Arrehnius equations used for the calculations of SiC oxide growth rate. The common values for SiC and Si are extracted from the reference .
Recently, semiconductor devices that work normally for a long time under harsh environments are demanded such as in nuclear power application or in space development field. Especially, after the disaster of Fukushima Dai-ichi nuclear power plant caused by the East-Japan great earthquake on March 11, 2011, the importance of such a
Prevention of the global warming is one of the most important and urgent subjects in the world. Technologies to reduce energy consumption should be the key for overcoming this problem, and one of which is the improvement in the efficiency of power devices.
Silicon carbide (SiC) semiconductor is one of the wideband gap semiconductors and the use of it is considered as the solution to achieve these performances because it has superior physical properties such as 3 times wider bandgap, 10 times larger electrical break-down field, and 3 times higher thermal conductivity, compared with Si semiconductor . Taking advantages of these properties, on-resistance for unipolar devices such as metal-oxide-semiconductor field-effect-transistors (MOSFETs) can, for example, be reduced by a factor of a few hundreds when replacing Si with SiC semiconductor. In addition, SiO2 film, utilized as an insulator in MOSFETs, can be grown on the SiC substrate surface by thermal oxidation, which is well compatible with the Si MOS device technologies . Moreover, the power and frequency ranges of SiC MOSFETs are around 1 kV break-down voltage and around 20 kHz switching frequency, respectively, which covers the wide power device application field.
For these reasons, the developments of SiC power MOSFETs have been very popular for a few decades. However, the on-resistances for MOSFETs fabricated practically are beyond the lower limit for Si, however, higher than the SiC limit by a few orders . As a result, conventional Si insulated gate bipolar transistors (IGBTs) still have most of the share in the application fields of power transistors. In the case of 1 kV break-down voltage device, the channel resistance is dominant to the total on-resistance. Therefore, controlling the channel layer,
In previous work, we have, for the first time, performed real-time observation of SiC thermal oxidation using an
At the beginning of this chapter, we review the thermal oxidation models for SiC as well as those for Si that have been previously proposed, to elucidate the oxidation mechanism of SiC and then we verify each of these SiC oxidation models by making comparison with the oxide growth rate data with various oxidation conditions and discuss the structure and nature of the SiC-oxide interface layer based on the oxidation model that we have proposed.
2. Thermal oxidation models for Si and SiC
2.1. Deal-Grove model and its related models
The kinetic model of Si oxidation that is most often taken as a reference is the one so-called Deal-Grove model proposed by Deal and Grove [6, 12]. According to this model, the beginning of oxidation is limited to the interfacial oxidation reaction and, after oxidation proceeds, the rate-imiting process is transferred from the interfacial reaction to the diffusion of oxidants in SiO2. This process is expressed by the following equation given by Deal and Grove as [6, 12]
2.2. Massoud empirical relation
It is well known that, in the case of dry oxidation, the oxidation rate of Si in the thin oxide thickness range cannot be reproduced by the D-G equation [6, 12] and, hence, several models to describe the growth rate enhancement in the thin oxide regime have been proposed. Among them, Massoud
2.3. Interfacial Si emission model for Si
Some Si oxidation models that describe the growth rate enhancement in the initial stage of oxidation have been proposed [14, 15, 17]. 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, the '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 layer 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 (
In the D-G model and the Massoud empirical relation, it has been considered that oxide growth occurs only or mainly at the Si-oxide interface. However, according to the interfacial Si emission model , Si atoms are emitted into the oxide layer, some of which encounter the oxidant inside the SiO2 layer to form SiO2. In addition to this, when the oxide is very thin, some of the emitted Si atoms can go through the oxide layer and reach the oxide surface, and are instantly oxidized, resulting in the formation of an SiO2 layer on the oxide surface. Therefore, there are two oxide growth processes other than the interfacial oxide growth,
where the is the emission ratio, the is the oxidation rate of Si interstitials inside SiO2, is the oxidation rate of Si interstitials on the oxide surface, and the superscript 'S' means the position at the oxide surface (
2.4. Si and C emission model for SiC
Since the density of Si atoms in 4H-SiC () is almost the same as that in Si () 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 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 . Figure 2. schematizes the Si and C emission model. 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,
where denotes the production ratio of CO.
