Properties and Applications of Silicon Carbide82 1 2 4 6 10 2 4 6 100 B/A [nm/h] 0.850.800.750.700.65 1000/T [K -1 ] 0.75 eV 1.31 eV 1.76 eV C-face Si-face fitted line Fig. 5. Arrhenius plots of the linear rate constant B/A for C- and Si-faces. been proposed (7–12). Among them, Massoud et al. (8; 9) have proposed an empirical relation for the oxide thickness dependence of oxidation rate, that is, the addition of an exponential term to the D-G equation, dX dt = B A + 2X + C exp  − X L  , (2) where C and L are the pre-exponential constant and the characteristic length, respectively. We have found that it is possible to fit the calculated values to the observed ones using eq. (2) much better than using eq. (1) in any cases, as shown by the dashed and solid lines, respec- tively, in Figs. 1–4. We discuss the temperature and oxygen partial pressure dependencies of the four parameters B/A, B, C, and L below. 3.4 Arrhenius Plots of the Fitting Parameter Figure 5 shows the Arrhenius plots of the linear rate constant B/A for C- and Si-faces. The values of B/A for Si-face are one order of magnitude smaller than those for C- face at any studied temperature, which is in agreement with the well-known experimental result indi- cating that the growth rate of Si-face is about 1/10 that of C-face. In the case of Si-face, the observed values of B/A are on a straight line with an activation energy of 1.31 eV. While for C-face, the values are on two straight lines, suggesting the existence of two activation ener- gies, i.e., 0.75 and 1.76 eV, and the break point in the activation energy is around 1000 ◦ C (14). As we have measured the growth rates of SiC Si-face in the oxide thickness range less than 100 nm, the diffusion limiting-step regime, in which the growth rate is inversely proportional to X, does not appear regardless of the temperatures used in this study. Therefore, the preci- sion in determining the values of B, related to the diffusion coefficient, is not sufficient, and thus, we do not discuss the value of B in this report. 0.1 2 4 1 2 4 10 2 4 C [nm/h] 0.850.800.750.700.65 1000/T [K -1 ] 1 2 4 10 2 4 100 2 4 L [nm] C-face C L Si-face C L Fig. 6. Arrhenius plots of pre-exponential constant and characteristic length of the growth rate enhancement (C and L) for C- and Si-faces. The values of C/ (B/A), which mean the magnitude of oxide growth enhance- ment, are around 2–6 for Si-face in the studied temperature range. On the other hand, those for C-face are less than 1. These results suggest that the growth rate enhancement phenomenon is more marked for Si-face than for C-face. The temperature dependences of the values of C and L for C- and Si-face shown in Fig. 6. Figure 6 shows that the values of C for Si-face are slightly smaller than those for C-face and almost independent of temperature, which is in contrast to the result for C-face. Figure 6 also shows that the values of L for the Si-face, around 3 nm at 1100 ◦ C, are smaller than those for C-face, around 6 nm at the same temperature, and increase with temperature, which is also in contrast to the result for C-face, i.e., almost independent of temperature. In the case of Si oxidation (8), the values of L are around 7 nm and almost independent of temperature, and the values of C increase with temperature. Therefore, it can be considered that the values of L and the temperature dependences of C and L for SiC C-face are almost the same as those for Si, but different from those for SiC Si-face. As seen in the oxide thickness dependence of the growth rate, the surface reaction-limiting-step regime, in which the growth rate is constant against the oxide thickness X, does not appear in the temperature range studied for SiC C- face (14; 16), as in the case for Si (8). This means that the oxidation mechanism of SiC C-face is in some sense similar to that of Si, but that of SiC Si-face is very different from that of Si. For SiC Si-face, the surface reaction rate is much smaller than the rate limited by oxygen diffusion, compared with the cases of SiC C-face and Si, which may cause the characteristics of the SiC Si-face oxidation to differ from those for SiC C-face and Si. Growth rate enhancement of silicon-carbide oxidation in thin oxide regime 83 1 2 4 6 10 2 4 6 100 B/A [nm/h] 0.850.800.750.700.65 1000/T [K -1 ] 0.75 eV 1.31 eV 1.76 eV C-face Si-face fitted line Fig. 5. Arrhenius plots of the linear rate constant B/A for C- and Si-faces. been proposed (7–12). Among them, Massoud et al. (8; 9) have proposed an empirical relation for the oxide thickness dependence of oxidation rate, that is, the addition of an exponential term to the D-G equation, dX dt = B A + 2X + C exp  − X L  , (2) where C and L are the pre-exponential constant and the characteristic length, respectively. We have found that it is possible to fit the calculated values to the observed ones using eq. (2) much better than using eq. (1) in any cases, as shown by the dashed and solid lines, respec- tively, in Figs. 1–4. We discuss the temperature and oxygen partial pressure dependencies of the four parameters B/A, B, C, and L below. 3.4 Arrhenius Plots of the Fitting Parameter Figure 5 shows the Arrhenius plots of the linear rate constant B/A for C- and Si-faces. The values of B/A for Si-face are one order of magnitude smaller than those for C- face at any studied temperature, which is in agreement with the well-known experimental result indi- cating that the growth rate of Si-face is about 1/10 that of C-face. In the case of Si-face, the observed values of B/A are on a straight line with an activation energy of 1.31 eV. While for C-face, the values are on two straight lines, suggesting the existence of two activation ener- gies, i.e., 0.75 and 1.76 eV, and the break point in the activation energy is around 1000 ◦ C (14). As we have measured the growth rates of SiC Si-face in the oxide thickness range less than 100 nm, the diffusion limiting-step regime, in which the growth rate is inversely proportional to X, does not appear regardless of the temperatures used in this study. Therefore, the preci- sion in determining the values of B, related to the diffusion coefficient, is not sufficient, and thus, we do not discuss the value of B in this report. 