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The solubility of carbon in pulled silicon crystals
J. Phys. Chem. Solids
Pergamon Press 1971. Vol. 32, pp. 1211-1219.
Printed in Great Britain.
T H E S O L U B I L I T Y OF C A R B O N IN P U L L E D S I L I C O N CRYSTALS A. R. B E A N and R. C. N E W M A N
J. J. Thomson Physical Laboratory, Whiteknights, Reading RG6 2AF, England
(Received 7 August 1970; in revised form 21 September 1970) Abstract-Single crystals of silicon grown by the Czochralski technique have been annealed at various temperatures in the range 600-1350~ l.R. measurements have been made of the strength of the absorption bands due to carbon (16"5 p.m) and oxygen (9 p.m). From the measurements, heats of solution of the two impurities of 53 + 6 and 38 _+4 kcal/mole have been deduced respectively. When carbon precipitates broad absorption is produced in the region of I2 p.m which is attributed to silicon carbide particles. The strength of this absorption is found to be consistent with the estimated loss of carbon from solution. Precipitation of silicon carbide was not observed in oxygen free crystals. 1. INTRODUCTION
IT IS now well established that silicon crystals may contain appreciable amounts of carbon. An i.r. absorption band due to the localized vibrations of 12C at 607 cm -1 (77~ has been ascribed to carbon atoms which occupy isolated substitutional sites[I,2]. In heat treated crystals other techniques have indicated the presence of silicon carbide particles [3,4], and it has been suggested that carbon may be present in interstitial sites or in the form of graphitic inclusions in epitaxially grown silicon [5]. Clearly a chemical or radio-activation analysis of a given sample would normally measure only its total carbon content and give little or no information about the form in which it was present. On the other hand, the use of a spectroscopic technique, with particular reference to i.r. absorption measurements, has one clear advantage since in principle it may allow the various possible configurations to be separately identified. This technique does however suffer from two disadvantages; (a) the strength of an absorption band has to be calibrated by examining samples which have a known concentration of the impurity in a specific form, and (b) certain configurations of the impurity may not give rise to any detectable absorption features. The strength of the i.r. absorption band due
to substitutional carbon was first calibrated from measurements made on pulled single crystals containing 14C, the total concentration of which was determined by a standard radiochemical technique; the band from 14C at 573 cm -~ is clearly resolved from that of a2C and hence no assumptions had to be made about the relative abundance of the two isotopes in these samples [ 1,2]. Apart from some other relatively very weak absorption bands, which were attributed to carbon-oxygen complexes[2], there were no other absorption features which could be related to the presence of carbon. With the assumption that no appreciable amount of carbon was present in any form other than simple isolated substitutional sites, it was then possible to determine a value for the apparent charge associated with the vibrational mode of these atoms as a9 = 2.6e [6]. This value is very high compared for example with substitutional B - ions which have "0 ~- e, but is in fact consistent with the corresponding value determined for silicon carbide crystals. The apparent charge ~/ is defined as .~2= A(e,)Z, where A is a local field correction and e* is the effective charge. In the work on the intrinsic reststrahl absorption in silicon carbide, A was assumed to take the value (e~+2)2/9, where e~o is the high frequency dielectric constant and a value of
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JPCS VoL 32 No. 6 H
1212
A.R.
B E A N and R. C. N E W M A N
e* = 0-9e was thereby obtained[7]; the apparent charge is thus "0 = 2.5e since ~ = 6.7. It follows that if a significant fraction of the carbon impurities had been present in some other form in the silicon crystals examined, the value of "0 would have had to be correspondingly greater, which does not seem to be plausible on physical grounds. Hence we regard the calibration as established, with only a small degree of possible error; this conclusion has received further support from other recent independent measurements which again showed overall self-consistency
[8]. It has already been mentioned that heat treatment of silicon may lead to the precipitation of silicon carbide, which is to be expected as a result of previous measurements that indicated that the solubility of carbon in silicon decreases as the temperature is decreased below the melting point[9]. Consequently, the strength of the i.r. band due to substitutional carbon should decrease if precipitation occurs and the residual strength should give a measure of the solid solubility of the impurity. Results will be presented in this paper which show that this is so. In addition, the precipitated silicon carbide particles might be expected to give rise to i.r. absorption in the spectral region near 12.6/xm. Again it will be shown that this does occur, although the detailed nature of the absorption is modified somewhat compared with that from a slab of pure silicon carbide. From these measurements, it has been possible to determine the solid solubility of substitutional carbon in pulled silicon single crystals as a function of temperature. These results, together with other apparently anomalous observations made on oxygen-free crystals will then be compared with the available information about the solubility of carbon in silicon as reported elsewhere. 2. EXPERIMENTAL DETAILS
Various crystals of high p-type resistivity (greater than 50~-cm), grown by either the
Czochralski or floating zone techniques, were first characterized by their i.r. absorption spectrum to determine their oxygen and carbon concentrations. Spectra were obtained at 77~ using the differential technique as described previously[2]. The concentration of oxygen present was determined from the calibration given by Pajot[10], while the concentration of substitutional carbon was estimated from our own previous calibration (see Fig. 2 of Ref. [2]). Most samples were then heated in an open silica tube for various times in the temperature range 600-1350~ other samples were heated in sealed-off evacuated silica tubes. After each heat treatment the sample was reground and repolished before it was examined optically; this was necessary to remove surface layers of silica and silicon carbide respectively t11]. In addition a few samples were given a prior irradiation by 2 MeV electrons at room temperature to a total dose of about l0 ''~ electrons cm -2 before they were annealed in the high temperature region; a discussion of the reasons for carrying out these treatments is deferred to Section 3. 3. HIGH TEMPERATURE HEAT TREATMENTS
3.1. Spectroscopic results Two samples each containing 1.4• 10 TM atom cm -3 of oxygen, and carbon concentrations of less than 10 '7 and 2 • 10TM atom cm -~ respectively were given successive anneals, each of one hour's duration, at 600 up to 1000~ in 50 ~ intervals. In both samples a large proportion of the dissolved interstitial oxygen precipitated at a temperature of 800~ as deduced from the observation of the formation of a broad absorption band near 9 p~m due to silica particles, and Rayleigh scattering in the spectral region from l-4/~m. Precipitation of the carbon, as judged from the fall in the strength of the local mode band at 607 cm-', did not occur until the second sample had been given a further heat treatment for 10 hr at 1040~ At the same time, an intense asym-
