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The effect of phosphorus background concentration on the diffusion of tin, arsenic and antimony in silicon
Materials Science and Engineering, B4 (1989) 1(17-112
107
The Effect of Phosphorus Background Concentration on the Diffusion of Tin, Arsenic and Antimony in Silicon A. NYLANDSTEI) LARSE;N, P. E. ANDERSEN, P. GA1DUK and K. KYLLESBECH LARSEN
Institute OfPhysics, Univers'it)of A arhus, DK-8000A arhus (' (1)enmark) IReceived May 30. 1989)
Abstract
"lhe effect of phosphorus background concentration on the di]]i4sion of tin, arsenic and antimony in silicon has been studied for phosphorus concentrations between about 9 x 10 ~'~ and 5 x 10 :° cm-~, corresponding to 10 <- n/n i <- 60. 7he effectiw, difJ'usion coefficients are found to be proportional to high power of n/n i ]'or all three impurities. These results are discussed within the framework of'the percolation model.
1. I n t r o d u c t i o n
The study of impurity diffusion in silicon under extrinsic conditions (extrinsic meaning n/ n~/> 1, where n and n~ are the actual and intrinsic carrier concentrations at the diffusion temperature respectively) is of great technological as well as fundamental interest, e.g. in very-large-scale integrated technology, which requires very shallow layers with high concentrations of dopants, or in the investigation of defect-impurity interaction and its dependence on different defect charge states. A number of investigations of impurity diffusion in silicon under extrinsic conditions have been reported in which the concentration of the diffusing impurity was kept low (below solubility limits) and in which the high background doping level was achieved by doping with either phosphorus or arsenic. These experimental conditions simplify the analysis very much because firstly the diffusing impurities do not precipitate, secondly the individual diffusion profiles can be analysed with concentration-independent diffusion coefficients and thirdly there is no electric field enhancement. Fair et al. [1J and Nishi et al. [2] studied the diffusion of antimony in silicon under such extrinsic conditions (n/ni <<.20). They found 0921-5107/89/$3.5(1
that Den (Sb) was proportional to (n/ni) ~ with a value of S between 2 and 3, i.e. higher than expected for diffusion via doubly charged negative vacancies (D~f~= (n/ni)2). Hoyt and Gibbons [3] studied arsenic diffusion in silicon for n~ n~ ~<60 and found an S value of 2.4. We have previously reported S values for antimony and tin in silicon of the order of 4 for 20 ~
The silicon samples were electronic-grade, dislocation-free, p-type (boron doped) 150 or 800 £2 cm, float-zone-refined monocrystals. The phosphorus background doping was established by implantation of phosphorus at an energy of 80 keV to doses between 2 x l015 and 1.2× 1() ~(' cm -2 Flat carrier density profiles extending to depths of at least 2000 A with carrier concentrations between 9 x 10 t9 and 5 x 1() 2{~ cm 3 were obtained after rapid thermal annealing (RTA) at 1075 °C for 20 s in an argon ambient [4]. Subsequently, tin, antimony or arsenic was implanted at an energy of 80 keV to doses of 2 x 1() 14 cm 2 (tin, antimony) or 4 x 10 ~4 cm z (arsenic), corresponding to maximum concentrations of 4 x 1()"~ cm 3 or 6 x 1() '~J cm -3 respectively. Annealing and diffusion were then achieved by RTA [6] in an argon ambient at a temperature of 1050 °C for a duration of 15 s (including the temperature rise time of about 5 s). Carrier density profiles (from the phosphorus background doping) and chemical profiles of tin, © Elsevier Sequoia/Printed in The Netherlands
108
antimony and arsenic were measured for all samples by respectively Hall effect-resistivity measurements combined with anodic oxidation and stripping in steps of 100 A [7] and Rutherford backscattering spectrometry (RBS) with 2 MeV He + ions. Some of the samples were studied by transmission electron microscopy (TEM) using a Carl Zeiss instrument operating at 100 kV. In some of the samples, in addition to the stable antimony a small amount ( 1 x 10 ~s cm : or less) of radioactive ~tgSb was implanted at the ISOLDE facility at CERN, and M6ssbauer spectra were measured fl)r the 24 keV y radiation emitted by the daughter ]19811 by employing a resonance-counting technique with CaSnO3 absorbers [8]. For some samples the background carrier concentration was measured before and after the last implantation and annealing by using duplicate samples. Within uncertainties the background carrier concentration did not change during the final annealing. 3. Results and discussion
