Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T11:28:28.108Z Has data issue: false hasContentIssue false
  • English
  • Français

On the kinetics of thermal donor formation in silicon

Published online by Cambridge University Press:  31 January 2011

Jeffrey T. Borenstein ,
David Peak  and
James W. Corbett
Jeffrey T. Borenstein
Affiliation:
Physics Department, SUNY at Albany, Albany, New York 12222
David Peak
Affiliation:
Physics Department, Union College, Schenectady, New York 12308
James W. Corbett
Affiliation:
Physics Department, SUNY at Albany, Albany, New York 12222
Get access

Abstract

A model for the kinetic growth of oxygen-related thermal donors in Czochralski silicon at about 450°C is presented. The model, which is based on the work of Suezawa and Sumino, derives forward reaction rates for the electrically active species by comparing analytic expressions for the early-time annealing kinetics with the infrared electronic absorption data. The analytic expressions, which are independent of the chemical structure of each species, result from three assumptions: (1) the donor defects beyond the first donor species (TD-1) are chemically stable at the donor formation temperature, (2) the reactions for the TD-1 and those electrically inactive clusters smaller than TD-1 are in equilibrium, and (3) the oxygen interstitial concentration remains constant for short annealing times. The parametrized values of the rate constants indicate that the forward rates of reaction vary widely between species, with a sharp peak at the reaction which takes the first electrically active species to the second. If the rate constants are taken to be of the form K = 4πRD, where R is the capture radius for the given forward reaction and D represents the effective diffusion coefficient, then the variation between reaction constants may be associated with differences in capture radii between species, with the diffusion coefficient assumed to be the value determined by Stavola et al. [Appl. Phys. Lett. 42, 73 (1983)] for “as-provided” material, which has an activation energy of 1.95 eV. The model is successfully applied to the two available sets of infrared absorption data (the Oeder-Wagner and Suezawa-Sumino data) when differences in the annealing temperatures and initial oxygen concentrations are taken into account. The best-fit parameters found by fitting the analytic expressions are then applied to a set of chemical reaction equations which characterize the formation rates of specific oxygen aggregates. The use of such a set of coupled, nonlinear differential equations, which must be solved numerically, introduces free parameters for the oxygen clusters smaller than the first thermal donor. It is shown that the assignments of a thermal donor core containing two, three, four, or five oxygen atoms are all capable of fitting the experimental data. This result indicates that a best fit to the kinetic data cannot be used to argue for a specific thermal donor core. Finally, the authors discuss possible mechanisms for the enhanced values of the capture radii.

