Evolution of thin film morphology: Modeling and simulations

Springer Series in Materials Science

Volumn 108, Issue , 2008, Pages 1-200

  Pelliccione, Matthew ^a   Lu, Toh Ming ^a  

^a Rensselaer Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85072833953     PISSN: 0933033X     EISSN: 21962812     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (191)

1. J.G. Amar, F. Family, P.-M. Lam: Dynamic scaling of the island-size distribution and percolation in a model of submonolayer molecular-beam epitaxy. Phys. Rev. B 50, 8781 (1994)
2. J.G. Amar, P.-M. Lam, F. Family: Groove instabilities in surface growth with diffusion. Phys. Rev. E 47, 3242 (1993)
3. J.G. Amar, P.-M. Lam, F. Family: Surface growth with long-range correlated noise. Phys. Rev. A 43, 4548 (1991)
4. G. Arfken, H. Weber: Mathematical Methods for Physicists, 5th edn (Harcourt Academic Press, New York 2001) p 711
5. P.B. Balbuena, J. M. Seminario: Molecular Dynamics: From Classical to Quantum Methods (Elsevier, New York 1999)
6. G.S. Bales, A.C. Redfield, A. Zangwill: Growth dynamics of chemical vapor deposition. Phys. Rev. Lett. 62, 776 (1989)
7. G.S. Bales, A. Zangwill: Growth dynamics of sputter deposition. Phys. Rev. Lett. 63, 692 (1989)
8. A.-L. Barabási, H.E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York 1995)
9. A.-L. Barabási, H.E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York 1995) p 19
10. A.-L. Barabási, H.E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York 1995) p 27
11. A.-L. Barabási, H.E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York 1995) p 213
12. A.-L. Barabási, H.E. Stanley: Fractal Concepts in Surface Growth (Cambridge University Press, New York 1995) p 289
13. D. Bensimon, B. Shraiman, S. Liang: On the ballistic model of aggregation. Physics Lett. A 102, 238 (1984)
14. G.E.P. Box, M.E. Muller: A note on the generation of random normal deviates. Ann. Math. Stat. 29, 610 (1958)
15. M. Boas: Mathematical Methods in the Physical Sciences, 2nd edn (John Wiley & Sons, New Jersey 1983) p 519
16. R. Bracewell: The Fourier Transform and Its Applications, 3rd edn (McGraw-Hill, New York 1999) pp 69–97
17. P. Brault, P. Dumas, F. Salvan: Roughness scaling of plasma-etched silicon surfaces. J. Phys.: Condens. Matter 10, L27 (1998)
18. C. Buzea, G. Beydaghyan, C. Elliott, K. Robbie: Control of power law scaling in the growth of silicon nanocolumn pseudo-regular arrays deposited by glancing angle deposition. Nanotechnology 16, 1986 (2005)
19. A.-C.-K. Chan, H. Wang, M.J. Chan: High quality thermal oxide on LPSOI formed by high temperature enhanced MILC. IEEE Electron Device Letters 22, 384 (2001)
20. R. Chiarello, V. Panella, J. Krim, C. Thompson: X-ray reflectivity and ad-sorption isotherm study of fractal scaling in vapor-deposited films. Phys. Rev. Lett. 67, 3408 (1991)
21. M. Constantin, C. Dasgupta, P.P. Chatraphorn, S.N. Majumdar, S. Das Sarma: Persistence in nonequilibrium surface growth. Phys. Rev. E 69 061608 (2004)
22. Image courtesy of George T. Dalakos, G.T. Dalakos, J.P. Plawsky, P.D. Persans: Topographic evolution during deposition of plasma-deposited hydrogenated silicon on glass. Phys. Rev. B 72, 205305 (2005)
23. S. Das Sarma, S.V. Ghaisas, J.M. Kim: Kinetic super-roughening and anomalous dynamic scaling in nonequilibrium growth models. Phys. Rev. E 49, 122 (1994)
24. S. Das Sarma, C.J. Lanczycki, R. Kotlyar, S.V. Ghaisas: Scale invariance and dynamical correlations in growth models of molecular beam epitaxy. Phys. Rev. E 53, 359 (1996)