In the case of Si oxidation, the interfacial reaction rate (eq. (5)) is introduced by assuming that the value of does not exceed the though the reaction rate decreases with increase of. Based on this idea, the interfacial reaction rate for SiC is thought to be given by multiplying decreasing functions for Si and C :
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 section.
Diffusion equations for Si and C interstitials, and oxidants can be written by modifying the those given by the interfacial Si emission model , that is,
where the prime means the variation for C atoms. It is noted that the and mean absorption of interstitials inside the oxide and they are assumed to be consist of two terms, as suggested by Uematsu
It has been believed that the oxidation rate in the thick oxide regime is solely limited by the in-diffusion of oxidant and the diffusivity of CO in SiO2 is much larger than that of O2. Thus, we assumed that the diffusion process of CO is insensitive to the oxide growth rate. The oxide growth rate is described as eq. (6), but the second term in the right-hand side (
Equations (8-10) were solved numerically using the partial differential equation solver ZOMBIE . The oxide thickness,
3. Results and Discussion
3.1. Differences in the oxidation process between C- and Si-face
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,
Figure 3 shows that the Si and C emission model reproduces the experimental values for both the C and Si faces better than the other two models. In particular, the dip in the thickness dependence of the growth rate seen around 20 nm for the C-face and 10 nm for the Si-face, 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.
As mentioned in Sec. 2.1, the growth rate in the thick oxide regime is determined by the parabolic rate constant
The parameters to be different between C- and Si-face in the deduced values were, , and. In next section, we will discuss the temperature dependence of these three parameters.
3.2. Oxidation rate at various oxidation temperatures
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) . 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, 26] the SiC oxidation can be described 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
Figure 5 shows the oxide growth rates for Si-face as a function of the oxide thickness at various 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 range in this study at any oxidation temperature. The reason for this constant thickness dependence is that, in the case of Si-face, interfacial reaction rate-limiting step continues up to several m in oxide thickness, as revealed in Sec. 3.1.
Figure 6 shows the temperature dependence of Si and C emission ratios (and, respectively) and initial interfacial reaction rate () for C- and Si-face deduced from the curve fits. The figure indicates that the activation energies of and are comparable between these polar faces, but the values of them for Si-face are larger than those for C-face, in particular, the for Si-face is remarkably large. It is noted that the values for C-face were just the same as those for Si(100)face. On the other hand, the activation energy of is a little larger for Si-face, while the values for these faces approach each other as elevating temperature.
In the simulation for Si oxidation, Uematsu
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 (
3.3. Oxidation rate at various oxygen partial pressures
To determine the oxygen pressure dependence of the SiC oxidation process,
Oxide thickness dependence of the oxide growth rates on 4H-SiC C-face (a) and Si-face (b) are shown in Fig. 7. As seen in the figure, we could obtain growth rate data in the extreme-thin oxide region down to a few nm more precisely by reducing the oxygen partial pressure less than 0.1 atm, compared with the case of measurements above 0.1 atm. For both faces, the oxide thickness dependence of growth rate less than 0.1 atm are basically similar to those of above 0.1 atm even if the partial pressure is lowered to 0.02 atm. Namely, just after the oxidation starts, the oxide growth rate rapidly decreases and at around 7 nm in thickness, the deceleration rate changes to gentle one (hereafter each oxidation stage is denoted as rapid and gentle deceleration stage, respectively). Because the growth rates at each of the deceleration stage well ride on a straight line in a semi-log plot (shown by dashed lines in Fig. 7) in respective stage, the oxide thickness dependence of oxide growth rate can be approximated by a sum of the two exponential functions , as,
where, and () are pre-exponential constants, and and () are characteristic lengths for the deceleration of oxide growth rate in each oxidation stage. The first and the second terms represent the rapid and gentle deceleration stage, respectively. Equation (11) means that, in the thin oxide regime, the oxide growth occurs by two ways and these proceed not in series but in parallel because the growth rate is given by the sum of two terms and is determined mainly by the faster one in each stage. Obviously, the and values correspond to the gradients of the fitted line in the rapid and gentle deceleration stage, respectively. As shown in Fig. 7, the value decreases with decreasing partial pressure, which corresponds to the more remarkable rapid deceleration. In contrast, the value is almost constant regardless of the partial pressure. This suggests that the oxidation process is different between the rapid and gentle deceleration stage. It is noted that the thickness at which the deceleration rate changes from rapid one to gentle one (termed '') is almost constant around 7 nm regardless of oxygen partial pressure and surface polarity. In the case of Si oxidation, a rapid deceleration stage has also been observed just after oxidation starts, and the thickness corresponding to is also almost independent of the oxygen partial pressure, though the growth rates at depend on the oxygen partial pressure [13, 31]. Therefore, it can be stated that is determined only by the thickness of the oxide layer for both the Si and SiC oxidation cases.