The doses and energies used for implantation in the present experiments were such that continuous amorphous layers were formed from the a-c interface to the surface. This, together with the high annealing temperature of the phosphorus implant of 1075 °C for 20 s, ensured that the epitaxial regrowth resulted in perfect crystalline layers without defects which could influence the subsequent diffusion of arsenic, antimony and tin [9]. This was confirmed by TEM. A detailed investigation of the influence of residual defects on the diffusion of arsenic and antimony in tin is presented in a separate paper [10]. In the final annealing at 1050 °C, during which the diffusion under consideration takes place, the epitaxial regrowth of the amorphous layer is completed during the temperature rise time. We have previously demonstrated [11] that arsenic does not diffuse to any measurable degree (by RBS) within this time for an annealing at 1050°C. Other investigators [12] have demonstrated that in contrast to phosphorus, neither arsenic nor antimony show any transient enhanced diffusion as a result of recrystallization. Thus in the following we will assume that the dominant part of the diffusion is unaffected by the epitaxial recrystallization or by residual defects after recrystallization. Figure 1 shows chemical profiles of arsenic
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measured by RBS before and after RTA at 1050°C for 15 s for an n/hi value of 40 ( n i ( 1 0 5 0 ° C ) = 0 . 8 7 3 x 1 0 > cm )). The carrier concentration (n) w a s determined by Hall measurements (see previous section) after the RBS measurement on the same sample used for the RBS measurement. A fit to the diffused profile is also shown in Fig. 1. This fit was obtained by letting the as-implanted profile spread out while obeying the diffusion equation with concentration-independent diffusion coefficients [13]. Effective diffusion coefficients extracted in this way from chemical profiles of arsenic, antimony and tin are shown in Fig. 2 as a function of n/n~ (open symbols) together with results published by Fair and coworkers [1, 14] for n/ni<~20 (full symbols). We will examine the results for each impurity separately.
3.1. Arsenic There is a clear transition from an (n/ni) °s dependence to an (n/ni)2s dependence of the diffusivity on n/ni at an n/n~ value of about 17, corresponding to a carrier concentration of 1.9 x 1020 cm-~. Fair et al.'s results were obtained by furnace annealing and without a Constant background carrier concentration. They interpreted their results as being indicative of a diffusion based on singly charged negative vacancies for n/n~ ~ 20. Hoyt and Gibbons [3] found for diffusion at t000 °C during RTA as well as furnace annealing a n (n/ni) 2x dependence for 20<~n/ n~ ~ 60 which they ~terpreted as being indicative of a diffusion based on doubly charged negative vacancies in this n/ni region, The deviation from
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an ( n/ni )2 dependence could be due, they claimed, to residual damage. We have previously shown [15] that the diffusion of high concentrations of arsenic (up to at least 7 x I(C ~ cm s), without a constant background carrier concentration, could be fitted adequately by including also doubly charged negative vacancies. We had, however, to postulate full electrical activity of the arsenic at the diffusion temperature in order to fit the data, an assumption which is in conflict with the presently accepted solubility value of 3 x 1(C ~ cm s at 1050°C [161.
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Three different regions of diffusivity vs. n/n~ can be identified. The first two have been previously related to diffusion via neutral (3"= 0.4) and doubly charged negative (S = 1.7) vacancies [1, 2]. At approximately the same n/ni value as in the case of arsenic the antimony diffusivity dependence on n/n i transforms into a n (IT~Hi) 3'~ dependence, i.e. into a very high power of n/ni. In the case of antimony, however, we are better off than in the case of arsenic because we can apply M6ssbauer spectroscopy to obtain information on the local surroundings of the antimony impurities at a microscopic level. For a survey of the application of M6ssbauer spectroscopy to the investigation of ion implantation and defects in semiconductors we refer to recent reviews [17, 18]. Suffice it here to say that from a M6ssbauer measurement one can obtain information on the electronic configuration of the impurity atom (via the isomer shift), the symmetry (via the quadrupole interaction) and the vibrational behaviour of the impurity atom (via the Debye-Waller factor). Figure 3 shows M6ssbauer spectra of antimony in silicon after annealing at 1050 °C for two different background carrier concentrations. The spectrum at the top, corresponding to a diffusivity in the S = 1.7 region (marked with an arrow in Fig. 2), consists of a line from substitutional antimony atoms, with an isomer shift of 1.77 mm s (at 77 K), and a weak line from surface-precipitated antimony atoms, with an isomer shift of 3.25 mm s-~ (at 77 K). From such spectra it can be estimated that approximately 6% of the antimony atoms are contained in these surface precipitates, the rest being in exact substitutional positions. The spectrum at the bottom, corresponding to a diffusivity in the S = 3.6 region (also marked with an arrow in Fig. 2), shows in addition to the substitutional line and the surface lines
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Fig. 3, ~'Sb M6ssbauer spectra measured at 77 K fo~ t~.o background doping levels. The corresponding points in Fig. 2 are marked by arrows. The Separation of the spectra into individual lines by the computer analysis is also shown.