25. S. Das Sarma, P. Tamborenea: A new universality class for kinetic growth: One-dimensional molecular-beam epitaxy. Phys. Rev. Lett. 66, 325 (1991)
26. P. Dennery, A. Krzywicki: Mathematics for Physicists (Dover, New York 1995)
27. L. Devroye: Non-Uniform Random Variate Generation (Springer-Verlag, New York 1986)
28. C.V. Dharmadhikari, A.O. Ali, N. Suresh, D.M. Phase, S.M. Chaudhari, V. Ganesan, A. Gupta, B.A. Dasannacharya: Dynamic scaling in growth of platinum films on Si(100). Mater. Sci. Eng. B 75, 29 (2000)
29. B. Dick, M.J. Brett, T. Smy, M. Belov, M.R. Freeman: Periodic submicrometer structures by sputtering. J. Vac. Sci. Technol. B 19, 1813 (2001)
30. B. Dick, M.J. Brett, T.J. Smy, M.R. Freeman, M. Malac, R.F. Egerton: Periodic magnetic microstructures by glancing angle deposition. J. Vac. Sci. Technol. A 18, 1838 (2000)
31. D. M. Dobkin, M. K. Zuraw, eds: Principles of Chemical Vapor Deposition (Springer, New York 2006)
32. Reprinted with permission from: J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang: Mechanisms for plasma and reactive ion etch-front roughening. Phys. Rev. B 61, 3012 (2000); Copyright 2000 by the American Physical Society
33. J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang: Numerical analysis of the noisy Kuramoto-Sivashinsky equation in 2+1 dimensions. Phys. Rev. E 59, 177 (1999)
34. J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang: Surface roughening in shadowing growth and etching in 2+1 dimensions. Phys. Rev. B 62, 2118 (2000)
35. J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang: Surface roughening in low-pressure chemical vapor deposition. Phys. Rev. B 64, 125411 (2001)
36. J.T. Drotar, Y.-P. Zhao, T.-M. Lu, G.-C. Wang: Why is KPZ type surface roughening so hard to observe?. Mat. Res. Soc. Proc. 648, 7.9.1 (2001)
37. L. Dubost, A. Rhallabi, J. Perrin, J. Schmitt: Growth of nodular defects during film deposition. J. Appl. Phys. 78, 3784 (1995)
38. S.F. Edwards, D.R. Wilkinson: The surface statistics of a granular aggregate. Proc. R. Soc. London Ser. A 381, 17 (1982)
39. F. Family: Scaling of rough surfaces: Effects of surface diffusion. J. Phys. A: Math. Gen. 19, L441 (1986)
40. F. Family, T. Vicsek: Dynamics of Fractal Surfaces (World Scientific Publishing Co., New Jersey 1991)
41. F. Family, T. Vicsek: Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J. Phys. A: Math. Gen. 18, L75 (1985)
42. G. Fisherman: Monte Carlo: Concepts, Algorithms, and Applications (Springer-Verlag, New York 1995)
43. H. Guclu, G. Korniss: Extreme fluctuations in small-world networks with relaxational dynamics. Phys. Rev. E 69, 065104 (2004)
44. K.H. Guenther: Microstructure of vapor-deposited optical coatings. Appl. Opt. 23, 3806 (1984)
45. S. Hassani: Mathematical Physics (Springer-Verlag, New York 1999)
46. M.M. Hawkeye, M.J. Brett: Narrow bandpass optical filters fabricated with one-dimensionally periodic inhomogeneous thin films. J. Appl. Phys. 100, 044322 (2006)
47. P.E. Hegeman, H.J.W. Zandvliet, G.A.M. Kip, A. van Silfhout: Kinetic roughening of vicinal Si(001). Surf. Sci. 311, L655 (1994)
48. B M. Henry, Z. Xie, H. Smith, K.R. Kirov, V.M. Burlakov, C.R.M. Grovenor, H.E. Assender, G.A.D. Briggs, P.L. Burn, M. Kano, Y. Tsukahara: Characterization and performance of TiO-based solar cells. Proc. SPIE 5938, 593817 (2005)
49. I. Hodgkinson, Q.H. Wu, S. Collett: Dispersion equations for vacuum-deposited tilted-columnar biaxial media. Appl. Opt. 40, 452 (2001)
50. I. Hodgkinson, Q.H. Wu, J. Hazel: Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide. Appl. Opt. 37, 2653 (1998)
51. B. Holley, A. Faghri: Analysis of pulsating heat pipe with capillary wick and varying channel diameter. Int. J. of Heat and Mass Trans. 48, 2635 (2005)
