Energetics of growing epilayer-substrate combinations of comparable bond strength and in Kurdjumov-Sachs orientation
Tóm tắt
In this paper we address the problems related to critical misfit and thickness in epilayer-substrate combinations of comparable bond strengths; specifically the case in which a pseudomorphic monolayer (ML) is stable and the critical thickness is about three MLs or less. Of particular interest are the average energies related to misfit strain f
KS and misfit dislocations (MDs)—in the latter case the individual contributions of the oscillatory strains 〈V〉 and the epilayer-substrate disregistry 〈V〉MD. The individual energies are of interest because they may play different roles in the realization of specific growth modes. The analytical approach involves the following assumptions: (a) a rigid substrate as source of a periodic epilayer atom-substrate interaction potential which we model in terms of a low order truncated Fourier series; and (b) an epilayer which (i) deforms harmonically with zero strain gradient normal to the film plane, (ii) grows in Kurdjumov-Sachs (KS) orientation due to small misfit. f
KS and in the layer-by-layer growth mode. Arguments are presented claiming that this interfacial situation may be approximated by a one-dimensional problem in which epilayer stiffness constants and equilibrium structure, as well as epilayer-substrate interaction depend on epilayer thickness; which poses a complex problem. An approximate solution could be obtained by assuming these quantities to be independent of thickness and proximities of the vacuum and the substrate. The most prominent conclusions are that the equilibrium density of MDs and hence the transition from misfit accommodation by MS to one containing MDs is a catastrophic process and that sustained minimum energy may require the overcoming of an energy barrier. While elementary implementation of the results to equilibrium growth mode theory suggests—independently of the catastrophic nature—that energetically favored misfit strain relief by misfit dislocations may, or may not, effect a transition to Stranski-Krastanov growth, a crude numerical calculation favors the transition. A proper implementation of the results require extensive numerical calculations and is planned for the near future.
Tài liệu tham khảo
E.Bauer, Z. Kristallogr. 110, 423 (1958).
J.H.van derMerwe, D.L.Tönsing, and P.M.Stoop, Surf. Sci. 312, 387 (1994).
F.C.Frank and J.H.van derMerwe, Proc. Roy. Soc. Ser. A. 198, 205, 216 (1949).
B.W.Dodson, Phys. Rev. Lett. 60, 2288 (1988).
J.H.van derMerwe, D.L.Tönsing, and P.M.Stoop, Thin Solid Films 237, 297 (1994).
G.Kurdjumov and G.Sachs, Z. Phys. 64, 325 (1930).
J.H.van derMerwe, Phil. Mag. A45, 127, 145 (1982).
H.Kunert and J.H.van derMerwe, in 23rd Anual Seminar on Theoretical Physics, edited by H.Geyer (Institute of Theoretical Physics, Stellenbosch, 1988), p. 185.
J.H.van derMerwe, E.Bauer, D.L.Tönsing, and P.M.Stoop, Phys. Rev. B49, 2127, 2137 (1994).
J.H.van derMerwe, J. Appl. Phys. 41, 4725 (1970).
C.A.B.Ball and J.H.van derMerwe, Phys. Stat. Sol. 38, 335 (1970).
P.M.Stoop, J.H.van derMerwe, and M.W.H.Braun, Phil. Mag. A63, 907 (1991).
P.M.Stoop, Interface Sci. 1, 243 (1993).
J.H.van derMerwe and G.J.Shiflet, Acta Metall. Mater. 42, 1199 (1994).
L.C.A.Stoop and J.H.van derMerwe, Thin Solid Films. 98, 65 (1982).
J.W.Matthews in Epitaxial Growth, Part 2, edited by J.W.Matthews (Academic Press, New York, 1975) p. 559.
M.Abramowitz and I.A.Stegun (eds.), Handbook of Mathematical Functions (Dover Publications, New York, 1968) p. 227.
D.L.Tönsing and J.H.van derMerwe, Phys. Rev. B44, 550 (1991).
D.L.Tönsing, P.M.Stoop, and J.H.van derMerwe, Surf. Sci. 277, 193 (1992).
J.Giergiel, J.Kirschner, J.Landgraf, J.Shen, and J.Woltersdorf, Surf. Sci. 310, 1 (1994).