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Tracer diffusion of Cu in CVD β-SiC
ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 69 (2008) 311–314 www.elsevier.com/locate/jpcs
Tracer diffusion of Cu in CVD b-SiC A. Suinoa, Y. Yamazakia, H. Nittaa,,1, K. Miuraa,2, H. Setoa,3, R. Kannoa,4, Y. Iijimaa,5, H. Satob, S. Takedab, E. Toyab, T. Ohtsukic a
Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-11, Sendai 980-8579, Japan b Process Materials Division, Toshiba Ceramics Co. Ltd., Oguni 999-1351, Japan c Laboratory of Nuclear Science, Graduate School of Science, Tohoku University, Mikamine 1-2-1, Sendai 982-0826, Japan
Abstract Tracer diffusion coefficients of 67Cu and 64Cu in CVD b-Silicon carbide (b-SiC) have been measured in the temperature range between 623 and 1373 K by use of a serial ion-beam sputter-microsectioning technique. The temperature dependence of the diffusion coefficient D 16 is expressed by DCu ¼ 8:2þ0:5 expð41 1 kJ mol1 RTÞ m2 s1 : The diffusion coefficient of Cu in b-SiC is larger than those of 0:5 10 Si and C by more than six orders of magnitude and those of Fe and Cr by one–three orders of magnitude. The activation energy for the diffusion of Cu is about one twentieth of that for the self-diffusion. The results suggest that an interstitial mechanism operates on the diffusion of Cu in b-SiC. r 2007 Published by Elsevier Ltd.
1. Introduction Silicon carbide (SiC) is recognized as a highly promised candidate for a high-temperature semiconductor device with the high heat conductivity and the wide band gap energy. On the other hand, SiC is well known as a hightemperature material because of the extremely high melting temperature (peritectic reaction at 2818 K). This quality also contributes to the semiconductor field. SiC instead of quartz glass is recently used as materials of tubes and boats for the high temperature heat treatments of large-sized silicon wafers. However, when sintered SiC tubes are used, metallic impurities evaporated from heating materials penetrate through the tubes and contaminate the silicon wafer, which is a serious problem to be solved. In practice, Corresponding author. Tel.:+81 222 153463; fax: +81 222 153465.
E-mail address: [email protected] (H. Nitta). Present address: Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan. 2 Present address: Nippon Yakin Kogyo Co. Ltd., Kawasaki 210-0823, Japan. 3 Present address: Fuji Heavy Industries Ltd., Ooizumi 370-0514, Japan. 4 Present address: Chiyoda Corporation, Yokohama 230-8601, Japan. 5 Present address: Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan. 1
0022-3697/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2007.07.007
sintered SiC tubes have been coated with CVD-SiC, which is found to be very effective in preventing the contamination of silicon wafers. The main metallic impurities contaminating silicon wafers through the tube are Fe, Cr, Al, Co, Ni, Cu and Na. Cu and Na result mainly from coolant and sweat, respectively. Especially, the 3d transition elements are known to affect remarkably on the performance of semiconductor devices [1]. Thus, the diffusion data on the 3d transition elements in CVD b-SiC are important for semiconductor fabrication. However, various conditions of SiC are unfavorable for diffusion experiments; it is often non-stoichiometric composition, it is very hard, it has extremely high melting temperature and it is difficult to obtain specimens of acceptable purity and single crystals. Impurities, grain boundaries, pores, and second phases cause many difficulties in the diffusion experiments. Nevertheless, reliable diffusion data on SiC are keenly required from both academic and technological interests. Tracer diffusion of 59Fe, 51Cr, and 57Co in CVD b-SiC (3C type) has been recently studied in the temperature range between 973 and 1873 K by the present authors [2,3]. Linear Arrhenius plots for the diffusion coefficients of Fe and Cr were observed. The activation energies for the diffusion of Fe and Cr were obtained to be 111 and
ARTICLE IN PRESS 312
