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Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights

Published online by Cambridge University Press:  28 May 2015

Leonardo Golubović*
Affiliation:
Physics Department, West Virginia University, Morgantown WV 26506-6315, USA
Artem Levandovsky
Affiliation:
Department of Physics and Astronomy, University of California, Riverside, CA 92521, USA
Dorel Moldovan
Affiliation:
Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803-6413, USA
*
Corresponding author. Email: [email protected]

Abstract

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We review recent theoretical progress in the physical understanding of far-from-equilibrium phenomena seen experimentally in epitaxial growth and erosion on crystal surfaces. The formation and dynamics of various interface structures (pyramids, ripples, etc.), and also kinetic phase transitions observed between these structures, can all be understood within a simple continuum model based on the mass conservation law and respecting the symmetries of the growing crystal surface. In particular, theoretical predictions and experimental results are compared for (001), (110) and (111) crystal surfaces.

Type
Review Article
Copyright
Copyright © Global-Science Press 2011

References

[1] See for example, Tsao, J.Y., Materials fundamentals of molecular beam epitaxy (World-Scientific, Singapore, 1993).Google Scholar
[2]Ehrlich, G. and Hudda, F.G., J. Chem. Phys. 44 (1966), 1039.CrossRefGoogle Scholar
[3]Schwoebel, R.L. and Shipsey, E.J., J Appl. Phys. 37 (1966), 3982; R.L. Schwoebel, J. Appl. Phys. 40 (1969), 614.Google Scholar
[4]Villain, J., J. Phys. I (France) 1 (1991), 19.Google Scholar
[5]Ernst, H.-J., Fabre, F., Folkerts, R. and Lapujoulade, J., Phys. Rev. Lett. 72 (1994), 112.CrossRefGoogle Scholar
[6]Johnson, M.D., Orme, C., Hunt, A.W., Graff, D., Sudijono, J., Sander, L.M. and Orr, B.G., Phys. Rev. Lett. 72 (1994), 116.Google Scholar
[7]Evans, J.W., Sanders, D.E., Thiel, P. A. and DePristo, A.E., Phys. Rev. B 41 (1990) 5410; J.W. Evans, Phys. Rev. B 43 (1993) , 3897.Google Scholar
[8]Vvedensky, D.D., Zangwill, A., Luse, C.N. and Wilby, M.R., Phys. Rev. E 48 (1993), 852.Google Scholar
[9]Siegert, M., in: Scale Invariance, Interfaces, and Non-Equilibrium Dynamics, eds. McKane, A.J., Droz, M., Vannimenus, J. and Wolf, D., NATO ASI Series B, Vol. 344 (Plenum, New York, 1995) pp. 165202.CrossRefGoogle Scholar
[10]Bartelt, M.C. and Evans, J.W., Phys. Rev. Lett. 75 (1995), 4250.CrossRefGoogle Scholar
[11]Smith, G.W., Pidduck, A.J., Whitehouse, C.R., Glasper, J.L. and Spowart, J., Cryst, J.. Growth 127 (1993), 996; C. Orme, M.D. Johnson, K.-T. Leung, B.G. Orr, P. Smilauer and D. Vvedensky, J. Cryst. Growth 150 (1995), 128.Google Scholar
[12]Van Nostrand, J.E., Chey, S.J., Hasan, M.-A., Cahill, D.G. and Greene, J.E., Phys. Rev. Lett. 74 (1995), 1127.CrossRefGoogle Scholar
[13]Thurmer, K., Koch, R., Weber, M. and Rieder, K.H., Phys. Rev. Lett. 75 (1995), 1767.Google Scholar
[14]Stroscio, J.A., Pierce, D.T., Stiles, M., Zangwill, A. and Sander, L.M., Phys. Rev. Lett. 75 (1995), 4246.Google Scholar
[15]Tsui, F., Wellman, J., Uher, C. and Clarke, R., Phys. Rev. Lett. 76 (1996), 3164; T. Michely, M. Kalff, G. Comsa, M. Strobel, and K.-H. Heinig, Phys. Rev. Lett. 86 (2001), 2589.Google Scholar
[16]Siegert, M. and Plischke, M., Phys. Rev. Lett. 73 (1994), 1517.Google Scholar
[17]Amar, J. and Family, F., Phys. Rev. B 54 (1996), 14742.Google Scholar