0.1 2 4 1 2 4 10 2 4 C [nm/h] 0.850.800.750.700.65 1000/T [K -1 ] 1 2 4 10 2 4 100 2 4 L [nm] C-face C L Si-face C L Fig. 6. Arrhenius plots of pre-exponential constant and characteristic length of the growth rate enhancement (C and L) for C- and Si-faces. The values of C/ (B/A), which mean the magnitude of oxide growth enhance- ment, are around 2–6 for Si-face in the studied temperature range. On the other hand, those for C-face are less than 1. These results suggest that the growth rate enhancement phenomenon is more marked for Si-face than for C-face. The temperature dependences of the values of C and L for C- and Si-face shown in Fig. 6. Figure 6 shows that the values of C for Si-face are slightly smaller than those for C-face and almost independent of temperature, which is in contrast to the result for C-face. Figure 6 also shows that the values of L for the Si-face, around 3 nm at 1100 ◦ C, are smaller than those for C-face, around 6 nm at the same temperature, and increase with temperature, which is also in contrast to the result for C-face, i.e., almost independent of temperature. In the case of Si oxidation (8), the values of L are around 7 nm and almost independent of temperature, and the values of C increase with temperature. Therefore, it can be considered that the values of L and the temperature dependences of C and L for SiC C-face are almost the same as those for Si, but different from those for SiC Si-face. As seen in the oxide thickness dependence of the growth rate, the surface reaction-limiting-step regime, in which the growth rate is constant against the oxide thickness X, does not appear in the temperature range studied for SiC C- face (14; 16), as in the case for Si (8). This means that the oxidation mechanism of SiC C-face is in some sense similar to that of Si, but that of SiC Si-face is very different from that of Si. For SiC Si-face, the surface reaction rate is much smaller than the rate limited by oxygen diffusion, compared with the cases of SiC C-face and Si, which may cause the characteristics of the SiC Si-face oxidation to differ from those for SiC C-face and Si. Properties and Applications of Silicon Carbide84 3.5 Oxygen Partial Pressure Dependencies of the Fitting Parameter We examined the oxygen partial pressure dependence of oxide growth rate at X = 0, i.e., C + B/A, for C-face. As a result, the value of C + B/A is propotional to oxygen partial pres- sure (17). When the oxide thickness X is nearly equal to 0, the oxide growth rate is essentially proportional to the quantity of oxidants that reach the interface between the oxide and SiC because this quantity is much lower than the number of Si atoms at the interface. Since the in- terfacial reaction rate when the oxide thickness X approaches 0 is considered to depend not on partial pressure but on oxidation temperature, the initial growth rate C + B/A is represented by the following expression: C + B A ∝ k 0 C I O2 (3) where k 0 is the interfacial reaction rate when the oxide thickness X approaches 0, C O2 is the concentration of oxidants, and the superscript ‘I’ means the position at the SiC–SiO 2 interface. According to the Henry’s law, the value of C I O2 is proportional to the oxygen partial pres- sure. Therefore, the initial growth rate C + B/A should be proportional to the oxygen partial pressure, which is consistent with the experimental results obtained in this study. While in the case of B/A, the oxygen partial pressure dependence showed a proportion to p 0.5−0.6 (16; 17). This non-linear dependence is also seen in the case of Si oxidation though the exponent is slightly higher. As will be described below, the value of B/A is considered as the quasi-state oxide growth rate and is determined by the balance between many factors, such as the quasi-steady concentration of C atoms at the interface, that of Si atoms emitted from the interface, interfacial reaction rate changing with oxide thickness. We believe that these are responsible for the non-linear dependence of B/A. 3.6 Discussion Some Si oxidation models that describe the growth rate enhancement in the initial stage of oxidation have been proposed (10–12; 18). The common view of these models is that the stress near/at the oxide–Si interface is closely related to the growth enhancement. Among these models, ‘interfacial Si emission model’ is known as showing the greatest ability to fit the experimental oxide growth rate curves. According to this model, Si atoms are emitted as interstitials into the oxide layers accompanied by oxidation of Si, which is caused by the strain due to the expansion of Si lattices during oxidation. The oxidation rate at the interface is initially large and is suppressed by the accumulation of emitted Si atoms near the interface with increasing oxide thickness, i.e., the oxidation rate is not enhanced in the thin oxide regime but is quickly suppressed with increasing thickness. To describe this change in the interfacial reaction rate, Kageshima et al. introduce the following equation as the interfacial reaction rate constant, k (10; 18): k = k 0  1 − C I Si C 0 Si  (4) where C I Si is the