(001) Surface during Ion Sputtering. Physical Review Letters, 72, 3040-3043. http://dx.doi.org/10.1103/PhysRevLett.72.3040
[11]	Eklund, E.A., Bruinsma, R., Rudnick, J. and Williams, R.S. (1991) Submicron-Scale Surface Roughening Induced by Ion Bombardment. Physical Review Letters, 67, 1759-1762. http://dx.doi.org/10.1103/PhysRevLett.67.1759
[12]	Krim, J., Heyvart, I., Haesendonck, D.V. and Bruynseraede, Y. (1993) Scanning Tunneling Microscopy Observation of Self-Affine Fractal Roughness in Ion-Bombarded Film Surfaces. Physical Review Letters, 70, 57-60. http://dx.doi.org/10.1103/PhysRevLett.70.57
[13]	Goswami, D.K. and Dev, B.N. (2003) Nanoscale Self-Affine Surface Smoothing by Ion Bombardment. Physical Review B, 68, Article ID: 033401. http://dx.doi.org/10.1103/PhysRevB.68.033401
[14]	Habenicht, S., Bolse, W., Lieb, K.P., Reimann, K. and Geyer, U. (1999) Nanometer Ripple Formation and Self-Affine Roughening of Ion-Beam-Eroded Graphite Surfaces. Physical Review B, 60, Article ID: R2200. http://dx.doi.org/10.1103/PhysRevB.60.R2200
[15]	Radjenovic, B. and Radmilovic-Radjenovic, M. (2012) The Effects of Isotropic Etching on Roughening and Smoothing of Nanostructure. Electronic Materials Letters, 8, 491-494. http://dx.doi.org/10.1007/s13391-012-2063-5
[16]	Radjenovic, B., Lee, J.K. and Radmilovic-Radjenovic, M. (2006) Sparse Field Level Set Method for Non-Convex Hamiltonians in 3D Plasma Etching Profile Simulations. Computer Physics Communications, 174, 127-132. http://dx.doi.org/10.1016/j.cpc.2005.09.010
[17]	Radjenovic, B. and Radmilovic-Radjenovic, M. (2012) The Effect of Different Etching Modes on the Smoothing of the Rough Surfaces. Materials Letters, 86, 165-167. http://dx.doi.org/10.1016/j.matlet.2012.07.068
[18]	Radjenovic, B. and Radmilovic-Radjenovic, M. (2013) Three-Dimensional Simulations with Fields and Particles in Software and Inflector Designs. Journal of Software Engineering and Applications, 6, 390-395. http://dx.doi.org/10.4236/jsea.2013.68048
[19]	Radjenovic, B. and Radmilovic-Radjenovic, M. (2014) The Implementation of the Surface Charging Effects in Three-Dimensional Simulations of SiO2 Etching Profile Evolution. Engineering, 6, 1-6.