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81 kJ mol1, respectively. These values are about one tenth of the activation energies 839 kJ mol1 for carbon [4] and 911 kJ mol1 for silicon [5]. Because of extremely small activation energies for the diffusion of Fe and Cr, it can be concluded that an interstitial mechanism is predominant to the diffusion of Fe and Cr in b-SiC [3]. On the other hand, the temperature dependence of the diffusion coefficients of Co shows a strongly curved Arrhenius line. The diffusion coefficient of Co above 1673 K is higher than that of Fe, while at lower temperatures it is much lower than that of Fe. The difference in the diffusivities at 1173 K is more than three orders of magnitude. This suggests that cobalt atoms diffuse by an interstitial mechanism at higher temperatures and by a substitutional mechanism at lower temperatures. However, the Arrhenius lines for the diffusion of Fe, Cr, and Co cross to those for the self-diffusion [4,5] at about 2000 K, which is much lower than 2818 K for the peritectic reaction of SiC. This is strange to the general feature of the diffusion behavior of interstitial mechanism in metals, because the diffusion coefficient via the interstitial mechanism is much higher than the selfdiffusion coefficient in a matrix metal even at the melting temperature. Recently, Linnarsson et al. [6] have studied the diffusion of 13C in 4H–SiC with isotopic 13C enriched epitaxial structure made by vapor phase epitaxy in the temperature range from 2373 to 2623 K. Furthermore, Ru¨schenschmidt et al. [7] have studied the diffusion of 13C and 30Si in 4H–SiC with isotopically enriched 28Si12C/natSiC heterostructures made by chemical vapor phase epitaxy in the temperature range from 2273 to 2473 K. Secondary ion mass spectrometry was used in these experiments. It was found that the self-diffusion coefficients of Si [7] and C [6,7] was of the same order of magnitude but several orders of magnitude smaller than earlier data reported by Hon et al. [4,5]. The activation energy for the diffusion of carbon has been obtained to be 820 [6] and 733 kJ mol1 [7]. As seen later, the Arrhenius lines extraporated to the peritectic temperature Tp ( ¼ 2818 K) for the diffusion of Fe, Cr, Co [3] are far above the Arrhenius lines [6,7] for the diffusion of C and Si in SiC. This is consistent with well known feature of interstitial diffusion in metals and in silicon [1]; interstitial atoms have very high diffusivities with very small activation energies. In the 3d transition elements, Cu is known as an awkward element for semiconductor devices [1]; a donor state is formed; precipitates which affect the performance of semiconductor devices are easily formed because the solubility and the diffusivity of Cu in silicon are the largest among the 3d transition metals. Thus, quantitative information on the diffusion behavior of Cu in CVD b-SiC is vital to semiconductor fabrication. However, the diffusion and penetration behavior of Cu in b-SiC has not been known. In the present study, experiments on the diffusion of Cu in CVD b-SiC have been carried out with the radioactive
tracers 67Cu and 64Cu using a serial ion-beam sputtermicrosectioning technique which enables us to measure submicron diffusion profiles at low temperatures far below the melting temperature of SiC. 2. Experimental procedure High purity polycrystalline SiC plates made by a chemical vapor deposition technique were supplied by Toshiba Ceramics Co. Ltd. The source materials of Si and C were SiHxCly and CnH2n+2, which reacted on a special graphite substrate. One surface of the specimen was polished mirror-likely. The external view of the CVD-SiC plate was gray and opaque. The specimen size was 10 mm2 and 0.5 mm thick. The mean grain size was about 10 mm. The polytype, crystallinity and orientation of the CVD-SiC were evaluated by the X-ray diffraction method using Ni-filtered Cu-Ka radiation. The concentrations of Na, Al, K, Ca, V, Cr, Ni, Cu and Mg in CVD-SiC were 0.01 ppm and that of Fe was 0.03 ppm. Two radioisotopes of 64Cu and 67Cu were used for the diffusion experiment. The radioisotope 64Cu (g-rays, 0.0075 MeV-14.1% and 0.0083 MeV-1.9%; half-life, 12.7 h) in a form of CuCl2 in 1 kmol m3 HCl solution was purchased from Japan Atomic Energy Research Institute. On the other hand, the radioisotope 67Cu (g-ray 0.185 MeV: half-life 2.58d) was produced by 68Zn(g,p) 67 Cu reaction with a linear electron accelerator in Tohoku University. Zinc grains (99.999% purity) about 500 mg were sealed in a quartz tube under vacuum and irradiated with bremsstrahlung (50 MeV electrons) for 8 h. The average beam current was 120 mA. After irradiation, the zinc target was transferred into 20 ml beaker and dissolved in a small volume of 2 N hydrochloric acid (HCl). Target material (natZn) and radioactive