concentration of Si interstitials emitted at the interface and the C 0 Si is the solubility limit of Si interstitials in SiO 2 . It is noted that, in the Deal-Grove model (5), the function k is assumed to be constant regardless of the oxidation thickness. By the way, since the density of Si atoms in SiC (4.80 ×10 22 cm −3 ) (19) is almost the same as that in Si (5 ×10 22 cm −3 ) and the residual carbon is unlikely to exist at the oxide–SiC interface in the early stage of SiC oxidation, the stress near/at the interface is considered to be almost identical to the case of Si oxidation. Therefore, it is probable that atomic emission due to the interfacial stress also occurs for SiC oxidation and it also accounts for the growth enhancement in SiC oxidation. In addition, in the case of SiC oxidation, we should take C emission as well as Si emission into account because SiC consists of Si and C atoms. Recently, we have proposed a SiC oxidation model , termed "Si and C emission model", taking the Si and C emissions into the oxide into account, which lead to a reduction of interfacial reaction rate (20). Considering Si and C atoms emitted from the interface during the oxidation as well as the oxidation process of C, the reaction equation for SiC oxidation can be written as, SiC +  2 − ν Si − ν C − α 2  O 2 → ( 1 − ν Si ) SiO 2 + ν Si Si +ν C C + αCO + ( 1 − ν C − α ) CO 2 , (5) where ν and α denote the interfacial emission rate and the production rate of CO, respectively. In the case of Si oxidation, the growth rate in thick oxide regime is determined by the parabolic rate constant B as is obvious if we consider the condition A  2X for eqs. (1,2). Song et al. proposed a modified Deal-Grove model that takes the out-diffusion of CO into account by modifying the parabolic rate constant B by a factor of 1.5 (called ‘normalizing factor’ (21)), and through this model, explained the oxidation process of SiC in the parabolic oxidation rate regime (6). For the Si and C emission model, the normalizing factor corresponds to the coefficient of the oxidant shown in eq. (5), i.e. (2 − ν Si − ν C − α/2). Since Song’s model assumed that there is no interfacial atomic emission (i.e. ν Si = ν C = 0) and carbonaceous products consist of only CO (i.e. α = 1), for this case, it is obvious that the coefficient of the oxidant in eq. (5) equals 1.5. Actually, it has been found in our study that this coefficient is 1.53 by fitting the calculated growth rates to the measured ones (20). Therefore, for C-face, the parameters ν Si , ν C , and α should be close to those assumed in the Song’s model. While for Si-face, this coefficient results in a lower value. According to our recent work (20; 22), the most significant differences between C- and Si-face oxidation are those in k 0 and ν Si . Therefore, it can be consider that the difference in ν Si leads to that in the coefficient of oxidant. Anyway, it is believed that the different B from that of Si oxidation is necessary to reproduce the growth rate in the diffusion rate-limiting region (4; 6; 21; 23) because CO and CO 2 production is neglected. In the case of Si oxidation, the interfacial reaction rate (i.e. eq. (4)) is introduced by assuming that the value of C I Si does not exceed the C 0 Si though the reaction rate decreases with increase of C I Si . Based on this idea, the interfacial reaction rate for SiC is thought to be given by multi- plying decreasing functions for Si and C (20): k = k 0  1 − C I Si C 0 Si  1 − C I C C 0 C  . (6) Growth rate enhancement of silicon-carbide oxidation in thin oxide regime 85 3.5 Oxygen Partial Pressure Dependencies of the Fitting Parameter We examined the oxygen partial pressure dependence of oxide growth rate at X = 0, i.e., C + B/A, for C-face. As a result, the value of C + B/A is propotional to oxygen partial pres- sure (17). When the oxide thickness X is nearly equal to 0, the oxide growth rate is essentially proportional to the quantity of oxidants that reach the interface between the oxide and SiC because this quantity is much lower than the number of Si atoms at the interface. Since the in- terfacial reaction rate when the oxide thickness X approaches 0 is considered to depend not on partial pressure but on oxidation temperature, the initial growth rate C + B/A is represented by the following expression: C + B A ∝ k 0 C I O2 (3) where k 0 is the interfacial reaction rate when the oxide thickness X approaches 0, C O2 is the concentration of oxidants, and the superscript ‘I’ means the position at the SiC–SiO 2 interface. According to the Henry’s law, the value of C I O2 is proportional to the oxygen partial pres- sure. Therefore, the initial growth rate C + B/A should be proportional to the oxygen partial pressure, which is consistent with the experimental results obtained in this study. While in the case of B/A, the oxygen partial pressure dependence showed a proportion to p 0.5−0.6 (16; 17). This non-linear dependence is also seen in the case of Si oxidation though the exponent is slightly higher. As will be described below, the value of B/A is considered as the quasi-state oxide growth rate and is determined by the balance between many factors, such as the quasi-steady concentration of C atoms at the interface, that of Si atoms emitted from the interface, interfacial reaction rate changing with oxide thickness. We believe that these are responsible for the non-linear dependence of B/A. 3.6 Discussion Some Si oxidation models that describe the growth rate enhancement in the initial stage of oxidation have been proposed (10–12; 18). The common view of these models is that the stress near/at the oxide–Si interface is closely related to the growth