# Anomalous Properties of the Dislocation-Free Interface between Si(111) Substrate and 3C-SiC(111) Epitaxial Layer

^{*}

## Abstract

**:**

_{3}m

_{1}. The calculations have shown that Si atoms in silicon carbide at the interface, which are the most distant from the Si atoms of the substrate and do not form a chemical bond with them (there are only 12% of them), provide a sharp peak in the density of electronic states near the Fermi energy. As a result, the interface acquires semimetal properties that fully correspond to the ellipsometry data.

## 1. Introduction

_{4}is also a supplement to obtain a uniform $~$100 nm thick SiC layer without voids and pits [2]. The second way is a rapid penetration of CO gas into a great depth of the Si substrate. It seems that this mechanism is realized due to dislocation lines and other defects in the initial silicon substrate [5]. As a result, a porous SiC layer is formed inside the substrate under a flat $~$100 nm thick SiC film, which is a combination of various SiC polytypes and SiC nanotubes. A thickness of the porous SiC can reach 3–10 µm. According to reaction (1), the volume of the formed SiC is equal to the volume of voids in this layer, since the volume of a Si cell is 2 times the volume of a 3C-SiC cell. A micrograph of a typical 3C-SiC(111)/Si(111) cut is shown in Figure 1.

## 2. Experimental Technique and Ellipsometric Analysis

_{4}(5%) was added to the CO gas. The technological details of the process of epitaxy by the method of substitution of atoms are given in the review [2]. The 3C-SiC films obtained in such a way had a thickness of 40–120 nm when grown on Si(111) and of 30–60 nm when grown on Si(100). It should be noted that at the given temperature, pressure, and gas flow rate, silicon dioxide SiO

_{2}is not formed. Analysis of the pressure–flow rate phase diagram for this system showed [8] that silicon dioxide SiO

_{2}can be formed at elevated CO pressures due to the reaction $2\mathrm{SiO}=\mathrm{Si}+{\mathrm{SiO}}_{2}$. At a given temperature and flow rate the critical CO pressure at which SiO

_{2}starts to form is $~1000\mathrm{Pa}$.

_{CO}= 150 Pa, the silane volume fraction of 5%, and the growth time of 20 min. The same figure shows the theoretical ellipsometric spectrum obtained in the framework of the simplest model consisting of only one layer of the film. That is, the lowest layer is the Si substrate containing, within the Bruggeman EMA approximation [6], pores and 3C-SiC in equal volume fractions. On it lies the only layer of this model—the SiC layer containing, in the EMA approximation, voids, and graphite in equal volume fractions. On top of this layer is a standard layer for ellipsometry that describes the roughness of a film, i.e., the material of the film, to which 50% of voids are added in the EMA approximation. One can see from Figure 2 that this simplest ellipsometric model describes without any problems the properties of SiC layers obtained on Si(100) by the method of coordinated substitution of atoms. It should be emphasized that this method is characterized by the presence of some amount of voids and graphite in SiC, which leads to a significant decrease in the height of the peaks in Figure 2 [9]. This feature was explained from a theoretical point of view in [10]. The point is that the method of coordinated substitution of atoms is characterized by the formation of a noticeable amount of silicon vacancies in SiC. The silicon vacancies can be generated both chemically on the SiC surface and due to the effect of ascending diffusion in the bulk of SiC [11]. Further, during the growth, one of the four neighboring C atoms moves to the silicon vacancy, which lowers the energy of the system by 1.5 eV [10]. For this, the carbon atom must overcome an activation barrier with a height of 3.1 eV [10]. Since the typical values of the SiC synthesis temperature are 1200–1300 °C, the thermal fluctuations are quite enough to overcome this barrier. As a result, an almost flat cluster of 4 C atoms is formed with the C—C bond length of 1.57 Å and with the inseparably associated voids with a characteristic diameter of 3.8 Å at the sites of the displaced C atoms [10]. We name such formations in SiC carbon-vacancy structures. Quantum-chemical calculations of the dielectric constant of SiC with the carbon-vacancy structures showed that their contribution is adequately described by the EMA model, in which SiC contains voids and graphite in equal volume fractions [10]. In particular, the ellipsometric analysis of the spectrum of the sample in Figure 2 gives the following results. The volume of the Si substrate contains 1% of pores and SiC, the SiC layer has a thickness of 50 nm and contains 5% of the carbon-vacancy structures, i.e., 5% of pores and 5% of graphite, the roughness is 6 nm.