impurities produced as byproducts were chemically separated by an anion exchange method. No radioactive impurity of 65Zn was detected in the g-ray measurement using Ge (Li) detector. After the solution dried up to a small volume, the radioisotope 67Cu was finally obtained in a form of CuCl2 in a hydrochloric solution. Some drops of the radioactive solution were dried on a flat surface of the specimen under a heating lamp. Another specimen from which the diffusion profile was analyzed after diffusion was put on the radioactive surface of the specimen and bound with a molybdenum wire. The couple of the specimens was sealed in a quartz tube at a pressure less than 5.3104 Pa and annealed at a temperature in the range from 623 to 1373 K for 2.1 to 58.8 ks in an electric furnace controlled to within 71 K. A serial ion-beam sputter-microsectioning technique was employed to measure the penetration profiles of 67Cu and 64 Cu. Details of the ion-beam sputter-microsectioning method were described elsewhere [8]. The sputtering chamber was pumped to a vacuum of 5 104 Pa, and pure argon gas (99.9995% purity) was introduced to the ion gun. The operating conditions of the ion-beam system
ARTICLE IN PRESS A. Suino et al. / Journal of Physics and Chemistry of Solids 69 (2008) 311–314
were as follows: beam voltage, 300 V; beam current, 10 mA; accelerating voltage, 100 V; cathode filament current, 3.7 A; argon gas pressure, 5 102 Pa. The sputtered section was collected on an aluminum foil step by step, by winding it like a roll of film in a camera, without interrupting the beam current. For each specimen about 30 successive sections were sputtered. The thickness of each section was determined from the individual sputtering time and sputtering rate, which was kept constant by controlling the argon gas pressure and the beam current. The sputtering rate was measured from the net reduction in thickness and the total time of sputtering. The thickness of the section removed was determined with the help of an interferometric microscope by analyzing the interference step between the protected and sputtered parts of the surface. The intensity of the g-rays from each section of the aluminum foil was measured using a well-type Tl-activated NaI scintillation detector in conjunction with a 1024channel pulse-height analyzer.
313
Fig. 1. Examples of penetration profiles for diffusion of 67Cu and 64Cu in b-SiC.
3. Results and discussion Penetration profiles of the tracer were analyzed using the solution of Fick’s second law for one-dimensional volume diffusion of a tracer from an infinitesimally thin surface layer into a sufficiently long rod [9], 2 M x Iðx; tÞ / Cðx; tÞ ¼ pffiffiffiffiffiffiffiffi exp , (1) 4Dt pDt where I(x,t) and C(x,t) are the intensities of the radioactivity and the concentration, respectively, of the tracer at a distance x from the original surface after a diffusion time t; D is the volume diffusion coefficient of the tracer; and M is the total amount of the tracer deposited on the surface before the diffusion. Fig. 1 shows the typical plots of ln I(x,t) vs. x2 for the diffusion of 67Cu and 64Cu in b-SiC. The linearity observed in Fig. 1 proves that Eq. (1) holds, and thus it can be said that the volume diffusion has been concerned. The diffusion coefficients DCu calculated from the slope of these plots are listed in Table 1. 64Cu was used to determine the diffusivity only at 1373 K. Fig. 2 shows the Arrhenius plot of DCu determined in b-SiC together with those of selfdiffusion coefficients of Si [7] and C [6,7] and the diffusion coefficients of Fe, Cr and Co [3]. The diffusion coefficient of 64Cu at 1373 K is located well on a linear Arrhenius line for the diffusion coefficient of 67Cu, as expected from a general feature of isotope effect, which is at most only a few percents; no difference in the diffusivities between 64Cu and 67Cu has been detected in this experiment. The temperature dependence of DCu can be expressed as 16 expð41 1 kJ mol1 RTÞ m2 s2 . DCu ¼ 8:2þ0:5 0:5 10 (2) The diffusion coefficient of Cu is extremely larger than the self-diffusion coefficients of Si [7] and C [6,7] and is
Table 1 Diffusion coefficients of
67
Cu and
64
Cu in b-SiC
T/K
t/ks
Dcu/m2s1
1373* 1273 1173 1073 973 873 773 623
3.0 2.4 3.0 2.1 3.3 5.5 12.6 58.8
2.10 1017 1.61 1017 1.15 1017 8.41 1018 5.09 1018 2.74 1018 1.36 1018 2.66 1019
Asterisk represents the diffusivities determined using the radioisotope 64 Cu.
