N_iO_i - pre-cursor to STDs and the NNO

Wagner et al [174] have reported two weak LVMs at 810 and 1018 cm^-1 (813 and 1020 cm^-1 at room temperature [100]) which were seen in the same materials as the NNO defects. These were also reproduced in experiments by Berg Rasmussen et al [103] in implanted Si after annealing at 600$^\circ$C. These modes are correlated, and disappear after annealing at 650$^\circ$C. Long time annealing at 600$^\circ$C increases their concentration at the expense of N₂ modes and the O defect responsible for the 1012 cm^-1 mode, suggesting that oxygen and nitrogen complexes are breaking up while this defect is forming. They are always of a much weaker intensity than the NNO vibrational modes. These modes have not to our knowledge ever been properly characterised, and their origin is unknown.

After high temperature pre-annealing even the N₂ pairs are broken up, and it seems reasonable that in material with a high O_i concentration, some of the N_i could diffuse to O_i before reaching a second N_i and reforming a pair. This N_iO_i would form as an intermediate structure between N_i and either N_iO_2i or N_2iO_i, and is a possible source of the 810 and 1018 cm^-1 vibrational modes (there are other alternatives, see below). If this is the source of the modes it would be important since it shows clear evidence of a N-O precursor to the N_iO_2i defect, and adds much support to the claim that the N_iO_2i shallow thermal donor can form in silicon (see Chapter 8).

We examined N_i-O_i using the 149 atom cluster Si₇₉H₆₈NO. In the neutral charge state the defect has roughly planar C_1h symmetry with a deep donor level close to that of isolated N_i (see Figure 8.2). This eliminates it as a model for the shallow thermal donor. The N atom moves very slightly out of plane by 0.156 Å which allows its lone pair to become more assymetric, similar to the nitrogen coordination in ammonia, NH₃. This is discussed further below. The O atom sits in a stable bond-centred location with Si-O lengths of 1.639 and 1.665 Å with the shorter bond on the Si shared with the N, and a Si-O-Si bond angle of 146$^\circ$ (see Figure 7.5). The N-Si bonds are 1.680, 1.834 and 1.832 Å, with the shorter bond once more shared with the Si bonded to the oxygen.

  

Figure 7.5: The N_iO_i defect in the neutral charge state. Lengths in Å, angles in degrees.

  

Figure 7.6: The N_iO_i defect in the +1, neutral, and -1 charge state. The core Si atom has a p-type orbital in the plane of the defect that is empty in the +1 charge state. This is partially and fully occupied in the neutral and -1 charge states respectively, which is reflected in the change in bonding character.

  

Figure 7.7: Kohn-Sham wavefunction for the partially occupied level of N_iO_i in the neutral charge state. Note that the diagram is reversed from the ball and stick diagrams, i.e. the O atom is on the right of the plot. The wavefunction lies primarily on the core Si atom, and is localised on the side away from the O_i atom.

The deep donor level is concentrated on a $\langle$110$\rangle$ p- type orbital located on the central Si atom. This atom moves away from the O. The asymmetry of the defect allows the donor wavefunction to concentrate on the lobe of the p-type orbital furthest from the oxygen, thus minimising the Coulombic repulsion with O. This explains why the donor level remains deep in the gap. A plot of the Kohn-Sham wavefunction for this level is given in Figure 7.7. This electronic behaviour is discussed further in Section 8.10.

Since the defect possesses such a deep level it raises the possibility that it could act as an acceptor, trapping an additional electron to fully populate this level. The implantation used to add isotopic N/O creates radiation defects, pinning the fermi-level near to midgap. Both the isotope implanted and as-grown material were n-type[100] with no difference in modes, which suggests the defects possessed the same charge state in both. This suggests that the defects would be negatively charged. We therefore calculated the structure and vibrational modes of the defect in both the neutral and negative charge states.

In the -1 charge state the core Si atom starts to form a bond with its Si next neighbour on the opposite side to the oxygen; this bond shortens to 2.35 Å, dilating the Si-Si back bond to 3.16 Å (see Figure 7.5). Thus the lone pair on the core Si appears to have migrated out of the defect core and onto a next neighbour Si atom of the defect. There is little change in the Si-O-Si lengths (1.63 and 1.65 Å, 153$^\circ$ bond angle), however the N-Si lengths dilate as the core Si is pulled away from the N, the new lengths being 1.66, 1.86 and 1.93 Å.

