Investigation of Mo defects in 4H polytype of silicon carbide by means of density functional theory
Silicon carbide (SiC) is a compound semiconductor that can be crystallized in several forms, called polytypes. These consist of Si-C biatom layers which can have cubic (k) or hexagonal (h) local symmetry. As some poltytypes have wide band gap, they can be utilized in high temperature and high power electronics. In addition, porous form of SiC is proven to be a bioinert material. As a novel application, certain polytypes (3C, 4H, 6H) doped by transition metal atoms are proposed to be employed as fluorescent biomarkers.
Tracking biomolecules has a high significance in medical practice as well as in scientific research. As a notable family of biomarkers, fluorescent nanoparticles can be utilized in this field. It is highly desirable that the emission to be in the near-infrared (NIR) region, because of the low absorption window of biological cells for this range (in wavelength) of light [1]. According to preliminary studies, molybdenum(Mo)-doped 4H and 6H SiC show NIR emission with the energy values of 1.15 eV and 1.11 eV, respectively [2]. It is also clear that the corresponding photoluminescence (PL) center has the spin state S=1, and the symmetry of C3v, as it was revealed by ESR and MCDA measurements [2].
In accordance with previous ab-initio calculations [3], the two most stable configurations formed by Mo in SiC host are MoSi either at k or h site and Mo-ASV (asymmetric split vacancy) complex at h-h sites. In order to characterize this system in detail, calculations by means of density functional theory (DFT) have been carried out. During our study, particularly the so-called HSE06 range-separated hybrid functional [4] was applied to calculate the electronic structure and adiabatic charge transition levels. By HSE06 both defect and the host material can be described with high accuracy, since this functional is capable to reproduce correctly the band gap and bulk properties [5]. However, to characterize such strongly correlated states like electrons on the open d-shell of Mo impurity, HSE06 may need to be corrected by an additional occupation-dependent Vw screening potential to achieve satisfying accuracy [6]. Thus, we start our investigation by checking HSE06 carefully for the current defect configurations in neutral charge state, and as a result, HSE06 was found to be able to describe these defects within the expected accuracy (~0.05 eV). It is worth noting, that spin-orbit splitting was reported to be below 1 meV by an earlier study [1]. Hence, it is out of consideration in our recent investigation.
Our main purpose was to calculate the electronic structure of these Mo-related defects in 4H-SiC. Calculations were carried out on a 576-atom supercell with a Mo atom substituting a Si atom at the k and h sites for MoSi defect, and at an h-h divacancy obtaining Mo-ASV complex. For determining one-electron wavefunctions plane wave basis set with 420 eV cutoff and PAW-potentials [7] were used as implemented in Vienna Ab initio Simulation Package (VASP) code [8]. As a next step, charge transition levels were calculated. In order to overcome self-interaction persisting in the case of charged Mo defect configurations, Freysoldt correction [9] was applied for the total energy of the supercell.
Firstly, results of optical analysis for the involved Mo-related defects are under discussion. In the case of MoSi defects we found that the Kohn-Sham levels appearing in the band gap agree in ~0.1 eV at k and h sites. In neutral charge state a two-fold degenerated e level appears at ~EV + 0.9 eV in the gap (Fig. 2.) occupied by two electrons with the same spin state, where EV is the valence band maximum energy. Neutral MoSi defect has S=1 ground state in C3v symmetry showing 3A2 character as explained by group theory. In accordance with preliminary experimental data [2] only neutral MoSi may provide the observed PL sign. In this scope, two possible transitions can be obtained: from the defect level to the conduction band edge (EC), or from the valence band edge to the defect level. The transition energies of these excitations can be well approximated by the (+|0) and (0|-) charge transition levels referenced to the EC and EV. For k situated MoSi the energy of (+|0) level is EC-2.22 eV and the value for (0|-) level is EV + 3.09 eV. These values for h site are EC – 2.25 eV and EV + 2.87 eV for (+|0) and (0|-) levels, respectively. These values are about two times larger than the preliminary reported ZPL energies of 1.15 eV in 4H-SiC. Therefore our results imply that MoSi defects are not likely to be responsible for the Mo-related PL center. From now on, Mo-ASV complex will be highlighted.
For Mo-ASV complex three defect levels appear in the band gap. This implies that intra-defect-level optical transitions may occur, which cannot be approximated by charge transition levels. In neutral charge state the lowest energy level is a double degenerate e level fully occupied by four electrons at EV + 0.32 eV. Besides, there is an a1 level at EV + 2.72 eV and another two-fold degenerate e level at EV + 2.79 eV (Fig. 4.). As experimental data show that the Mo-related PL center has the spin state S = 1, only (2-) and (2+) charged Mo-ASV may responsible for the corresponding PL sign. These charge states can occur in n-type and p-type SiC samples, respectively. In experiments, PL center was observed in p-type SiC. According to charge transition levels (2-) charge state can be stable only n-type samples, thus Mo-ASV(2+) should be responsible for the Mo-related PL (and ESR) center. The ground state of the corresponding charge state has 3A2 symmetry. Selection rules indicate from the experiments that the excited state should show 3A2 symmetry, as well. This fact implies that both the ground and excited states could be multi-determinant in nature. In addition, the singlet 1E might also couple to the ground state triplet by phonons. Consequently, accurate calculations of transition energies between the ground and excited states are very challenging.
In summary, in relation with experimental data related to the corresponding PL center only the Mo-ASV(2+) defect configuration cannot be excluded as the source of the observed PL and ESR signs. The exact nature of the excited states still need further investigation.
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