one–three orders of magnitude larger than the diffusion coefficients of Fe and Cr [3] in the temperature range examined. Furthermore, the value of the activation energy for the diffusion of Cu is about one twentieth of those for Si and C, a half of that for Cr and one third of that for Fe. Since the activation energy for the diffusion of Cu in b-SiC is very small, the contribution of diffusion along grain boundaries and dislocations on the volume diffusion should be discussed. Fig. 3 shows a plot of ln I(x,t) vs. x for the diffusion of Cu in b-SiC at 1373 K. The sample is the same as sample A in Fig. 1. The general feature of the curve is in agreement with the type B kinetics behavior along dislocations: almost Gaussian portion at the near-surface region and a long-linear tail, as has been observed for the dislocation diffusion of Fe, Cr and Co in b-SiC [3]. The near-surface region in the depth of 0.47 mm corresponds to the volume diffusion, as shown in Fig. 1. On the other hand, the long-linear tail at the deeper region corresponds to diffusion along dislocations. The contribution of grain
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dislocations is estimated to be seven orders of magnitude larger than that for the volume diffusion. The penetration profile shown in Fig. 3 and the submicron profile for the volume diffusion suggest that the influence of short circuit paths on the volume diffusion is negligible. Therefore, it is concluded that the very fast Cu diffusion with the small activation energy in b-SiC is attributed not to the contribution of diffusion along grain boundaries and dislocations but to an interstitial mechanism. As seen in Fig. 2, very high diffusivities of 3d transition elements, in particular Cu, in b-SiC are of the same tendency reported in the diffusion behavior in silicon [1]. 4. Conclusion
Fig. 2. Arrhenius plot of diffusion coefficient of copper in comparison with those for carbon, silicon, iron, chromium and cobalt. C[04L] and C[04R] represent the Arrhenius lines for C diffusion obtained by Linnarsson et al. and Ru¨schenschmiddt et al., respectively.
Tracer diffusion of copper in CVD b-SiC has been studied in the temperature range from 623 to 1373 K using an ion-beam sputter-microsectioning technique. The Arrhenius plot of the diffusion coefficient of Cu shows a good linearity with the pre-exponential factor 8.3 1016 m2s1 and the activation energy 41 kJ mol1. The value of the activation energy for Cu is about one twentieth of those for Si and C, a half of that for Cr and one third of that for Fe. This suggests that the diffusion of Cu in b-SiC operates on an interstitial mechanism like as the diffusion of Fe and Cr. Acknowledgments The authors are grateful to the technical staff of the Laboratory of Nuclear Science, Tohoku University. The authors are indebted to Toshiba Ceramics Co. Ltd. for support of this work. References
Fig. 3. Plot of ln I(x,t) vs. x for the diffusion of Cu in b-SiC at 1373 K.
boundary diffusion in the profile of Fig. 3 is negligible because the mean grain size is 10 mm, which is much larger than the depth of profile. The value of the diffusivity along
[1] K. Graff, Metal Impurities in Silicon-Device Fabrication, second ed., Springer, Berlin, 1999, p. 5. [2] C.G. Lee, Y. Iijima, Defect. Diff. Forum 143 (1997) 1153. [3] K. Takano, H. Nitta, H. Seto, C.G. Lee, K. Yamada, Y. Yamazaki, H. Sato, S. Takeda, E. Toya, Y. Iijima, Sci. Tech. Adv. Mater. 2 (2001) 381. [4] M.H. Hon, R.F. Davis, J. Mater. Sci. 14 (1979) 2411. [5] M.H. Hon, R.F. Davis, D.E. Newbury, J. Mater. Sci. 15 (1980) 2073. [6] M.K. Linnarsson, M.S. Janson, J. Zhang, E. Janze´n, B.G. Svensson, J. Appl. Phys. 95 (2004) 8469. [7] K. Ru¨schenschmidt, H. Bracht, N.A. Stolwijk, M. Laube, G. Pensl, G.R. Brandes, J. Appl. Phys. 96 (2004) 1458. [8] Y. Iijima, K. Yamada, H. Katoh, J.K. Kim, K. Hirano, in: T. Takagi (Ed.), In: Proceedings of 13th Symposium on Ion Sources and Ionassisted Techniques, Ionics, The Ion Engineering Society of Japan, Tokyo, 1990, p. 179. [9] P. Shewmon, Diffusion in Solids, second ed., TMS, PA, 1989, p. 14.