THE SOLUBILITY OF CARBON metric band of halfwidth of about 60 c m - ' and peak absorption at 12.0/zm was produced, similar to that observed previously by Balkanski et al. in polycrystalline silicon [ 12]. Although both the width and position of the peak varied somewhat with further heat treatments at higher temperatures (see Fig. 1), the integrated absorption remained essentially constant at a value of 230 cm-'-'; at the highest temperatures there was an indication that this value was reduced by about 10 per cent, but this is not considered to be particularly significant because of the errors involved in measurement. When the anneal temperature was increased above I050~ the concentrations of both the dissolved oxygen and carbon increased as shown in Figs. 2 and 3. In order to ensure that equilibrium conditions had been reached at each temperature, the samples were heated for successive periods of up to 100hr at temperatures in the region of 1000~ and for 2 to 3 hr at 1350~ and examined at various stages during each treatment; in no cases were there significant differences in the measurements at a given temperature. Similar measurements were then performed in a second series of anneals in which the temperature was reduced. These results were entirely consistent with the first set which indicates that a genuine equilibrium situation was achieved in the samples examined. Apart from errors of measurement, the determination of the carbon solubility at the lowest temperature may have been in some error because of the uncertainty of the carbon concentration in the untreated float-zone silicon reference sample used in the differential transmission measurements: this may have been as high as 5 x 10J~ atom cm -3. F r o m the results shown in Fig. 3, the heat of solution of substitutional carbon is found to be 5 3 • kcal/mole (2-3 eV). An extrapolation of this data to the melting point yields a solubility of 4.5 • 1017 atom cm -3 which is substantially lower than the carbon content of 2 x 10 TM atom cm -a of the sample in its
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as-grown state;' this point will be discussed in Section 4. Figure 2 indicates that the heat of solution of oxygen in interstitial sites is 3 8 • kcal/ mole (1.65___0.15 eV), which is significantly greater than the value of 22 kcai/mole obtained by Hrostowski and Kaiser[13]. In this previous work, measurements were made on samples which had been annealed in the limited temperature range from 1000-1250~ These measurements were made with a nominal sample temperature of 4.2~ although it is clear from Fig. 1 of Ref. [13] that the
61 //',y
,%... 2
_j,// ) 800 Energy,
~".
850 cm -I
"._
900
Fig. 1. D i f f e r e n t i a l A b s o r p t i o n Spectra at 80~ o f heattreated silicon. C u r v e a sample 2, ~'-'C+ t:~C, after 4 hr at 13 ]0~ Curve b sample I, r'-C after 60 hr at I040~
Curve c sample I, r-'C after 10 hr at 1240~ Curve d sample 5, ~C+ ~:'C,after I hrat 1350~ The spectra have been vertically displaced relative to one another for convenienceof representation. actual sample temperature was considerably higher than this value (cf. Fig. 2 of Ref. [10]), and furthermore, the instrumental resolution must have been much lower than the intrinsic linewidth of the oxygen vibrational absorption band. It was pointed out that there was a difficulty in determining the integrated absorption in this band particularly at the lower temperatures because of the underlying in-
1214
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B E A N and R. C. N E W M A N
trinsic absorption arising from the silicon lattice and also from the very broad band due to the precipitated silica which has a peak at around 1100 cm -1. In fact, further inspection of Fig. 1 of Ref. [13] indicates that the magnitude of this latter absorption becomes smaller, as the fraction of precipitated oxygen increases which is clearly unreasonable and is not consistent with the present observations. It seems possible therefore that the integrated absorption in the oxygen 9/xm band was overestimated for samples annealed at the lower, temperatures and that the quoted solubilities were higher than they should have been. This could then explain the difference in the two values of the heats of solution. It should be pointed out that there is not any discrepancy in the value of the solubility at a temperature of 1250~ when allowance i s made for the modified calibration of Pajot as used in the present work. At this temperature; the integrated absorption in the 9/.~m band is large and hence subtraction of background absorption will make only minor corrections'. It is clear therefore that the measurements are difficult to interpret in a completely unambiguous manner. It should be remembered that the part of the background absorption due to the silicon lattice has been eliminated in the present work, because of the technique of measurement used. Since our measurements also extend to higher temperatures of 1350~ we consider that the present estimate of the heat of solution is likely to be more reliable than that previously reported. Finally our results give some indication that the solubility of oxygen may be decreased slightly when carbon is present, although this is a relatively small effect. At this stage, it should be emphasized that a single heat treatment of other similar samples containing high concentrations of both oxygen and carbon did not lead to significant precipitation of either impurity, although a second heat treatment did produce this effect. It would appear that nucleation sites are produced during the cooling procedure which facilitate
the precipitation process in the second heat treatment. Consequently, an attempt was made to produce such sites by a completely different process. Previously untreated samples were therefore irradiated by 2 M e V electrons at room temperature to total doses of 5 • 1018 electrons cm -z (or 1019 cm-2); the effects of such a treatment have been discussed elsewhere [14]. These samples were then given a single anneal in the high temperature region which did lead to precipitation of both carbon and oxygen, and the residual solubility was entirely consistent with the measurements shown in Figs. 2 and 3. It was concluded that I
I
I
18
17"5
--
17
16"5 t.) O 04
h
6-0
.
r
.
6"5
O
I
7.0
.
I
7.5
10 4 / T ~ K Fig. 2. 9 [C] ~) [C] [ ] [C] L~ [C]
Dissolved = = = =
oxygen concentrations a f t e r heat treatment 2. ]0 TM atoms cm -3, increasing temperatures, sample I 2.101~ atoms cm -3, decreasing temperatures, sample I 2 . 1 0 '~ atoms cm -3, sample 2 2 . 1 0 TM atoms cm -z, sample 3
X [C] < I017 atoms cm -'~,
sample 4
the irradiation did have the desired effect of producing nucleation sites, which are most likely to be vacancy or interstitial clusters. One of these samples contained approximately equal concentrations of tzC and t3C,
THE SOLUBILITY OF CARBON
and it w a s noted that the broad band in the region of 12/xm was shifted somewhat to lower energies and a small subsidiary and relatively sharp feature was produced at 12.61/xm. The halfwidth of this feature was about 7 cm -1 while its contribution to the total absorption relative to the broad band was about 4 per cent. It was definitely established by successive grinding and repolishing of the sample that this was not a feature due to surface contamination [ l 1] and its presence is somewhat puzzling since no corresponding feature was observed in another sample containing only '2C. I
I
I
I
18
o
Z o_
17
o~
u
16
;
g
I~ 6"0
I
o ] 6-5
104/ Fig. 3.
