Abstract
A systematic theory is presented that models the effects of interstitial oxygen on the deformation behavior of silicon. The theory is based on calculation of the dependence of the dislocation velocity on the applied stress in the crystal and determination of the locking and unlocking stresses for dislocation motion. Internal stresses in the oxygen-hardened crystals are modeled by the superposition of the unlocking stress, a back stress due to the interaction between mobile dislocations, and an internal stress that arises from the interaction between a dislocation and the oxygen cloud around other dislocations. The initiation of dislocation multiplication is modeled as a two-step thermally activated process; the first step is the unlocking of the dislocation and the second step is the formation of jogs along the dislocation line. The coupled model for oxygen transport and dislocation motion is used to simulate crystal deformation in dynamic experiments and to reproduce stress-strain curves. The predictions of the initial stage of deformation are in good agreement with the experimental data of Yonenaga et al. [J. Applied Phys. 56, 2346 (1984)].
Similar content being viewed by others
References
S.K. Ghandi, VLSI Fabrication Principles: Silicon and Gallium Arsenide (Wiley, New York, 1983).
K. V. Ravi, Imperfections and Impurities in Semiconductor Silicon (Wiley, New York, 1981).
J. R. Patel and A. R. Chaudhuri, Phys. Rev. 143, 601 (1966).
H. Alexander and P. Haasen, Solid State Phys. 22, 27 (1968).
H.G. Brion, P. Haasen, and H. Siethoff, Acta Metall. 19, 283 (1971).
K. Sumino, in Defects and Properties of Semiconductors: Defect Engineering, edited by J. Chikawa, K. Sumino, and K. Wada (KTK Scientific Publishers, Tokyo, 1987), p.227.
G. Jacob, in Proc. Semi-Insulating III-V Materials Conf., Evian, 2 (1982).
Y. Seki, J. Watanabe, and J. Matsui, J. Appl. Phys. 49, 822 (1978).
J. C. Mikkelsen, Jr., in Oxygen, Carbon, Hydrogen, and Nitrogen in Crystalline Silicon, edited by J. C. Mikkelsen, Jr., S. J. Pearton, J. W. Corbett, and S. J. Pennycook (Mater. Res. Soc. Symp. Proc. 59, Pittsburgh, PA, 1986), pp. 3,19.
W. Lin and K. E. Benson, Annu. Rev. Mater. Sci. 17, 293 (1987).
K. Sumino, H. Harada, and I. Yonenaga, Jpn. J. Appl. Phys. 19, L49 (1980).
K. Sumino and I. Yonenaga, Jpn. J. Appl. Phys. 20, L685 (1981).
D. Maroudas and R.A. Brown, J. Appl. Phys. 69, 3865 (1991).
D. Maroudas and R.A. Brown, Appl. Phys. Lett. 58, 1842 (1991).
A.H. Cottrell and B.A. Bilby, Proc. Phys. Soc. London A62, 49 (1949).
A.H. Cottrell and M.A. Jawson, Proc. R. Soc. London A199, 104 (1949).
H. Yoshinaga and S. Morozumi, Philos. Mag. 23, 1367 (1971).
M. Needels, J. D. Joannopoulos, Y. Bar-Yam, and S. T. Pantelides, Phys. Rev. B43, 4208 (1991).
I. Yonenaga, K. Sumino, and K. Hoshi, J. Appl. Phys. 56, 2346 (1984).
M. Imai and K. Sumino, Philos. Mag. A 47, 599 (1983).
R. Bullough and R.C. Newman, Rep. Prog. Phys. 33, 101 (1970).
S. Nandedkar and J. Narayan, Philos. Mag. A 56, 625 (1987).
J. P. Hirth and J. Lothe, Theory of Dislocations (Wiley, New York, 1982).
F. R. N. Nabarro, Theory of Crystal Dislocations (Dover, New York, 1987).
K. Sumino and M. Imai, Philos. Mag. A 47, 753 (1983).
P. Haasen, Z. Phys. 167, 461 (1962).
M. Suezawa, K. Sumino, and I. Yonenaga, Phys. Status Solidi A 51, 217 (1979).
O. W. Dillon, Jr., C. T. Tsai, and R. J. DeAngelis, J. Cryst. Growth 82, 50 (1987).
J. C. Lambropoulos, J. Cryst. Growth 84, 349 (1987).
Landolt-Bornstein: Crystal and Solid State Physics, edited by K.H. Hellwege (Springer, Berlin, 1979), Vol. 11, p. 116.
M.D. Kluge, J.R. Ray, and A. Rahman, J. Chem. Phys. 85, 4028 (1986).
J. R. Ray, Comput. Phys. Rep. 8, 109 (1988).
J. D. Eshelby, in Vacancies ‘76, edited by R. E. Smallman and J. E. Harris (The Metals Society, U.K., 1976), p. 3; also see Ref. 24, p. 403.
A. H. Cottrell, Dislocations and Plastic Flow in Crystals (Oxford University Press, 1953).
K. Sumino and H. Harada, Philos. Mag. A 44, 1319 (1981).
W. G. Johnston and J. J. Gilman, J. Appl. Phys. 30, 129 (1959).
W.G. Johnston and J.J. Gilman, J. Appl. Phys. 31, 632 (1960).
J.CM. Li, J. Appl. Phys. 32, 593 (1961).
H. Wiedersich, J. Appl. Phys. 33, 854 (1962).
J. R. Low, Jr. and A. M. Turkalo, Acta Metall. 10, 215 (1962).
R. Labusch, Phys. Status Solidi 10, 645 (1965).
I. Yonenaga and K. Sumino, Phys. Status Solidi A 50, 685 (1978).
B. Boley and J. Weiner, Theory of Thermal Stresses (Wiley, New York, 1960).
E. Orowan, Proc. Phys. Soc. London 52, 8 (1940).
K. Sumino, Mater. Sci. Eng. 13, 269 (1974).
E. Schmid and W. Boas, Plasticity of Crystals (Hughes, London, 1968).
A. S. Jordan, R. Caruso, and A. R. Von Neida, Bell System Technol. J. 59, 593 (1980).
G. Müller, R. Rupp, J. Volkl, H. Wolf, and W. Blum, J. Cryst. Growth 71, 771 (1985).
D. Maroudas and R.A. Brown, J. Cryst. Growth 108, 399 (1991).
A. S. Krausz and H. Eyring, Deformation Kinetics (Wiley, New York, 1975).
M.I. Heggie, B. Jones, and A. Umerski, in Atomic Scale Calculations of Structure in Materials, edited by M. S. Daw and M.A. Schlüter (Mater. Res. Soc. Symp. Proc. 193, Pittsburgh, PA, 1990), p. 277.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maroudas, D., Brown, R.A. Constitutive modeling of the effects of oxygen on the deformation behavior of silicon. Journal of Materials Research 6, 2337–2352 (1991). https://doi.org/10.1557/JMR.1991.2337
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/JMR.1991.2337