Titanium impurities in silicon, diamond, and silicon carbide

Brazilian Journal of Physics, vol. 34, no. 2B, June, 2004 602 Titanium Impurities in Silicon, Diamond, and Silicon Carbide L. V. C. Assali† , W. V. M. Machado† , and J. F. Justo‡ † ‡ Instituto de Fı́sica, Universidade de São Paulo, CP 66318, 05315-970, São Paulo, SP, Brazil Escola Politécnica, Universidade de São Paulo, CP 61548, 05424-970, São Paulo, SP, Brazil Received on 31 March, 2003 We carried a theoretical investigation on the electronic and structural properties of titanium impurities in silicon, diamond, and silicon carbide. The calculations were performed using the spin-polarized full-potential linearized augmented plane wave method in the supercell approach. The atomic configurations and transition and formation energies of isolated Ti impurities were computed. 1 Introduction Since transition metal impurities affect the electronic and optical properties of semiconductors [1], it is important to understand the role of such unavoidable impurities on those properties. At the same time, transition metals in semiconductors can be used in other unusual situations. The energy levels related to transition metal impurities are aligned with respect to each other for the same group of isovalent semiconducting compounds [2]. Therefore, this defect-related level could be used as a reference to determine an important property in semiconductors: the valence band offset in the interface between two compounds [3]. Titanium, vanadium and chromium are native impurities which are incorporated during growth of several type-IV and type IV-IV semiconductors [4, 5]. The properties of the titanium impurity in those materials are also interesting from a fundamental point of view, since it has a 3d2 4s2 atomic configuration, being isoelectronic with the host atoms. In the specific case of silicon carbide, experimental data indicates that titanium is stable in a silicon site [6], and while it is electrically active in 4H-SiC, it is inactive in 3C-SiC [4]. Although the nearest-neighbor local structure for a substitutional Ti impurity is essentially the same in either hexagonal or cubic material, such distinction in the electrical activity behavior has been associated with the large difference in the materials bandgap (εg ) for the polytypes (εg ranging from 2.42 eV for the 3C-SiC to 3.33 eV for the 2H-SiC). Deep level transient spectroscopy (DLTS) experiments on Ti in 4H-SiC show that Ti introduces gap levels near the bottom of the conduction band [5]. Since εg is considerably smaller in 3C-SiC than in 4H-SiC, the Ti-related energy levels would be pinned in the conduction band for the 3C-SiC, and therefore they would be undetectable. Here, we have carried a theoretical investigation on the electronic and the atomic structure, the spin state, and the stability of Ti impurities in silicon carbide, silicon, and dia- mond. We computed the Ti-related acceptor transition energies in all those materials, and using the model by Langer and Heinrich [2], we determined the valence band offset among Si, SiC, and diamond. 2 The FP-LAPW method The calculations were performed within the framework of the density functional theory [7, 8], using the total energy full-potential linearized augmented plane wave (FP-LAPW) method, implemented in the WIEN97 package [9], combined with the exchange-correlation potential of PerdewBurke-Ernzerhof [10]. We considered reference supercells of 54 atoms for the cubic crystals and of 56 atoms for the hexagonal (2H-SiC) crystal. For the bulk SiC, a convergence in total energy was achieved using 5.8/R (maximum length of the plane-waves), where R is the smallest radius of spheres which defines the host atoms. We used RSi = 1.5 a.u. and RC = 1.2 a.u. For bulk Si, the convergence criteria was 6.0/R, with RSi = 1.8 a.u., and for diamond, it was 7.0/R, with RC = 1.2 a.u. For simulations involving titanium impurities, RTi = 1.2 a.u. was used. The full Brillouin zone (BZ) was sampled by a 63 grid of k-points [11], which reduces to 16 k-points in the irreducible BZ (IBZ) in the primitive cell. Self-consistent interactions were performed until convergence on both the total energy (10−4 eV per unit cell) and total charge in the atomic spheres (10−5 electronic charges per atom) were achieved. Total energy minimizations, with respect to variations in the lattice parameters, lead to values of a = 4.38 Å (aexpt = 4.360 Å [12]) in 3C-SiC, a = 3.09 Å and c = 5.05 Å (aexpt = 3.076 Å and cexpt = 5.035 Å [12]) in 2H-SiC, a = 5.46 Å (aexpt = 5.431 Å [12]) in silicon, and a = 3.57 Å (aexpt = 3.567 Å [12]) in diamond. For the supercell calculations, the BZ was sampled by a 2 × 2 × 2 grid [11], corresponding to a unique point to integrate the IBZ. For such calculations, the convergence cri- L. V. C. Assali et al. teria for total energy and electronic charge were the same as described earlier [13, 14, 15]. The atomic positions were relaxed until the forces were smaller than 1mRy/a.u. Here, we investigated only substitutional Ti, since it has been recently shown by total energy calculations that the interstitial Ti is considerably less stable than the substitutional one in silicon carbide [13, 14]. 603 S=0 in a Td point symmetry (fig. 1e) and the four nearestneighboring carbon atoms relax outward by 19 %. The impurity introduces a fully occupied t2 energy level and a pair of unoccupied levels (e plus t2 ) in the gap. The results for this center are similar to those of the TiC s center in 3C-SiC. Silicon Ti 3C-SiC Ti(Si) 2H-SiC Ti(Si) 3C-SiC Ti(C) Diamond Ti t2 3 Substitutional Ti in SiC, Si, and diamond t2 Ec t2 t2 e Ev Figure 1 displays the impurity induced energy levels, based on the Kohn-Sham eigenvalues, for the neutral substitutional Ti impurity in Si, in diamond, in 3C- and 2H-SiC at the Γ point. In the Td crystal field, the Ti 3d-derived states split into two energy levels with t2 and e symmetries. In silicon, the Tis impurity (fig. 1a) introduces a fullyoccupied t2 level in the valence band and an unoccupied e level in the bandgap. The center presents an effective spin S=0, and has a Td point symmetry. This result is fully consistent with a previous theoretical investigation [16], although such investigation did not take atomic relaxations into account. Here, the four nearest-neighboring atoms undergo an outward relaxation of 6.0 % (with respect to the crystalline interatomic distance). In 3C-SiC, the TiSi s center (substitutional Ti in the Si site) introduces no energy levels in the band gap (fig. 1b). The center also shows an effective spin S=0 and a Td point symmetry. The four nearest-neighbors undergo an outward relaxation of 6.6 %. The Ti-related energy levels are unoccupied resonant levels in the conduction band, where the e level lies below the t2 level. Therefore, when a Ti atom replaces a Si atom, it undergoes a p-d hybridization, binding to the four nearest-neighboring carbon atoms. The Ti impurity reconstructs the Si vacancy dangling bo (...truncated)