52. P. Hrudey, A. Popta, J. Sit, M. Brett: Photonic device applications of nanoengineered thin film materials. Proc. SPIE 5931, 593113 (2005)
53. P. Jain, J.S. Juneja, T. Karabacak, E.J. Rymaszewski, T.-M. Lu: Surface roughness evolution in amorphous tantalum oxide films deposited by pulsed reactive sputtering. In: Morphological and Compositional Evolution of Thin Films, ed by M.J. Aziz, N.C. Bartelt, I. Berbezier, J.B. Hannon, S.J. Hearne. Mat. Res. Soc. Proc. 749, W5.11 (2003)
54. J.H. Jeffries, J.-K. Zuo, M.M. Craig: Instability of kinetic roughening in sputter-deposition growth of Pt on glass. Phys. Rev. Lett. 76, 4931 (1996)
55. M.D. Johnson, C. Orme, A.W. Hunt, D. Graff, J. Sudijono, L.M. Sander, B.G. Orr: Stable and unstable growth in molecular beam epitaxy. Phys. Rev. Lett. 72, 116 (1994)
56. K. Kaminska, A. Amassian, L. Martinu, K. Robbie: Growth of vacuum evaporated ultraporous silicon studied with spectroscopic ellipsometry and scanning electron microscopy. J. Appl. Phys. 97, 013511 (2005)
57. T. Karabacak, T.-M. Lu: Shadowing growth and physical self-assembly. In: Handbook of Theoretical and Computational Nanotechnology, ed by M. Rieth, W. Schommers (American Scientific Publishers, California 2005) ch 69
58. Reprinted with permission from: T. Karabacak, J.P. Singh, Y.-P. Zhao, G.-C. Wang, T.-M. Lu: Scaling during shadowing growth of isolated nanocolumns. Phys. Rev. B 68, 125408 (2003); Copyright 2003 by the American Physical Society
59. Reprinted with permission from: T. Karabacak, Y.-P. Zhao, G.-C. Wang, T.-M. Lu: Growth-front roughening in amorphous silicon films by sputtering. Phys. Rev. B 64, 085323 (2001); Copyright 2001 by the American Physical Society
60. T. Karabacak, Y.-P. Zhao, G.-C. Wang, T.-M. Lu: Growth front roughening in silicon nitride films by plasma-enhanced chemical vapor deposition. Phys. Rev. B 66, 075329 (2002)
61. M. Kardar, G. Parisi, Y.C. Zhang: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889 (1986)
62. R.-P.-U. Karunasiri, R. Bruinsma, J. Rudnick: Thin-film growth and the shadow instability. Phys. Rev. Lett. 62, 788 (1989)
63. E. Katzav: Self-consistent expansion for the molecular beam epitaxy equation. Phys. Rev. E 65, 032103 (2002)
64. P. Keblinski, A. Maritan, F. Toigo, R. Messier, J.R. Banavar, Continuum model for the growth of interfaces. Phys. Rev. E 53, 759 (1996)
65. S.R. Kennedy, M.J. Brett, H. Miguez, O. Toader, S. John: Optical properties of a three-dimensional silicon square spiral photonic crystal. Photonics and Nanostruct. Fundam. and Appl. 1, 37 (2003)
66. S. Kennedy, M.J. Brett, O. Toader, S. John: Fabrication of tetragonal square spiral photonic crystals. Nano Lett. 2, 59 (2001)
67. S.V. Kesapragada, D. Gall: Anisotropic broadening of Cu nanorods during glancing angle deposition. Appl. Phys. Lett. 89, 203121 (2006)
68. J.M. Kim, S. Das Sarma: Discrete models for conserved growth equations. Phys. Rev. Lett. 72, 2903 (1994)
69. S. Kim, N. Koratkar, T. Karabacak, T.-M. Lu: Water electrolysis activated by Ru nanorod array electrodes. Appl. Phys. Lett. 88, 263106 (2006)
70. B. Kozma, M.B. Hastings, G. Korniss: Diffusion processes on power-law small-world networks. Phys. Rev. Lett. 95, 018701 (2005)
71. B. Kozma, M.B. Hastings, G. Korniss: Roughness scaling for Edwards-Wilkinson relaxation in small-world networks. Phys. Rev. Lett. 92, 108701 (2004)
72. J. Krug, P. Meakin: Columnar growth in oblique incidence ballistic deposition: Faceting, noise reduction, and mean-field theory. Phys. Rev. A 43, 900 (1991)
