立方晶体外延应变薄膜稳定性分析
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摘要
对立方晶体外延应变薄膜的弹性场与稳定性进行了线性分析,在扰动幅度的一阶近似下,得到了扰动应力的表达式,表明扰动应力分别与晶格错配、扰动幅度成正比,随着扰动波长或各向异性率的增大而下降.同时也得到了区别平面膜是否稳定的临界扰动波长的表示式,临界扰动波长随着各向异性率的增加而增加.
The elastic fields and stability of epitaxially strained thin films of cubic crystals are linearly analyzed.Expressions of the perturbated stresses to first order of perturbation amplitude are derived, which show that the stresses are directly proportional to the lattice mismatch and the perturbation amplitude, and decrease with increasing perturbation wavelength and anisotropic ratio. The critical perturbation wavelength distinguishing that the flat film for the perturbation is stable or unstable is obtained, which increases with increasing anisotropy ratio.
The elastic fields and stability of epitaxially strained thin films of cubic crystals are linearly analyzed.Expressions of the perturbated stresses to first order of perturbation amplitude are derived, which show that the stresses are directly proportional to the lattice mismatch and the perturbation amplitude, and decrease with increasing perturbation wavelength and anisotropic ratio. The critical perturbation wavelength distinguishing that the flat film for the perturbation is stable or unstable is obtained, which increases with increasing anisotropy ratio.
引文
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[20] Holy V, Springholz G, Pinczolits M, et al. Strain induced vertical and lateral correlations in quantum dot superlattices[J]. Phys. Rev. Lett., 1999,83:56.
[21] Mullins W W. Theory of thermal grooving[J]. J. Appl. Phys., 1957,28:333.
[22] Cullis A G, Robbins D J, Pidduck A J, et al. The characteristics of strain-modulated surface undulations formed upon epitaxial Si1-xGex alloy layers on Si[J]. J. Crystal Growth, 1992,123:333.
[23] Freund L B, Suresh S. Thin Film Materials:Stress, Defect Formation and Surface Evolution[M]. Cambridge:Cambridge University Press, 2003.
[2] Mo Y W, Savage D E, Swartzentruber B S, et al. Kinetic pathway in Stranski-Krastanov growth of Ge on Si(001)[J]. Phys. Rev. Lett., 1990,65:1020.
[3] Massies J, Grandjen N. Oscillation of the lattice relaxation in layer-by-layer epitaxial growth of highly strained materials[J]. Phys. Rev. Lett., 1993,71:1411.
[4] Ramachandran T R, Heitz R, Chen P, et al. Mass transfer in Stranski-Krastanow growth of InAs on GaAs[J].Appl. Phys. Lett., 1997,70:640
[5] Kamins T I, Carr E C, Williams R S, et al. Deposition of three-dimensional Ge islands on Si(001)by chemical vapor deposition at atmospheric and reduced pressures[J]. J. Appl. Phys., 1997,81:211.
[6] Floro J A, Chason E, Twesten R D, et al. SiGe Coherent Islanding and Stress Relaxation in the High Mobility Regime[J]. Phys. Rev. Lett., 1997,79:3946.
[7] Floro J A, Chason E, Freud L B, et al. Evolution of coherent islands in Si1-xGex/Si(001)[J]. Phys. Rev.B., 1999,59:1990.
[8] Tromp R M, Ross F M, Reuter M C. Instability-driven SiGe island growth[J]. Phys. Rev. Lett., 2000,84:641.
[9] Perovic D D, Bahierathan B, Lafontaine H, et al. Kinetic critical thickness for surface wave instability vs.misfit dislocation formation in GexSi1-x/Si(100)heterostructures[J]. Physica A, 1997,239:11.
[10] Osten H J, Zeindl H P, Bugiel E. Considerations about the critical thickness for pseudomorphic Si1-xGex growth on Si(001)[J]. J. Cryst. Growth, 1994,143:94.
[11] Asaro R J, Tiller W A. Interface morphology development during stress corrosion cracking[J]. Metall.Trans., 1972,3:1789.
[12] Grinfeld M Ya. Instability of the separation boundary between a nonhydrostatically stressed elastic body and melt[J]. Sov. Phys. Dokl., 1986,31:831
[13] Hack J E, Chen S P, Srolovitz D J. A kinetic criterion for quasi-brittle fracture[J]. Acta. Metall.,1989,37:1957.
[14] Yang W H, Srolovitz D J. Cracklike surface instabilities in stressed solids[J]. Phys. Rev. Lett., 1993,71:1593.
[15] Eisenberg Helen R, Kandel Daniel. Origin and properties of the wetting layer and early evolution of epitaxially strained thin films[J]. Phys. Rev. B., 2002,66:155429.
[16] Politi P, Grenet G, Marty A, et al. Instability in crystal growth by atomic or molecular beams[J]. Phys.Rep., 2000,324:271.
[17] Springholz G, Holy V, Mayer P. Self-organized ordering in self-assembled quantum dot superlattices[J].Mater. Sci. Eng. B., 2002,88:143.
[18] Pei Q X, Lu C, Wang Y Y. Effect of elastic anisotropy on the elastic fields and vertical alignment of quantum dots[J]. J. Appl. Phys., 2003,93:1487.
[19] Pei Q X, Quek S S, Guo J Y, et al. Elastic fields in quantum dots arrays:A three-dimensional finite element study[J]. Engineering Analysis with Boundary Elements, 2008,32:309.
[20] Holy V, Springholz G, Pinczolits M, et al. Strain induced vertical and lateral correlations in quantum dot superlattices[J]. Phys. Rev. Lett., 1999,83:56.
[21] Mullins W W. Theory of thermal grooving[J]. J. Appl. Phys., 1957,28:333.
[22] Cullis A G, Robbins D J, Pidduck A J, et al. The characteristics of strain-modulated surface undulations formed upon epitaxial Si1-xGex alloy layers on Si[J]. J. Crystal Growth, 1992,123:333.
[23] Freund L B, Suresh S. Thin Film Materials:Stress, Defect Formation and Surface Evolution[M]. Cambridge:Cambridge University Press, 2003.