Dissolved
I
I 7"0
T ~ K
carbon concentrations treatment. 9 sample I, increasing temperatures | sample l, decreasing temperatures [] sample 2.
after heat
The results described above all relate to pulled crystals. In order to compare the behaviour of carbon in oxygen free samples, two samples from a particular crystal grown
1215
by the floating' zone technique and with dislocation densities of about 104 cm -2 were given similar heat treatments in open silica tubes. The first sample showed some very anomalous results. After treatments at 1260~ the concentration of substitutional carbon increased from its initial value of 4 • 1017 to 9 • 1017 atoms cm -3, only to fall again to its original value after subsequent treatments. The second sample was heated for 9 hr at each of a number of temperatures between 550 and 1300~ which led to no significant changes in the carbon concentration. In neither sample was a band produced at 12/~m, but very weak absorption was observed at wavelengths around 21/zm which is in the band mode region for silicon[6]. Attempts to induce precipitation by giving a sample a prior electron irradiation treatment also failed. Since these heat treatments were carried out in air, diffusion of oxygen into the samples occurred at the high temperatures. For one sample an estimate was made of the diffusion coefficient on the assumption of an error function complement distribution and using a surface concentration equal to the solubility at 1260~ shown in Fig. 2. The estimated value of D was found to be 1-8• 10-a cm 2 sec -1 which is considered to be consistent with the value of 9 • 10-1~ cm 2 sec -1 calculated from the accepted variation with temperature o f D = 0-21 exp (--2.55 eV/kT) cm 2 sec -1 [15]. 3.2. Interpretation o f the band at 12/xm The band in the region of 12/~m was only produced when a large fraction of carbon had been removed from normal substitutional sites. The most simple explanation is that it arises from precipitated particles of silicon carbide. However, the position of the peak absorption is different from that of 12-6/zm found from slabs of silicon carbide[7], and the width of the line is also much greater. These differences can be explained since (a) the precipitates are in the form of small particles and (b) they are embedded in a matrix of high dielectric constant. The theory relevant
1216
A.R. BEAN and R. C. NEWMAN
to absorption under these conditions has been reviewed recently by Ruppin and Englman [16] and their results will now be used to analyse the present observations. Absorption by ionic crystalline particles of a finite size occurs via surface modes at energies above that of the normal frequency of absorption corresponding to the transverse optic mode tOT at the F point in the zone. F o r a small spherical particle of radius R (where V T R ~ 1) embedded in a medium of dielectric constant eM, absorption will occur at tO, given by:-
precipitation probably did not occur. Particles with other non-spherical shapes will however produce absorption at wavelengths above and below 11-95/zm (oJ0. The magnitude of the absorption now has to be considered. This will be estimated only for small spherical particles, in which case the absorption coefficient is given by:K = 3kolma
(4)
where a ~ - -e--eM - m
9+ 29
tot 2 = 9149 +A) tot~ e~ + 2eu(1 + A)
(1)
and 47rp 1 -- (to/toT)2 -- i y t o / t o r
where 6 [ eo + 2 9
(2)
47rp = (Co--e~o) and k0 is the wavevector of the incident radiation. These expressions apply and e0 and e~ are the low and high frequency to unit volume of the precipitate and so the dielectric constants of the material of the absorption has to be scaled down according to particle. F o r silicon carbide e0----10-0, e~---- the number of carbon atoms which have 6.7 and for silicon eu = 11"8. Hence the posi- precipitated in unit volume of silicon. If 7 tion o f the peak absorption corresponds to is taken as 0.0107 corresponding to the width h = 11-95 ~m (R ~< 1 ~m), 12-25 ttm (R - 3 of the reststrahl band of fl-SiC[7] the integp.m) and 12-6p~m (R ~> 12/zm). From other rated absorption deduced from the above evidence on the precipitation of silicon equations is 2 2 0 c m -~, assuming a volume carbide, it is thought that the particle size in fraction of silicon carbide of 4.1 • 10-5 (corthe present samples is of the order of, or responding to a loss of 2 • 10 '8 carbon atoms smaller than 1/zm, in which case a simpler cm -3 from solution). At this stage, it should expression may be used to determine tog; be made clear that if the particles were a l l that is:spherical, the predicted band should have a peak absorption coefficient of 25 c m - ' and toi ~ _ Eo - - e M ( 1 - - 4 r r / N i ) half-width of about 9 cm -1. This may be (3) ~ 2 9 -- 9 ( 1 -- 47r/Ni) compared with the observed band which has a maximum absorption coefficient of about where Ni is an appropriate depolarizing factor 3 - 4 cm-' and a much larger half-width of 60 cm -1. This result suggests that the prethat depends on the shape of the particle. F o r cylinders and planar particles N = 0 for at cipitate particles have a range of ellipsoidal least one principal axis and this should lead to shapes, each particle giving rise to absorption absorption at tot (12.60/zm). In general this at a slightly different wavelength; this interwas not observed, there being negligible pretation would not however be expected to absorption at wavelengths greater than about greatly modify the estimate of the total integ12.3/xm. It follows that under the present rated absorption in the band. The variations experimental conditions, rod and plat 9 in the shape of the observed band are now
THE SOLUBILITY OF CARBON
easilyexplained as modifications of the form and size of the particles as a function of the annealing treatment given to the samples. Moreover, the total calculated absorption from the silicon carbide is entirely consistent with the absolute number of carbon atoms lost from substitutional sites on the basis of our previous calibration. The shift of the main band to lower energies in the sample containing 13C is also explained, although the reason for the relatively weak feature at 12.6 /xm is still not clear. This peak which at first sight appears to correspond to COTfor Si~2C would obviously be expected to occur at a lower energy due to the presence of the Iac if this were the correct interpretation. However this discrepency is considered to be of minor significance in the context of the present work and will not be discussed further. 4. DISCUSSION
It has been shown that substitutional carbon impurities in pulled silicon single crystals precipitate to form silicon carbide particles after suitable heat treatments, and the silicon carbide gives rise to optical absorption which is explicable in terms of the theory discussed by Ruppin and Englman[16]. It has also been demonstrated that the magnitude of the absorption arising from the precipitated phase is consistent, within experimental error, with that to be expected from the measured loss of carbon from solution. The solubility of carbon as a function of temperature may now be compared with the values determined in earlier diffusion measurements involving 14C. The present results, which are consistent with a heat of solution of 53 + 6 kcal/mole, are considered to be more reliable than the former[9] which suggested a lower yalue of 34 kcal/mole. However, there does appear to be a discrepancy at temperatures close to the melting point of silicon, since the diffusion measurements gave surface concentrations as high as 1-1.5 • 1018 cm -3, whereas the extrapolated value from the optical measurements was only
1217
