3. Results and Discussion

count by modifying the parabolic rate constant *B* by a factor of 1.5 (called 'normalizing factor' eEFfd\_z\* z0\$.+1#\$z0\$%/z)+ !(\_z0\$!5z!4,(%\*! z0\$!z+4% 0%+\*z,.+!//z+"z%z%\*z0\$!z,.+(%z+4¥ % 0%+\*z .0!z .!#%)!z eJf^z+.z 0\$!z %z \* zz!)%//%+\*z)+ !(\_z 0\$!z\*+.)(%6%\*#z "0+.z+..!¥ sponds to the coefficient of the oxidant shown in eq. (7), *i.e.* (2hSih<sup>C</sup> \_ / 2). Since Song's model assumed that there is no interfacial atomic emission (*i.e.* hSi=h<sup>C</sup> =0) and carbonaceous products consist of only CO (*i.e.* \_ =1), for this case, the coefficient of the oxidant in eq. (7) equals 1.5, which is the same as the normalizing factor. Actually, our experiments revealed this coefficient to be 1.53 [19], which is almost equal to the measured value from Song *et al.* Therefore, our results support the assumption in the Song's model that \_ =1 and we believe that the obtained *B* values to be different from that of Si oxidation [5, 7, 23, 24] despite the fact that the native oxide is SiO2 regardless of Si and SiC were due to the contribution from z,.+ 10%+\*z%\*z%z+4% 0%+\*^z\$%(!z%\*z0\$!z/!z+"z0\$!z%w"!\_z/%\*!z0\$!z%\*"(1!\*!z+"z+45¥ gen diffusion was significant at thicknesses above several *µm* as seen in Fig. 3, we could not determine the value of\_. The value of \_ is thought to depend on the areal density of carbon

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in the substrate. Thus, we regard the \_ value of the Si-face as equal to that of C-face.

The parameters to be different between C- and Si-face in the deduced values werehSi, hC, and *k*0. In next section, we will discuss the temperature dependence of these three parameters.

Figure 4. Oxide thickness dependence of oxide growth rates at various oxidation temperatures for (0001¯ )C-face. The

Figure 4 shows the oxide growth rates as a function of oxide thickness, observed for the dry oxidation of C-face at various oxidation temperatures (circles) and those given by the Si and C emission model (the solid curves) [25]. The figure indicates that the Si and C emission model reproduces the oxide growth rate curves for all of the temperatures measured. As

circles and the solid curves denote measured growth rates and calculated ones, respectively.

3.2. Oxidation rate at various oxidation temperatures

#### 3.1. Differences in the oxidation process between C- and Si-face

Figure 3. Oxide thickness dependence of growth rates on C- and Si-faces.

Figure 3 shows the oxide growth rates observed for 4H-SiC C face at 1090°C (circles) and Si face at 1100°C (triangles). The oxide growths were executed under dry oxygen ambient at a pressure of 1 atm. The experimental details can be found in the references [8, 9, 10]. Also shown in the figure are the growth rates given by the Si and C emission model (blue solid lines), the Si emission model, and the model that does not take account of both Si and C emission, *i.e.*, the D-G model (red broken line and black double broken line, respectively). We note that the same parameters were used for these three SiC oxidation models.

Figure 3 shows that the Si and C emission model reproduces the experimental values for +0\$z0\$!zz\* z%z"!/z!00!.z0\$\*z0\$!z+0\$!.z03+z)+ !(/^z \*z,.0%1(.\_z0\$!z %,z%\*z0\$!z0\$%'¥ ness dependence of the growth rate seen around 20 nm for the C-face and 10 nm for the Siface, which cannot be reproduced by the Si emission model or the D-G 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.

