**3. Results**

Figure 2a,b show a photo image of a two-inch 4H-SiC crystal grown with the PVT process and a visible-light-emitting luminescence of a fluorescent 4H-SiC sample excited by a 325 nm pulsed laser source. The spot diameter of the 325 nm laser source was about 10 mm, and the greenish light was emitted from inside the 4H-SiC crystal sample shown in Figure 2b. The 4H-SiC crystal that was grown was cut in the form of a wafer and was subjected to slicing and then polishing in a direction perpendicular to the c-axis on the Si face before the PL measurement.

The XRD patterns of S1, S2, and S3 (pristine, A, and B, respectively) showed peaks corresponding to 3C-SiC (β-SiC phase), as shown in Figure 3. These peaks at 35.7◦, 41.2◦, 59.9◦, and 71.6◦ are attributed to the (111), (200), (220), and (311) planes of the β-SiC phase, respectively [18,19].

Figure 4 shows two prominent peaks at 36◦ and 76◦, which are the reflections from the (0004) and (0008) planes, which correspond to 4H-SiC [20,21]. In addition, all peaks are good agreemen<sup>t</sup> with ICSD card 98-016-4971. Furthermore, a few peaks of low intensity that were separated by almost equal intervals were also observed. These weak diffraction peaks were due to the (0005), (0006), and (0007) planes [21]. Their appearance was due to

the double diffraction effect, as explained by other researchers [21]. Herein, for the highly purified 4H-SiC, the small periodic peaks between the main peaks that were related to the double diffraction effect could indicate the polytype of a SiC crystal with small periodic peaks due to the periodic stacking layers in the c-direction on the crystal [21]. For our XRD results, after the purification process (S2 and S3), small periodic peaks were also observed, as shown in Figure 4. In addition, the S1 sample had no small periodic peaks due to the large amounts of impurities. However, these XRD results could not be evaluated for 4H-SiC crystals with lower impurity doping levels. Thus, in this work, we investigated 4H-SiC crystal samples in terms of the trace impurity doping level by using the Raman and PL techniques.

**Figure 2.** (**a**) Photo image of a two-inch 4H-SiC crystal grown with the PVT process with 3C-SiC powder and (**b**) a visible-light-emitting fluorescent 4H-SiC sample excited by a 325 nm laser source.

**Figure 3.** X-ray diffraction (XRD) patterns of three differently treated starting materials of 3C-SiC powder (S1, S2, and S3).

The Raman spectra of the 4H-SiC crystals that were grown are shown in Figure 5. The three characteristic peaks of the 4H-SiC samples were detected at approximately 795, 800, and 970 cm<sup>−</sup><sup>1</sup> [22–24]. In Figure 5a, the two characteristic peaks at 795 and 800 cm<sup>−</sup><sup>1</sup> correspond to the transverse optical (TO) phonon [22,23]. The peak at 970 cm<sup>−</sup><sup>1</sup> is the longitudinal optical (LO) phonon mode of 4H-SiC [22,23].

Figure 5b shows that the LO peaks (from 991 to 981 cm<sup>−</sup>1) in the Raman spectra of the three 4H-SiC crystal samples were altered with respect to the starting material (S1, S2, and S3). The Raman shifts of the LO peak for two samples (S2 and S3) occurred at significantly lower wavenumbers than those of S1. It may be considered that the reason was that the LO phonon mode also caused a shift in the peaks toward lower frequencies, which could probably be attributed to the decrease in the grain size, internal stress from impurities, and the atomic size effect [22–28]. The peak breadth and reduced intensity of the S1 sample were the result of the increase in the free carrier concentration, as shown in

Figure 5b. The Raman features of the LO (or LOPC) modes are very useful in determining the structural properties of SiC and have been shown to allow the estimation of the nitrogen concentration [29]. As the starting material was purified, S1 to S3, the Raman spectra showed a decreasing nitrogen concentration with the shift toward lower energies, as well as a change in the intensity of the LOPC. The peak intensity of the LOPC increased and the peak position shifted to lower wavenumbers through the elimination of the nitrate element under various purification conditions, such as oxidation and reduction reactions.

**Figure 4.** X-ray diffraction (XRD) patterns of the 4H-SiC crystal samples prepared with the PVT process with three different starting materials (S1, S2, and S3).

**Figure 5.** Raman spectra of the three 4H–SiC crystal samples: (**a**) wide scan and (**b**) narrow scan of the LO peak.

