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Distributions of kinetic pathways in strain relaxation of heteroepitaxial films

  • Dustin Andersen (a1) and Robert Hull (a1)

The kinetic relaxation pathways for strained heteroepitaxial films are mapped using a process simulator that integrates experimental and model descriptions of the energetic and kinetic parameters that define the nucleation, propagation, and interaction of strain relieving dislocations. This paper focuses on Ge x Si1−x /Si(100), but the methodologies described should be extendible to other systems. The kinetic pathways for strain evolution are plotted for film growth as functions of the primary kinetic parameters: growth temperature, growth rate, and initial lattice mismatch, generating relaxation surfaces for parameter pairs. Sensitivity analyses are presented of how deviations from mean parameters disperse the resultant relaxation surfaces. Finally, multi-parameter “fingerprinting” of the dislocation array is shown to illustrate how fundamental kinetic mechanisms—particularly dislocation nucleation mechanisms—define the final dislocation array. The overarching goal is to establish a robust framework for predicting, interrogating, and optimizing strain relaxation pathways and underlying mechanisms, for misfit dislocations in strained heteroepitaxial films.

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1. Hull, R., Andersen, D., Parveneh, H., and Bean, J.C.: Materials genomics of thin film strain relaxation by misfit dislocations. J. Appl. Phys. 118, 225306 (2015).
2. Andersen, D. and Hull, R.: Effect of asymmetric strain relaxation on dislocation relaxation processes in heteroepitaxial semiconductors. J. Appl. Phys. 121, 075302 (2017).
3. Van der Merwe, J.H.: Crystal interfaces. Part I. Semi-infinite crystals. J. Appl. Phys. 34, 117 (1963).
4. Van der Merwe, J.H.: Equilibrium structure of a thin epitaxial film. J. Appl. Phys. 41, 4725 (1970).
5. Van der Merwe, J.H.: Misfit dislocation generation in epitaxial layers. Crit. Rev. Solid State Mater. Sci. 17, 187 (1991).
6. Matthews, J.W. and Blakeslee, A.E.: Defects in epitaxial multilayers: I. Misfit dislocations. J. Cryst. Growth 27, 118 (1974).
7. Matthews, J.W. and Blakeslee, A.E.: Defects in epitaxial multilayers: II. Dislocation pile-ups, threading dislocations, slip lines and cracks. J. Cryst. Growth 29, 273 (1975).
8. Matthews, J.W. and Blakeslee, A.E.: Defects in epitaxial multilayers: III. Preparation of almost perfect multilayers. J. Cryst. Growth 32, 265 (1976).
9. Dodson, B.W. and Tsao, J.Y.: Relaxation of strained-layer semiconductor structures via plastic flow. Appl. Phys. Lett. 51, 1325 (1987).
10. Coppeta, R.A., Holec, D., Ceric, H., and Grasser, T.: Evaluation of dislocation energy in thin films. Philos. Mag. 95, 186 (2015).
11. Re, M., Scalese, S., Mirabella, S., Terrasi, A., Priolo, F., Rimini, E., Berti, M., Coati, A., Drigo, A., Carnera, A., De Salvador, D., Spinella, C., and La Mantia, A.: Structural characterization and stability of Si1−x Ge x /Si(100) heterostructures grown by molecular beam epitaxy. J. Cryst. Growth 227–228, 749 (2001).
12. Liu, J.P., Kong, M.Y., Liu, X.F., Li, J.P., Huang, D.D., Li, L.X., and Sun, D.Z.: Strain-induced morphological evolution and preferential interdiffusion in SiGe epitaxial film on Si(100) during high-temperature annealing. J. Cryst. Growth 201/202, 556 (1999).
13. Hollander, B., Mantl, S., Stritzker, B., Jorke, H., and Kasper, E.: Strain measurements and thermal stability of Si1−x Ge x /Si strained layers. J. Mater. Res. 4, 163 (1989).
14. Alexander, H. and Haasen, P.: Dislocations and plastic flow in the diamond structure. Solid State Phys. 22, 27 (1969).
15. Imai, M. and Sumino, K.: In situ X-ray topographic study of the dislocation mobility in high-purity and impurity-doped silicon crystals. Philos. Mag. A 47, 599 (1983).
16. Yonenaga, I.: Dislocation velocities and mechanical strength of bulk GeSi crystals. Phys. Status Solidi A 171, 41 (1999).
17. Hagen, W. and Strunk, H.: A new type of source generating misfit dislocations. Appl. Phys. 17, 85 (1978).
18. Rajan, K. and Denhoff, M.: Misfit dislocation structure at a Si/Si x Ge1−x strained-layer interface. J. Appl. Phys. 62, 1710 (1987).
19. Rzaev, M., Schaffler, F., Vdovin, V., and Yugova, T.: Misfit dislocation nucleation and multiplication in fully strained SiGe/Si heterostructures under thermal annealing. Mater. Sci. Semicond. Process. 8, 137 (2005).
20. Hull, R. and Bean, J.C.: Variation in misfit dislocation behavior as a function of strain in the GeSi/Si system. Appl. Phys. Lett. 54, 925 (1989).