4 - 5 • 1017 at6m cm -a. The higher value certainly appears to be the more reasonable, since it has been demonstrated that as-grown crystals may contain up to 2-3 • 1018 carbon atom cm-312, 17]. This would imply that the solubility rises to its maximum value at a temperature which is only slightly lower than the melting point and that the relation [C] = A exp (-- AH/RT) certainly does not hold close to this temperature. A determination of the solubility close to the melting temperature is of interest because it is related to the solubility in molten silicon via the segregation coefficient k. Evidence obtained from the distribution of 14C along the length of grown silicon crystals has suggested that k is less than unity, although the two values of 0.00511] and 0.09118] that have been quoted are not consistent. However it is well known that this method of determining k is not very accurate if k ~< 0.1, since the precise value obtained depends upon a detailed examination of the very last part of the crystal to freeze. If it is assumed that k = 0 - 1 , it is implied that the solubility of carbon in molten silicon at the melting point is about 2-3 • 1019 atom cm -3, which is an order of magnitude greater than that which has been reported[19]. The liquid solubility was determined by measuring the weight of solid silicon carbide which dissolved in a measured weight of liquid silicon which was itself in contact with solid silicon. This experimental result is however open to the criticism that carbon from other sources, such as the original solid silicon and from the ambient in which the melting was carried our, may have partially saturated the liquid and so limited the amount of silicon carbide which dissolved. It would appear that this problem could only be resolved by repeating the experiment and using a4C as a tracer. The present results have indicated that precipitation only occurs in pulled crystals
1218
A.R.
B E A N and R. C. N E W M A N
which also contain substantial amounts of oxygen. A possible implication of this result that precipitated silica particles act as nucleation centres for the growth of silicon carbide is supported by other observations of the precipitated phase using the technique of the microbeam analyser[4]. It has also been found that a single heat treatment of an as grown crystal does not in general lead to significant precipitation of either the carbon or oxygen. It is well known that heating silicon under the conditions used in the present work can lead to the introduction of copper and other metallic impurities. It is possible that these elements in precipitated form, or alternatively vacancy clusters produced by such precipitation can act as nuclei for oxygen precipitation in a second treatment of the same sample. The fact that a prior electron irradiation treatment has also been found to induce precipitation in a single anneal suggests that vacancy aggregates could well be important. Hence it may be speculated that oxygen precipitates on vacancy clusters and these particles then act as nuclei for the growth of silicon carbide particles. It has been suggested elsewhere[20] that the detailed behaviour of copper precipitation may also be related to the carbon content of samples but this is difficult to assess as detailed measurements of the carbon content of the samples examined were not reported. In any case, there would not appear to be any discrepancies in these various observations. The question of the detailed behaviour of carbon in oxygen free crystals is still somewhat open. The present results, taken in conjunction with other observations relating to electron irradiation damage[21] seem to suggest that not all the carbon may be present on substitutional sites. Since there is also no indication that the impurity is present as a precipitated silicon carbide phase, it is implied that it must be present in interstitial sites or as graphitic inclusions. The former possibility seems to be unlikely in view of infra-red measurements made on electron irradiated
material[22]. The second possibility certainly cannot be ruled out and evidence for carbon in this form has been reported in epitaxial layers[5]. Such inclusions may not give rise to any detectable i.r. absorption, although no adequate explanation has yet been found for the weak band mode absorption found in such samples as reported in this work. Finally, it is necessary to consider the estimates of carbon contents of crystals obtained by chemical and other methods. In some cases very high values of up to and even greater than 1019 atom cm -3 have been reported[23-25]. Clearly there is no limit to the amount of carbon which may be incorporated as silicon carbide since this is a distinct second phase. This may provide an explanation of some of the results, particularly those relating to polycrystalline material and epitaxial layers[5] where heat treatment of silicon can produce a substantial surface coating of silicon carbide [ 1 I]. One of our own previous determinations, based on optical microscopic measurements of the size of preciptate particles[9], is now considered to be too high since the size of the particles was probably overestimated because of the techniques used (for a discussion of this see for example Ref. [26]). Great care must also be exercised in estimating 'blanks' in straightforward chemical methods. In other possible methods including bombardment of samples by high energy heavy ions to produce nuclear reactions with 12C there are again certain problems. Such treatments usually produce a surface coating of cracked organic material on the samples. It may then be possible, under the conditions of the irradiation, to produce interstitial carbon atoms which diffuse into a surface layer since such atoms are almost certainly mobile at room temperature [ 14, 21 ]. These interstitials could then recombine with vacancies also produced by the irradiation and so carbon may actually be introduced into material which was originally free of this impurity. It is concluded finally that great care is
THE SOLUBILITY OF CARBON
necessary in estimating the total carbon content of a given silicon sample and it appears that further work is necessary to clarify the situation with respect to oxygen free crystals. In pulled material the present results, taken in conjunction with previous work, do appear to be self consistent and indicate that the carbon is probably present only as substitutional impurities or as silicon carbide precipitates. Acknowledgements-The authors wish to thank Mr. R. L. Rouse of A E I ] G E C for making available the crystals used in this investigation. One of us A. R. B. thanks the S.R.C. for a research studentship, and we should also like to thank Professor E. W. J. Mitchell for his interest and providing the laboratory electron irradiation facilities. REFERENCES
I. N E W M A N R. C. and W I L L I S J. B.,J. Phys. Chem. Solids 26, 373 (1965). 2. N E W M A N R. C. and S M I T H R. S.,J. Phys. Chem. Solids 30, 1493 (1969). 3. N E W M A N R. C., Proc. Phys. Soc. 76, 993 (1960). 4. S H U L ' P I N A I. L., Z A S L A V S K I I A. 1. and D E D E G K A E V T. T., Soviet Phys.-solid State 10, 1070 (1968). 5. R A I - C H O U D H U R Y P., N O R E I K A A. J. and T H E O D O R E M. L., J. electrochem. Soc. 116. 97 (1969). 6. N E W M A N R. C.,Adv. Phys. 18,545 (1969). 7. S P I T Z E R W. G., K L E I N M A N D. A. and F R O S C H C.J. Phys. Rev. 113, 133 (1959). 8. B A K E R J. A . , T U C K E R T. N., M O Y E R N. E. and B U S C H E R T R. C., J. appl. Phys. 39~ 4365 (1968). 9. N E W M A N R. C. and W A K E F I E L D J., J. Phys. Chem. Solids 19, 230 (1961), Metallurgy of Semi-
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Pergamon Press 1971. Vol. 32, pp. 1211-1219.
