Boron-doping of cubic SiC for intermediate band solar cells: a scanning transmission electron microscopy study

Boron (B) has the potential for generating an intermediate band in cubic silicon carbide (3C-SiC), turning this material into a highly efficient absorber for single-junction solar cells. The formation of a delocalized band demands high concentration of the foreign element, but the precipitation behavior of B in the 3C polymorph of SiC is not well known. Here, probe-corrected scanning transmission electron microscopy and secondary-ion mass spectrometry are used to investigate precipitation mechanisms in B-implanted 3C-SiC as a function of temperature. Point-defect clustering was detected after annealing at 1273 K, while stacking faults, B-rich precipitates and dislocation networks developed in the 1573 - 1773 K range. The precipitates adopted the rhombohedral B13C2 structure and trapped B up to 1773 K. Above this temperature, higher solubility reduced precipitation and free B diffused out of the implantation layer. Dopant concentrations E19 at.cm-3 were achieved at 1873 K.


Introduction
An intermediate band (IB) in the energy band gap of a semiconductor allows photons with lower energy than the band gap to excite electrons from the valence to the conduction band, increasing the photocurrent generated [1]. Due to the potential for enhanced efficiency in energy conversion, intermediate-band solar cells are promising candidates for the next generation of photovoltaic devices. Theoretical efficiencies of 63% have been estimated for IB solar cells under concentrated sunlight [1], a value considerably higher than the maximum efficiency of 40% expected for conventional single p-n junctions [2].
Realization of IB solar cells has faced challenges in finding a semiconductor/dopant system with band gap in the 1.9 -2.5 eV range and suitably positioned intermediate band. Cubic silicon carbide (3C-SiC) has a nearly ideal band gap of 2.36 eV at room temperature, combined with useful electronic properties [3], and boron (B) has been proposed to form a deep acceptor level 0.7 eV above the valence edge (E v ) of 3C-SiC [4]. Thus, B-doped 3C-SiC is a promising absorber system for highly efficient photovoltaic devices.
The hydrogen-like model with the values of permittivity and effective hole mass reported for 3C-SiC [5] estimates 10 19 -10 20 at.cm −3 as the minimum concentration of shallow acceptors for their energy levels to merge into impurity bands. However, the two acceptor levels associated with B in 3C-SiC are rather deep (with positions at ∼ E v + 0.3 eV and ∼ E v +0.7 eV [4]), which may push the required concentration to even higher values, emphasizing the need of assessing and controlling the precipitation behavior in the system. Limited work has been carried out on doping 3C-SiC with B and the literature available is essentially theoretical due to the difficult synthesis of high quality crystals [6][7][8][9]. Recent improvements in growth techniques are renewing experimental efforts on bulk 3C-SiC [10,11], and the optical activity deduced so far from absorption and emission spectra of B-implanted 3C-SiC indicates, indeed, IB behavior [12,13]. Nevertheless, ascertaining the electronic configuration of the system demands heavily doped and structurally sound 3C-SiC samples, and thus processing conditions above the B solvus.
In the present work, sublimation-grown 3C-SiC crystals were implanted with B at elevated temperatures and the samples were subsequently annealed in the 1273 -2073 K temperature range. Crystalline defects and precipitation mechanisms were investigated by scanning transmission electron microscopy (STEM) using variable collection angles to evidence specific local features. Correlation of the microstructural observations with secondary-ion mass spectrometry (SIMS) data was used to evaluate B solubility.