The change in bonding with charge state is shown in Figure 7.6, and shows an interesting effect. In the +1 charge state the core p-type orbital is empty and thus there is an attraction between it and the O$^{\delta-}$ atom. It therefore shifts off site towards the oxygen. However in the neutral charge state this orbital is occupied and so there is now a driving force to form a covalent bond with its Si next-neighbour on the other side. Since this Si atom is fully coordinated already then it has to choose between bonding to the core Si and bonding to its standard neighbour along $\langle$110$\rangle$. In practise it appears to form an extended bond between the two with roughly equal bond lengths (see Figure 7.5). Finally in the -1 charge state there are now sufficient electrons to completely fill the dangling p-type bond. However it is energetically more favourable to form instead a Si-Si bond with this next neighbour along $\langle$110$\rangle$, thus creating a dangling bond on the Si atom further from the defect core. This is probably since the dangling bond, if it were to stay on the core Si, would have to sit quite close to the oxygen atom, so the defect can lower the overall Coulombic repulsion by moving it out of the defect centre in this way. Whether it would be possible to grow this defect in p-type material and observe the shifted +1 behaviour is an open question.

The vibrational modes are given in Table 7.2. As can be seen, there is extremely good agreement between the calculated and experimental values. The change in charge state has only a small effect on the modes. The modes for the -1 charge state are slightly better than the neutral result and add weight to the suggestion that the defect is negatively charged, however there is not sufficient difference to allow us to distinguish the defect charge state purely on this basis. The experimental resolution was 6 cm^-1 and most of the isotopic shifts lie well within this accuracy. The 805 cm^-1 mode appears experimentally as a shoulder to the stronger 813 cm^-1 mode due to NNO, and as this barely shifts with O isotope it could mask any movement in the 805 cm^-1 mode.

Both the N and O atoms have one very short Si bond with their mutually shared Si atom. This is extremely similar to the oxygen pair (see Chapter 6), where the two oxygen atoms bind tightly to their shared Si atom. This is due to the large electronegativities of both the oxygen and nitrogen atom, which draw charge from their Si neighbours, making the shared Si atom strongly $\delta+$. However the binding for the N_iO_i defect will be much stronger than that of the oxygen dimer, since as well as this electrostatic bonding there is the additional binding due to strain compensation with is absent in the dimer. This is in agreement with their dissociation temperatures; oxygen dimers are not important in TD formation above about 450$^\circ$C whereas the N_iO_i modes anneal out at 650$^\circ$C.

 We originally relaxed this defect with the N atom starting exactly in-plane, but this is a metastable minimum. Allowing the N extremely small out-of-plane relaxation allows the wavefunction of its lone pair to distribute correctly. Without this the N does not attract as much surrounding charge, decreasing the polarisation of the surrounding lattice and so weakening the strong shared bonds with the neighbouring Si in the N-Si-O chain. This then shifts their vibrational modes, leading to an incorrect ordering of the N and O modes. These earlier modes are included in Table 7.2 for reference.

Note that these results for N_iO_i differ to those given in earlier work performed using semi-empirical PM3 clusters[180], where it was suggested that N_iO_i represented a single, rather shallow, EMT donor.

 

Defect Source

¹⁴N ¹⁵N

N_i Experiment [170,181] 690 17

Theory [145] 700 17

582 15

¹⁴N¹⁶O ¹⁵N¹⁶O ¹⁴N¹⁷O ¹⁴N¹⁸O

N_iO_i Experiment [100,174] 1020 8 9

813 18 This work

-1 1014 3 20 37

875 20 5 11

745 14 28

Neutral 992 2 21 39

850 21 3 8

694 12 23

Local Minimum 954 25

(see Section 7.5) 828 20 38

625 15

N_2iO_2i ¹⁴N¹⁴N ¹⁶O¹⁶O ¹⁶O¹⁸O ¹⁸O¹⁶O ¹⁸O¹⁸O

This work 1142

1100 26 13 42 963

868 17 23 37

767 1 2 741

629 2 3

591 12 3 17

¹⁶O¹⁶O ¹⁴N¹⁴N ¹⁴N¹⁵N ¹⁵N¹⁴N ¹⁵N¹⁵N

1142 1 31 32

1100 1 1

963 26 1 28

868 1 1

767 17 18

741 17 17