73. Y. Kuo: Thin Film Transistors: Materials and Processes (Springer-Verlag, New York 2003).
74. Z.W. Lai, S. Das Sarma: Kinetic growth with surface relaxation: Continuum versus atomistic models. Phys. Rev. Lett. 66, 2348 (1991)
75. A. Lakhtakia: Sculptured thin films: Accomplishments and emerging uses. Mater. Sci. Eng. C 19, 427 (2002)
76. A. Lakhtakia, R. Messier: Sculptured Thin Films: Nanoengineered Morphology and Optics, (SPIE Press Monograph vol PM143, 2005).
77. C.-H. Lam, L.M. Sander: Surface growth with power-law noise. Phys. Rev. Lett. 69, 3338 (1992)
78. P.-M. Lam, F. Family: Dynamics of a height-conserved surface-growth model with spatially correlated noise. Phys. Rev. A 44, 7939 (1991)
79. Z. Lang, W. Xiuqin: Formation of nodular defects as revealed by simulation of a modified ballistic model of depositional growth. J. Mat. Sci. 33, 1487 (1998)
80. H. Leschhorn, L.-H. Tang: Comment on ‘Elastic string in a random potential’. Phys. Rev. Lett. 70, 2973 (1993)
81. S. Liang, L.P. Kadanoff: Scaling in a ballistic aggregation model. Phys. Rev. A 31, 2628 (1985)
82. C.-H. Lin, F. Yuan, C.-R. Shie, K.-F. Chen, B.-C. Hsu, M.H. Lee, W.W. Pai, C.W. Liu: Roughness-enhanced reliability of MOS tunneling diodes. IEEE Electron Device Letters 23, 431 (2002)
83. A.V. Limaye, R.E. Amritkar: Theory of growth of ballistic aggregates. Phys. Rev. A 34, 5085 (1986)
84. A. Lisfi, J.C. Lodder: Magnetic domains in Co thin films obliquely sputtered on a polymer substrate. Phys. Rev. B 63, 174441 (2001)
85. F. Liu, M.T. Umlor, L. Shen, J. Weston, W. Eads, J.A. Barnard, G.J. Mankey: The growth of nanoscale structured iron films by glancing angle deposition. J. Appl. Phys. 85, 5486 (1999)
86. G.P. Lepage: A new algorithm for adaptive multidimensional integration. J. Comp. Phys. 27, 192 (1978)
87. J.M. López: Scaling approach to calculate critical exponents in anomalous surface roughening. Phys. Rev. Lett. 83, 4594 (1999)
88. J.M. López, M.A. Rodríguez: Lack of self-affinity and anomalous roughening in growth processes. Phys. Rev. E 54, R2189 (1996)
89. J.M. López, M.A. Rodríguez: Growth of interfaces with strong quenched disorder: Columnar media. Phys. Rev. E 52, 6442 (1995)
90. J.M. López, M.A. Rodríguez, R. Cuerno: Superroughening versus intrinsic anomalous scaling of surfaces. Phys. Rev. E 56, 3993 (1997)
91. T.-M. Lu, H.-N. Yang, G.-C. Wang: When interface gets rough…. Mat. Res. Soc. Symp. Proc. 367, 283 (1995)
92. For review, see T.-M. Lu, Y.-P. Zhao, J.T. Drotar, T. Karabacak, G.-C. Wang: Novel mechanisms on the growth morphology of films. In: Morphological and Compositional Evolution of Thin Films, ed by M.J. Aziz, N.C. Bartelt, I. Berbezier, J.B. Hannon, S.J. Hearne. Mat. Res. Soc. Proc. 749, W1.2 (2003)
93. 2. Phys. Rev. Lett. 92, 256102 (2004)
94. 2. Phys. Rev. B 56, 4085 (1997)
95. J. Mahan: Physical Vapor Deposition of Thin Films (John Wiley & Sons, Inc., New York 2000)
96. J. Mahan: Physical Vapor Deposition of Thin Films (John Wiley & Sons, Inc., New York 2000) p 29
97. J. Mahan: Physical Vapor Deposition of Thin Films (John Wiley & Sons, Inc., New York 2000) p 153
98. E. Main, T. Karabacak, T.-M. Lu: Continuum model for nanocolumn growth during oblique angle deposition. J. Appl. Phys. 95, 4346 (2004)