a dominating line with an isomer shift of 2.53 mm s- ~ (at 77 K), the intensity of which corresponds to an antimony fraction of about 80%. A detailed discussion of the results from M6ssbauer spectroscopy on this system has been published in ref. 5. The appearance of the new line with an isomer shift of 2.53 mm s--~ reflects the formation of a new defect complex containing antimony and is correlated to the onset of the (n/nl) 3s dependence of the diffusivity. A plausible structure of t h e complex is a (neutral) complex of the form Sb-P-vacancy, formed by the interaction of, for example, a negative E centre and a positively charged Sb + ion. We will return to this complex shortly.
3.3. Tin Fewer data are available for tin than for arsenic and antimony. A region, however, in which the diffusivity depends on a very high power of n/n i ((n/ni)49) can clearly be identified. From the present data we are not able to identify an n/n~ value at which the diffusivity changes from a low power dependence on n/n~ to a high power. With the
Ill combination of RTA and RBS it is very difficult to measure diffusion coefficients below about 1 × 10 14 cm 2 s i Preliminary M6ssbauer measurements of tin in silicon at high n/n i values [41 indicate the existence of a line with an isomer shift of about 2.5 mm s i in addition to the substitutional line, i.e. similar to what is observed for antimony. On the basis of the data of Figs. 2 and 3 we can conclude that for 20 <~ n/n i -< 6() all three impurities diffuse via mechanisms in which the diffusion coefficients depend on n/n i to a power S which is significantly higher than 2, the value expected for a diffusion via doubly charged negative vacancies. T h e onset of this new diffusivity occurs at approximately the same n/n, value for arsenic and antimony, corresponding to carrier concentrations of 1.9 × l(i > and 2.3 × 10 > cm 3 respectively, and for tin at a value which we can only estimate as being smaller than 2.3 x 102o cm 3. This onset is accompanied by the appearance of a new defect complex which has been observed for antimony and probably also for tin by M6ssbauer spectroscopy. Unfortunately, this kind of information cannot be easily obtained for arsenic owing to the lack of a suitable radioactive isotope. In view of the similarities between the diffusivities of these three impurities in silicon at carrier concentrations higher than about 2 × 10 > cm -~, it seems ,justified to look for a c o m m o n mechanism. Mathiot and Pfister [19] have shown that their percolation model developed for high concentration phosphorus diffusion can account for the antimony diffusion data shown in Fig. 2 with a percolation threshold of C* = 2.5 x 10 2o cm -~, in excellent agreement with the threshold observed in the present investigation of 2.3 x 102o cm 3 for antimony. We are at present trying to model the arsenic data of Fig. 2 with the percolation model and the preliminary results are very promising. According to Mathiot and Pfister [1 9], for n/ n i = 4 0 about 30% of the antimony atoms are involved in S b - V pairs in the close vicinity of phosphorus atoms and the new M/Sssbauer line with an isomer shift of 2.53 mm s ~ could arise from these S b - V pairs perturbed by the phosphorus atoms. T h e r e is, however, one serious problem connected with this interpretation. M6ssbauer spectroscopy is rather insensitive to the local surrounding beyond the nearest-neighbour shell. In a percolation cluster in which the phosphorus atom can be in a fifth-neighbour position from the antimony atom, the M6ssbauer
spectrum will not be influenced by the presence of the phosphorus atom, but appears identical to the spectrum of an S b - V pair with an isomer shift at 2.3 mm s 1 [201 or to that of a substitutional antimony atom with an isomer shift of 1.77 mm s ~. An exception would be the situation in which the loosely bound percolation cluster stabilizes itself and becomes a stable defect with the phosphorus atom and the vacancy as nearest neighbours to the antimony atom during the cooling down from the diffusion temperature to room temperature or even lower, at which temperature the M6ssbauer measurements are performed. We are presently investigating this possibility. A point which we have not yet commented on is the decreasing S values from tin (3;=4.9) through antimony ( S = 3 . 6 ) to arsenic (S=2.8). Nishi et al. [2] found that the enhancement at 1100 °C of the phosphorus diffusivity was significantly smaller than that of antimony and pointed out the difference in the interstitial fractions of the respective diffusivities as a possible source of the difference. To our knowledge, the interstitial fraction of the tin diffusivity is not known; however, the observation that the S value for arsenic is smaller than that for antimony is in agreement with this suggestion.