enhancement. Among these models, ‘interfacial Si emission model’ is known as showing the greatest ability to fit the experimental oxide growth rate curves. According to this model, Si atoms are emitted as interstitials into the oxide layers accompanied by oxidation of Si, which is caused by the strain due to the expansion of Si lattices during oxidation. The oxidation rate at the interface is initially large and is suppressed by the accumulation of emitted Si atoms near the interface with increasing oxide thickness, i.e., the oxidation rate is not enhanced in the thin oxide regime but is quickly suppressed with increasing thickness. To describe this change in the interfacial reaction rate, Kageshima et al. introduce the following equation as the interfacial reaction rate constant, k (10; 18): k = k 0  1 − C I Si C 0 Si  (4) where C I Si is the concentration of Si interstitials emitted at the interface and the C 0 Si is the solubility limit of Si interstitials in SiO 2 . It is noted that, in the Deal-Grove model (5), the function k is assumed to be constant regardless of the oxidation thickness. By the way, since the density of Si atoms in SiC (4.80 ×10 22 cm −3 ) (19) is almost the same as that in Si (5 ×10 22 cm −3 ) and the residual carbon is unlikely to exist at the oxide–SiC interface in the early stage of SiC oxidation, the stress near/at the interface is considered to be almost identical to the case of Si oxidation. Therefore, it is probable that atomic emission due to the interfacial stress also occurs for SiC oxidation and it also accounts for the growth enhancement in SiC oxidation. In addition, in the case of SiC oxidation, we should take C emission as well as Si emission into account because SiC consists of Si and C atoms. Recently, we have proposed a SiC oxidation model , termed "Si and C emission model", taking the Si and C emissions into the oxide into account, which lead to a reduction of interfacial reaction rate (20). Considering Si and C atoms emitted from the interface during the oxidation as well as the oxidation process of C, the reaction equation for SiC oxidation can be written as, SiC +  2 − ν Si − ν C − α 2  O 2 → ( 1 − ν Si ) SiO 2 + ν Si Si +ν C C + αCO + ( 1 − ν C − α ) CO 2 , (5) where ν and α denote the interfacial emission rate and the production rate of CO, respectively. In the case of Si oxidation, the growth rate in thick oxide regime is determined by the parabolic rate constant B as is obvious if we consider the condition A  2X for eqs. (1,2). Song et al. proposed a modified Deal-Grove model that takes the out-diffusion of CO into account by modifying the parabolic rate constant B by a factor of 1.5 (called ‘normalizing factor’ (21)), and through this model, explained the oxidation process of SiC in the parabolic oxidation rate regime (6). For the Si and C emission model, the normalizing factor corresponds to the coefficient of the oxidant shown in eq. (5), i.e. (2 − ν Si − ν C − α/2). Since Song’s model assumed that there is no interfacial atomic emission (i.e. ν Si = ν C = 0) and carbonaceous products consist of only CO (i.e. α = 1), for this case, it is obvious that the coefficient of the oxidant in eq. (5) equals 1.5. Actually, it has been found in our study that this coefficient is 1.53 by fitting the calculated growth rates to the measured ones (20). Therefore, for C-face, the parameters ν Si , ν C , and α should be close to those assumed in the Song’s model. While for Si-face, this coefficient results in a lower value. According to our recent work (20; 22), the most significant differences between C- and Si-face oxidation are those in k 0 and ν Si . Therefore, it can be consider that the difference in ν Si leads to that in the coefficient of oxidant. Anyway, it is believed that the different B from that of Si oxidation is necessary to reproduce the growth rate in the diffusion rate-limiting region (4; 6; 21; 23) because CO and CO 2 production is neglected. In the case of Si oxidation, the interfacial reaction rate (i.e. eq. (4)) is introduced by assuming that the value of C I Si does not exceed the C 0 Si though the reaction rate decreases with increase of C I Si . Based on this idea, the interfacial reaction rate for SiC is thought to be given by multi- plying decreasing functions for Si and C (20): k = k 0  1 − C I Si C 0 Si  1 − C I C C 0 C  . (6) Properties and Applications of Silicon Carbide86 100 80 60 40 20 0 Growth rate [nm/s] 5004003002001000 Oxide thickness [nm] Si emission Deal-Grove model Si and C emission meas. SiC C-face 1090 o C Fig. 7. Oxide thickness dependence of growth rates for C-faces. This equation implies that the growth rate in the initial stage of oxidation should reduce by two steps because the accumulation rates for Si and C interstitials should be different from each other, and hence, the oxidation time when the concentration of interstitial saturates should be different between Si and C interstitial. This prediction will be evidenced in the next paragraph. Figure 7 shows the oxide growth rates observed for C - face at 1090 ◦ C (circles). Also shown in the figure are the growth rates given by the Si and C emission model (solid lines), the Si emission model, and the model that does not take account of both Si and C emission, i.e., the Deal-Grove model (broken line and double broken line, respectively). We note that the same parameters were used for these three SiC oxidation models. Figure 7 shows that the Si and C emission model reproduces the experimental values better than the other two models. In particular, the dip in the thickness dependence of the growth rate seen around 20 nm (pointed by the arrow in the figure), which cannot be reproduced by the Si emission model or the Deal- Grove model no matter how well the calculation are tuned, can be well reproduced by the Si and C emission model. These results suggest that the C interstitials play an important role in the reduction of the oxidation rate, similarly to the role of the Si interstitials. Moreover, from the fact that the drop in growth rate in the initial stage of oxidation is larger for the Si and C emission model than in the case of taking only Si emission into account, we found that the accumulation of C interstitials is faster than that of Si interstitials and that the accumulation of C interstitials is more effective in the thin oxide regime. 