### 4 Conclusions

State-of-the-art technologies as well as novel modeling and simulation approaches for SiC device fabrication steps, in particular, oxidation and post-implantation annealing, have been presented. More concretely, the main focus has been on thermal oxidation and electrical activation of various dopants. Important SiC properties, applications, and device fabrication technologies have been discussed, followed by a brief overview of TCAD. The required background for modeling and simulation of oxidation and annealing has been provided and the developed models and model extensions - representing the core contributions of this thesis - have been discussed in detail. The modeling approaches have been verified with process and device simulations based on reference SiC-based applications.

SiC is a semiconductor with an energy bandgap of 3.2 eV and is thus highly desirable for high-power and high-temperature applications due to its outstanding electric breakdown field of 3 MV/cm and thermal conductivity of 3.7 W/cmK. As many other materials, SiC exhibits various polytypes, which differ in the stacking sequence of the layers. For semiconductor device applications 4H-SiC is the most promising SiC polytype and thus commonly utilized and is therefore the focus of this work. Due to the hexagonal structure of SiC many crystallographic faces are available. However, typically the $$(0001)$$ Si-, $$(11\bar {2}0)$$ a-, $$(1\bar {1}00)$$ m-, or $$(000\bar {1})$$ C-face is considered due to the crystal symmetry.

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The first part of the thesis deals with thermal oxidation of SiC, which is one of the most important processing steps of fabricating MOS devices in order to form SiO2, i.e., an oxide with an energy bandgap of 8.9 eV. Oxidation of SiC is a complex non-linear chemical process and thus requires accurate modeling techniques in order to be able to correctly predict oxide thicknesses. To set the stage, the three SiC oxidation modeling techniques, i.e., the Deal-Grove model, Massoud’s model, and the C and Si emission model, have been presented and discussed in detail. The most accurate and advanced model is to this day Massoud’s model, which has thus been used to fit experimental data and to obtain model parameters with low numerical fitting errors. Due to the orientation dependence of SiC (induced by the hexagonal crystal structure of 4H-SiC), the model parameters have been obtained for the four crystal faces, i.e., Si, a, m, and C. In order to introduce temperature dependence into the parameters, the growth rate coefficients have been fitted with the Arrhenius equation to obtain activation energies and pre-exponential factors for each crystal orientation: 4 model parameters times 4 faces times 2 Arrhenius parameters result in 32 parameters, which have all been analyzed and calibrated. Interface reaction rates of SiC oxidation are similar for the Si- and C-face as well as for the a- and m-face, but for these orientations, the areal density of atoms and the mechanical stress effects are different. The oxidation rates are therefore the highest for the C-face followed by the m-, a-face, and lastly the Si-face. All the growth rate coefficients play an important role in the oxidation anisotropy of SiC. From the predicted oxidation growth rates it has been concluded that the saturation of the oxide growth is highest for the Si-face and the initial oxide enhancement is strongest for the m- and a-face.

In order to be able to utilize the obtained oxidation parameters in an actual process simulation, an interpolation method has been proposed to compute oxidation growth rate coefficients for arbitrary 3D problems. The interpolation method includes a well-known anisotropy of the oxidation of the Si- and C-face, as well as the anisotropic behavior of the m- and a-face. The interpolation method consists of six maxima and six minima (corresponding to the crystal symmetry in the shape of a star) in the x-y plane, which intersects with the origin of the unit cell. In the x-z and y-z planes the method consists of a tangent-continuous union of two half-ellipses. The interpolation method has been used together with Massoud’s model to perform 2D and 3D simulations of the thermal oxidation of SiC. These results have been proven to be in a good agreement with experimental findings from the literature.

Additionally, ReaxFF MD simulations have been performed in order to investigate the early stage of SiC oxidation for various crystallographic faces. The time evolution of the Si, C, and O atoms incorporated into the crystal structure has been extracted and analyzed for the considered oxidation temperatures ranging from 900°C to 1200° C. Oxide thicknesses have been accurately determined from the simulation results showing that even in the early stage of SiC oxidation (up to 1 ns) an orientation dependence is evident. The initial oxide thickness has been found to be approximately 2.7 nm. The comparison between the emitted Si and C species from the SiC crystal has shown a three-times higher emission of the C interstitials. An unexpected maximum has been observed for the time evolution of the Si and C emission rates between 104 and 105 fs. Emissions of Si and C have been observed to be orientation-dependent as well. The calculated growth rates indicate that the C-face has the highest oxidation rate, followed by the m-, a-, and Si-face. Furthermore, the differences in growth rates between the various faces are decreasing with time.

The second part of the thesis focuses on the electrical activation of dopants in SiC, introducing three novel modeling approaches, i.e., the activation ratio model, the semi-empirical model, and the transient model. All the discussed models enable to augment process simulations by an accurate prediction of the active concentration of dopants, but differ in the number of independent variables, i.e., annealing temperature, total implanted concentration, and annealing time. Each of the models has been fitted to the pre-processed experimental data of Al-, B-, P-, and N-implanted SiC. The obtained model parameters have in turn been fitted with the Arrhenius equation to incorporate temperature dependence. Extensive simulations have been performed to characterize and evaluate each of the models via comparisons to reference experimental data. The activation ratio model has predicted a 50\% activation for P-, N-, Al-, and B-implanted SiC at annealing temperatures 1475°C, 1515° C, 1570°C, and 1640°C, respectively. Results from the semi-empirical model have shown that for low-dose implantations (1015 cm-3) relatively high activation ratios have been achieved for the temperatures below 1200°C, e.g., a full activation was achieved at 1070°C for Al- and 1010°C for B-implanted SiC. In contrast, for high-dose implantations (1020 cm-3) the full activation of Al impurities was not achieved even at very high temperatures (> 2200°C), but B impurities reached full activation (> 90\%) at 2010° C. Results from the transient model have further corroborated that the annealing time has profound effects for anneals with < 30 min and that the activation is dopant-specific. For the cases of annealing time < 1 min, the dopants have been fully activated for temperatures above 2000°C. For longer annealing times (> 1 min) the donor- and acceptor-type dopants have exhibited various differences in annealing temperatures as well as the total implanted concentrations. On top of that, simulation results have suggested that the saturation effects of the SiC activation processes are temperature-dependent.

To sum up, this thesis presents key contributions to SiC modeling capabilities in the area of oxidation and annealing. The formulated research goals presented in Section 1.4 have been met. The novel modeling capabilities as well as the empirically determined parameters enable highly accurate predictions of 2D and in particular 3D oxidation and annealing processing steps and are thus of paramount importance to TCAD processing tools. All developed models have been calibrated and evaluated using extensive process and device simulation studies. Finally, many fundamental questions have been answered, based on the obtained results, further extending the understanding of SiC on the material but also on the device fabrication level.