[18]Moldovan, D. and Golubovic, L., Phys. Rev. E 61, 6190 (2000).Google Scholar
[19]Siegert, M., Phys. Rev. Lett. 81 (1998), 5481.Google Scholar
[20]Bray, A. J., Adv. Phys. 34 (1994), 357.Google Scholar
[21]Golubovic, L. and Karunasiri, R.P.U., Phys. Rev. Lett. 66 (1991), 3156.Google Scholar
[22]Golubovic, L., Phys. Rev. Lett. 78 (1997), 90.Google Scholar
[23]Golubovic, L., Moldovan, D. and Peredera, A., Phys. Rev. Lett. 81 (1998), 3387; L. Golubovic, D. Moldovan and A. Peredera, Phys. Rev. E 61 (2000), 1703.Google Scholar
[24]Moldovan, D. and Golubovic, L., Phys. Rev. Lett. 82 (1999) 2884; D. Moldovan and L. Golubovic, Phys. Rev. E 60 (1999), 4377.CrossRefGoogle Scholar
[25]Golubovic, L., Levandovsky, A., and Moldovan, D., Phys. Rev. Lett. 89 (2002), 266104.Google Scholar
[26]Levandovsky, A., Golubovic, L., and Moldovan, D., Phys. Rev. E74 (2006), 061601.Google Scholar
[27]Levandovsky, A. and Golubovic, L., Phys. Rev. E 76 (2007), 041605.Google Scholar
[28]Golubovic, L. and Levandovsky, A., Phys. Rev. E 77 (2008), 051606.Google Scholar
[29]Levandovsky, A. and Golubovic, L., Phys. Rev. B 69 R (2004), 241402.Google Scholar
[30]de Mongeot, F. B., Costantini, G., Boragno, C., and Valbusa, U., Phys. Rev. Lett. 84 (2000), 2446. This study was the first one to report the ripple rotation transition on a (110) crystal surface, for the case of the Ag(110) surface (epitaxial growth), and to reveal an intermediate state intervening in the transition.Google Scholar
[31]Costantini, G., Rusponi, S., de Mongeot, F. B., Boragno, C., and Valbusa, U., J. Phys.: Cond. Matter 13 (2001), 5875.Google Scholar
[32]Albrecht, M., Fritzsche, H. and Gradmann, U., Surf. Sci. 294 (1993), 1.Google Scholar
[33]Molle, A., de Mongeot, F. B., Molinari, A., Xiaerding, F., Boragno, C., and Valbusa, U., Phys. Rev. Lett. 93 (2004), 256103. This study revealed the Rhomboidal Pyramid state to be present in the erosion on Cu(110) and Rh(100) surfaces.Google Scholar
[34]de Mongeot, F. B., Zhu, W., Molle, A., Buzio, R., Boragno, C., Valbusa, U., Wang, E. G., and Zhang, Z., Phys. Rev. Lett. 91 (2003), 016102.Google Scholar
[35]Molle, A., de Mongeot, F. B., Molinari, A., Boragno, C., and Valbusa, U., Phys. Rev. B 73 (2006), 155418.CrossRefGoogle Scholar
[36]de Mongeot, F. B., Costantini, G., Boragno, C., and Valbusa, U., Europhys. Lett. 58 (2002), 537.Google Scholar
[37]Broekmann, P., Mewe, A., Wormeester, H., and Poelsema, B., Phys. Rev. Lett. 89(2002), 146102.Google Scholar
[38]Stoldt, C. R., Caspersen, K. J., Bartelt, M. C., Jenks, C. J., Evans, J. W., and Thiel, P. A., Phys. Rev. Lett. 85 (2000), 800.Google Scholar
[39]Caspersen, K. J., Stoldt, C. R., Layson, A. R., Bartelt, M. C., Thiel, P. A., and Evans, J. W., Phys. Rev. B 63 (2001), 085401.Google Scholar
[40]Caspersen, K. J., Layson, A. R., Stoldt, C. R., Fournee, V., Thiel, P. A., and Evans, J. W., Phys. Rev. B 65 (2002), 193407.Google Scholar
[41] For review, see Krug, J., Adv. in Phys. 46 (1997), 139, and Physica A 313 (2002), 47. See also, J.W. Evans, P.A. Thiel, and M.C. Bartelt, Surf. Sci. Reports 61 iss. 1-2 (2006), 1.Google Scholar
[42] See, e.g., Haken, H., Synegetics (Springer-Verlag, 1978).Google Scholar
[43]Toner, J. and Nelson, D. R., Phys. Rev. B 23 (1981), 316.Google Scholar
[44]Zuo, J.-K. and Wendelken, J. F., Phys. Rev. Lett 78, 2791 (1997).Google Scholar
[45]Li, M. and Evans, J. W., Phys. Rev. Lett. 95 (2005), 256101; ibid. 96 (2006), 079902 E, and Phys. Rev. B 73 (2006), 125434.Google Scholar
[46]J. Amar, Phys. Rev. B 60 (1999), R 11 317.Google Scholar