/z)!\*0%+\*! z%\*z!^zE^D\_z0\$!z#.+30\$z.0!z%\*z0\$!z0\$%'z+4% !z.!#%)!z%/z !0!.)%\*! z5z0\$!z,.¥ abolic rate constant *B* as is obvious if we consider the condition that *A* 2*X* for eqs. (1, 4). Song *et al.*z,.+,+/! zz)+ %"%! z!(w.+2!z)+ !(z0\$0z0'!/z0\$!z+10w %""1/%+\*z+"zz%\*0+z¥ count by modifying the parabolic rate constant *B* by a factor of 1.5 (called 'normalizing factor' eEFfd\_z\* z0\$.+1#\$z0\$%/z)+ !(\_z0\$!5z!4,(%\*! z0\$!z+4% 0%+\*z,.+!//z+"z%z%\*z0\$!z,.+(%z+4¥ % 0%+\*z .0!z .!#%)!z eJf^z+.z 0\$!z %z \* zz!)%//%+\*z)+ !(\_z 0\$!z\*+.)(%6%\*#z "0+.z+..!¥ sponds to the coefficient of the oxidant shown in eq. (7), *i.e.* (2hSih<sup>C</sup> \_ / 2). Since Song's model assumed that there is no interfacial atomic emission (*i.e.* hSi=h<sup>C</sup> =0) and carbonaceous products consist of only CO (*i.e.* \_ =1), for this case, the coefficient of the oxidant in eq. (7) equals 1.5, which is the same as the normalizing factor. Actually, our experiments revealed this coefficient to be 1.53 [19], which is almost equal to the measured value from Song *et al.* Therefore, our results support the assumption in the Song's model that \_ =1 and we believe that the obtained *B* values to be different from that of Si oxidation [5, 7, 23, 24] despite the fact that the native oxide is SiO2 regardless of Si and SiC were due to the contribution from z,.+ 10%+\*z%\*z%z+4% 0%+\*^z\$%(!z%\*z0\$!z/!z+"z0\$!z%w"!\_z/%\*!z0\$!z%\*"(1!\*!z+"z+45¥ gen diffusion was significant at thicknesses above several *µm* as seen in Fig. 3, we could not determine the value of\_. The value of \_ is thought to depend on the areal density of carbon in the substrate. Thus, we regard the \_ value of the Si-face as equal to that of C-face.

The parameters to be different between C- and Si-face in the deduced values werehSi, hC, and *k*0. In next section, we will discuss the temperature dependence of these three parameters.

Figure 4. Oxide thickness dependence of oxide growth rates at various oxidation temperatures for (0001¯ )C-face. The circles and the solid curves denote measured growth rates and calculated ones, respectively.

#### 3.2. Oxidation rate at various oxidation temperatures

3. Results and Discussion

188 Physics and Technology of Silicon Carbide Devices

3.1. Differences in the oxidation process between C- and Si-face

Figure 3. Oxide thickness dependence of growth rates on C- and Si-faces.

more effective in the thin oxide regime.

Figure 3 shows the oxide growth rates observed for 4H-SiC C face at 1090°C (circles) and Si face at 1100°C (triangles). The oxide growths were executed under dry oxygen ambient at a pressure of 1 atm. The experimental details can be found in the references [8, 9, 10]. Also shown in the figure are the growth rates given by the Si and C emission model (blue solid lines), the Si emission model, and the model that does not take account of both Si and C emission, *i.e.*, the D-G model (red broken line and black double broken line, respectively).

Figure 3 shows that the Si and C emission model reproduces the experimental values for +0\$z0\$!zz\* z%z"!/z!00!.z0\$\*z0\$!z+0\$!.z03+z)+ !(/^z \*z,.0%1(.\_z0\$!z %,z%\*z0\$!z0\$%'¥ ness dependence of the growth rate seen around 20 nm for the C-face and 10 nm for the Siface, which cannot be reproduced by the Si emission model or the D-G 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

/z)!\*0%+\*! z%\*z!^zE^D\_z0\$!z#.+30\$z.0!z%\*z0\$!z0\$%'z+4% !z.!#%)!z%/z !0!.)%\*! z5z0\$!z,.¥ abolic rate constant *B* as is obvious if we consider the condition that *A* 2*X* for eqs. (1, 4). Song *et al.*z,.+,+/! zz)+ %"%! z!(w.+2!z)+ !(z0\$0z0'!/z0\$!z+10w %""1/%+\*z+"zz%\*0+z¥

We note that the same parameters were used for these three SiC oxidation models.