99. S. Majaniemi, T. Ala-Nissila, J. Krug: Kinetic roughening of surfaces: Derivation, solution, and application of linear growth equations. Phys. Rev. B 53, 8071 (1996)
100. B.B. Mandelbrot: Self-affine fractals and fractal dimension. Physica Scripta 32, 257 (1985)
101. A. Margolina, H.E. Warriner: Growth in a restricted solid on solid model with correlated noise. J. Stat. Phys. 60, 809 (1990)
102. J. Mathews, R. L. Walker: Mathematical Methods of Physics, 2nd edn (Addison-Wesley, New York 1970)
103. S.G. Mayr, K. Samwer: Tailoring the surface morphology of amorphous thin films by appropriately chosen deposition conditions. J. Appl. Phys. 91, 2779 (2002)
104. P. Meakin: Fractals, Scaling, and Growth Far from Equilibrium (Cambridge University Press, New York 1998)
105. P. Meakin: Fractals, Scaling, and Growth Far from Equilibrium (Cambridge University Press, New York 1998) p 420
106. P. Meakin: Fractals, Scaling, and Growth Far from Equilibrium (Cambridge University Press, New York 1998) p 553
107. P. Meakin, J. Krug: Scaling structure in simple screening models for columnar growth. Phys. Rev. A 46, 4654 (1992)
108. P. Meakin, R. Jullien: Restructuring effect in the rain model for random deposition. J. Physique 48, 1651 (1987)
109. P. Meakin, R. Jullien: Spatially correlated ballistic deposition on one-and two-dimensional surfaces. Phys. Rev. A 41, 983 (1990)
110. P. Meakin, R. Jullien: Spatially correlated ballistic deposition on one-and two-dimensional surfaces. Europhys. Lett. 9, 71 (1989)
111. P. Meakin, P. Ramanlal, L.M. Sander, R.C. Ball: Ballistic deposition on surfaces. Phys. Rev. A 34, 5091 (1986)
112. T. Michely, J. Krug: Islands, Mounds, and Atoms: Patterns and Processes in Crystal Growth Far from Equilibrium (Springer-Verlag, New York 2003)
113. D. Moldovan, L. Golubovic: Interfacial coarsening dynamics in epitaxial growth with slope selection. Phys. Rev. E 61, 6190 (2000)
114. W.W. Mullins: Theory of thermal grooving. J. Appl. Phys. 28, 333 (1957)
115. 20 thin films. J. Appl. Phys. 91, 7206 (2002)
116. F. Ojeda, R. Cuerno, R. Salvarezza, L. Vázquez: Dynamics of rough interfaces in chemical vapor deposition: Experiments and a model for silica films. Phys. Rev. Lett. 84, 3125 (2000)
117. S. Pal, D.P. Landau: Monte Carlo simulation and dynamic scaling of surfaces in MBE growth. Phys. Rev. B 49, 10597 (1994)
118. G. Palasantzas: Roughness spectrum and surface width of self-affine fractal surfaces via the K-correlation model. Phys. Rev. B 48, 14472 (1993)
119. G. Palasantzas: Self-affine fractals and the limit H → 0. Phys. Rev. E 49, 1740 (1994)
120. G. Palasantzas, J. Krim: Effect of the form of the height-height correlation function on diffuse x-ray scattering from a self-affine surface. Phys. Rev. B 48, 2873 (1993)
121. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd edn (McGraw-Hill, New York 1984) pp 102–103
122. Reprinted with permission from: M. Pelliccione, T. Karabacak, C. Gaire, G.-C. Wang, T.-M. Lu: Mound formation in surface growth under shadowing. Phys. Rev. B 74, 125420 (2006); Copyright 2006 by the American Physical Society
123. M. Pelliccione, T. Karabacak, T.-M. Lu: Breakdown of dynamic scaling in surface growth under shadowing. Phys. Rev. Lett. 96, 146105 (2006)