Figure 6a shows the PL spectra of the 4H-SiC crystal samples prepared using different starting materials at room temperature (*T* = 298 K). The measurements were carried out with a 325 nm exciting laser source, and the PL emission spectra are shown in Figure 6a. All of the samples showed a wide non-Gaussian symmetric peak located at 533 nm that corresponds to the N-B donor–acceptor pair (DAP) emission [22,23]. The peak intensity of the N-B DAP emissions for S2 was observed to be high, resulting in an increase in the N-B DAP density at room temperature (*T* = 298 K) [30–32]. The N-B DAP emissions of S1 were the weakest, although the concentrations of N and B were the highest among the three 4H-SiC crystal samples according to the ICP-OES data in Table 2. The reason could be that

the N-B DAP emissions of S1 were affected by the N-Al DAP emissions at 420 nm [30–32]. These luminescence properties are directly correlated with energy-level transitions in semiconductors. The recombination of donor–acceptor pairs for 4H-SiC crystals with an indirect band gap forms a free exciton and a phonon. This type of recombination introduces a complex donor–acceptor recombination mechanism. Thus, the impurity concentration may have a critical influence on the luminescence properties [30–32].

**Figure 6.** PL spectra of 4H-SiC crystal samples measured at (**a**) room temperature (*T* = 298 K) and (**b**) an extremely low temperature (*T* = 50 K) in a wavelength range of 300 to 900 nm.


**Table 2.** Elemental composition measured by ICP-OES and an element analyzer with the different 4H-SiC crystal samples (ppm: part per million, mg/kg).

Figure 6b shows the PL spectra of the three types of 4H-SiC crystal samples at extremely low temperatures (*T* = 50 K). Both N-Al and N-B DAP emissions were observed at 420 and 580 nm, respectively, at extremely low temperatures [30–32]. The peak intensity of the N-Al DAP emissions was observed to be the highest in S1. The peak intensities of the N-B DAP emissions for S2 were observed to be high, suggesting an increase in the N-B DAP density at extremely low temperatures [30–32]. The peak intensity of the N-B DAP emissions increased with the nitrogen concentration. As shown in the magnified image of Figure 6b, sample S2 showed a weak PL peak at 370 nm in the low-temperature PL spectra, which was caused by the emission of nitrogen from the nitrogen-bounce excitation [30–32]. Meanwhile, the N-B DAP emissions of S1 at 533 nm were the weakest due to the N-Al DAP emissions at 420 nm [30–32]. In the case of sample S1, the N-Al DAP emissions were dominant in the spectra at 420 nm, and they were affected by visible-green-light luminescence quenching at 533 nm.

To better understand the relationship between the impurities and PL properties, ICP-OES and an elemental analysis were performed to investigate the elemental composition of B, Al, and N in the three 4H-SiC crystal samples (S1, S2, and S3). The results are presented in Table 2.

From the obtained results, the concentration of each element was converted into units of atoms/cm<sup>3</sup> so that the recombination ratio of the donor–acceptor (RDA) (*C*D-A and 2*C*B/(*C*N − *C*B)) could be calculated using Equation (1) [22,23]. The B, Al, and N concentrations were defined as *C*B, *C*Al, and *C*N, respectively. The parameter *C*D-A was calculated as a function of *C*B − (*C*Al − *C*N) [31–33]. The calculated concentrations are listed in Table 3.

$$C\_{\rm D \cdot A} = \ln C\_{\rm B} - (\ln C\_{\rm Al} - \ln C\_{\rm N}) \tag{1}$$

**Table 3.** Calculated concentrations of B, N, and Al using the ICP-OES results (atoms/cm3).


The DAP recombination rate is an efficient measure of emission luminescence [33–35]. The RDA is proportional to the donor concentration (*C*D) and acceptor concentration (*C*A). The correlation between *C*D, *C*A, and the PL properties in SiC samples has already been shown [22]. The increase in PL intensity of N-B DAP for S2 was shown to be due to an increase in *C*N. The Aukerman and Millea model [33–35] suggests that the correlation between the DAP recombination and concentration causes an increase in PL intensity with the increase in the difference between *C*N and *C*B, which is called the N-B concentration gap. When the N-B concentration gap is larger than *C*B, it becomes saturated. When the N-B concentration gap exceeds twice the value of *C*B, the PL emission intensity decreases due to non-radiative defects (non-emission), as shown in the S3 sample [32].

