Introduction

Carbon is a common and important impurity in silicon, typically occurring in concentrations of around 10 -10 cm , and predominantly occupying substitutional sites, C . Upon irradiation, mobile silicon interstitials (Si ) can be captured by C , forming the interstitial carbon defect C [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The defect is characterized by two local vibrational bands at 920 and 931 cm , whose absorption intensities are in a ratio of approximate 2:1. This suggested to the earliest workers a trigonal defect [2]. However, later work with lightly irradiated p-type Si was able to correlate an electron paramagnetic resonance, EPR, spectrum with the infra-red absorption. The EPR showed that C possessed symmetry [4]. The hyperfine splitting on C showed that the highest occupied state in C consisted of a localized p-orbital centered on the C atom. Deep level transient spectroscopic (DLTS) measurements gave a donor level at +0.28 eV. These results suggested a model of the defect shown in Fig. 1.

More recent EPR and DLTS investigations on n-type material [5] found an acceptor level at -0.10 eV and that C also possessed symmetry. The similarity between the re-orientation barriers of the defects in both charge states ( 0.8 eV) indicated that they possess the same structure. However, no hyperfine splitting of the EPR line due to C with C or Si was observed, possibly because the partially occupied acceptor state is extended over a number of Si atoms and has only a small overlap with carbon.

The defect is associated with a 856 meV photoluminescence (PL) line and uniaxial stress measurements revealed that the symmetry of the defect was also (monoclinic I) [6]. It is just possible that the neutral defect possesses trigonal symmetry and reorients to in a charged state when a carrier is thermally trapped before radiative recombination occurs. However, unambiguous confirmation that the symmetry of the neutral defect is indeed and not trigonal came from the response of the two LVMs of the neutral defect to uniaxial stress [7]. These experiments showed that the symmetries of the 920 and 931 cm LVMs were and respectively. Thus it appears that the defect adopts the structure shown in Fig. 1 in all three charge states and consists of a C and Si atom sharing a single lattice site with a 100 orientation [4, 5, 7]. However, this model gives no natural explanation of the near degeneracy of the local vibrational modes of the defect, or their 2:1 ratio in absorption intensities.

Several theoretical calculations have been performed on the C defect, all finding the 100 structure to be the ground state configuration [8, 9, 10, 11, 12]. The calculated vibrational modes of the various defect configurations [9] provides further evidence for the configuration in Fig. 1. For this model they were 1005 cm and 853 cm for the and the modes respectively, in fair agreement with experiment. None of the three possible symmetry configurations possessed two high frequency modes.

The energy barrier to reorientation of the defect among the equivalent 100 orientations has been calculated by Tersoff [10]. He found this to be 0.7 eV for a saddle point where the C atom lies at a bond centered (BC) site along 111 . This is in good agreement with experimental reorientation and migration barriers around 0.8 eV [4, 5, 13]. More recent calculations on the migration/reorientation barriers of the defect have calculated these to be 0.51 eV via a saddle point with symmetry [11] and 0.77 eV via a H-site [12] The migration/reorientation pathway considered by Capaz et al [11] involved a low energy, 0.51 eV, four-fold coordinated carbon atom at the saddle point. This path involves C moving through the lattice and at the same time reorienting and hence explains why the barriers to migration and reorientation are the same. The path via a BC defect was also considered but they found it involve a 2.5 eV barrier which is considerably greater than that found by Tersoff. The structural data from this recent ab initio supercell calculation [11] for the neutral defect is given in Table 1.

The di-carbon defect C -C is formed when Si:C, containing a low oxygen-content, is e-irradiated at room temperature creating mobile C defects which are subsequently trapped by C [1]. The defect is bi-stable taking the A-form in the charged states and the B-form in the neutral one. EPR and DLTS studies [14] showed that (C -C ) defects possessed symmetry, and they gave rise to acceptor and donor levels at -0.17 and +0.09 eV. The EPR data also found that the carbon atoms were inequivalent, and the g-tensors were perturbed by stress in a very similar way to those of the charged C defect. The model proposed from the experimental data is very similar to that of C , the symmetry being lowered by the presence of a second carbon atom at a substitutional site shown in Fig. 2. This configuration of the C -C defect is known as the A-form, and is the stable configuration for both singly ionized states.

For high e-irradiation fluences, the Fermi level is around mid gap and the neutral B-form of the defect is formed [14, 15]. This state is diamagnetic, but an excited triplet state B has been observed by optically detected magnetic resonance (ODMR) [16]. This revealed that the symmetry of the B-form is for T > 30 K, and otherwise. Hyperfine interactions on C detected by ODMR indicated that the carbon atoms are nearly equivalent. DLTS studies on the metastable B form, which has trapped a carrier, show that has shallow donor and acceptor levels at +0.07 and -0.11 eV respectively. It has also been possible to observe EPR from the metastable B form, but not from B . B is also found to have symmetry for T > 15 K and again below this temperature. The ODMR results suggest that the two C atoms lie close to neighboring substitutional sites, with a silicon interstitial, Si , close to a BC site lying between them. This configuration is illustrated in Fig. 3.

There are three peculiar features with this model. Firstly, if Si lay at the BC site, then the resulting symmetry would give a partially occupied e-level. This would probably be split through a Jahn-Teller distortion resulting in Si moving away from the BC site. However, the distortion cannot be too great if the reorientation energy around the C-C axis is to remain small. Nevertheless, the observed donor and acceptor levels are split by 0.97 eV, whereas a small distortion would lead to a difference in donor and acceptor levels of at most 0.5 eV being an estimate for the Hubbard U-correlation energy. On the other hand, if the distortion is not small, then the reorientation energy might be substantial and the symmetry of the defect would not be .

A second difficulty comes from the vibrational modes of the defect. The B-form gives rise to a zero phonon luminescence line at 969 meV. The fine structure associated with this line reveals two local vibrational modes at 543.0 and 579.5 cm ( C) which shift by 10.1 and 14.9 cm respectively for C samples. However, in a sample containing a mixture of C and C, additional lines are observed which are shifted only by 0.1 and 0.6 cm . Indeed, the original PL investigations failed to find distinct modes in the mixed case, and incorrectly suggested that the defect only contained one C atom. These tiny shifts confirmed that two carbon atoms were present in the defect, but implied that they are almost dynamically decoupled [17, 18]. It has been suggested that the this decoupling arises because the two C-Si bonds are almost orthogonal to each other [14]. Even if this was the case, it would require that the C-Si stretch modes lie around 550 cm . This is unlikely since the reduced coordination of Si will result in a shorter C-Si bond, and hence the C-Si stretch should be larger than the highest mode of C which occurs at 607 cm [19].

A third peculiarity is that the positive and negative charge states of the B-form are metastable, with energy differences with the A form of only a few hundredths of an eV in all three charge states. Similarly, the barriers between the forms are only 0.1-0.2 eV. As the bonding in the two forms is quite different and bond energies are of the order of 1 eV, it is surprising that these energy difference are so small.

Theoretical modelling of the di-carbon defect is still in its early stages, and to date three groups have examined the centre [9, 12, 24]. The first two focused on the relative energies of the A and B forms, and in our previous work, we analysed local modes of the B form only. The findings of the previous calculations relating to the defect energies are summarised in Table 4.

We discuss the standard models, and analyze their structure and vibrational modes in this paper. The method is discussed in section II, and applied to the C defect in III and the di-carbon center in IV. We give our conclusions in V.