Printed in Great Britain.
T H E S O L U B I L I T Y OF C A R B O N IN P U L L E D S I L I C O N CRYSTALS A. R. B E A N and R. C. N E W M A N
J. J. Thomson Physical Laboratory, Whiteknights, Reading RG6 2AF, England
(Received 7 August 1970; in revised form 21 September 1970) Abstract-Single crystals of silicon grown by the Czochralski technique have been annealed at various temperatures in the range 600-1350~ l.R. measurements have been made of the strength of the absorption bands due to carbon (16"5 p.m) and oxygen (9 p.m). From the measurements, heats of solution of the two impurities of 53 + 6 and 38 _+4 kcal/mole have been deduced respectively. When carbon precipitates broad absorption is produced in the region of I2 p.m which is attributed to silicon carbide particles. The strength of this absorption is found to be consistent with the estimated loss of carbon from solution. Precipitation of silicon carbide was not observed in oxygen free crystals. 1. INTRODUCTION
IT IS now well established that silicon crystals may contain appreciable amounts of carbon. An i.r. absorption band due to the localized vibrations of 12C at 607 cm -1 (77~ has been ascribed to carbon atoms which occupy isolated substitutional sites[I,2]. In heat treated crystals other techniques have indicated the presence of silicon carbide particles [3,4], and it has been suggested that carbon may be present in interstitial sites or in the form of graphitic inclusions in epitaxially grown silicon [5]. Clearly a chemical or radio-activation analysis of a given sample would normally measure only its total carbon content and give little or no information about the form in which it was present. On the other hand, the use of a spectroscopic technique, with particular reference to i.r. absorption measurements, has one clear advantage since in principle it may allow the various possible configurations to be separately identified. This technique does however suffer from two disadvantages; (a) the strength of an absorption band has to be calibrated by examining samples which have a known concentration of the impurity in a specific form, and (b) certain configurations of the impurity may not give rise to any detectable absorption features. The strength of the i.r. absorption band due
to substitutional carbon was first calibrated from measurements made on pulled single crystals containing 14C, the total concentration of which was determined by a standard radiochemical technique; the band from 14C at 573 cm -~ is clearly resolved from that of a2C and hence no assumptions had to be made about the relative abundance of the two isotopes in these samples [ 1,2]. Apart from some other relatively very weak absorption bands, which were attributed to carbon-oxygen complexes[2], there were no other absorption features which could be related to the presence of carbon. With the assumption that no appreciable amount of carbon was present in any form other than simple isolated substitutional sites, it was then possible to determine a value for the apparent charge associated with the vibrational mode of these atoms as a9 = 2.6e [6]. This value is very high compared for example with substitutional B - ions which have "0 ~- e, but is in fact consistent with the corresponding value determined for silicon carbide crystals. The apparent charge ~/ is defined as .~2= A(e,)Z, where A is a local field correction and e* is the effective charge. In the work on the intrinsic reststrahl absorption in silicon carbide, A was assumed to take the value (e~+2)2/9, where e~o is the high frequency dielectric constant and a value of
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JPCS VoL 32 No. 6 H
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A.R.
B E A N and R. C. N E W M A N
e* = 0-9e was thereby obtained[7]; the apparent charge is thus "0 = 2.5e since ~ = 6.7. It follows that if a significant fraction of the carbon impurities had been present in some other form in the silicon crystals examined, the value of "0 would have had to be correspondingly greater, which does not seem to be plausible on physical grounds. Hence we regard the calibration as established, with only a small degree of possible error; this conclusion has received further support from other recent independent measurements which again showed overall self-consistency
[8]. It has already been mentioned that heat treatment of silicon may lead to the precipitation of silicon carbide, which is to be expected as a result of previous measurements that indicated that the solubility of carbon in silicon decreases as the temperature is decreased below the melting point[9]. Consequently, the strength of the i.r. band due to substitutional carbon should decrease if precipitation occurs and the residual strength should give a measure of the solid solubility of the impurity. Results will be presented in this paper which show that this is so. In addition, the precipitated silicon carbide particles might be expected to give rise to i.r. absorption in the spectral region near 12.6/xm. Again it will be shown that this does occur, although the detailed nature of the absorption is modified somewhat compared with that from a slab of pure silicon carbide. From these measurements, it has been possible to determine the solid solubility of substitutional carbon in pulled silicon single crystals as a function of temperature. These results, together with other apparently anomalous observations made on oxygen-free crystals will then be compared with the available information about the solubility of carbon in silicon as reported elsewhere. 2. EXPERIMENTAL DETAILS
Various crystals of high p-type resistivity (greater than 50~-cm), grown by either the
Czochralski or floating zone techniques, were first characterized by their i.r. absorption spectrum to determine their oxygen and carbon concentrations. Spectra were obtained at 77~ using the differential technique as described previously[2]. The concentration of oxygen present was determined from the calibration given by Pajot[10], while the concentration of substitutional carbon was estimated from our own previous calibration (see Fig. 2 of Ref. [2]). Most samples were then heated in an open silica tube for various times in the temperature range 600-1350~ other samples were heated in sealed-off evacuated silica tubes. After each heat treatment the sample was reground and repolished before it was examined optically; this was necessary to remove surface layers of silica and silicon carbide respectively t11]. In addition a few samples were given a prior irradiation by 2 MeV electrons at room temperature to a total dose of about l0 ''~ electrons cm -2 before they were annealed in the high temperature region; a discussion of the reasons for carrying out these treatments is deferred to Section 3. 3. HIGH TEMPERATURE HEAT TREATMENTS