Figure 4 shows the oxide growth rates as a function of oxide thickness, observed for the dry oxidation of C-face at various oxidation temperatures (circles) and those given by the Si and C emission model (the solid curves) [25]. The figure indicates that the Si and C emission model reproduces the oxide growth rate curves for all of the temperatures measured. As mentioned above, some articles have suggested that [7, 23, 26fz0\$!z%z+4% 0%+\*z\*z!z !¥ scribed by using the D-G model. However, there are several issues in the application of D-G model to SiC oxidation, in which unreasonable parameter values are needed to fit to the measured oxide growth rates. For example, the activation energy of parabolic oxidation-rate constant *B* for SiC Si-face and (112 ¯0)\_ -face significantly different from that for Si is required to fit the growth rate curve despite the fact that both of oxides on SiC and Si are SiO2. In accordance with Si and C emission model, on the contrary, the oxide growth rates of SiC for all of the temperatures measured can be derived using just the same diffusivities as those for Si regardless of oxidation temperatures. This shows that the Si and C emission model is more valid than the D-G model to explain SiC oxidation process.

Figure 5. Oxide thickness dependence of oxide growth rates at various oxidation temperatures for (0001)Si-face. The circles and the solid curves denote measured growth rates and calculated ones, respectively.

Figure 6. Arrehnius plots of%Si, %C, and *k*0 (circles, squares, and triangles, respectively) for Si- and C-face.

orientation does not affect the oxidation process any more.

In the simulation for Si oxidation, Uematsu *et al.* have found that the hSi depends on surface orientation of the substrate [17]. Therefore, it is possible that the differences in hSi and hC also appear between SiC C- and Si-face. Obviously, a high Si emission ratio leads to a low oxide growth rate, as shown in eqs. (5, 8). Therefore, it is considered that the high Si emission ratio is one of the causes for the low oxidation rate for Si-face [28]. Uematsu *et al.* also found that the *k*<sup>0</sup> also depends on surface orientation, which is probably due to the difference in surface density of the Si-Si bonds available for the reaction with oxidants [17]. In the case of SiC, the areal density of such reaction-available bonds on Si-face is lower than that on C-face by a factor of three, which is roughly coincident with the difference in observed data (%#^zId^z¥ cording to the report from Ref. [27], in the cases of extremely high oxidation temperature (~1500°C), the oxide growth rate is comparable between C- and Si-face, which is different from the fact that the oxide growth rates for the C-face are about eight times larger than those for the Si-face in the several 10 nm thickness region at around 1100°C and atmospheric oxygen pressure. We consider that such a high temperature oxidation proceeds with another mechanism such as 'active oxidation' (*i.e.* oxidizing with evaporation), so that the substrate

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Figure 5 /\$+3/z0\$!z+4% !z#.+30\$z.0!/z"+.z%w"!z/zz"1\*0%+\*z+"z0\$!z+4% !z0\$%'\*!//z0z2.%¥ ous oxidation temperatures. The calculated curves also well agree with the measured data. The figure indicates that the values obtained are almost constant in the larger thickness .\*#!z%\*z0\$%/z/01 5z0z\*5z+4% 0%+\*z0!),!.01.!^z\$!z.!/+\*z"+.z0\$%/z+\*/0\*0z0\$%'\*!//z !¥ pendence is that, in the case of Si-face, interfacial reaction rate-limiting step continues up to several *µ*m in oxide thickness, as revealed in Sec. 3.1.

Figure 6 shows the temperature dependence of Si and C emission ratios (hSiandhC\_z .!/,!¥ tively) and initial interfacial reaction rate (*k*0) for C- and Si-face deduced from the curve fits. The figure indicates that the activation energies of hSiand h<sup>C</sup> are comparable between these polar faces, but the values of them for Si-face are larger than those for C-face, in particular, the hSi for Si-face is remarkably large. It is noted that the hSi values for C-face were just the same as those for Si(100)face. On the other hand, the activation energy of *k*0 is a little larger for Si-face, while the *k*0 values for these faces approach each other as elevating temperature.

mentioned above, some articles have suggested that [7, 23, 26fz0\$!z%z+4% 0%+\*z\*z!z !¥ scribed by using the D-G model. However, there are several issues in the application of D-G model to SiC oxidation, in which unreasonable parameter values are needed to fit to the measured oxide growth rates. For example, the activation energy of parabolic oxidation-rate

to fit the growth rate curve despite the fact that both of oxides on SiC and Si are SiO2. In accordance with Si and C emission model, on the contrary, the oxide growth rates of SiC for all of the temperatures measured can be derived using just the same diffusivities as those for Si regardless of oxidation temperatures. This shows that the Si and C emission model is