4. Conclusion By performing in-situ spectroscopic ellipsometry, we have, for the first time, observed the growth enhancement in oxide growth rate at the initial stage of SiC oxidation, which means that the D-G model is not suitable for SiC oxidation in the whole thickness regime, as in the case of Si oxidation. We have also observed the occurrence of the oxide growth rate enhance- ment at any oxidation temperature and oxygen partial pressure measured both in the cases of C- and Si-faces. We found that the growth rate of SiC for both polar faces can be well represented by the empirical equation proposed by Massoud et al. using the four adjusting parameters B/A, B, C, and L, and that the values of B/A, C, and L, and the temperature de- pendences of C and L for Si-face are different from those for C-face. Finally, we have discussed the mechanism of the growth rate enhancement in the initial stage of oxidation by comparing with the oxidation mechanism of Si. 5. References [1] H. Matsunami: Jpn. J. Appl. Phys. Part 1 43 (2004) 6835. [2] S. Yoshida: Electric Refractory Materials, ed. Y. Kumashiro (Dekker, New York, 2000) 437. [3] V. V. Afanas’ev and A. Stesmans: Appl. Phys. Lett. 71 (1997) 3844. [4] K. Kakubari, R. Kuboki, Y. Hijikata, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum 527- 529 (2006) 1031. [5] B. E. Deal and A. S. Grove: J. Appl. Phys. 36 (1965) 3770. [6] Y. Song, S. Dhar, L. C. Feldman, G. Chung and J. R. Williams: J. Appl. Phys. 95 (2004) 4953. [7] A. S. Grove: Physics and Technology of Semiconductor Devices (John Wiley & Sons, New York, 1967) 31. [8] H. Z. Massoud, J. D. Plummer, and E. A. Irene: J. Electrochem. Soc. 132 (1985) 2685. [9] H. Z. Massoud, J. D. Plummer, and E. A. Irene: J. Electrochem. Soc. 132 (1985) 2693. [10] H. Kageshima, K. Shiraishi, and M. Uematsu: Jpn. J. Appl. Phys. Part 2 38 (1999) L971. [11] S. Ogawa and Y. Takakuwa: Jpn. J. Appl. Phys. 45 (2006) 7063. [12] T. Watanabe, K. Tatsumura, and I. Ohdomari: Phys. Rev. Lett. 96 (2006) 196102. [13] T. Iida, Y. Tomioka, M. Midorikawa, H. Tsukada, M. Orihara, Y. Hijikata, H. Yaguchi, M. Yoshikawa, H. Itoh, Y. Ishida, and S. Yoshida: Jpn. J. Appl. Phys. Part 1 41 (2002) 800. [14] T. Yamamoto, Y. Hijikata, H. Yaguchi, and S. Yoshida: Jpn. J. Appl. Phys 46 (2007) L770. [15] T. Yamamoto, Y. Hijikata, H. Yaguchi, and S. Yoshida: Jpn. J. Appl. Phys. 47 (2008) 7803. [16] T. Yamamoto, Y. Hijikata, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum. 600-603 (2009) 667. [17] K. Kouda, Y. Hijikata, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum. 645-648 (2010) 813. [18] M. Uematsu, H. Kageshima, and K. Shiraishi: J. Appl. Phys. 89 (2001) 1948. [19] Y. Hijikata, H. Yaguchi, S. Yoshida, Y. Takata, K. Kobayashi, H. Nohira, and T. Hattori: J. Appl. Phys. 100 (2006) 053710. [20] Y. Hijikata, H. Yaguchi, and S. Yoshida: Appl. Phys. Express 2 (2009) 021203. [21] E. A. Ray, J. Rozen, S. Dhar, L. C. Feldman, and J. R. Williams: J. Appl. Phys. 103 (2008) 023522. [22] Y. Hijikata, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum 615-617 (2009) 489. [23] Y. Hijikata, T. Yamamoto, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum 600-603 (2009) 663. Growth rate enhancement of silicon-carbide oxidation in thin oxide regime 87 100 80 60 40 20 0 Growth rate [nm/s] 5004003002001000 Oxide thickness [nm] Si emission Deal-Grove model Si and C emission meas. SiC C-face 1090 o C Fig. 7. Oxide thickness dependence of growth rates for C-faces. This equation implies that the growth rate in the initial stage of oxidation should reduce by two steps because the accumulation rates for Si and C interstitials should be different from each other, and hence, the oxidation time when the concentration of interstitial saturates should be different between Si and C interstitial. This prediction will be evidenced in the next paragraph. Figure 7 shows the oxide growth rates observed for C - face at 1090 ◦ C (circles). Also shown in the figure are the growth rates given by the Si and C emission model (solid lines), the Si emission model, and the model that does not take account of both Si and C emission, i.e., the Deal-Grove model (broken line and double broken line, respectively). We note that the same parameters were used for these three SiC oxidation models. Figure 7 shows that the Si and C emission model reproduces the experimental values better than the other two models. In particular, the dip in the thickness dependence of the growth rate seen around 20 nm (pointed by the arrow in the figure), which cannot be reproduced by the Si emission model or the Deal- Grove model no matter how well the calculation are tuned, can be well reproduced by the Si and C emission model. These results suggest that the C interstitials play an important role in the reduction of the oxidation rate, similarly to the role of the Si interstitials. Moreover, from the fact that the drop in growth rate in the initial stage of oxidation is larger for the Si and C emission model than in the case of taking only Si emission into account, we found that the accumulation of C interstitials is faster than that of Si interstitials and that the accumulation of C interstitials is more effective in the thin oxide regime. 