As mentioned above, the existence of a rapid deceleration stage in the oxide growth rate just after oxidation starts (
We fitted the experimental data at each partial pressure with two straight lines, as shown by the dashed lines in Fig. 7, and derived the initial growth rate of the two deceleration stages, and, by extrapolating the straight line to
The value of
If the initial growth rate in the rapid deceleration stage is also followed by eq. (12), it can be expressed that, where is the interfacial reaction rate when oxidation starts. As the value of is also unlikely to depend on oxygen partial pressure, should be also proportional to oxygen pressure. While, as seen in Fig. 8, is not proportional to
It has been considered that oxide growth occurs only or mainly at the Si-oxide (SiC-oxide) interface, so far. However, according to the interfacial Si emission model [14, 17] for Si oxidation and the Si and C emission model  for SiC oxidation, Si atoms (Si and C atoms) emit into the oxide layer, and some of which meet with oxidant inside the oxide to form SiO2. When the thickness of the oxide is very thin, a part of the emitted Si atoms can go through the oxide layer and reach the oxide surface, and then are instantly oxidized, resulting in the formation of a SiO2 layer on the oxide surface. Therefore, there are two oxide growth processes other than the interfacial oxide growth, The oxygen flux impinging from a gaseous atmosphere of pressure
The oxygen flux impinging from a gaseous atmosphere of pressure
As has been mentioned above, in the rapid deceleration stage, the growth rate is determined with the oxidation rate of the emitted Si interstitials on the oxide surface (termed 'surface oxide growth'), while in the gentle deceleration stage, it is determined by the oxidation rate at the SiC-oxide interface and that of the emitted Si interstitials inside the SiO2 layer (termed 'interfacial oxide growth' and 'internal oxide growth', respectively). The surface oxide growth rate depends little on partial pressure and, in contrast, the interfacial and internal oxide growth rates are proportional to partial pressure. It is therefore predicted from these pressure dependence that the rapid deceleration becomes more remarkable (
Figure 9 compares the observed oxide growth rates at various oxygen partial pressures on SiC () C-face (a) and (0001) Si-face (b) with the growth rates given by the Si and C emission model (solid lines). It is noted that all the parameters used in the calculations other than the solubility limit of oxygen in SiO2 The corresponding solubility limit of oxygen is derived by multiplying partial pressure by that for 1 atm,
The corresponding solubility limit of oxygen is derived by multiplying partial pressure by that for 1 atm,
Figure 10 shows the calculation results of, , and at 0.1 and 0.01 atm on Si-face. The figure indicates that the curve for 0.01 atm is much higher than that for 0.1 atm by a factor of about 5 orders, though the is still lower than. This result confirms that the low pressure oxidation enhances the oxide growth on the surface, as discussed above, which is probably due to the reduction in the oxygen concentration at the interface and inside the oxide. Conversely, the and curves for 0.01 atm are lower than those for 0.1 atm by factors of 2 orders and 1 order, respectively. Since the is higher than in general, it is found that the growth rate in the gentle deceleration stage to be proportional to pressure is due to the proportional increase in. Moreover, a careful look confirms the deceleration of in the very-thin oxide region (
3.4. Discussion on Si and C emission phenomenon and its relation to the interface layer
So far, we specify the oxidation mechanism of SiC from the viewpoint of the Si and C emission phenomenon. In this section, we will discuss the structure and the formation mechanism of the interface layer between SiC-SiO2, which has been considered as the crucial issue for the practical use of SiC-MOSFET, in the light of interfacial Si and C emission.