Experimental
High-quality 3C-SiC single crystals were grown on 4H-SiC substrates by sublimation epitaxy (details on the process can be found elsewhere [11]). Implantation with 11 B + ions was carried out at elevated temperatures (673 and 773 K) along a direction close to {111} 3C-SiC using multiple energies (100 to 575 keV) with a total dose of 4 -13 × 10 16 atoms.cm -2 to form box-like concentration profiles of about 1, 2 and 3 at.% B (used henceforth to designate the doping level in the material). The profiles extended about 600 nm in depth either directly below the free surface or buried with a start at ∼ 300 nm. Post-implantation annealing was carried out in the 1273 -1973 K temperature range for 3600 s and at 2073 K for 1.4 × 10 4 s.
Prior to annealing, the samples were protected by a pyrolized resist film (carbon cap) after native oxide etching. The pyrolysis was performed in forming gas at 1173 K for 6 -9 × 10 2 s and the carbon cap was removed by dry thermal oxidation at 1173 K for 2 -3 × 10 2 s before the measurements.
Absence of extended structural defects in the sublimation-grown 3C-SiC single crystals was confirmed by conventional transmission electron microscopy (TEM) prior to the B implantation. The observations were performed close to 110 zone axes for easy detection of the typical stacking faults on {111} planes. The implanted and annealed samples were investigated by TEM and by annular bright-field (ABF), low-angle annular dark field (ADF) and high-angle annular dark field (HAADF) STEM. The microscopy work was performed with a DCOR Cs probe-corrected FEI Titan G2 60-300 instrument with 0.08 nm of nominal spatial resolution. Chemical information was obtained by X-ray energy dispersive spectroscopy (EDS) with a Bruker SuperX EDS system, comprising four silicon drift detectors, and by electron energy loss spectroscopy (EELS) with a GIF Quantum 965 EELS Spectrometer. TEM sample preparation was performed by focused ion beam with a JEOL JIB 4500 multibeam system. Lattice images were indexed using fast Fourier transforms (FFT) and strain was evaluated by geometric phase analysis (GPA) using the FRWRtools plugin [14] implemented in Digital Micrograph (Gatan Inc). The crystallographic orientations between precipitate variants and the 3C-SiC matrix were investigated using crystallographic data retrieved from the literature [15]. The Carine Crystallography 3.1 package [16] was employed to associate stereographic projections to the respective lattices. Phase diagrams of the B-C-Si system [17][18][19] have been used to interpret the microstructural configurations.
Boron concentration across sample depth was measured by SIMS using a Cameca IMS 7f microanalyzer with a primary sputtering beam of 10 keV O − 2 ions rasterized over 150×150 µm 2 with lateral resolution of 1 µm and detection of 11 B + secondary ions. Absolute values of B concentration were obtained via calibration with ion-implanted reference samples. The depth of the sputtered crater was measured using a Dektak 8 stylus profilometer and a constant erosion rate was assumed for conversion of sputter time to depth.