3.1. Spectroscopic results Two samples each containing 1.4• 10 TM atom cm -3 of oxygen, and carbon concentrations of less than 10 '7 and 2 • 10TM atom cm -~ respectively were given successive anneals, each of one hour's duration, at 600 up to 1000~ in 50 ~ intervals. In both samples a large proportion of the dissolved interstitial oxygen precipitated at a temperature of 800~ as deduced from the observation of the formation of a broad absorption band near 9 p~m due to silica particles, and Rayleigh scattering in the spectral region from l-4/~m. Precipitation of the carbon, as judged from the fall in the strength of the local mode band at 607 cm-', did not occur until the second sample had been given a further heat treatment for 10 hr at 1040~ At the same time, an intense asym-
THE SOLUBILITY OF CARBON metric band of halfwidth of about 60 c m - ' and peak absorption at 12.0/zm was produced, similar to that observed previously by Balkanski et al. in polycrystalline silicon [ 12]. Although both the width and position of the peak varied somewhat with further heat treatments at higher temperatures (see Fig. 1), the integrated absorption remained essentially constant at a value of 230 cm-'-'; at the highest temperatures there was an indication that this value was reduced by about 10 per cent, but this is not considered to be particularly significant because of the errors involved in measurement. When the anneal temperature was increased above I050~ the concentrations of both the dissolved oxygen and carbon increased as shown in Figs. 2 and 3. In order to ensure that equilibrium conditions had been reached at each temperature, the samples were heated for successive periods of up to 100hr at temperatures in the region of 1000~ and for 2 to 3 hr at 1350~ and examined at various stages during each treatment; in no cases were there significant differences in the measurements at a given temperature. Similar measurements were then performed in a second series of anneals in which the temperature was reduced. These results were entirely consistent with the first set which indicates that a genuine equilibrium situation was achieved in the samples examined. Apart from errors of measurement, the determination of the carbon solubility at the lowest temperature may have been in some error because of the uncertainty of the carbon concentration in the untreated float-zone silicon reference sample used in the differential transmission measurements: this may have been as high as 5 x 10J~ atom cm -3. F r o m the results shown in Fig. 3, the heat of solution of substitutional carbon is found to be 5 3 • kcal/mole (2-3 eV). An extrapolation of this data to the melting point yields a solubility of 4.5 • 1017 atom cm -3 which is substantially lower than the carbon content of 2 x 10 TM atom cm -a of the sample in its
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as-grown state;' this point will be discussed in Section 4. Figure 2 indicates that the heat of solution of oxygen in interstitial sites is 3 8 • kcal/ mole (1.65___0.15 eV), which is significantly greater than the value of 22 kcai/mole obtained by Hrostowski and Kaiser[13]. In this previous work, measurements were made on samples which had been annealed in the limited temperature range from 1000-1250~ These measurements were made with a nominal sample temperature of 4.2~ although it is clear from Fig. 1 of Ref. [13] that the
61 //',y
,%... 2
_j,// ) 800 Energy,
~".
850 cm -I
"._
900
Fig. 1. D i f f e r e n t i a l A b s o r p t i o n Spectra at 80~ o f heattreated silicon. C u r v e a sample 2, ~'-'C+ t:~C, after 4 hr at 13 ]0~ Curve b sample I, r'-C after 60 hr at I040~
Curve c sample I, r-'C after 10 hr at 1240~ Curve d sample 5, ~C+ ~:'C,after I hrat 1350~ The spectra have been vertically displaced relative to one another for convenienceof representation. actual sample temperature was considerably higher than this value (cf. Fig. 2 of Ref. [10]), and furthermore, the instrumental resolution must have been much lower than the intrinsic linewidth of the oxygen vibrational absorption band. It was pointed out that there was a difficulty in determining the integrated absorption in this band particularly at the lower temperatures because of the underlying in-
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B E A N and R. C. N E W M A N
trinsic absorption arising from the silicon lattice and also from the very broad band due to the precipitated silica which has a peak at around 1100 cm -1. In fact, further inspection of Fig. 1 of Ref. [13] indicates that the magnitude of this latter absorption becomes smaller, as the fraction of precipitated oxygen increases which is clearly unreasonable and is not consistent with the present observations. It seems possible therefore that the integrated absorption in the oxygen 9/xm band was overestimated for samples annealed at the lower, temperatures and that the quoted solubilities were higher than they should have been. This could then explain the difference in the two values of the heats of solution. It should be pointed out that there is not any discrepancy in the value of the solubility at a temperature of 1250~ when allowance i s made for the modified calibration of Pajot as used in the present work. At this temperature; the integrated absorption in the 9/.~m band is large and hence subtraction of background absorption will make only minor corrections'. It is clear therefore that the measurements are difficult to interpret in a completely unambiguous manner. It should be remembered that the part of the background absorption due to the silicon lattice has been eliminated in the present work, because of the technique of measurement used. Since our measurements also extend to higher temperatures of 1350~ we consider that the present estimate of the heat of solution is likely to be more reliable than that previously reported. Finally our results give some indication that the solubility of oxygen may be decreased slightly when carbon is present, although this is a relatively small effect. At this stage, it should be emphasized that a single heat treatment of other similar samples containing high concentrations of both oxygen and carbon did not lead to significant precipitation of either impurity, although a second heat treatment did produce this effect. It would appear that nucleation sites are produced during the cooling procedure which facilitate
the precipitation process in the second heat treatment. Consequently, an attempt was made to produce such sites by a completely different process. Previously untreated samples were therefore irradiated by 2 M e V electrons at room temperature to total doses of 5 • 1018 electrons cm -z (or 1019 cm-2); the effects of such a treatment have been discussed elsewhere [14]. These samples were then given a single anneal in the high temperature region which did lead to precipitation of both carbon and oxygen, and the residual solubility was entirely consistent with the measurements shown in Figs. 2 and 3. It was concluded that I
I
I
18
17"5
--
17
16"5 t.) O 04
h
6-0
.
r
.
6"5
O
I
7.0
.