124. Reprinted with permission from: M. Pelliccione, T.-M. Lu: Self-shadowing in ballistic fan formation from point seeds. Phys. Rev. B 75, 245431 (2007); Copyright 2007 by the American Physical Society
125. C.-K. Peng, S. Havlin, M. Schwartz, H.E. Stanley: Directed polymer and ballistic-deposition growth with correlated noise. Phys. Rev. A 44, R2239 (1991)
126. R. Pétri, P. Brault, O. Vatel, D. Henry, E. André, P. Dumas, F. Salvan: Silicon roughness induced by plasma etching, J. Appl. Phys. 75, 7498 (1994)
127. J. Poortmans, V. Arkhipov, eds: Thin Film Solar Cells: Fabrication, Characterization and Applications (John Wiley & Sons, New York 2006)
128. F. Porcú, F. Prodi: Ballistic accretion on seeds of different sizes. Phys. Rev. A 44, 8313 (1991)
129. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edn (Cambridge University Press, New York 2007)
130. R. Rabady, I. Avrutsky: Reduced surface roughness of solid thin films prepared by alternating-bias, radio-frequency magnetron sputtering. J. Opt. Soc. Am. B 20, 2174 (2003)
131. M. Raible, S.J. Linz, P. Hänggi: Amorphous thin film growth: Minimal deposition equation. Phys. Rev. E 62, 1691 (2000)
132. P. Ramanlal, L.M. Sander: Theory of ballistic aggregation. Phys. Rev. Lett. 54, 1828 (1985)
133. D.C. Rapaport: The Art of Molecular Dynamics Simulation (Cambridge University Press, New York 2004)
134. D. Reicher, P. Black, K. Jungling: Defect formation in hafnium dioxide thin films. Appl. Opt. 39, 1589 (2000)
135. S.M. Rossnagel, T.S. Kuan: Alteration of Cu conductivity in the size effect regime. J. Vac. Sci. Technol. B 22, 240 (2004)
136. P.I. Rovira, R.A. Yarussi, R.W. Collins, V.C. Venugopal, A. Lakhtakia, R. Messier, K. Robbie, M.J. Brett: Rotating-compensator multichannel transmission ellipsometry of a thin-film helicoidal bianisotropic medium. Thin Solid Films 313, 373 (1998)
137. R.A. Roy, R.Messier: Preparation-physical structure relations in SiC sputtered films. J. Vac. Sci. Tech. A 2, 312 (1984)
138. M. Saitou: Anomalous scaling of nickel surfaces in pulse-current electrodepo-sition growth. Phys. Rev. B 66, 073416 (2002)
139. J. Shao, S. Wang, Z. Shen, X. Fu, H. He, Z. Fan: Glancing angle deposited thin films and their applications in laser systems. Proc. SPIE 6403, 640312 (2006)
140. M. Siegert: Coarsening dynamics of crystalline thin films. Phys. Rev. Lett. 81, 5481 (1998)
141. M. Siegert, M. Plischke: Slope selection and coarsening in molecular beam epitaxy. Phys. Rev. Lett. 73, 1517 (1994)
142. S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley: X-ray and neutron scattering from rough surfaces. Phys. Rev. B 38, 2297 (1988)
143. A.H.M. Smets, W.M.M. Kessels, M.C.M. van de Sanden: Temperature dependence of the surface roughness evolution during hydrogenated amorphous silicon film growth. Appl. Phys. Lett. 82, 865 (2003)
144. D.L. Smith: Thin Film Deposition: Principles and Practice (McGraw-Hill, New York 1995) p 307
145. W.A. Smith: Elementary Numerical Analysis (Prentice Hall, New Jersey 1986) p 21
146. I.M. Sokolov, J. Mai, A. Blumen: Paradoxal diffusion in chemical space for nearest-neighbor walks over polymer chains. Phys. Rev. Lett. 79, 857 (1997)