Acknowledgments T h e authors are indebted to Dr. G. Weyer and Dr. P. Tidemand-Petersson for their contributions and useful discussions.
References 1 R.B. [=air, M. L. Manda and J. J. Worlman, ,/. ,:ltater. Rex., 1 (1986) 705. K. Nishi, K. Sakamoto and ,I. Meda, ,/. AppI. l'hsv, 5{J
(]986)4177. 3 J. L. Hoyt and J. F. Gibbons, MRS&'mt). I'roc., 52 (198,6) 15. 4 P. E. Andersen, A. Nylandsted Larsen, P. TidemandPetersson and G. Weyer, Appl. l'hys. Lell., 53(198;8)755. 5 A. Nylandsted Larsen, P. Tidemand-Petersson, P. E. Andersen and G. Weyer, lnst. I'hvs. (o;(t: Ser., 95 (1989) 499. 6 A. Nylandsted Larsen and V. E. Borisenko. Al?pl. l'h)w. A, ,('~ (1984) 51. 7 R. Galloni and A. Sardo. Ret'. A'
112 11 A. Nylandsted Larsen, S. Yu. Shiryaev, E. Schwartz Sorensen and E Tidemand-Petersson, Appl. Phys. Lett., 48(1986) 1805. 12 S. Solmi and M. Servidori, in D. Stievenard and J. C. Bourgoin (eds.), Ion Implantation in Semiconducu~t:s', Trans. Techn. Publ., 1988, p. 65. 13 E. Schwartz Sorensen, personal communication, 1987. 14 R. B. Fair and J. C. C. Tsai, J. Electrochem. Soc., 122 (1975) 1689. 15 S. Yu. Shiryaev, A. Nylandsted Larsen, E. Schwartz
16 17 18 19 20
Sorenscn and P. Tidcmand-Pcicrsson. \ t ~ i l~zslr~o~. Methods B, 19-20(1987 507. D. Nobili, EMIS Datarevie~s 5c,. 4 1988) 401. ~'\. Nylandsted Larsen, J. \~< Peterscn and (i. Wcye~, Mater. Sci. Fon~m, 3~'-4l 1 ~ ~ ~ I:~7, G. Langouche, tt3perfine lnter,~clions, 45(1989) 199. 1). Mathiot and J. C. Pfistet~ J ,Ippl. Phys., 65 (1989i t~70. S. l)amgaard, J. W. Peterscn and G. Weyer. ttypeljine Interactions, 10 i 1981 ~,75 I
107
The Effect of Phosphorus Background Concentration on the Diffusion of Tin, Arsenic and Antimony in Silicon A. NYLANDSTEI) LARSE;N, P. E. ANDERSEN, P. GA1DUK and K. KYLLESBECH LARSEN
Institute OfPhysics, Univers'it)of A arhus, DK-8000A arhus (' (1)enmark) IReceived May 30. 1989)
Abstract
"lhe effect of phosphorus background concentration on the di]]i4sion of tin, arsenic and antimony in silicon has been studied for phosphorus concentrations between about 9 x 10 ~'~ and 5 x 10 :° cm-~, corresponding to 10 <- n/n i <- 60. 7he effectiw, difJ'usion coefficients are found to be proportional to high power of n/n i ]'or all three impurities. These results are discussed within the framework of'the percolation model.