21. Freund, L.B.: A criterion for arrest of a threading dislocation in a strained epitaxial layer due to an interface misfit dislocation in its path. J. Appl. Phys. 68, 2073 (1990).
22. Stach, E.A., Schwarz, K.W., Hull, R., Ross, F.M., and Tromp, R.M.: New mechanism for dislocation blocking in strained layer epitaxial growth. Phys. Rev. Lett. 84, 947 (2000).
23. Hull, R., Bean, J.C., Bahnck, D., Peticolas, L.J. Jr., Short, K.T., and Unterwald, F.C.: Interpretation of dislocation propagation velocities in strained Ge x Si1−x /Si(100) heterostructures by the diffusive kink pair model. J. Appl. Phys. 70, 2052 (1991).
24. Hull, R. and Bean, J.C.: New insights into the microscopic motion of dislocations in covalently bonded semiconductors by in situ transmission electron microscope observations of misfit dislocations in thin strained epitaxial layers. Phys. Status Solidi A 138, 533 (1993).
25. Tuppen, C.G. and Gibbings, C.J.: The kinetics of dislocation glide in SiGe alloy layers. J. Electron. Mater. 19, 1101 (1990).
26. Houghton, D.C.: Strain relaxation kinetics in Si1−x Ge x /Si heterostructures. J. Appl. Phys. 70, 2136 (1991).
27. Yuan, Q., Thesis, M.S.: Misfit Strain Relaxation Mechanisms in Thin Films (University of Virginia, 1999).
28. Willis, J.R., Jain, S.C., and Bullough, R.: Work hardening and strain relaxation in strained-layer buffers. Appl. Phys. Lett. 59, 920 (1991).
29. Gillard, V.T., Nix, W.D., and Freund, L.B.: Role of dislocation blocking in limiting strain relaxation in heteroepitaxial films. J. Appl. Phys. 76, 7280 (1994).
30. Kujofsa, T., Cheruku, S., Yu, W., Outlaw, B., Xhurxhi, S., Obst, F., Sidoti, D., Bertoli, B., Rago, P.B., Suarez, E.N., Jain, F.C., and Ayers, J.E.: Relaxation dynamics and threading dislocations in ZnSe and ZnS y Se1−y /GaAs(001) heterostructures. J. Electron. Mater. 42, 2764 (2013).
31. Jain, U., Jain, S.C., Nijs, J., Willis, J.R., Bullough, R., Mertens, R.P., and Van Overstraeten, R.: Calculation of critical-layer-thickness and strain relaxation in Ge x Si1−x strained layers with interacting 60 and 90° dislocations. Solid-State Electron. 36, 331 (1993).
32. Menendez, J.: Analytical strain relaxation model for Si1−x Ge x /Si epitaxial layers. J. Appl. Phys. 105, 063519 (2009).
33. Gosling, T.J., Jain, S.C., and Harker, A.H.: The kinetics of strain relaxation in lattice-mismatched semiconductor layers. Phys. Status Solidi A 146, 713 (1994).
34. Tan, E.H. and Sun, L.Z.: Dislocation dynamics in semiconductor thin film-substrate systems. Mater. Res. Soc. Symp. Proc. 795, 47 (2004).
35. Schwarz, K.W., Cai, J., and Mooney, P.M.: Comparison of large-scale layer-relaxation simulations with experiment. Appl. Phys. Lett. 85, 2238 (2004).
36. Fertig, R.S. and Baker, S.P.: Simulation of dislocations and strength in thin films: A review. Prog. Mater. Sci. 54, 874 (2009).
37. Schwarz, K.W.: Discrete dislocation dynamics study of strained-layer relaxation. Phys. Rev. Lett. 91, 145503 (2003).
38. Kasper, E., Herzog, H.J., and Kibbel, H.: A one-dimensional SiGe superlattice grown by UHV epitaxy. Appl. Phys. 8, 199 (1975).
39. Stach, E.A., Hull, R., Tromp, R.M., Reuter, M.C., Copel, M., LeGoues, F.K., and Bean, J.C.: Effect of the surface upon misfit dislocation velocities during the growth and annealing of SiGe(001) heterostructures. J. Appl. Phys. 83, 1931 (1998).
40. Hull, R.: Metastable strained layer configurations in the SiGe/Si system. In Properties of Silicon Germanium and SiGe: Carbon, Kasper, E. and Lyutovich, K., eds. (IEE INSPEC, London, U.K., 2000); pp. 2141.
41. Whaley, G.J. and Cohen, P.I.: Relaxation of strained InGaAs during molecular beam epitaxy. Appl. Phys. Lett. 57, 144 (1990).
42. Floro, J.A., Chason, E., and Lee, S.R.: Real time measurement of epilayer strain using a simplified wafer curvature technique. Mater. Res. Soc. Symp. Proc. 405, 381 (1996).
43. Yaguchi, H., Fujita, K., Fukatsu, S., Shiraki, Y., and Ito, R.: Strain relaxation in MBE-grown Si1−x Ge x /Si(100) heterostructures by annealing. Jpn. J. Appl. Phys. 30, 1450 (1991).
44. Bai, G., Nicolet, M-A., Chern, C.H., and Wang, K.L.: Strain relief of metastable GeSi layers on Si(100). J. Appl. Phys. 75, 4475 (1994).
45. Kuhne, H.: On a substituting, sticking and trapping model of CVD Si1−x G x layer growth. J. Cryst. Growth 125, 291 (1992).
46. Xiaojun, J. and Junwu, L.: Dependence of Ge x Si1−x epitaxial growth on GeH4 flow using chemical vapour deposition. J. Mater. Sci.: Mater. Electron. 8, 405 (1997).
47. Yang, X. and Tao, M.: A kinetic model for Si1−x Ge x growth from SiH4 and GeH4 by CVD. J. Electrochem. Soc. 154, H53 (2007).
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