147. D. Sornette: Critical Phenomena in Natural Sciences: Chaos, Fractals, Selfor-ganization and Disorder: Concepts and Tools (Springer, New York 2004) p 254
148. B.A. Sperling, J.R. Abelson: Kinetic roughening of amorphous silicon during hot-wire chemical vapor deposition at low temperature. J. Appl. Phys. 101, 024915 (2007) and references therein
149. M.R. Spiegel, J. Liu: Schaum’s Outlines: Mathematical Handbook of Formulas and Tables, 2nd edn (McGraw-Hill, New York 1999) p 109 eqn 18.71
150. H.E. Stanley: Introduction to Phase Transition and Critical Phenomena (Ox-ford University Press, New York 1971) p 108
151. C. Stolz, R. Tench, M. Kozlowski, A. Fornier: A comparison of nodular defect seed geometries from different deposition techniques. Proc. SPIE 2714, 374 (1996)
152. J.A. Stroscio, D.T. Pierce, M.D. Stiles, A. Zangwill, L.M. Sander: Coarsening of unstable surface features during Fe(001) homoepitaxy. Phys. Rev. Lett. 75, 4246 (1995)
153. S.M. Sze, K.K. Ng: Physics of Semiconductor Devices, 3rd edn (John Wiley & Sons, New York 2006)
154. D.M. Tanenbaum, A.L. Laracuente, A. Gallagher: Surface roughening during plasma-enhanced chemical-vapor deposition of hydrogenated amorphous silicon on crystal silicon substrates. Phys. Rev. B 56, 4243 (1997)
155. C. Tang, S. Alexander, R. Bruinsma, B.E. Shaw: Scaling theory for the growth of amorphous films. Phys. Rev. Lett. 64, 772 (1990)
156. F. Tang, T. Karabacak, L. Li, M. Pelliccione, G.-C. Wang, T.-M. Lu: Power-law scaling during shadowing growth of nanocolumns by oblique angle deposition. J. Vac. Sci. Tech. A 25, 160 (2007)
157. F. Tang, D.-L. Liu, D.-X. Ye, Y.-P. Zhao, T.-M. Lu, A. Vijayaraghavan: Magnetic properties of Co nanocolumns fabricated by oblique-angle deposition. J. Appl. Phys. 93, 4194 (2003)
158. R. Teki, N. Koratkar, T. Karabacak, T.-M. Lu: Enhanced photoemission from nanostructured surface topologies. Appl. Phys. Lett. 89, 193116 (2006)
159. J.A. Thornton: High rate thick film growth. Annu. Rev. Mater. Sci. 7, 239 (1977)
160. E.S. Tok, S.W. Ong, H.C. Kang: Dynamical scaling of sputter-roughened surfaces in 2+1 dimensions. Phys. Rev. E 70, 011604 (2004)
161. F. Tsui, J. Wellman, C. Uher, R. Clarke: Morphology transition and layer-by-layer growth of Rh(111). Phys. Rev. Lett. 76, 3164 (1996)
162. J.E. Van Nostrand, S.J. Chey, M.-A. Hasan, D.G. Cahill, J.E. Greene: Surface morphology during multilayer epitaxial growth of Ge(001). Phys. Rev. Lett. 74, 1127 (1995)
163. J.A. Venables: Introduction to Surface and Thin Film Processes (Cambridge University Press, New York 2000) p 144
164. D. Vick, T. Smy, B. Dick, S. Kennedy, M.J. Brett: Growth behavior of engineered porous thin films-Measurement and modeling. Mat. Res. Soc. Symp. Proc. 648, 3.43.1 (2001)
165. J. Villain: Continuum models of crystal growth from atomic beams with and without deposition. J. Phys. I (France) 1, 19 (1991)
166. For review, E.G. Wang: Handbook of Theoretical and Computational Nanotechnology, ed by M. Rieth, W. Schommers (American Scientific, California 2006) p 256
167. G.-C. Wang, T.-M. Lu: Physical realization of two-dimensional Ising critical phenomenon: Oxygen chemisorbed on a W(112) surface. Phys. Rev. B 31, 5918 (1985)
168. G.N. Watson: A Treatise on the Theory of Bessel Functions (Cambridge University Press, New York 1944) p 410