Journal of Physics and Chemistry of Solids 69 (2008) 311–314 www.elsevier.com/locate/jpcs
Tracer diffusion of Cu in CVD b-SiC A. Suinoa, Y. Yamazakia, H. Nittaa,,1, K. Miuraa,2, H. Setoa,3, R. Kannoa,4, Y. Iijimaa,5, H. Satob, S. Takedab, E. Toyab, T. Ohtsukic a
Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 6-6-11, Sendai 980-8579, Japan b Process Materials Division, Toshiba Ceramics Co. Ltd., Oguni 999-1351, Japan c Laboratory of Nuclear Science, Graduate School of Science, Tohoku University, Mikamine 1-2-1, Sendai 982-0826, Japan
Abstract Tracer diffusion coefficients of 67Cu and 64Cu in CVD b-Silicon carbide (b-SiC) have been measured in the temperature range between 623 and 1373 K by use of a serial ion-beam sputter-microsectioning technique. The temperature dependence of the diffusion coefficient D 16 is expressed by DCu ¼ 8:2þ0:5 expð41 1 kJ mol1 RTÞ m2 s1 : The diffusion coefficient of Cu in b-SiC is larger than those of 0:5 10 Si and C by more than six orders of magnitude and those of Fe and Cr by one–three orders of magnitude. The activation energy for the diffusion of Cu is about one twentieth of that for the self-diffusion. The results suggest that an interstitial mechanism operates on the diffusion of Cu in b-SiC. r 2007 Published by Elsevier Ltd.
1. Introduction Silicon carbide (SiC) is recognized as a highly promised candidate for a high-temperature semiconductor device with the high heat conductivity and the wide band gap energy. On the other hand, SiC is well known as a hightemperature material because of the extremely high melting temperature (peritectic reaction at 2818 K). This quality also contributes to the semiconductor field. SiC instead of quartz glass is recently used as materials of tubes and boats for the high temperature heat treatments of large-sized silicon wafers. However, when sintered SiC tubes are used, metallic impurities evaporated from heating materials penetrate through the tubes and contaminate the silicon wafer, which is a serious problem to be solved. In practice, Corresponding author. Tel.:+81 222 153463; fax: +81 222 153465.