_{CO}= 100 Pa (the proportion of silane in CO was 5%). Different thicknesses of SiC films grown under the same conditions, but on Si substrates of different orientations (in this case (111) and (100)) are explained by the different hydraulic diameters of channels in the SiC crystal along which CO and SiO gases move towards each other [5]. Figure 4 also shows the best theoretical dependence for this spectrum, obtained in the framework of a rather complex two-layer model with various additives and a classical EMA interface layer between SiC and Si. Moreover, the optical constants of SiC have been chosen as the most optimal, namely in the form of a sum of 3 Tauc-Lorentz oscillators [7], which should have ensured an acceptable agreement between the model and experiment. Nevertheless, as can be seen from Figure 4, no efforts can successfully describe the region of low photon energies up to about 3.3 eV. The experiment gives a rather strong change in the dielectric constant ε in this region, while theory can provide only a slight change in ε (for the given SiC thickness) since SiC is transparent in this region. For the same reason, using the classic EMA interface layer between SiC and Si gives nothing. Note also that ellipsometric analysis does not reveal the presence of silicon dioxide SiO

_{2}in the samples of either the first type or the second type.

## 3. Analysis of a 3C-SiC(111)/Si(111) Interface Obtained by the Epitaxial Method of Coordinated Substitution of Atoms

_{3}m

_{1}symmetry. If we consider the interface between Si(111) and the C surface of SiC(111), then SiC will attract not 1 but as many as 3 Si atoms out of 16 (in full accordance with the requirement of P

_{3}m

_{1}symmetry). Consequently, the deformation energy of the interface will be somewhat higher, but not much. Thus, it follows from the quantum-chemical calculations that the surface of a 3C-SiC(111) film growing on Si(111) by the method of coordinated substitution of atoms should be of the C-type since the Si-type surface is oriented toward silicon. A comparison of the total energy of the entire system for these two cases is beyond the scope of this work since here it is necessary to take into account the real reconstruction of the SiC surface [15].

## 4. Ellipsometric Analysis of the 3C-SiC(111)/Si(111) Samples with an Account of the Semimetal Layer at the Interface

_{2}is the imaginary part of the dielectric constant (the real part ε

_{1}is calculated from ε

_{2}using the Kramers-Kronig relation [6]), A, E

_{0}, C, E

_{g}are minimization parameters of the model. E

_{g}has the meaning of the bandgap, E

_{0}is the position of the oscillator peak, A is its amplitude, C is its half-width. If E

_{g}= 0, then expression (3) is simplified, and the number of the minimization parameters of the model is reduced to 3. We emphasize that the thickness of the first layer (i.e., semimetal) h

_{1}(Figure 9) strongly correlates with the amplitude of oscillator A. Therefore, it is impossible to determine together h

_{1}and A from the experimental data, since a change in h

_{1}in the range from 0.5 to 5 nm almost does not lead to a change in the error function. In this work, the thickness of the semimetal layer h

_{1}is assumed to be equal to the average interface roughness determined by microscopic exploration, that is, h

_{1}= 2 nm.

_{2}(Figure 9), containing in equal proportions voids and graphite, i.e., carbon-vacancy structures. Since their concentration is low (from 0 to 8%), it is not necessary to use the Bruggeman model, the simpler Maxwell-Garnett model [6] is sufficient. Finally, on top of the second layer, there is a roughness of thickness h

_{r}(Figure 9), i.e., the Bruggeman mixture of 50% of the material of the second layer and 50% of voids [6]. For h

_{1}= 2 nm and E

_{g}= 0, this ellipsometric model contains only 7 minimization parameters. There is practically no correlation between these parameters, so they are uniquely determined by the measured ellipsometric spectrum. Figure 10 shows both experimental and theoretical dependences of the pseudodielectric constant ε of the 3C-SiC(111)/Si(111) sample on the photon energy E. One can see that taking into account the interface layer with semimetallic optical properties (3) (at E

_{g}= 0) makes it possible for the first time to adequately describe the experimental ellipsometric data (Figure 10). In particular, for the sample under study, h

_{2}= 48 nm, h

_{r}= 5 nm, the volume concentration of SiC and voids in the substrate is 28%, and the concentration of carbon-vacancy structures in SiC is 0.5%. The dielectric constant of the interface layer is shown in Figure 11. We emphasize that for almost all 3C-SiC(111)/Si(111) samples produced by the method of coordinated substitution of atoms, the maximum of the ε

_{2}function for the interface layer is about 2 eV. Since the half-width of the TL peak is also close to 2 eV, E

_{g}is always very close or equal to 0. The conductivity of the interface layer can be estimated by comparing its dielectric constant with the dielectric constant of the conductor, in particular, in Figure 11, the dashed line indicates ε

_{2}of a conductor in the Drude model [17] with a resistivity of 4 × 10

^{−7}Ohm m and a scattering time of conduction electrons 4 × 10

^{−1}

^{6}s (this is about 2 times worse than that of lead). That is, in the frequency range of an electric field of 700 THz and over, the interface layer conducts current like a bad metal. However, in the region of low frequencies, its conductivity deteriorates significantly and becomes similar to the conductivity of a semiconductor with a zero bandgap [17]. In general, the conductivity of the interface layer is determined by a sharp narrow peak in the density of electronic states near the Fermi energy (Figure 10).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Micrograph of a section of a 3C-SiC(111)/silicon (Si)(111) sample grown by the method of substitution of atoms.