169. D.J. Watts: Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton University Press, New Jersey 1999)
170. D.J. Watts, S.H. Strogatz: Collective dynamics of ’small-world’ networks. Nature (London) 393, 440 (1998)
171. T.A. Witten Jr, L.M. Sander: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47, 1400 (1981)
172. D.E. Wolf, J. Villain: Growth with surface diffusion. Europhys. Lett. 13, 389 (1990)
173. 2 nanorods. Opt. Lett. 31, 601 (2006)
174. Reprinted with permission from: H.-N. Yang, Y.-P. Zhao, A. Chan, T.-M. Lu, G.-C. Wang: Sampling-induced hidden cycles in correlated random rough surfaces. Phys. Rev. B 56, 4224 (1997); Copyright 1997 by the American Physical Society
175. H.-N. Yang, Y.-P. Zhao, G.-C. Wang, T.-M. Lu: Noise-induced roughening evolution of amorphous Si films grown by thermal evaporation. Phys. Rev. Lett. 76, 3774 (1996)
176. A. Yanguas-Gil, J. Cotrino, A. Barranco, A.R. González-Elipe Influence of the angular distribution function of incident particles on the microstructure and anomalous scaling behavior of thin films. Phys. Rev. Lett. 96, 236101 (2006)
177. J.H. Yao, H. Guo: Shadowing instability in three dimensions. Phys. Rev. E 47, 1007 (1993)
178. J. Yao, C. Roland, H. Guo: Interfacial dynamics with long-range screening. Phys. Rev. A 45, 3903 (1992)
179. D.-X. Ye, T.-M. Lu: Fanlike aggregations on seeds by parallel ballistic flux: Experimental results and Monte Carlo simulations of the growth of three-dimensional Si structures. Phys. Rev. B 75, 115420 (2007)
180. D.-X. Ye, Z.-P. Yang, A.S.P. Chang, J. Bur, S.-Y. Lin, T.-M. Lu, R.Z. Wang, S. John: Experimental realization of a well-controlled 3D silicon spiral photonic crystal. J. Phys. D: Appl. Phys. 40, 2624 (2007)
181. J. Yu, J.G. Amar: Dynamical scaling behavior in two-dimensional ballistic deposition with shadowing. Phys. Rev. E 66, 021603 (2002)
182. Y.-C. Zhang: Growth anomaly and its implications. Physica A 170, 1 (1990)
183. Y.-C. Zhang: Non-universal roughening of kinetic self-affine surfaces. J. Physique 51, 2129 (1990)
184. Y.-P. Zhao, J.T. Drotar, G.-C. Wang, T.-M. Lu: Morphology transition during low-pressure chemical vapor deposition. Phys. Rev. Lett. 87, 136102 (2001)
185. Y.-P. Zhao, J.T. Drotar, G.-C. Wang, T.-M. Lu: Roughening in plasma etch fronts of Si(100). Phys. Rev. Lett. 82, 4882 (1999)
186. Y.-P. Zhao, J.B. Fortin, G. Bonvallet, G.-C. Wang, T.-M. Lu: Kinetic roughening in polymer film growth by vapor deposition. Phys. Rev. Lett. 85, 3229 (2000)
187. Y.-P. Zhao, G.-C. Wang, T.-M. Lu: Characterization of Amorphous and Crystalline Rough Surface: Principles and Applications (Academic Press, New York 2001)
188. Y.-P. Zhao, D.-X. Ye, P.-I. Wang, G.-C. Wang, T.-M. Lu: Fabrication of Si nanocolumns and Si square spirals of self-assembled monolayer colloid substrates. Int. J. Nanosci. 1, 87 (2002)
189. C.M. Zhou, D. Gall: Competitive growth of Ta nanopillars during glancing angle deposition: Effect of surface diffusion. J. Vac. Sci. Technol. A 25, 312 (2007)
190. S. Zorba, Y. Shapir, Y. Gao: Fractal-mound growth of pentacene thin films. Phys. Rev. B 74 245410 (2006)
191. J.-K. Zuo, J.F. Wendelken: Evolution of mound morphology in reversible homoepitaxy on Cu(100). Phys. Rev. Lett. 78, 2791 (1997)