E-mail address: [email protected] (H. Nitta). Present address: Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan. 2 Present address: Nippon Yakin Kogyo Co. Ltd., Kawasaki 210-0823, Japan. 3 Present address: Fuji Heavy Industries Ltd., Ooizumi 370-0514, Japan. 4 Present address: Chiyoda Corporation, Yokohama 230-8601, Japan. 5 Present address: Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, Morioka 020-8551, Japan. 1
0022-3697/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.jpcs.2007.07.007
sintered SiC tubes have been coated with CVD-SiC, which is found to be very effective in preventing the contamination of silicon wafers. The main metallic impurities contaminating silicon wafers through the tube are Fe, Cr, Al, Co, Ni, Cu and Na. Cu and Na result mainly from coolant and sweat, respectively. Especially, the 3d transition elements are known to affect remarkably on the performance of semiconductor devices [1]. Thus, the diffusion data on the 3d transition elements in CVD b-SiC are important for semiconductor fabrication. However, various conditions of SiC are unfavorable for diffusion experiments; it is often non-stoichiometric composition, it is very hard, it has extremely high melting temperature and it is difficult to obtain specimens of acceptable purity and single crystals. Impurities, grain boundaries, pores, and second phases cause many difficulties in the diffusion experiments. Nevertheless, reliable diffusion data on SiC are keenly required from both academic and technological interests. Tracer diffusion of 59Fe, 51Cr, and 57Co in CVD b-SiC (3C type) has been recently studied in the temperature range between 973 and 1873 K by the present authors [2,3]. Linear Arrhenius plots for the diffusion coefficients of Fe and Cr were observed. The activation energies for the diffusion of Fe and Cr were obtained to be 111 and
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81 kJ mol1, respectively. These values are about one tenth of the activation energies 839 kJ mol1 for carbon [4] and 911 kJ mol1 for silicon [5]. Because of extremely small activation energies for the diffusion of Fe and Cr, it can be concluded that an interstitial mechanism is predominant to the diffusion of Fe and Cr in b-SiC [3]. On the other hand, the temperature dependence of the diffusion coefficients of Co shows a strongly curved Arrhenius line. The diffusion coefficient of Co above 1673 K is higher than that of Fe, while at lower temperatures it is much lower than that of Fe. The difference in the diffusivities at 1173 K is more than three orders of magnitude. This suggests that cobalt atoms diffuse by an interstitial mechanism at higher temperatures and by a substitutional mechanism at lower temperatures. However, the Arrhenius lines for the diffusion of Fe, Cr, and Co cross to those for the self-diffusion [4,5] at about 2000 K, which is much lower than 2818 K for the peritectic reaction of SiC. This is strange to the general feature of the diffusion behavior of interstitial mechanism in metals, because the diffusion coefficient via the interstitial mechanism is much higher than the selfdiffusion coefficient in a matrix metal even at the melting temperature. Recently, Linnarsson et al. [6] have studied the diffusion of 13C in 4H–SiC with isotopic 13C enriched epitaxial structure made by vapor phase epitaxy in the temperature range from 2373 to 2623 K. Furthermore, Ru¨schenschmidt et al. [7] have studied the diffusion of 13C and 30Si in 4H–SiC with isotopically enriched 28Si12C/natSiC heterostructures made by chemical vapor phase epitaxy in the temperature range from 2273 to 2473 K. Secondary ion mass spectrometry was used in these experiments. It was found that the self-diffusion coefficients of Si [7] and C [6,7] was of the same order of magnitude but several orders of magnitude smaller than earlier data reported by Hon et al. [4,5]. The activation energy for the diffusion of carbon has been obtained to be 820 [6] and 733 kJ mol1 [7]. As seen later, the Arrhenius lines extraporated to the peritectic temperature Tp ( ¼ 2818 K) for the diffusion of Fe, Cr, Co [3] are far above the Arrhenius lines [6,7] for the diffusion of C and Si in SiC. This is consistent with well known feature of interstitial diffusion in metals and in silicon [1]; interstitial atoms have very high diffusivities with very small activation energies. In the 3d transition elements, Cu is known as an awkward element for semiconductor devices [1]; a donor state is formed; precipitates which affect the performance of semiconductor devices are easily formed because the solubility and the diffusivity of Cu in silicon are the largest among the 3d transition metals. Thus, quantitative information on the diffusion behavior of Cu in CVD b-SiC is vital to semiconductor fabrication. However, the diffusion and penetration behavior of Cu in b-SiC has not been known. In the present study, experiments on the diffusion of Cu in CVD b-SiC have been carried out with the radioactive