1. I n t r o d u c t i o n
The study of impurity diffusion in silicon under extrinsic conditions (extrinsic meaning n/ n~/> 1, where n and n~ are the actual and intrinsic carrier concentrations at the diffusion temperature respectively) is of great technological as well as fundamental interest, e.g. in very-large-scale integrated technology, which requires very shallow layers with high concentrations of dopants, or in the investigation of defect-impurity interaction and its dependence on different defect charge states. A number of investigations of impurity diffusion in silicon under extrinsic conditions have been reported in which the concentration of the diffusing impurity was kept low (below solubility limits) and in which the high background doping level was achieved by doping with either phosphorus or arsenic. These experimental conditions simplify the analysis very much because firstly the diffusing impurities do not precipitate, secondly the individual diffusion profiles can be analysed with concentration-independent diffusion coefficients and thirdly there is no electric field enhancement. Fair et al. [1J and Nishi et al. [2] studied the diffusion of antimony in silicon under such extrinsic conditions (n/ni <<.20). They found 0921-5107/89/$3.5(1
that Den (Sb) was proportional to (n/ni) ~ with a value of S between 2 and 3, i.e. higher than expected for diffusion via doubly charged negative vacancies (D~f~= (n/ni)2). Hoyt and Gibbons [3] studied arsenic diffusion in silicon for n~ n~ ~<60 and found an S value of 2.4. We have previously reported S values for antimony and tin in silicon of the order of 4 for 20 ~
The silicon samples were electronic-grade, dislocation-free, p-type (boron doped) 150 or 800 £2 cm, float-zone-refined monocrystals. The phosphorus background doping was established by implantation of phosphorus at an energy of 80 keV to doses between 2 x l015 and 1.2× 1() ~(' cm -2 Flat carrier density profiles extending to depths of at least 2000 A with carrier concentrations between 9 x 10 t9 and 5 x 1() 2{~ cm 3 were obtained after rapid thermal annealing (RTA) at 1075 °C for 20 s in an argon ambient [4]. Subsequently, tin, antimony or arsenic was implanted at an energy of 80 keV to doses of 2 x 1() 14 cm 2 (tin, antimony) or 4 x 10 ~4 cm z (arsenic), corresponding to maximum concentrations of 4 x 1()"~ cm 3 or 6 x 1() '~J cm -3 respectively. Annealing and diffusion were then achieved by RTA [6] in an argon ambient at a temperature of 1050 °C for a duration of 15 s (including the temperature rise time of about 5 s). Carrier density profiles (from the phosphorus background doping) and chemical profiles of tin, © Elsevier Sequoia/Printed in The Netherlands
108
antimony and arsenic were measured for all samples by respectively Hall effect-resistivity measurements combined with anodic oxidation and stripping in steps of 100 A [7] and Rutherford backscattering spectrometry (RBS) with 2 MeV He + ions. Some of the samples were studied by transmission electron microscopy (TEM) using a Carl Zeiss instrument operating at 100 kV. In some of the samples, in addition to the stable antimony a small amount ( 1 x 10 ~s cm : or less) of radioactive ~tgSb was implanted at the ISOLDE facility at CERN, and M6ssbauer spectra were measured fl)r the 24 keV y radiation emitted by the daughter ]19811 by employing a resonance-counting technique with CaSnO3 absorbers [8]. For some samples the background carrier concentration was measured before and after the last implantation and annealing by using duplicate samples. Within uncertainties the background carrier concentration did not change during the final annealing. 3. Results and discussion
The doses and energies used for implantation in the present experiments were such that continuous amorphous layers were formed from the a-c interface to the surface. This, together with the high annealing temperature of the phosphorus implant of 1075 °C for 20 s, ensured that the epitaxial regrowth resulted in perfect crystalline layers without defects which could influence the subsequent diffusion of arsenic, antimony and tin [9]. This was confirmed by TEM. A detailed investigation of the influence of residual defects on the diffusion of arsenic and antimony in tin is presented in a separate paper [10]. In the final annealing at 1050 °C, during which the diffusion under consideration takes place, the epitaxial regrowth of the amorphous layer is completed during the temperature rise time. We have previously demonstrated [11] that arsenic does not diffuse to any measurable degree (by RBS) within this time for an annealing at 1050°C. Other investigators [12] have demonstrated that in contrast to phosphorus, neither arsenic nor antimony show any transient enhanced diffusion as a result of recrystallization. Thus in the following we will assume that the dominant part of the diffusion is unaffected by the epitaxial recrystallization or by residual defects after recrystallization. Figure 1 shows chemical profiles of arsenic
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measured by RBS before and after RTA at 1050°C for 15 s for an n/hi value of 40 ( n i ( 1 0 5 0 ° C ) = 0 . 8 7 3 x 1 0 > cm )). The carrier concentration (n) w a s determined by Hall measurements (see previous section) after the RBS measurement on the same sample used for the RBS measurement. A fit to the diffused profile is also shown in Fig. 1. This fit was obtained by letting the as-implanted profile spread out while obeying the diffusion equation with concentration-independent diffusion coefficients [13]. Effective diffusion coefficients extracted in this way from chemical profiles of arsenic, antimony and tin are shown in Fig. 2 as a function of n/n~ (open symbols) together with results published by Fair and coworkers [1, 14] for n/ni<~20 (full symbols). We will examine the results for each impurity separately.