Type
Articles
Information
Journal of Materials Research , Volume 1 , Issue 4 , August 1986 , pp. 527 - 536
Copyright
Copyright © Materials Research Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Fuller, C. S., Ditzenberger, N. B., Hannay, N. B., and Buehler, E., Phys. Rev. 96, 833 (1954).Google Scholar
2Kaiser, W., Frisch, H. L., and Reiss, H., Phys. Rev. 112, 1546 (1958).CrossRefGoogle Scholar
3Fuller, C. S. and Logan, R. A., J. Appl. Phys. 28, 1427 (1957).Google Scholar
4Corbett, J. W., McDonald, R. S., and Watkins, G. D., J. Phys. Chem. Solids 25, 873 (1964).CrossRefGoogle Scholar
5Graff, K., Gallrath, E., Ades, S., Goldbach, G., and Tolg, G., Solid State Electron. 16, 887 (1973).CrossRefGoogle Scholar
6Gaworzewski, P. and Schmalz, K., Phys. Stat. Sol. A 55, 699 (1979).CrossRefGoogle Scholar
7Pajot, B., Compain, H., Lerouille, J., and Clerjaud, B., Physica 117B and 118B, 110 (1983).Google Scholar
8Oeder, R. and Wagner, P., in Defects in Semiconductors II, edited by Mahajanand, S.Corbett, J. W. (North-Holland, New York, 1983),p. 107.Google Scholar
9Suezawa, M. and Sumino, K., Mater. Lett. 2, 85 (1983).CrossRefGoogle Scholar
10Suezawa, M. and Sumino, K., Phys. Stat. Sol. A 82, 235 (1984).CrossRefGoogle Scholar
11Ourmazd, A., Schroter, W., and Bourret, A., J. Appl. Phys. 56, 1670 (1984).CrossRefGoogle Scholar
11Stavola, M., Patel, J. R., Kimerling, L. C., and Freeland, P. E., Appl. Phys. Lett. 42, 73 (1983).CrossRefGoogle Scholar
13Waite, T. R., J. Chem. Phys. 28, 103 (1958).CrossRefGoogle Scholar
14Corbett, J. W., Frisch, H. L., and Snyder, L. C., Mater. Lett. 2, 209 (1984).CrossRefGoogle Scholar
15Borenstein, J. T., Corbett, J. W., Herder, M., Sahu, S. N., and Snyder, L. C., J. Phys. C 19, 2893 (1986).CrossRefGoogle Scholar
16Borenstein, I.T. and Corbett, J. W., Phys. Lett. A 115, 55 (1986).CrossRefGoogle Scholar
17Helmreich, D. and Sirtl, E., in Semiconductor Silicon, edited by Huff, H. R. and Sirtl, E. (Electrochemical Society, Princeton, NJ, 1977), p. 626.Google Scholar
18Gosele, U. and Tan, T. Y., Appl. Phys. A 28, 79 (1982).CrossRefGoogle Scholar
19Newman, R. C., Oates, A. S., and Livingston, F. M., J. Phys. C 16, 1667 (1983).Google Scholar
20Snyder, L. C. and Corbett, J. W., Thirteenth International Conference on Defects in Semiconductors, edited by Kimerling, L. C. and Parsey, J. M. Jr., (Metallurgical Society of AIME, Coronado, CA, 1984), p. 693.Google Scholar
21Keller, W. W., J. Appl. Phys. 55, 3471 (1984).CrossRefGoogle Scholar
22Robertson, J. and Ourmazd, A., Appl. Phys. Lett. 46, 559 (1985).CrossRefGoogle Scholar
23Lindstrom, J. L., Svensson, B., and Corbett, J. W., Phys. Stat. Sol. A 91, K107 (1985).CrossRefGoogle Scholar
24Kohn, W., in Solid State Physics, Vol. 5, edited by Seitz, F. and Turnbull, D. (Academic, New York, 1957), p. 257.Google Scholar
25Kohn, W. and Luttinger, J. M., Phys. Rev. 98, 915 (1955).Google Scholar
26Faulkner, R. A., Phys. Rev. 184, 713 (1969).CrossRefGoogle Scholar
27Ramdas, A.K. and Rodriguez, S., Rep. Prog. Phys. 44, 1297 (1981).CrossRefGoogle Scholar
28Borenstein, J. T., Ph.D. thesis, Suny/Albany, 1986.Google Scholar
29Rath, H.J., Stallhofer, P., Huber, D., and Schmitt, B. F., J. Electrochem. SOC. 131, 1920 (1984).CrossRefGoogle Scholar
30Wagner, P., MRS Proceedings, Symposium K, Boston, 1985 (to be published).Google Scholar
31Kaiser, W., Phys. Rev. 105, 1751 (1957).CrossRefGoogle Scholar
32Cazcarra, V. and Zunino, P., J. Appl. Phys. 51, 4206 (1980).CrossRefGoogle Scholar
33Kaiser, W., Keck, P. H., and Lange, C. F., Phys. Rev. 101, 1254 (1956).CrossRefGoogle Scholar
34Tan, T. Y., Kleinhenz, R., and Schneider, C. P., in Oxygen, Carbon, Hydrogen and Nitrogen in Silicon, edited by Pearton, S. J., Corbett, J. W., Mikkelsen, J. C., and Pennycook, S. J. (Materials Research Society, Pittsburgh, 1986).Google Scholar
35Newman, R. C., J. Phys. C 18, L967 (1985).Google Scholar
36Sahu, S.N. (unpublished).Google Scholar
37Reiss, H., J. Appl. Phys. 30, 1141 (1959).CrossRefGoogle Scholar
38Frenkel, J., Kinetic Theory of Liquids (Clarendon, Oxford, 1946).Google Scholar
39Lothe, J. and Pound, G. M., in Nucleation, edited by Zettle-moyer, A. C. (Dekker, New York, 1969), p. 109.Google Scholar
40Peak, D., Frisch, H. L., and Corbett, J. W., Radiat. Effects 11, 149 (1971).CrossRefGoogle Scholar
41Peak, D. and Corbett, J. W., Phys. Rev. B 5, 1220 (1972).CrossRefGoogle Scholar
42Peak, D. and Corbett, J. W., J. Stat. Phys. 17, 97 (1977).CrossRefGoogle Scholar
43Peak, D. and Corbett, J. W., Radiat. Effects 36, 197 (1978).CrossRefGoogle Scholar
44Oehrlein, G.S., Lindstrom, J. L., and Cohen, S. A., in Thirteenth International Conference on Defects in Semiconductors, edited by Kimerling, L. C. and Parsey, J. M. Jr., (Metallurgical Society of AIME, Coronado, CA, 1984), p. 701.Google Scholar