Figure 5. Oxide thickness dependence of oxide growth rates at various oxidation temperatures for (0001)Si-face. The

Figure 5 /\$+3/z0\$!z+4% !z#.+30\$z.0!/z"+.z%w"!z/zz"1\*0%+\*z+"z0\$!z+4% !z0\$%'\*!//z0z2.%¥ ous oxidation temperatures. The calculated curves also well agree with the measured data. The figure indicates that the values obtained are almost constant in the larger thickness .\*#!z%\*z0\$%/z/01 5z0z\*5z+4% 0%+\*z0!),!.01.!^z\$!z.!/+\*z"+.z0\$%/z+\*/0\*0z0\$%'\*!//z !¥ pendence is that, in the case of Si-face, interfacial reaction rate-limiting step continues up to

Figure 6 shows the temperature dependence of Si and C emission ratios (hSiandhC\_z .!/,!¥ tively) and initial interfacial reaction rate (*k*0) for C- and Si-face deduced from the curve fits. The figure indicates that the activation energies of hSiand h<sup>C</sup> are comparable between these polar faces, but the values of them for Si-face are larger than those for C-face, in particular, the hSi for Si-face is remarkably large. It is noted that the hSi values for C-face were just the same as those for Si(100)face. On the other hand, the activation energy of *k*0 is a little larger for Si-face, while the *k*0 values for these faces approach each other as elevating temperature.

circles and the solid curves denote measured growth rates and calculated ones, respectively.

several *µ*m in oxide thickness, as revealed in Sec. 3.1.

more valid than the D-G model to explain SiC oxidation process.

¯0)\_ -face significantly different from that for Si is required

constant *B* for SiC Si-face and (112

190 Physics and Technology of Silicon Carbide Devices

Figure 6. Arrehnius plots of%Si, %C, and *k*0 (circles, squares, and triangles, respectively) for Si- and C-face.

In the simulation for Si oxidation, Uematsu *et al.* have found that the hSi depends on surface orientation of the substrate [17]. Therefore, it is possible that the differences in hSi and hC also appear between SiC C- and Si-face. Obviously, a high Si emission ratio leads to a low oxide growth rate, as shown in eqs. (5, 8). Therefore, it is considered that the high Si emission ratio is one of the causes for the low oxidation rate for Si-face [28]. Uematsu *et al.* also found that the *k*<sup>0</sup> also depends on surface orientation, which is probably due to the difference in surface density of the Si-Si bonds available for the reaction with oxidants [17]. In the case of SiC, the areal density of such reaction-available bonds on Si-face is lower than that on C-face by a factor of three, which is roughly coincident with the difference in observed data (%#^zId^z¥ cording to the report from Ref. [27], in the cases of extremely high oxidation temperature (~1500°C), the oxide growth rate is comparable between C- and Si-face, which is different from the fact that the oxide growth rates for the C-face are about eight times larger than those for the Si-face in the several 10 nm thickness region at around 1100°C and atmospheric oxygen pressure. We consider that such a high temperature oxidation proceeds with another mechanism such as 'active oxidation' (*i.e.* oxidizing with evaporation), so that the substrate orientation does not affect the oxidation process any more.


tive to the variation of d and d ¦

tials that reach the oxide surface.

3.3. Oxidation rate at various oxygen partial pressures

initial stage of oxidation in more detail [11, 30].

To determine the oxygen pressure dependence of the SiC oxidation process, *ex-situ*z)!/1.!¥

ments from 10-3 to 4 atm have been carried out [23, 27]. However, both of these studies did

not examine the initial oxidation process in detail, partly because *in-situ*z.!(w0%)!z+/!.2¥

tions were not possible. We performed *in-situ* real-time measurements at reduced partial

,.!//1.!/z !03!!\*z C^Dz \* z D^Cz 0)\_z \* z "+1\* z 0\$!z ,.!/!\*!z +"z 0\$!z %\*%0%(z #.+30\$z .0!z !\*¥

hancement to be similar to the case at atmospheric pressure [10]. Recently, we observed the

SiC oxidation process under low oxygen partial pressures down to 0.02 atm to examine the

z3\$!\*z0\$!/!z2(1!/z.!z(.#!z!\*+1#\$z0+z/%\*'z((z0\$!z%\*0!./0%¥

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Table 1. Arrehnius equations used for the calculations of SiC oxide growth rate. The common values for SiC and Si are extracted from the reference [17].