Microstructure evolution
STEM images obtained directly after implantation and after annealing at 1273 K are shown in figure 1 together with corresponding concentration profiles obtained by SIMS. At low collection angles, the implanted regions exhibited homogenous but distinctive contrast compared to the underlying material ( figure 1(a)). This is expected to result from displaced Si atoms rather than from the introduction of the weakly-scattering B atoms [20]. In silicon, scattering induced by lattice displacement around a single substitutional B atom peaks at 40 mrad and several atoms superimposed along the atomic columns can add up to significant scattering [21]. A similar behavior is proposed for SiC, where B preferentially substitutes Si [22]. At high collection angles (98 -200 mrad), no contrast between the implanted layers and the underlying material was discerned (figure 1 (b)) due to filtering of the electrons scattered to lower angles by point defects. After annealing at 1273 K, local contrast variations were detected in the implanted layer at low collection angles (figure 1 (c)), while no significant changes occured in the concentration profile (figure 1(d)). Due to the greater contribution from coherent scattering at low/moderate collection angles, ABF and ADF images are more sensitive to defocus and thickness variations, and to the presence of strain, than HAADF images [21]. However, the extremely fine variations observed in figure 2 (a) are not expected to originate from a tilted or wavy specimen, or from local differences in thickness. Furthermore, any changes in the electron exit wave resulting from the presence of amorphous layers on the top and lower surfaces of the TEM sample would not be confined to the implanted layer (see uniform contrast below the implanted layer in figure 1 (c)). Geometric phase analysis of both ABF and HAADF images was carried out with 111 and 002 passbands to investigate whether such contrast variations resulted from strain (see figure 2 (c) and (d)). Indeed, apparent strain localization perpendicular to (111) planes, compatible with the presence of edge-on dislocations, was found in the ABF images (figure 2 (c)). However, these defect configurations were not confirmed by GPA performed on the HAADF images (figure 2 (d)). Closer inspection of the atomically resolved ABF images revealed sharp contrast reversals along (111) planes (see magnified inset in figure 2 (e)), which do not correspond to consistent displacements of the heavier Si columns, as evidenced in figure 2 (f). Therefore, the contrast variations at low collection angles resulted probably from amplitude and phase changes induced on the electron wave by emergent clustering of the point defects generated by implantation. After annealing at 1673 K, a large density of stacking faults was observed on (111) planes parallel to the surface, whereas a lower fault density was present on concurrent {111} planes ( figure 3 (a) and (b)). The absence of these defects in the samples annealed at lower temperatures (see Figure 2) implies that additional thermally activated lattice rearrangements occurred at 1673 K. A mottled contrast compatible with the presence of clusters or precipitates was barely discernible in BF TEM (see arrows in figure 3 (b)), while no significant changes were detected in the B concentration profiles ( figure 3 (c)). Different types of contrast were observed after heat treatment at even higher temperatures, as shown in figure 4. Extended structural defects, such as dislocations and stacking faults, separating mosaics with slightly different crystallographic orientations, were present in ABF and ADF images after annealing at 1773 K ( figure 4 (a,d) and (b,e), respectively), while low-mass precipitates were the dominating feature in HAADF images ( figure 4 (c,f)). Annealing at 1873 K resulted in lower defect density but large precipitates pinned curved dislocations (figure 4 (g) to (i)). The lower precipitate density and larger precipitate size at 1873 K (2 at. % B) compared to 1773 K (3 at. % B) points to lower nucleation rate, as expected for lower undercooling and/or lower supersaturation (lower initial concentration and higher solubility). Ostwald ripening after precipitation may also have contributed to the increased particle size [24]. The microstructural changes occurring during the heat treatments are summarized in figure 5 (a) using ADF images, where both extended structural defects and low-mass precipitates present distinctive contrast. The observations suggest that precipitation was controlled by diffusion at the lower annealing temperatures and by driving force (supersaturation and undercooling) at the higher temperatures, with highest rate at around 1773 K (see also Figure  4 (f)). Quantitative evaluation of precipitation parameters was complicated by the diffusive fluxes out of the implanted layer, which promoted precipitate dissolution. Nevertheless, a qualitative description is schematized in ( figure 5 (b)).
Complete elimination of defects was not accomplished in the conditions studied, since Lomer-Cottrell locks [23] and precipitates stabilized by extended defects were detected after annealing at 2073 K for 1.4 × 10 4 s (see arrows in figure 5 (a)). Structural defects, such as precipitates, stacking faults and dislocations, are inherently associated with electronic transitions and can contribute to the optical and electrical activity of the material, potentially masking/mimicking IB behavior in absorption/emission spectra. Figure 5: (a) ADF images obtained from 3C-SiC implanted with B (same magnification). The B concentration and annealing temperature are indicated, respectively, above and below each image. (b) Qualitative illustration of the microstructural evolution in the implanted layer with annealing temperature. The precipitate density was estimated from the initial concentration and approximate precipitate size assuming spherical shape.

Precipitate phase
Despite the low fluorescence yield of B (EDS) and the overlapping of the B-K edge with the strong Si-L2,3 edge (EELS), the local spectroscopy techniques demonstrated that the low mass precipitates were rich in B (red tint in figure 6). The boride precipitates tended to adopt platelet morphologies but their atomic structure was not easily resolved due to the intrinsically weaker B scattering and the strong contribution of the embedding 3C-SiC matrix (see figure 7 (a) to (c)).
Stacking faults running in the matrix often terminated at precipitates (see arrows in figures 4 and 7), in some instances in association with Lomer-Cottrell locks ( figure 7 (d)). Since stacking faults were absent both in as-implanted samples and after annealing at 1273 K (figures 1 and 2), these defects were generated during precipitate growth, probably through a stress relaxation mechanism. Therefore, precipitation has additional deleterious implications on the overall structural quality of the B-doped 3C-SiC crystals.   Boron carbide is a well-known semiconductor with electronic properties dominated by hopping-type carrier transport [28]. This is relevant in the context of the present investigation because the optical behavior of B-doped 3C-SiC may be masked by the presence of B 13 C 2 precipitates acting as embedded quantum dots with electronic transitions in spectral ranges similar to those expected for an IB in 3C-SiC. Luminescence peaks exhibited by boron carbide have been attributed to localized gap states and transitions between such states and the energy bands [29,30]. Specific characteristics of the boride determined from optical absorption, photoluminescence and charge transport data are: band gap of 2.09 eV, several disorderinduced intermediate gap states extending 1.2 eV above E v , excitonic level at 1.56 eV above E v , electron trap level around 0.27 eV below the bottom of the conduction band, and 20 (Ωcm) −1 conductivity for the B 13 C 2 stoichiometry at room temperature [29,30]. The typical random distribution of twins parallel to {1101} B 13 C 2 [25][26][27] is likely to contribute to the complex electronic configuration of this compound and to play a significant role in charge carrier recombination.