I
7.5
10 4 / T ~ K Fig. 2. 9 [C] ~) [C] [ ] [C] L~ [C]
Dissolved = = = =
oxygen concentrations a f t e r heat treatment 2. ]0 TM atoms cm -3, increasing temperatures, sample I 2.101~ atoms cm -3, decreasing temperatures, sample I 2 . 1 0 '~ atoms cm -3, sample 2 2 . 1 0 TM atoms cm -z, sample 3
X [C] < I017 atoms cm -'~,
sample 4
the irradiation did have the desired effect of producing nucleation sites, which are most likely to be vacancy or interstitial clusters. One of these samples contained approximately equal concentrations of tzC and t3C,
THE SOLUBILITY OF CARBON
and it w a s noted that the broad band in the region of 12/xm was shifted somewhat to lower energies and a small subsidiary and relatively sharp feature was produced at 12.61/xm. The halfwidth of this feature was about 7 cm -1 while its contribution to the total absorption relative to the broad band was about 4 per cent. It was definitely established by successive grinding and repolishing of the sample that this was not a feature due to surface contamination [ l 1] and its presence is somewhat puzzling since no corresponding feature was observed in another sample containing only '2C. I
I
I
I
18
o
Z o_
17
o~
u
16
;
g
I~ 6"0
I
o ] 6-5
104/ Fig. 3.
Dissolved
I
I 7"0
T ~ K
carbon concentrations treatment. 9 sample I, increasing temperatures | sample l, decreasing temperatures [] sample 2.
after heat
The results described above all relate to pulled crystals. In order to compare the behaviour of carbon in oxygen free samples, two samples from a particular crystal grown
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by the floating' zone technique and with dislocation densities of about 104 cm -2 were given similar heat treatments in open silica tubes. The first sample showed some very anomalous results. After treatments at 1260~ the concentration of substitutional carbon increased from its initial value of 4 • 1017 to 9 • 1017 atoms cm -3, only to fall again to its original value after subsequent treatments. The second sample was heated for 9 hr at each of a number of temperatures between 550 and 1300~ which led to no significant changes in the carbon concentration. In neither sample was a band produced at 12/~m, but very weak absorption was observed at wavelengths around 21/zm which is in the band mode region for silicon[6]. Attempts to induce precipitation by giving a sample a prior electron irradiation treatment also failed. Since these heat treatments were carried out in air, diffusion of oxygen into the samples occurred at the high temperatures. For one sample an estimate was made of the diffusion coefficient on the assumption of an error function complement distribution and using a surface concentration equal to the solubility at 1260~ shown in Fig. 2. The estimated value of D was found to be 1-8• 10-a cm 2 sec -1 which is considered to be consistent with the value of 9 • 10-1~ cm 2 sec -1 calculated from the accepted variation with temperature o f D = 0-21 exp (--2.55 eV/kT) cm 2 sec -1 [15]. 3.2. Interpretation o f the band at 12/xm The band in the region of 12/~m was only produced when a large fraction of carbon had been removed from normal substitutional sites. The most simple explanation is that it arises from precipitated particles of silicon carbide. However, the position of the peak absorption is different from that of 12-6/zm found from slabs of silicon carbide[7], and the width of the line is also much greater. These differences can be explained since (a) the precipitates are in the form of small particles and (b) they are embedded in a matrix of high dielectric constant. The theory relevant
1216
A.R. BEAN and R. C. NEWMAN
to absorption under these conditions has been reviewed recently by Ruppin and Englman [16] and their results will now be used to analyse the present observations. Absorption by ionic crystalline particles of a finite size occurs via surface modes at energies above that of the normal frequency of absorption corresponding to the transverse optic mode tOT at the F point in the zone. F o r a small spherical particle of radius R (where V T R ~ 1) embedded in a medium of dielectric constant eM, absorption will occur at tO, given by:-
precipitation probably did not occur. Particles with other non-spherical shapes will however produce absorption at wavelengths above and below 11-95/zm (oJ0. The magnitude of the absorption now has to be considered. This will be estimated only for small spherical particles, in which case the absorption coefficient is given by:K = 3kolma
(4)
where a ~ - -e--eM - m
9+ 29
tot 2 = 9149 +A) tot~ e~ + 2eu(1 + A)
(1)
and 47rp 1 -- (to/toT)2 -- i y t o / t o r
where 6 [ eo + 2 9
(2)
47rp = (Co--e~o) and k0 is the wavevector of the incident radiation. These expressions apply and e0 and e~ are the low and high frequency to unit volume of the precipitate and so the dielectric constants of the material of the absorption has to be scaled down according to particle. F o r silicon carbide e0----10-0, e~---- the number of carbon atoms which have 6.7 and for silicon eu = 11"8. Hence the posi- precipitated in unit volume of silicon. If 7 tion o f the peak absorption corresponds to is taken as 0.0107 corresponding to the width h = 11-95 ~m (R ~< 1 ~m), 12-25 ttm (R - 3 of the reststrahl band of fl-SiC[7] the integp.m) and 12-6p~m (R ~> 12/zm). From other rated absorption deduced from the above evidence on the precipitation of silicon equations is 2 2 0 c m -~, assuming a volume carbide, it is thought that the particle size in fraction of silicon carbide of 4.1 • 10-5 (corthe present samples is of the order of, or responding to a loss of 2 • 10 '8 carbon atoms smaller than 1/zm, in which case a simpler cm -3 from solution). At this stage, it should expression may be used to determine tog; be made clear that if the particles were a l l that is:spherical, the predicted band should have a peak absorption coefficient of 25 c m - ' and toi ~ _ Eo - - e M ( 1 - - 4 r r / N i ) half-width of about 9 cm -1. This may be (3) ~ 2 9 -- 9 ( 1 -- 47r/Ni) compared with the observed band which has a maximum absorption coefficient of about where Ni is an appropriate depolarizing factor 3 - 4 cm-' and a much larger half-width of 60 cm -1. This result suggests that the prethat depends on the shape of the particle. F o r cylinders and planar particles N = 0 for at cipitate particles have a range of ellipsoidal least one principal axis and this should lead to shapes, each particle giving rise to absorption absorption at tot (12.60/zm). In general this at a slightly different wavelength; this interwas not observed, there being negligible pretation would not however be expected to absorption at wavelengths greater than about greatly modify the estimate of the total integ12.3/xm. It follows that under the present rated absorption in the band. The variations experimental conditions, rod and plat 9 in the shape of the observed band are now
THE SOLUBILITY OF CARBON
easilyexplained as modifications of the form and size of the particles as a function of the annealing treatment given to the samples. Moreover, the total calculated absorption from the silicon carbide is entirely consistent with the absolute number of carbon atoms lost from substitutional sites on the basis of our previous calibration. The shift of the main band to lower energies in the sample containing 13C is also explained, although the reason for the relatively weak feature at 12.6 /xm is still not clear. This peak which at first sight appears to correspond to COTfor Si~2C would obviously be expected to occur at a lower energy due to the presence of the Iac if this were the correct interpretation. However this discrepency is considered to be of minor significance in the context of the present work and will not be discussed further. 4. DISCUSSION