In previous work, we have found that [32, 33] the photon energy dependence of the optical constants
According to the results from the real time observation , the thickness at which the interface layer thickness and the refractive index become constant (
Finally, we would like to introduce a recent innovation using oxidation about elimination of point defects. Hiyoshi and Kimoto invented an epoch-making idea, in which as-grown deep-level states such as a Z1/2 center can be eliminated by oxidation of SiC substrates . Taking into account the report from Storasta
We review the oxidation mechanism of SiC and the formation of the interface layer between SiC and SiO2. Though most of articles have reported that the Deal-Grove model also describes the SiC oxidation process, we pointed out the discrepancy in the application of Deal-Grove model, in which the oxide growth rate in the thin oxide region cannot be reproduced with this model. Aimed at the elucidation of SiC oxidation process in this thin oxide region, we proposed a kinetic model that accounts for SiC oxidation, termed the 'Si and C emission model', and showed that the model well reproduces the oxide growth rate over the entire thickness range including the thin oxide region for both the C and Si faces. The results indicated that the oxidation and emission of C and the emission of Si all need to be taken into account to describe the oxide growth process in SiC. A comparison of the parameters obtained for the C and Si faces from the curve fits revealed that the differences in initial interfacial reaction rate and Si emission ratio are contributing to the large difference in oxide growth rate between these polar faces.
We tried to apply the Si and C emission model to the oxide growth rate data at various oxidation temperatures and found that the model reproduces the oxide growth rate curves for all of the temperatures measured for both of the Si- and C-faces. Comparing with the parameters deduced from the curve fits, we discussed the differences in oxidation process between Si- and C-face. We also showed the parameters obtained in this study, some of which such as a diffusivity and solubility limit of C in SiO2 were firstly reported.
We have studied the oxygen partial pressure dependence of the SiC oxidation process on the Si- and C-faces. The oxide thickness dependence of the growth rate at sub-atmospheric oxygen partial pressures down to 0.02 atm show that, just after oxidation starts, the oxide growth rate rapidly decreases and the deceleration-rate changes to a gentle mode at around 7 nm in oxide thickness, which are probably the oxide surface growth mode and oxide internal/interfacial growth mode, respectively. We tried to reproduce the pressure dependence of oxide growth rates, however, it cannot be achieved, which is perhaps due to the inaccurate description for the oxide growth on the oxide surface.
Finally, we discussed the structure and formation mechanism of the SiC–oxide interface layer in terms of the Si and C emission phenomenon. We also introduced a recently invented technology on defect using oxidation,
The authors would like to thank Professor Uematsu of Keio University and Dr. Kageshima of NTT for their helpful advice and technical support for the simulation. This work was partially supported by a Grant-in-Aid for Scientific Research (24560365) from the Japan Society for the Promotion of Science.
- The oxygen flux impinging from a gaseous atmosphere of pressure p to the solid surface is 3x10p[m-2s-1]. Since the areal density of Si atoms on SiO2 is about 8x1018[m-2], the flux in the case that p=0.02 atm corresponds to 75 [monolayer/s], which is the oxygen flux necessary for the oxide growth rate of 105 nm/h.
- The corresponding solubility limit of oxygen is derived by multiplying partial pressure by that for 1 atm, i.e., C O 0 = p × C O 0 (1 atm).