In the oxide growth calculations, we gave the same parameters to C- and Si-face in the case that the parameters are related to SiO2 (*i.e.* d ¦ , *D*C, e<sup>1</sup> ¦ , e<sup>2</sup> ¦ , and*C*<sup>C</sup> 0 ). Through the curve fits for various oxidation temperatures, we obtained their Arrehnius equations. Table 1 addresses the Arrehnius equations for these common parameters such as *D*<sup>C</sup> as well as those related to the properties of SiO2 from Ref. [17]. It is noticed that the self-diffusivities of Si and O (*D*Si SD and*D*<sup>O</sup> SD, respectively, in Ref. [17]) have been transformed to ordinary diffusivities. Looking at the table, the activation energy of *D*C (0.57 eV) seems to be small. Indeed, *ab-initio* studies have reported the energy between 2-3 eV [29f^z!z/1,,+/!z"+.z0\$%/z %/.!,\*5z0\$0z+1.z+¥ tained value originates from not a segregation but a migration, that is, it is the diffusivity for z0+)/z0\$0z %""1/!z/z%\*0!./0%0%(/^z+0!z0\$0z0\$!z(1(0! z#.+30\$z.0!/z.!z-1%0!z%\*/!\*/%¥ tive to the variation of d and d ¦ z3\$!\*z0\$!/!z2(1!/z.!z(.#!z!\*+1#\$z0+z/%\*'z((z0\$!z%\*0!./0%¥

tials that reach the oxide surface.

for SiC

<sup>1</sup> \* 5×10<sup>8</sup>

<sup>1</sup> 1.04×1015exp(1.55eV/*kBT* )

<sup>1</sup> 1.04×1032exp(1.55eV/*kBT* )

<sup>1</sup> 1.46×1014exp(1.55eV/*kBT* )

<sup>1</sup> 1.46×1031exp(1.55eV/*kBT* )

<sup>0</sup> cm<sup>3</sup> 3.6×1024exp(1.07eV/*kBT* )

<sup>0</sup> cm<sup>3</sup> 3.6×1023exp(1.07eV/*kBT* )

common values

<sup>1</sup> 5×10<sup>8</sup>

<sup>1</sup> 8.1×10<sup>2</sup>

<sup>1</sup> 1.3×10<sup>2</sup>

<sup>0</sup> cm<sup>3</sup> 5.5×10<sup>16</sup>

Table 1. Arrehnius equations used for the calculations of SiC oxide growth rate. The common values for SiC and Si are

In the oxide growth calculations, we gave the same parameters to C- and Si-face in the case

various oxidation temperatures, we obtained their Arrehnius equations. Table 1 addresses the Arrehnius equations for these common parameters such as *D*<sup>C</sup> as well as those related to

the properties of SiO2 from Ref. [17]. It is noticed that the self-diffusivities of Si and O (*D*Si

at the table, the activation energy of *D*C (0.57 eV) seems to be small. Indeed, *ab-initio* studies have reported the energy between 2-3 eV [29f^z!z/1,,+/!z"+.z0\$%/z %/.!,\*5z0\$0z+1.z+¥ tained value originates from not a segregation but a migration, that is, it is the diffusivity for z0+)/z0\$0z %""1/!z/z%\*0!./0%0%(/^z+0!z0\$0z0\$!z(1(0! z#.+30\$z.0!/z.!z-1%0!z%\*/!\*/%¥

, *D*C, e<sup>1</sup> ¦ , e<sup>2</sup> ¦ , and*C*<sup>C</sup> 0

SD, respectively, in Ref. [17]) have been transformed to ordinary diffusivities. Looking

exp(0.57eV/*kBT* )

exp(3.43eV/*kBT* )

exp(1.64eV/*kBT* )

). Through the curve fits for

SD

<sup>1</sup> 2.0×10<sup>9</sup>