3.1. Arsenic There is a clear transition from an (n/ni) °s dependence to an (n/ni)2s dependence of the diffusivity on n/ni at an n/n~ value of about 17, corresponding to a carrier concentration of 1.9 x 1020 cm-~. Fair et al.'s results were obtained by furnace annealing and without a Constant background carrier concentration. They interpreted their results as being indicative of a diffusion based on singly charged negative vacancies for n/n~ ~ 20. Hoyt and Gibbons [3] found for diffusion at t000 °C during RTA as well as furnace annealing a n (n/ni) 2x dependence for 20<~n/ n~ ~ 60 which they ~terpreted as being indicative of a diffusion based on doubly charged negative vacancies in this n/ni region, The deviation from
109
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an ( n/ni )2 dependence could be due, they claimed, to residual damage. We have previously shown [15] that the diffusion of high concentrations of arsenic (up to at least 7 x I(C ~ cm s), without a constant background carrier concentration, could be fitted adequately by including also doubly charged negative vacancies. We had, however, to postulate full electrical activity of the arsenic at the diffusion temperature in order to fit the data, an assumption which is in conflict with the presently accepted solubility value of 3 x 1(C ~ cm s at 1050°C [161.
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Three different regions of diffusivity vs. n/n~ can be identified. The first two have been previously related to diffusion via neutral (3"= 0.4) and doubly charged negative (S = 1.7) vacancies [1, 2]. At approximately the same n/ni value as in the case of arsenic the antimony diffusivity dependence on n/n i transforms into a n (IT~Hi) 3'~ dependence, i.e. into a very high power of n/ni. In the case of antimony, however, we are better off than in the case of arsenic because we can apply M6ssbauer spectroscopy to obtain information on the local surroundings of the antimony impurities at a microscopic level. For a survey of the application of M6ssbauer spectroscopy to the investigation of ion implantation and defects in semiconductors we refer to recent reviews [17, 18]. Suffice it here to say that from a M6ssbauer measurement one can obtain information on the electronic configuration of the impurity atom (via the isomer shift), the symmetry (via the quadrupole interaction) and the vibrational behaviour of the impurity atom (via the Debye-Waller factor). Figure 3 shows M6ssbauer spectra of antimony in silicon after annealing at 1050 °C for two different background carrier concentrations. The spectrum at the top, corresponding to a diffusivity in the S = 1.7 region (marked with an arrow in Fig. 2), consists of a line from substitutional antimony atoms, with an isomer shift of 1.77 mm s (at 77 K), and a weak line from surface-precipitated antimony atoms, with an isomer shift of 3.25 mm s-~ (at 77 K). From such spectra it can be estimated that approximately 6% of the antimony atoms are contained in these surface precipitates, the rest being in exact substitutional positions. The spectrum at the bottom, corresponding to a diffusivity in the S = 3.6 region (also marked with an arrow in Fig. 2), shows in addition to the substitutional line and the surface lines
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44
Fig. 3, ~'Sb M6ssbauer spectra measured at 77 K fo~ t~.o background doping levels. The corresponding points in Fig. 2 are marked by arrows. The Separation of the spectra into individual lines by the computer analysis is also shown.
a dominating line with an isomer shift of 2.53 mm s- ~ (at 77 K), the intensity of which corresponds to an antimony fraction of about 80%. A detailed discussion of the results from M6ssbauer spectroscopy on this system has been published in ref. 5. The appearance of the new line with an isomer shift of 2.53 mm s--~ reflects the formation of a new defect complex containing antimony and is correlated to the onset of the (n/nl) 3s dependence of the diffusivity. A plausible structure of t h e complex is a (neutral) complex of the form Sb-P-vacancy, formed by the interaction of, for example, a negative E centre and a positively charged Sb + ion. We will return to this complex shortly.