Solubility of B in 3C-SiC
Changes in the concentration profiles compatible with long-range diffusion were only detected upon annealing at temperatures higher than 1773 K (see figure 10). At lower temperatures, the B 13 C 2 precipitates trapped B and the low concentration of solute available in the 3C-SiC matrix prevented any significant long-range diffusion, i.e., low solubility led to stable concentration profiles, suggesting apparent low diffusivity.
Since the equilibrium solid solubility as a function of temperature, C B 3C-SiC (T ), is given by the concentration in thermodynamic equilibrium with the B 13 C 2 phase, the concentration of free B immediately below the precipitation layer can be assumed ≤ C B 3C-SiC (T ). Thus, the consistent absence of precipitates below ∼ 1000 nm after annealing at 1873 K enables to infer from figure 10 (b) that C B 3C-SiC (1873K) ≥ 10 19 at.cm −3 . This value is comparable to the solubility reported for 6H-and 4H-SiC at 1873 K [31,32], with 10 20 at.cm −3 proposed for these polytypes at the temperature of the 3C-SiC + B 13 C 2 ↔ L eutectic reaction, expected to correspond to the equilibrium solid solubility limit (∼ 2500 K [17][18][19]). In the present study, the low precipitate density and high dilutions achieved hindered an evaluation of solubility at temperatures higher than 1873 K. Precise determination of solubility at high temperatures is challenging for nanometric sources given the relatively poor lateral resolution of SIMS and the transient nature of the B concentration profiles [33], with fast diffusion due to steep gradients around the precipitates. In addition, precipitates stabilized by extended defects were present in layers implanted with 1 at.% B even after annealing at 2073 K for 1.4×10 4 s (see figure 5 (a)), although the B concentration measured at those depths (∼ 200 nm) was only 10 17 at.cm −3 . Therefore, dissolution rather than diffusion may be the rate-controlling mechanism defining the concentration profiles at high temperatures, i.e., the 3C-SiC matrix may be rapidly depleted of B by fast diffusive fluxes in the neighborhood of slowly dissolving B 13 C 2 precipitates. In this case, the concentration measured immediately below the precipitation layer after relatively long heat treatments may, in fact, be significantly lower than the equilibrium solubility at the annealing temperature.

Conclusion
Annealing after implantation led to precipitation of B 13 C 2 that trapped B up to 1773 K. Therefore, the low solubility induced stable concentration profiles and resulted in apparently low B diffusivity. The precipitates adopted the (0001) B 13 C 2 //{111} 3C-SiC and 1100 B 13 C 2 // 110 3C-SiC orientation relation with the matrix and exhibited planar defects on {1101} B 13 C 2 . Strain generated by precipitate growth induced the formation of stacking faults and dislocations in 3C-SiC that contributed to lower the overall structural quality of the crystal. The presence of extended defects and precipitates may mask the presence of an IB in 3C-SiC and total elimination of these structures is challenging due to the locked configurations adopted. Correlation between SIMS concentration profiles and STEM observations enabled to infer that the solubility of B in perfect 3C-SiC crystals is ≥ 10 19 at.cm −3 at 1873 K. Our results suggest that for IB formation, alternative methods for introducing high concentrations of B into 3C-SiC should be sought.