To compare the correlation between the N-B concentrations and PL, we calculated the value of 2*C*B/(*C*N − *C*B). When N-B emissions were observed, the N impurity—substituted for C in the SiC lattice—made it difficult for the electrons/holes between the impurity levels to transition to non-radiative emission at 533 nm, resulting in luminescence quenching. In the S3 sample, there was no emission, as the calculated ratio of 2*C*B/(*C*N − *C*B) was 0.01 or less. In the S1 sample, Al and N existed in the hexagonal lattice of SiC, leading to a blue emission spectrum derived from the N-B DAP luminescence quenching. This shows that N-B DAP luminescence quenching can be extinguished depending on the concentrations of N and B impurities in 4H-SiC. When the calculated ratio of 2*C*B/(*C*N − *C*B) was less than 0.01, the PL intensity was enhanced. When the Al concentration (*C*Al) was high in 4H-SiC (S1), N-B DAP emissions could not be generated with the N-Al DAP emissions at 420 nm [30–32,35].

Based on the PL results, a schematic diagram of the proposed recombination paths of the main impurities in the 4H-SiC crystals is shown in Figure 7. When the wavefunction of an electron bound to a donor can interact with a hole that is bound to an acceptor, DAP recombination occurs. Typical DAP luminescence spectra were observed in 4H-SiC at room temperature (*T* = 298 K) and extremely low temperatures (*T* = 50 K). In Figure 7, the N-Al and N-B DAP PL spectra are shown. The N-Al DAP PL peaks were located in the relatively high-energy region, and the N-B DAP peaks appeared in the low-energy region because the Al acceptor levels were low, and the boron levels were relatively high. As described in Figure 7, the incorporation of B into 4H-SiC induced two boron-related levels, shallow boron and deep boron. In the N-B DAP PL, the deep boron centers were mainly involved in radiative recombination [30–32,35].

**Figure 7.** Schematic diagram of the proposed recombination paths with the elemental impurities incorporated into the 4H-SiC crystals.

The optical transmittance spectra of the 4H-SiC samples in the range of 200–1000 nm are shown in Figure 8a for samples S1 and S3. The optical transmittance of sample S1 was below 40%, and that of sample S3 was also above 40%. For the S1 sample, more N doping could decrease the optical transmissivity of the 4H-SiC crystal for wavelengths from 600 to 1000 nm. The absorption at 463 nm caused by nitrogen doping may weaken N-Al DAP emission extraction. Most importantly, Al and N co-doping caused the N donor and Al acceptor at hexagonal sites to be dominated in the SiC crystal, resulting in more non-radiative recombination and light absorption losses [22]. This absorption band was caused by the transition between the bottom levels of the conduction band and the top levels of the valence band, while the absorption band was caused by the induction of the energy level of the N impurities [35].

**Figure 8.** (**a**) Optical transmittance and (**b**) absorbance spectra of 4H-SiC crystal samples at room temperature (*T* = 298 K).

The absorption spectra of the 4H-SiC samples in the range of 200–1600 nm are shown in Figure 8b. The absorption peak at 463 nm caused by nitrogen doping may weaken the N-Al DAP emissions. These N-B DAP emissions of the 4H-SiC samples were responsible for the low optical transmissivity, and the light extraction of the N-B DAP emissions in the visible light range was weakened [22,23]. The aluminum and nitrogen co-doping led to the N donor and Al acceptor at the hexagonal sites dominating in the SiC crystal, resulting in more non-radiative recombination and light absorption losses [22,35].

The optical band gap (*E*g) was calculated from the transmittance spectra using the Tauc Equation (2) [36,37].

$$
\alpha l \mathbf{v} = A \cdot (l \mathbf{v} \mathbf{v} - E\_{\mathsf{E}})^{\mathsf{U}, \mathsf{D}} \tag{2}
$$

where α is the absorption coefficient, *A* is a constant, and *h*υ is the photon energy [36,37]. *E*g can be evaluated from the relation between α*h*υ and the photon energy (*h*υ), as shown

when plotting (α*h*υ)<sup>2</sup> vs. energy in Figure 9. The value of *E*g of the samples can then be determined by extrapolating a straight line to cross with the *h*υ axis at zero, as shown in Figure 9. The value of *E*g of the 4H-SiC that was grown was found to be 3.29 eV for both S1 and S3 [36,37].

**Figure 9.** Plots of the variation in (α*h*υ)<sup>2</sup> versus photon energy (*h*υ) of the 4H-SiC crystal samples grown with the PVT method with different 3C-SiC powders: (**a**) S1 sample and (**b**) S3 sample.