3.3. Tin Fewer data are available for tin than for arsenic and antimony. A region, however, in which the diffusivity depends on a very high power of n/n i ((n/ni)49) can clearly be identified. From the present data we are not able to identify an n/n~ value at which the diffusivity changes from a low power dependence on n/n~ to a high power. With the
Ill combination of RTA and RBS it is very difficult to measure diffusion coefficients below about 1 × 10 14 cm 2 s i Preliminary M6ssbauer measurements of tin in silicon at high n/n i values [41 indicate the existence of a line with an isomer shift of about 2.5 mm s i in addition to the substitutional line, i.e. similar to what is observed for antimony. On the basis of the data of Figs. 2 and 3 we can conclude that for 20 <~ n/n i -< 6() all three impurities diffuse via mechanisms in which the diffusion coefficients depend on n/n i to a power S which is significantly higher than 2, the value expected for a diffusion via doubly charged negative vacancies. T h e onset of this new diffusivity occurs at approximately the same n/n, value for arsenic and antimony, corresponding to carrier concentrations of 1.9 × l(i > and 2.3 × 10 > cm 3 respectively, and for tin at a value which we can only estimate as being smaller than 2.3 x 102o cm 3. This onset is accompanied by the appearance of a new defect complex which has been observed for antimony and probably also for tin by M6ssbauer spectroscopy. Unfortunately, this kind of information cannot be easily obtained for arsenic owing to the lack of a suitable radioactive isotope. In view of the similarities between the diffusivities of these three impurities in silicon at carrier concentrations higher than about 2 × 10 > cm -~, it seems ,justified to look for a c o m m o n mechanism. Mathiot and Pfister [19] have shown that their percolation model developed for high concentration phosphorus diffusion can account for the antimony diffusion data shown in Fig. 2 with a percolation threshold of C* = 2.5 x 10 2o cm -~, in excellent agreement with the threshold observed in the present investigation of 2.3 x 102o cm 3 for antimony. We are at present trying to model the arsenic data of Fig. 2 with the percolation model and the preliminary results are very promising. According to Mathiot and Pfister [1 9], for n/ n i = 4 0 about 30% of the antimony atoms are involved in S b - V pairs in the close vicinity of phosphorus atoms and the new M/Sssbauer line with an isomer shift of 2.53 mm s ~ could arise from these S b - V pairs perturbed by the phosphorus atoms. T h e r e is, however, one serious problem connected with this interpretation. M6ssbauer spectroscopy is rather insensitive to the local surrounding beyond the nearest-neighbour shell. In a percolation cluster in which the phosphorus atom can be in a fifth-neighbour position from the antimony atom, the M6ssbauer
spectrum will not be influenced by the presence of the phosphorus atom, but appears identical to the spectrum of an S b - V pair with an isomer shift at 2.3 mm s 1 [201 or to that of a substitutional antimony atom with an isomer shift of 1.77 mm s ~. An exception would be the situation in which the loosely bound percolation cluster stabilizes itself and becomes a stable defect with the phosphorus atom and the vacancy as nearest neighbours to the antimony atom during the cooling down from the diffusion temperature to room temperature or even lower, at which temperature the M6ssbauer measurements are performed. We are presently investigating this possibility. A point which we have not yet commented on is the decreasing S values from tin (3;=4.9) through antimony ( S = 3 . 6 ) to arsenic (S=2.8). Nishi et al. [2] found that the enhancement at 1100 °C of the phosphorus diffusivity was significantly smaller than that of antimony and pointed out the difference in the interstitial fractions of the respective diffusivities as a possible source of the difference. To our knowledge, the interstitial fraction of the tin diffusivity is not known; however, the observation that the S value for arsenic is smaller than that for antimony is in agreement with this suggestion.
Acknowledgments T h e authors are indebted to Dr. G. Weyer and Dr. P. Tidemand-Petersson for their contributions and useful discussions.
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