4. Conclusion By performing in-situ spectroscopic ellipsometry, we have, for the first time, observed the growth enhancement in oxide growth rate at the initial stage of SiC oxidation, which means that the D-G model is not suitable for SiC oxidation in the whole thickness regime, as in the case of Si oxidation. We have also observed the occurrence of the oxide growth rate enhance- ment at any oxidation temperature and oxygen partial pressure measured both in the cases of C- and Si-faces. We found that the growth rate of SiC for both polar faces can be well represented by the empirical equation proposed by Massoud et al. using the four adjusting parameters B/A, B, C, and L, and that the values of B/A, C, and L, and the temperature de- pendences of C and L for Si-face are different from those for C-face. Finally, we have discussed the mechanism of the growth rate enhancement in the initial stage of oxidation by comparing with the oxidation mechanism of Si. 5. References [1] H. Matsunami: Jpn. J. Appl. Phys. Part 1 43 (2004) 6835. [2] S. Yoshida: Electric Refractory Materials, ed. Y. Kumashiro (Dekker, New York, 2000) 437. [3] V. V. Afanas’ev and A. Stesmans: Appl. Phys. Lett. 71 (1997) 3844. [4] K. Kakubari, R. Kuboki, Y. Hijikata, H. Yaguchi, and S. Yoshida: Mater. Sci. Forum 527- 529 (2006) 1031. [5] B. E. Deal and A. S. Grove: J. Appl. Phys. 36 (1965) 3770. [6] Y. Song, S. Dhar, L. C. Feldman, G. Chung and J. R. Williams: J. Appl. Phys. 95 (2004) 4953. [7] A. S. 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Magnetic Properties of Transition-Metal-Doped Silicon Carbide Diluted Magnetic Semiconductors 89 Magnetic Properties of Transition-Metal-Doped Silicon Carbide Diluted Magnetic Semiconductors Andrei Los and Victor Los X Magnetic Properties of Transition-Metal-Doped Silicon Carbide Diluted Magnetic Semiconductors Andrei Los 1, 2 and Victor Los 3 1 ISS Ltd., Semiconductors and Circuits Lab 2 Freescale Semiconductor Ukraine LLC 3 Institute of Magnetism, National Academy of Sciences Kiev, Ukraine 1. Introduction Possibility to employ the spin of electrons for controlling electronic device operation has long been envisaged as a foundation for future extremely low power amplifying and logic devices, polarized light emitting diodes, new generation magnetic field sensors, high density 3D magnetic memories, etc. (Gregg et al., 2002; Žutić et al., 2004; Bratkovsky, 2008). While metal-metal and metal-insulator spin-electronic (or spintronic) devices have already found their application as hard drive magnetic field sensors and niche nonvolatile memories, diluted magnetic semiconductors (DMSs), i.e. semiconductors with a fraction of the atoms substituted by magnetic atoms, are expected to become a link enabling integration of spin-electronic functionality into traditional electron-charge-based semiconductor technology. Following the discovery of carrier-mediated ferromagnetism due to transition metal doping in technologically important GaAs and InAs III-V compound semiconductors (Munekata et at., 1989; Ohno et al., 1996), a wealth of research efforts have been invested in the past two decades into investigations of magnetic properties of DMSs. Ferromagnetic semiconductors were, of course, not new at the time and carrier-mediated ferromagnetism, a lever allowing electrical control of the magnetic ordering, had also been demonstrated albeit only at liquid helium temperatures (Pashitskii & Ryabchenko, 1979; Story et al., 1986). The achievement of the ferromagnetic ordering temperature, the Curie temperature T C , in excess of 100 K in (Ga, Mn) As compounds was a significant step towards practical semiconductor spintronic device implementation. A substantial progress has been achieved in increasing the ordering temperature in this material system and T C as high as 180 K has been reported (Olejník et al., 2008). (Ga, Mn) As has effectively become a model magnetic semiconductor material with its electronic, magnetic, and optical properties understood most deeply among the DMSs. Still, however, one needs the Curie temperature to be at or above room temperature for most practical applications. Mean-field theory of ferromagnetism (Dietl et al., 2000; Dietl et al., 2001), predicting that above room temperature carrier-mediated ferromagnetic ordering may be possible in certain wide bandgap diluted magnetic semiconductors, including a family of III-nitrides and ZnO, had spun a great deal of interest to magnetic properties of these materials. The resulting 5 Properties and Applications of Silicon Carbide90 flurry of activities in this area led to apparent early successes in fabricating the DMS samples exhibiting ferromagnetism above room temperature (Pearton et al., 2003; Hebard et al., 2004). Ferromagnetic ordering in these samples was attributed to formation of homogeneous DMS alloys which, however, was in many cases later refuted and explained differently, by, for instance, impurity clustering, at the time overlooked by standard characterization techniques. Much theoretical understanding has been gained since then on the effects of exchange interaction, self-compensation, spinodal decomposition, etc. Given that various effects may mimic the “true DMS” behaviour, a careful investigation of the microscopic picture of magnetic moments formation and their interaction, as well as attraction of different complementary experimental techniques is required for a realistic understanding and prediction of the