tracers 67Cu and 64Cu using a serial ion-beam sputtermicrosectioning technique which enables us to measure submicron diffusion profiles at low temperatures far below the melting temperature of SiC. 2. Experimental procedure High purity polycrystalline SiC plates made by a chemical vapor deposition technique were supplied by Toshiba Ceramics Co. Ltd. The source materials of Si and C were SiHxCly and CnH2n+2, which reacted on a special graphite substrate. One surface of the specimen was polished mirror-likely. The external view of the CVD-SiC plate was gray and opaque. The specimen size was 10 mm2 and 0.5 mm thick. The mean grain size was about 10 mm. The polytype, crystallinity and orientation of the CVD-SiC were evaluated by the X-ray diffraction method using Ni-filtered Cu-Ka radiation. The concentrations of Na, Al, K, Ca, V, Cr, Ni, Cu and Mg in CVD-SiC were 0.01 ppm and that of Fe was 0.03 ppm. Two radioisotopes of 64Cu and 67Cu were used for the diffusion experiment. The radioisotope 64Cu (g-rays, 0.0075 MeV-14.1% and 0.0083 MeV-1.9%; half-life, 12.7 h) in a form of CuCl2 in 1 kmol m3 HCl solution was purchased from Japan Atomic Energy Research Institute. On the other hand, the radioisotope 67Cu (g-ray 0.185 MeV: half-life 2.58d) was produced by 68Zn(g,p) 67 Cu reaction with a linear electron accelerator in Tohoku University. Zinc grains (99.999% purity) about 500 mg were sealed in a quartz tube under vacuum and irradiated with bremsstrahlung (50 MeV electrons) for 8 h. The average beam current was 120 mA. After irradiation, the zinc target was transferred into 20 ml beaker and dissolved in a small volume of 2 N hydrochloric acid (HCl). Target material (natZn) and radioactive impurities produced as byproducts were chemically separated by an anion exchange method. No radioactive impurity of 65Zn was detected in the g-ray measurement using Ge (Li) detector. After the solution dried up to a small volume, the radioisotope 67Cu was finally obtained in a form of CuCl2 in a hydrochloric solution. Some drops of the radioactive solution were dried on a flat surface of the specimen under a heating lamp. Another specimen from which the diffusion profile was analyzed after diffusion was put on the radioactive surface of the specimen and bound with a molybdenum wire. The couple of the specimens was sealed in a quartz tube at a pressure less than 5.3104 Pa and annealed at a temperature in the range from 623 to 1373 K for 2.1 to 58.8 ks in an electric furnace controlled to within 71 K. A serial ion-beam sputter-microsectioning technique was employed to measure the penetration profiles of 67Cu and 64 Cu. Details of the ion-beam sputter-microsectioning method were described elsewhere [8]. The sputtering chamber was pumped to a vacuum of 5 104 Pa, and pure argon gas (99.9995% purity) was introduced to the ion gun. The operating conditions of the ion-beam system
ARTICLE IN PRESS A. Suino et al. / Journal of Physics and Chemistry of Solids 69 (2008) 311–314
were as follows: beam voltage, 300 V; beam current, 10 mA; accelerating voltage, 100 V; cathode filament current, 3.7 A; argon gas pressure, 5 102 Pa. The sputtered section was collected on an aluminum foil step by step, by winding it like a roll of film in a camera, without interrupting the beam current. For each specimen about 30 successive sections were sputtered. The thickness of each section was determined from the individual sputtering time and sputtering rate, which was kept constant by controlling the argon gas pressure and the beam current. The sputtering rate was measured from the net reduction in thickness and the total time of sputtering. The thickness of the section removed was determined with the help of an interferometric microscope by analyzing the interference step between the protected and sputtered parts of the surface. The intensity of the g-rays from each section of the aluminum foil was measured using a well-type Tl-activated NaI scintillation detector in conjunction with a 1024channel pulse-height analyzer.
313
Fig. 1. Examples of penetration profiles for diffusion of 67Cu and 64Cu in b-SiC.
