Reply to comments of F. F. Morehead
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a good correspondence between Figs. (5) and (7) for«/ «, > 1. A much simpler expression [than that in Eq. (10), Ref. 1] for the effective diffusivity of Sb with heavy B doping is D,-/( 1 + H C B ) , which is quite accurate enough since C B > C Sb > P, where P is the concentration of pairs. Finally, we present an alternative analysis of the data in Fig. 5 of Ref. 1. These data are reasonably well represented4 by a version of Eq. (1) of Ref. 1, D_Dt[\+P{n/ni)+Y{n/nl)2]
where D, is D f. Afitto the data yields /? ~ 1, y ~ 0.1 for n/tij > 1. Here we assume that the temperature dependence of /? and y is small compared to that of Dt and «,. Activation energies for D ~ and D r in Eq. (1), Ref. 1, which are meaningfully different from that of-Df, cannot be reliably estimated from these data. Equation (5) is also consistent with the data5 of Nishi etal., a citation omitted by Ref. 1. If the binding in the pairs between Sb + and B~ is coulombic, we can estimate a binding energy of 0.65 eV, which would give the pairing constant il a value of [exp(0.65 eV/kT)]/5XlO 2 2 cm3 (decreased binding with increasing temperature). If the reduction factor to
DSb for pairing (1 +flCB) ' is rewritten for C B / «, ~ « , / « , then the factor is roughly independent of T and is given by 15(«/«,)/[ 1 + 15(«/n ; ) ] for n/nt < 1 and 900 °C < T< 1200 °C. By including this correction inEq. (5) we get
DSb
[1 + («/«,) + 0.l(n/ni)2] (6)
which fits the data in Fig. 7 of Ref. 1 for «/«, < 1. Equation (6) indicates that the reduction in Sb diffusivity caused by heavy B doping is due both to pairing and to the elimination of contributions to Sb diffusion from V ~ and F = vacancies. The latter effect is somewhat more important, in contradiction to the conclusions of Ref. 1.
REFERENCES 'R. B. Fair, M. L. Manda, and J. J. Wortman, J. Mater. Res. 1, 705 (1986). 2 B. Tuck, Introduction to Diffusion in Semiconductors (Peregrinus, England, 1974), p. 138 and ff. 3 F. M. Smits, Proc. IRE46, 1049 (1958). 4 S. M. Hu and S. Schmidt, J. Appl. Phys. 39, 4272 (1968). 5 K. Nishi, K. Sakamoto, and J. Ueda, J. Appl. Phys. 59,4177 (1986).
Reply to comments of F. F. Morehead Richard B. Fair Microelectronics Center of North Carolina, Research Triangle Park, North Carolina 27709 (Received 11 May 1987; accepted 11 May 1987) The expression used for electric field in the article being discussed is not appropriate for the experimental conditions, but there is a built-in electric field present that affects Sb diffusion. Thus the calculated values of D , = are reasonably within the experimental error of the data on which the calculations are based. Our conclusions that V vacancies do not play an important role in Sb diffusion and that Sb-B pairs are responsible for retarded Sb diffusion in high-concentration B-doped Si are supported.
F. F. Morehead has pointed out some apparent inconsistencies in our article. On the first point regarding Eq. (2) for the electric field, the intuition here is that the large As background doping levels used in our experiments were all much gre
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