properties of this complex class of materials. Silicon carbide is another wide bandgap semiconductor which has been considered a possible candidate for spin electronic applications. SiC has a long history of material research and device development and is already commercially successful in a number of applications. The mean field theory (Dietl et al., 2000; Dietl et al., 2001) predicted that semiconductors with light atoms and smaller lattice constants might possess stronger magnetic coupling and larger ordering temperatures. Although not applied directly to studying magnetic properties of SiC, these predictions make SiC DMS a promising candidate for spintronic applications. Relatively little attention has been paid to investigation of magnetic properties of SiC doped with TM impurities, and the results obtained to date are rather modest compared to many other DMS systems and are far from being conclusive. Early experimental studies evidenced ferromagnetic response in Ni-, Mn-, and Fe-doped SiC with the values of the Curie temperature T C varying from significantly below to close to room temperature (Theodoropoulou et al., 2002; Syväjärvi et al., 2004; Stromberg et al., 2006). The authors assigned the magnetic signal to either the true DMS behaviour or to secondary phase formation. Later experimental reports on Cr-doped SiC suggested this material to be ferromagnetic with the T C ~70 K for Cr concentration of ~0.02 wt% (Huang & Chen, 2007), while above room temperature magnetism with varying values of the atomic magnetic moments was observed for Cr concentration of 7-10 at% in amorphous SiC (Jin et al., 2008). SiC doped with Mn has become the most actively studied SiC DMS material. Experimental studies of Mn-implanted 3C-SiC/Si heteroepitaxial structure (Bouziane et al., 2009), of C- incorporated Mn-Si films grown on 4H-SiC wafers (Wang et al., 2007), a detailed report by the same authors on structural, magnetic, and magneto-optical properties of Mn-doped SiC films prepared on 3C-SiC wafers (Wang et al., 2009) as well as studies of low-Mn-doped 6H- SiC (Song et al., 2009) and polycrystalline 3C-SiC (Ma et al., 2007) all suggested Mn to be a promising impurity choice for achieving high ferromagnetic ordering temperatures in SiC DMS. Researchers recently turned to studying magnetic properties of TM-doped silicon carbide nanowires (Seong et al., 2009). Theoretical work done in parallel in an attempt to explain the available experimental data and to obtain guidance for experimentalists was concentrated on first principles calculations which are a powerful tool for modelling and predicting DMS material properties. Various ab initio computational techniques were used to study magnetic properties of SiC DMSs theoretically. Linearized muffin-tin orbital (LMTO) technique was utilized for calculating substitution energies of a number of transition metal impurities in 3C-SiC (Gubanov et al., 2001; Miao & Lambrecht, 2003). The researchers found that Si site is more favourable compared to C site for TM substitution. This result holds when lattice relaxation effects are taken into account in the full-potential LMTO calculation. Both research teams found that Fe, Ni and Co were nonmagnetic while Cr and Mn possessed nonzero magnetic moments in the 3C-SiC host. Calculation of the magnetic moments in a relaxed supercell containing two TM atoms showed that both Mn and Cr atoms ordered ferromagnetically. Ferromagnetic ordering was later confirmed for V, Mn, and Cr using ultrasoft pseudopotential plane wave method (Kim et al., 2004). In another ab initio study, nonzero magnetic moments were found for Cr and Mn in 3C-SiC using full potential linearized augmented plane wave (FLAPW) calculation technique and no relaxation procedure accounting for impurity–substitution- related lattice reconstruction (Shaposhnikov & Sobolev, 2004). The authors additionally studied magnetic properties of TM impurities in 6H-SiC substituting for 2% or 16% of host atoms. It was found that on Si site in 6H-SiC Cr and Mn possessed magnetic moments in both concentrations, while Fe was magnetic only in the concentration of 2%. Ultrasoft pseudopotentials were used for calculations of magnetic moments and ferromagnetic exchange energy estimations for the case of Cr doping of 3C-SiC (Kim & Chung, 2005). In a later reported study (Miao & Lambrecht, 2006) the authors used FP-LMTO technique with lattice relaxation to compare electronic and magnetic properties of 3C- and 4H-SiC doped with early first row transition metals. Spin polarization was found to be present in V, Cr, and Mn-doped SiC. The authors of (Bouziane et al., 2008) additionally studied the influence of implantation-induced defects on electronic structure of Mn-doped SiC. The results of the cited calculations were also somewhat sensitive to the particular calculation technique employed. Here, we attempt to create a somewhat complete description of SiC-based diluted magnetic semiconductors in a systematic study of magnetic states of first row transition metal impurities in SiC host. Improving prior research, we do this in the framework of ab initio FLAPW calculation technique, perhaps one of the most if not the most accurate density functional theory technique at the date, combined with a complete lattice relaxation procedure at all stages of the calculation of magnetic moments and ordering temperatures. Accounting for the impurity-substitution-caused relaxation has been found crucial by many researchers for a correct description of a DMS system. We therefore are hopefully approaching the best accuracy of the calculations possible with the ground state density functional theory. We analyze the details