3. Results and discussion Penetration profiles of the tracer were analyzed using the solution of Fick’s second law for one-dimensional volume diffusion of a tracer from an infinitesimally thin surface layer into a sufficiently long rod [9], 2 M x Iðx; tÞ / Cðx; tÞ ¼ pffiffiffiffiffiffiffiffi exp , (1) 4Dt pDt where I(x,t) and C(x,t) are the intensities of the radioactivity and the concentration, respectively, of the tracer at a distance x from the original surface after a diffusion time t; D is the volume diffusion coefficient of the tracer; and M is the total amount of the tracer deposited on the surface before the diffusion. Fig. 1 shows the typical plots of ln I(x,t) vs. x2 for the diffusion of 67Cu and 64Cu in b-SiC. The linearity observed in Fig. 1 proves that Eq. (1) holds, and thus it can be said that the volume diffusion has been concerned. The diffusion coefficients DCu calculated from the slope of these plots are listed in Table 1. 64Cu was used to determine the diffusivity only at 1373 K. Fig. 2 shows the Arrhenius plot of DCu determined in b-SiC together with those of selfdiffusion coefficients of Si [7] and C [6,7] and the diffusion coefficients of Fe, Cr and Co [3]. The diffusion coefficient of 64Cu at 1373 K is located well on a linear Arrhenius line for the diffusion coefficient of 67Cu, as expected from a general feature of isotope effect, which is at most only a few percents; no difference in the diffusivities between 64Cu and 67Cu has been detected in this experiment. The temperature dependence of DCu can be expressed as 16 expð41 1 kJ mol1 RTÞ m2 s2 . DCu ¼ 8:2þ0:5 0:5 10 (2) The diffusion coefficient of Cu is extremely larger than the self-diffusion coefficients of Si [7] and C [6,7] and is
Table 1 Diffusion coefficients of
67
Cu and
64
Cu in b-SiC
T/K
t/ks
Dcu/m2s1
1373* 1273 1173 1073 973 873 773 623
3.0 2.4 3.0 2.1 3.3 5.5 12.6 58.8
2.10 1017 1.61 1017 1.15 1017 8.41 1018 5.09 1018 2.74 1018 1.36 1018 2.66 1019
Asterisk represents the diffusivities determined using the radioisotope 64 Cu.
one–three orders of magnitude larger than the diffusion coefficients of Fe and Cr [3] in the temperature range examined. Furthermore, the value of the activation energy for the diffusion of Cu is about one twentieth of those for Si and C, a half of that for Cr and one third of that for Fe. Since the activation energy for the diffusion of Cu in b-SiC is very small, the contribution of diffusion along grain boundaries and dislocations on the volume diffusion should be discussed. Fig. 3 shows a plot of ln I(x,t) vs. x for the diffusion of Cu in b-SiC at 1373 K. The sample is the same as sample A in Fig. 1. The general feature of the curve is in agreement with the type B kinetics behavior along dislocations: almost Gaussian portion at the near-surface region and a long-linear tail, as has been observed for the dislocation diffusion of Fe, Cr and Co in b-SiC [3]. The near-surface region in the depth of 0.47 mm corresponds to the volume diffusion, as shown in Fig. 1. On the other hand, the long-linear tail at the deeper region corresponds to diffusion along dislocations. The contribution of grain
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dislocations is estimated to be seven orders of magnitude larger than that for the volume diffusion. The penetration profile shown in Fig. 3 and the submicron profile for the volume diffusion suggest that the influence of short circuit paths on the volume diffusion is negligible. Therefore, it is concluded that the very fast Cu diffusion with the small activation energy in b-SiC is attributed not to the contribution of diffusion along grain boundaries and dislocations but to an interstitial mechanism. As seen in Fig. 2, very high diffusivities of 3d transition elements, in particular Cu, in b-SiC are of the same tendency reported in the diffusion behavior in silicon [1]. 4. Conclusion
Fig. 2. Arrhenius plot of diffusion coefficient of copper in comparison with those for carbon, silicon, iron, chromium and cobalt. C[04L] and C[04R] represent the Arrhenius lines for C diffusion obtained by Linnarsson et al. and Ru¨schenschmiddt et al., respectively.
Tracer diffusion of copper in CVD b-SiC has been studied in the temperature range from 623 to 1373 K using an ion-beam sputter-microsectioning technique. The Arrhenius plot of the diffusion coefficient of Cu shows a good linearity with the pre-exponential factor 8.3 1016 m2s1 and the activation energy 41 kJ mol1. The value of the activation energy for Cu is about one twentieth of those for Si and C, a half of that for Cr and one third of that for Fe. This suggests that the diffusion of Cu in b-SiC operates on an interstitial mechanism like as the diffusion of Fe and Cr. Acknowledgments The authors are grateful to the technical staff of the Laboratory of Nuclear Science, Tohoku University. The authors are indebted to Toshiba Ceramics Co. Ltd. for support of this work. References
Fig. 3. Plot of ln I(x,t) vs. x for the diffusion of Cu in b-SiC at 1373 K.
boundary diffusion in the profile of Fig. 3 is negligible because the mean grain size is 10 mm, which is much larger than the depth of profile. The value of the diffusivity along
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