**Figure 2.**Dependence of the pseudodielectric function (ε

_{1}is its real part, ε

_{2}is its imaginary part) of a silicon carbide (SiC)/Si(100) sample on the photon energy, measured in the range of 0.5–9.3 eV by an ultraviolet ellipsometer J.A. Woollam VUV-WASE with a rotating analyzer (solid line). The dashed line is the same relationship calculated using the Effective Media Approximation (EMA) model.

**Figure 3.**Dependence of the pseudodielectric function (ε

_{1}is its real part, ε

_{2}is its imaginary part) on the photon energy of a SiC/Si(111) sample grown by the CVD method by Advanced Epi using patented technology (solid line). The dashed line is the same relationship calculated using the EMA model.

**Figure 4.**Dependence of the pseudodielectric function (ε

_{1}is its real part, ε

_{2}is its imaginary part) on the photon energy of a 3C-SiC/Si(111) sample grown by the method of substitution of atoms on a Si(111) substrate for 15 min at T = 1280 °C and CO pressure p

_{CO}= 100 Pa (solid line). The dashed line is the best theoretical dependence for this spectrum, obtained within a complex two-layer model using EMA.

**Figure 5.**X-ray diffraction spectrum of a 3C-SiC(111)/Si(111) sample grown by the method of coordinated substitution of atoms.

**Figure 6.**Atomic configuration corresponding to the optimal dislocation-free 3C-SiC(111)/Si(111) interface, calculated by the methods of quantum chemistry in the framework of DFT. The symmetry of the system corresponds to P

_{3}m

_{1}. The red color highlights those Si atoms at the SiC boundary that do not form bonds with the Si atoms of the substrate since they are too far from those.

**Figure 7.**Dependence of the density of electronic states of the system under study on energy (curve 1). The Fermi energy corresponds to 0. Curve 2 is the contribution of p-electrons of those Si atoms at the SiC boundary that do not form bonds with the Si atoms of the substrate (highlighted in red in Figure 6 and by arrows in Figure 8).

**Figure 8.**View of the optimal dislocation-free interface 3C-SiC (111)/Si (111) perpendicular to the interface. Arrows show Si atoms at the SiC interface, which do not form bonds with Si atoms of the substrate.

**Figure 9.**Universal two-layer ellipsometric model describing the optical properties of 3C-SiC(111)/Si(111) samples produced by the method of coordinated substitution of atoms. The optical constants of the intermediate layer separating 3C-SiC and Si are described by the Tauc-Lorentz (TL) oscillator.

**Figure 10.**Comparison between the experimental (solid line) and theoretical (dashed line) dependences of the pseudodielectric constant ε on the photon energy of a 3C-SiC(111)/Si(111) sample grown by the method of substitution of atoms on a Si(111) substrate. The theoretical curve was obtained on the basis of an ellipsometric model with a semimetal layer at the interface (Figure 9).

**Figure 11.**Dependence of the dielectric constant (ε

_{1}is its real part, ε

_{2}is its imaginary part) of the interface layer of a semimetal on the photon energy, measured in the range of 0.5–9.3 eV by an ultraviolet ellipsometer J.A. Woollam VUV-VASE with a rotating analyzer on the assumption that the thickness of the semimetal interface layer is h

_{1}= 2 nm.

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Kukushkin, S.A.; Osipov, A.V.
Anomalous Properties of the Dislocation-Free Interface between Si(111) Substrate and 3C-SiC(111) Epitaxial Layer. *Materials* **2021**, *14*, 78.
https://doi.org/10.3390/ma14010078

**AMA Style**

Kukushkin SA, Osipov AV.
Anomalous Properties of the Dislocation-Free Interface between Si(111) Substrate and 3C-SiC(111) Epitaxial Layer. *Materials*. 2021; 14(1):78.
https://doi.org/10.3390/ma14010078

**Chicago/Turabian Style**

Kukushkin, Sergey A., and Andrey V. Osipov.
2021. "Anomalous Properties of the Dislocation-Free Interface between Si(111) Substrate and 3C-SiC(111) Epitaxial Layer" *Materials* 14, no. 1: 78.
https://doi.org/10.3390/ma14010078