of magnetic moments formation and of their change with the unit cell volume, as well as of the host lattice reconstruction due to impurity substitution. Such analysis leads to revealing multiple magnetic states in TM-doped SiC. We also study, for the first time, particulars of exchange interaction for different TM impurities and provide estimates of the magnetic ordering temperatures of SiC DMSs. 2. Methodology and computational setup 2.1 SiC-TM material system Crystal lattice of any SiC polytype can be represented as a sequence of hexagonal close- packed silicon-carbon bilayers. Different bilayer stacking sequences correspond to different polytypes. For example, for the most technologically important hexagonal 4H polytype, the stacking sequence is ABAC (or, equivalently, ABCB), where A, B, and C denote hexagonal bilayers rotated by 120º with respect to each other (Bechstedt et al., 1997). The stacking sequence for another common polytype, the cubic 3C-SiC, is ABC. Although in all SiC [...]... magnetic properties of TM-doped SiC are studied for 3C (Zincblende) and 4H (Wurtzite) SiC polytypes We start with calculations of the lattice parameters and electronic structure of pure 3C- and 4H-SiC The primitive cell of pure cubic 3C-SiC consists of single silicon- carbon pair Another way of representing this type of lattice is with a sequence of Magnetic Properties of Transition-Metal-Doped Silicon Carbide. .. total number of atoms is about 4 % in the case of 4H-SiC and about 5% in the case of 3C-SiC As already mentioned, such concentrations are typical for experimental, including SiC, DMS systems  94 Properties and Applications of Silicon Carbide Calculations of SiC DMS ordering temperatures require adding another TM impurity atom to the supercells These supercells are shown in Fig 2 In the case of 3C-SiC,... difference between the FM- and AFM-ordered supercells containing a pair of TM 1 04 Properties and Applications of Silicon Carbide atoms This is the amount of energy needed to flip the spin of one of these atoms and thus change magnetic ordering of the supercell from FM to AFM or vice versa; therefore, this energy is counted per supercell The second quantity EFMNM is the amount of total energy needed to... functions of the majority e and t2 states hybridize with the antiferromagnetically aligned e and t2 states of the opposite spin channel As a result, the lower in energy states are shifted to even lower energies and the higher states are shifted to 106 Properties and Applications of Silicon Carbide higher energies The energy is gained by reduction of the energy of filled states The mechanisms of ferromagnetic... cell consists of 3 Si-C bilayers or 6 atoms Both cells are, of course, equivalent from the computational point of view and must produce identical results The unit cell of 4H-SiC consists of 4 Si-C bilayers or 8 atoms Then, the lattice parameters, electronic structure and magnetic properties are calculated for 3C- and 4H-SiC doped with TM impurity In the calculations, to model the lattice of doped single... Mn bonds to the surrounding C atoms and extend significantly beyond the nearest 108 Properties and Applications of Silicon Carbide neighbours Charge density isosurfaces of filled anti-bonding Mn states, corresponding to an equal value of this quantity, are shown in Fig 8 for two different 4H-SiC FM-ordered supercells of Fig 2 (c) and (d), demonstrating the smallest and largest ordering temperatures,... containing Co or Ni atoms expand even further, with their relative (to pure SiC with the same unit cell volume) volumes reaching 13% for Ni and 4% for Co at the average volume value of 78 a.u.3/atom At the same time, relaxation of the rest of the supercell reduces with the Si atoms returning to the positions characteristic to pure material, 100 Properties and Applications of Silicon Carbide indicating that... the calculations of magnetic moments and properties of different magnetic states TM, Si, and C atoms added by periodicity and not being part of the supercells are shown having smaller diameters compared to the similar atoms in the supercells Layers with the hexagonal and quasicubic symmetries in 4H-SiC are marked by h anc c, respectively Investigation of the magnetic moment formation and related lattice... value of the Curie temperature reaching 550 K in one of the atomic configurations Given the long-range character of Mn-Mn exchange interaction in SiC host, among the TM impurities Mn is perhaps the most promising candidate for achieving room temperature 110 Properties and Applications of Silicon Carbide DMS behaviour The analysis of the band structure of (Si, Mn) C suggests that ferromagnetic coupling... impurity band, the energy is gained by aligning atomic spins in parallel This leads to broadening of this band and shifting of the weight of the electron distribution to lower energies This is Zener’s double exchange mechanism which leads to ferromagnetism (Sato et al., 20 04; Akai, 1998) The width of the impurity band and thus the energy gain due to double exchange scales as the square root of impurity . cases of SiC C-face and Si, which may cause the characteristics of the SiC Si-face oxidation to differ from those for SiC C-face and Si. Properties and Applications of Silicon Carbide8 4 3.5 Oxygen. 89 Magnetic Properties of Transition-Metal-Doped Silicon Carbide Diluted Magnetic Semiconductors Andrei Los and Victor Los X Magnetic Properties of Transition-Metal-Doped Silicon Carbide Diluted. realistic understanding and prediction of the properties of this complex class of materials. Silicon carbide is another wide bandgap semiconductor which has been considered a possible candidate for