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The Relationship between the Microscopic Properties of Semiconducting Grain Boundaries and their Orientation

Published online by Cambridge University Press:  16 February 2011

Eugen Tarnow ,
Tomas Arias ,
P. D. Bristowe ,
P. Dallot ,
G. P. Francis ,
J. D. Joannopoulos  and
M. C. Payne
Eugen Tarnow
Affiliation:
Xerox Palo Alto Research Center, 3333 Coyote Hill Rd, Palo Alto, CA 94304
Tomas Arias
Affiliation:
Massachusetts Institute of Technology, Dept. of Physics, Cambridge, MA 02139
P. D. Bristowe
Affiliation:
Massachusetts Institute of Technology, Dept. of Physics, Cambridge, MA 02139
P. Dallot
Affiliation:
Massachusetts Institute of Technology, Dept. of Physics, Cambridge, MA 02139
G. P. Francis
Affiliation:
Cavendish Laboratory, Cambridge, CB3 OHE, England
J. D. Joannopoulos
Affiliation:
Massachusetts Institute of Technology, Dept. of Physics, Cambridge, MA 02139
M. C. Payne
Affiliation:
Cavendish Laboratory, Cambridge, CB3 OHE, England
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Abstract

The microscopic structure of a tilt and a twist boundary in germanium are explored using a state-of-the-art total energy calculation. The structure of the tilt boundary (Σ = 5 (310)) is found to be simple as it exhibits a well defined minimum energy structure, consistent with previous experimental and theoretical results on this and other tilt boundaries. The structure of the twist boundary (Σ = 5 (100)), however, is found to be very complex. The boundary bonds are distorted and weak, and their weakness makes the twist boundary exhibit a wealth of local energy minima. The different types of energy minima for the twist boundaries are identified and studied in some detail. We summarize the consequence of the orientation of the two crystal grains upon the microscopic structure of the boundaries, and speculate about future applications.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 193: Symposium Q – Atomic Scale Calculations of Structure in Materials , 1990 , 235
Copyright
Copyright © Materials Research Society 1990

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References

REFERENCES

1. See articles in “Structure and Properties of Internal Interfaces”, ed. by Ruhle, M., Baluffi, R.W., Fischmeister, H. and Sass, S.L., J. de Physique 46, C–4 (1985).Google Scholar
2. Majid, I., Bristowe, P.D. and Baluffi, R.W., Phys. Rev. B 40, 2779 (1989).Google Scholar
3. Bourret, A. and Bacmann, J.J., Revue Phys. Appl. 22, 563 (1987).Google Scholar
4. Grovenor, C.R.M., J. Phys. C: Solid State Phys. 18, 4079 (1985).Google Scholar
5. See papers in “Interface Science and Engineering '87”, J. de Physique Colloque, 49, C5 (1988).Google Scholar
6. See papers in “Polycrystalline Semiconductors”, Springer Proceedings in Physics, Vol. 35 (1989).Google Scholar
7. Car, R. and Parrinello, M., Phys. Rev. Lett. 55, 2471 (1985).Google Scholar
8. Payne, M.C., Joannopoulos, J.D., Allan, D.C., Teter, M.P. and Vanderbilt, D.H., Phys. Rev. Lett. 56, 2656 (1986).Google Scholar
9. Starkloff, Th. and Joannopoulos, J.D., Phys. Rev. B 16, 5212 (1977).Google Scholar
10. It is important to assert the validity of the size of the force cutoff, since different criteria are used in different types of calculations. Our 0.1 eV/Å is used among those performing ab-initio calculations while 10−5 eV/Å is commonly used in empirical calculations such as the embedded atom scheme. One can estimate the equivalent error in the total energy as follows. The energy gain in the harmonic approximation is 1/2kx2 and the force is kx where x is the (unknown) displacement from the equilibrium position. That means that the energy can be written in terms of the force two ways: E = (1/2)F2/k and E = (1/2)Fx. The smallest force constant that is likely to occur is about 0.5 eV/Å coming from bond bending and the largest x that is even remotely likely to occur once we are close to convergence is 0.5Å. We can now make two different estimates of the energy convergence resulting from a force smaller than 0.1 eV/Å: E < 0.01 eV and E < 0.025 eV. The error is smaller of the two. Using the worst case scenario in which all the atoms in the cell have the maximal force we find that the error arising from the non-zero forces is smaller than 3.8 meV/Å2.Google Scholar
11. Payne, M.C., Bristowe, P.D. and Joannopoulos, J.D., J. de Physique Colloque 49, C5–151 (1988).Google Scholar
12. Bourret, A. and Rouviere, J.L., Centre d'Etudes Nucleaire de Grenoble preprint.Google Scholar
13. Thomson, R.E. and Chadi, D.J., Phys. Rev. B 29, 889 (1984).Google Scholar
14. DiVincenzo, D.P., Alerhand, O.L., Schluter, M. and Wilkins, J.W., Phys. Rev. Lett. 56, 1925 (1986).Google Scholar
15. Chou, M.Y., Cohen, M.L., and Louie, S.G., Phys. Rev. B 32, 7979(1985).Google Scholar