It has been shown that substitutional carbon impurities in pulled silicon single crystals precipitate to form silicon carbide particles after suitable heat treatments, and the silicon carbide gives rise to optical absorption which is explicable in terms of the theory discussed by Ruppin and Englman[16]. It has also been demonstrated that the magnitude of the absorption arising from the precipitated phase is consistent, within experimental error, with that to be expected from the measured loss of carbon from solution. The solubility of carbon as a function of temperature may now be compared with the values determined in earlier diffusion measurements involving 14C. The present results, which are consistent with a heat of solution of 53 + 6 kcal/mole, are considered to be more reliable than the former[9] which suggested a lower yalue of 34 kcal/mole. However, there does appear to be a discrepancy at temperatures close to the melting point of silicon, since the diffusion measurements gave surface concentrations as high as 1-1.5 • 1018 cm -3, whereas the extrapolated value from the optical measurements was only
1217
4 - 5 • 1017 at6m cm -a. The higher value certainly appears to be the more reasonable, since it has been demonstrated that as-grown crystals may contain up to 2-3 • 1018 carbon atom cm-312, 17]. This would imply that the solubility rises to its maximum value at a temperature which is only slightly lower than the melting point and that the relation [C] = A exp (-- AH/RT) certainly does not hold close to this temperature. A determination of the solubility close to the melting temperature is of interest because it is related to the solubility in molten silicon via the segregation coefficient k. Evidence obtained from the distribution of 14C along the length of grown silicon crystals has suggested that k is less than unity, although the two values of 0.00511] and 0.09118] that have been quoted are not consistent. However it is well known that this method of determining k is not very accurate if k ~< 0.1, since the precise value obtained depends upon a detailed examination of the very last part of the crystal to freeze. If it is assumed that k = 0 - 1 , it is implied that the solubility of carbon in molten silicon at the melting point is about 2-3 • 1019 atom cm -3, which is an order of magnitude greater than that which has been reported[19]. The liquid solubility was determined by measuring the weight of solid silicon carbide which dissolved in a measured weight of liquid silicon which was itself in contact with solid silicon. This experimental result is however open to the criticism that carbon from other sources, such as the original solid silicon and from the ambient in which the melting was carried our, may have partially saturated the liquid and so limited the amount of silicon carbide which dissolved. It would appear that this problem could only be resolved by repeating the experiment and using a4C as a tracer. The present results have indicated that precipitation only occurs in pulled crystals
1218
A.R.
B E A N and R. C. N E W M A N
which also contain substantial amounts of oxygen. A possible implication of this result that precipitated silica particles act as nucleation centres for the growth of silicon carbide is supported by other observations of the precipitated phase using the technique of the microbeam analyser[4]. It has also been found that a single heat treatment of an as grown crystal does not in general lead to significant precipitation of either the carbon or oxygen. It is well known that heating silicon under the conditions used in the present work can lead to the introduction of copper and other metallic impurities. It is possible that these elements in precipitated form, or alternatively vacancy clusters produced by such precipitation can act as nuclei for oxygen precipitation in a second treatment of the same sample. The fact that a prior electron irradiation treatment has also been found to induce precipitation in a single anneal suggests that vacancy aggregates could well be important. Hence it may be speculated that oxygen precipitates on vacancy clusters and these particles then act as nuclei for the growth of silicon carbide particles. It has been suggested elsewhere[20] that the detailed behaviour of copper precipitation may also be related to the carbon content of samples but this is difficult to assess as detailed measurements of the carbon content of the samples examined were not reported. In any case, there would not appear to be any discrepancies in these various observations. The question of the detailed behaviour of carbon in oxygen free crystals is still somewhat open. The present results, taken in conjunction with other observations relating to electron irradiation damage[21] seem to suggest that not all the carbon may be present on substitutional sites. Since there is also no indication that the impurity is present as a precipitated silicon carbide phase, it is implied that it must be present in interstitial sites or as graphitic inclusions. The former possibility seems to be unlikely in view of infra-red measurements made on electron irradiated
material[22]. The second possibility certainly cannot be ruled out and evidence for carbon in this form has been reported in epitaxial layers[5]. Such inclusions may not give rise to any detectable i.r. absorption, although no adequate explanation has yet been found for the weak band mode absorption found in such samples as reported in this work. Finally, it is necessary to consider the estimates of carbon contents of crystals obtained by chemical and other methods. In some cases very high values of up to and even greater than 1019 atom cm -3 have been reported[23-25]. Clearly there is no limit to the amount of carbon which may be incorporated as silicon carbide since this is a distinct second phase. This may provide an explanation of some of the results, particularly those relating to polycrystalline material and epitaxial layers[5] where heat treatment of silicon can produce a substantial surface coating of silicon carbide [ 1 I]. One of our own previous determinations, based on optical microscopic measurements of the size of preciptate particles[9], is now considered to be too high since the size of the particles was probably overestimated because of the techniques used (for a discussion of this see for example Ref. [26]). Great care must also be exercised in estimating 'blanks' in straightforward chemical methods. In other possible methods including bombardment of samples by high energy heavy ions to produce nuclear reactions with 12C there are again certain problems. Such treatments usually produce a surface coating of cracked organic material on the samples. It may then be possible, under the conditions of the irradiation, to produce interstitial carbon atoms which diffuse into a surface layer since such atoms are almost certainly mobile at room temperature [ 14, 21 ]. These interstitials could then recombine with vacancies also produced by the irradiation and so carbon may actually be introduced into material which was originally free of this impurity. It is concluded finally that great care is
THE SOLUBILITY OF CARBON
necessary in estimating the total carbon content of a given silicon sample and it appears that further work is necessary to clarify the situation with respect to oxygen free crystals. In pulled material the present results, taken in conjunction with previous work, do appear to be self consistent and indicate that the carbon is probably present only as substitutional impurities or as silicon carbide precipitates. Acknowledgements-The authors wish to thank Mr. R. L. Rouse of A E I ] G E C for making available the crystals used in this investigation. One of us A. R. B. thanks the S.R.C. for a research studentship, and we should also like to thank Professor E. W. J. Mitchell for his interest and providing the laboratory electron irradiation facilities. REFERENCES
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