Impurity LDOS

The situation changes drastically when the Mo atom is placed at the site of the nonmetal sublattice in TiC and TiN. For such an anomalous type of substitution, the impurity LDOS in TiC exhibits three maxima A, B and C (Fig. 7.10), one of which (A) corresponds to the hybridisation of the Mo d states with Ti d and s functions, which, in turn, are hybridised with 2p-orbitals of the neighbouring C atoms. Peaks B and C can be attributed to local interactions of Ti-Mo type (in the [MoTi ] cluster). For TiN, the intensities of peaks B and C are enhanced further, and they, being located at the nitride DOS minimum, acquire a pronounced atom-like (nonbonding) character. The data of Table 7.1 show that the greatest energy gain is achieved for solid solutions of TiC-Mo type, when Mo enters the Ti sites. A much weaker effect is observed for the TiN-Mo system, where Mo-N bonds are far weaker as compared with Mo-C interactions. 

The presence of a defect in the lattice (impurity, surface, vacancy...) breaks the symmetry and induces perturbations of the electronic structure in its vicinity. Thus it is convenient to introduce the concept of local density of states (LDOS) at site i ... 

The LDOS have been calculated using 10 exact levels in the continued fraction expansion of the Green functions. For clean surfaces the quantities A Vi are the same for all atoms in the same plane they have been determined up to p = 2, 4, 6 for the (110), (100) and (111) surfaces, respectively, and neglected beyond. The cluster C includes the atoms located at the site occupied by the impurity and at al the neighbouring sites up to the fourth nearest neighbour. 

In a next step the possibility to image sub-surface impurities in metal surfaces by STM has been investigated [102]. The STM images were calculated for room temperature in the Tersoff and Hamann [105] approximation to determine the tunneling current I(r, U) for a gap voltage U. The local density of states (LDOS) of the sample is expressed in n(r , z, Sp+ s) [106] at the position... 

Taking into account the formation of direct C-C, N-C, etc. bonds when N2 molecules or excess C are introduced into the MX phases, one should expect sharp changes in the shape of the LDOS of the p impurities in the nonmetal sublattice. Instead of one occupied p-band formed by the usual impurity states in the ideal crystal, the 2p-orbitals of the central (in microclusters ) atoms are split into two subbands. One is located near the bottom of the p-d-band, while the other gives rise to a narrow peak near the Fermi level. According to the classification scheme of the gas molecules (Nj, CO, Oj, etc.), such states can be considered as bonding and antibonding ones. 

The LDOSs of a single B impurity in TiC, TiN, VN and MoC have been calculated by Ivanovsky (1988) and Anisimov et al (1986a) using the LMTO-GF method. These calculations show that the B2p-type LDOS overlaps completely with the main valence-bonding band of the carbide, while B2s states are localised between C2s and p-d-TiC subbands. 

Similar results were obtained for the VC-B and MoC-B systems. Only a small decrease in the B2p-M(nd) states overlap was observed with an increase of the atomic number of the metal. Transformation of the electron states of the isolated B impurity depending on the band structure of the matrix (TiC and TiN) shows that B LDOSs are again determined by the relative energies of the impurity and crystal states. The increase of the interval between the states (from TiC-B to TiN-B) leads to an enhancement of the impurity state localisation, which in the case of TiO-B results in a clear pseudoatomic type for the LDOS of the impurity. 

These peculiarities in the distribution of the impurity states are defined primarily by the nearest neighbourhood of M or C vacancies. The electronic states of these atoms interact strongly with outer orbitals of the Be atoms, which fill these vacancies in the soUd solution. As follows from Chapter 4, the vacancy states of C defects in TiC and NbC produce intensive DOS peaks near the Fermi level and result in an increase of the electron density along the M-M bonds near the defect. The shape of these states is determined by the admixtures of Be2p functions. Similar features are seen in the LDOS of Be in position (2) and M defects, revealing the dominant hybridisation of the impurity states and C2p-orbitals. 

Thus the LDOS of the Be impurity (and those of the other p elements considered above) depends mainly on the nature of the immediate vicinity of the impurity in the crystal, while the band structure of the matrix is of... 

For elements at the end of the d series (Ni, Cu), the shape of the LDOS curve is again different. The impurity band is shifted to the lower edge of the bonding band and is accompanied by the formation of narrow atom-like peaks near the edge of the p-d-band with energy intervals corresponding to the DOS minima of the initial binary phases. 

The KVV spectra of the impurity (Fig. 8.20) are of particular interest here. As with LDOS curves, the shape of the O impurity Auger spectra differs drastically for the two O sites which model the possible ways of carbide oxidation. As can be seen, the three main peaks in the spectrum... 

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