Bond-center site

In Chapter 8, Stavola and Pearton discuss the local vibrational modes of complexes in Si that contain hydrogen or deuterium. They also show how one can use applied stress and polarized light to determine the symmetry of the defects. In the case of the B-H complex, the bond-center location of H is confirmed by vibrational and other measurements, although there are some remaining questions on the stress dependence of the Raman spectrum. The motion of H in different acceptor-H complexes is discussed for the Be-H complex, the H can tunnel between bond-center sites, while for B-H the H must overcome a 0.2 eV barrier to move between equivalent sites about the B. In the case of the H-donor complexes, instead of bonding directly to the donor, H is in the antibonding site beyond the Si atom nearest to the donor. The main experimental evidence for this is that nearly the same vibrational frequency is obtained for the different donor atoms. There is also a discussion of the vibrational modes of H tied to crystal defects such as those introduced by implantation. The relationship of the experimental results to recent theoretical studies is discussed throughout. 

Throughout the remaining sections of this chapter, various configurations for complexes that include hydrogen will be discussed. Figure 1 shows a schematic of a [110] plane that includes a substitutional impurity. The following sites for an H atom attached to the impurity are labeled the bond-centered site (BC), the tetrahedral interstitial site (T), the antibonding site (AB), and the C-site (C). 

Experimental data from Bech Nielsen s study is shown in Fig. 6 and Fig. 7. The data show that implanted 2H is found predominantly in bond-center sites. This qualitative conclusion can be drawn immediately from the raw channeling data, especially the 111 planar scans, and does not depend on the details of the model used to subsequently analyze the data in greater detail. Si—Si bonds run perpendicularly across the 111 planar channel. At zero tilt, a strong flux peak of planar channeled ions is focused on the bond centered site and causes the peak seen in the data at this angle. However, back-bonded sites are hidden in the wall of this channel, which is unusually thick and consists of two planes of atoms close together. Thus, the ion flux near the back-bonded sites is low when the tilt angle is small, hence the dip in nuclear reaction yield calculated for this site. Bech Nielsen (1988) found that this data pointed to there being a minority of the 2H... 

Fig. 9. Calculated angular scans for 700 keV 3He ions in (110) silicon for different 2H lattice sites the tetrahedral interstitial site (T), a back-bonded site 1.5 A from a lattice site (BB), and a bond-centered site (BC). From Marwick et al. (1988).

The experimental data show that most of the deuterium atoms in the samples examined occupy bond-center sites. The attribution of this site comes both from the observation of a flux peak in the 111 plane (Fig. 11), and of a dip in the (110) axial channel (Fig. 12), together with the channeling simulations shown in Fig. 9 and Fig. 10. Just as in the case of FI-implanted silicon, the qualitative observation of a flux peak in the 111 planar data rules out any possibility of a back-bonded site for the 2H, although some calculations of the B—H structure have suggested this site. The data were analyzed on the assumption that they could be fitted by a combination of a small number of sites of high symmetry. First, the excess hydrogen, i.e., the part of the hydrogen concentration in Fig. 8... 

Fig. 11. Channeling data for the 111 plane (Marwick et al., 1987, 1988), showing data for the nuclear reaction with 2H atoms in the sample and the yield of elastically backscattered 3He ions. The central peak in the 2H scan is important evidence that the 2H atoms occupy bond-center sites. The solid line is a fit to the data, as described in the text.

Bech Nielsen et a/. s experimental channeling data for the (100) axial channels is shown in Fig. 14. Together with 111 planar data, which showed a pronounced flux peak, these data clearly indicate a near bond-center site for the 2H. According to Bech Nielsen s analysis, the best fit to the data was obtained with 87% of the 2H atoms in the sample assigned to near BC sites and the rest to T sites. However, the attribution of the minority component could be influenced by radiation effects during the analysis, as will be discussed later. 

Fig. 14. Axial channeling scans from Nielsen et al. (1988) showing the yield from the (3He, ap) reaction with 2H in B—H pairs and the Si crystal host dip. The solid lines show a fit to the experimental data with the Statistical Equilibrium model for 87% of the 2H in a near bond-center site and the remainder in a T site.

There appears to be a low barrier between adjacent sites for normal muonium in Si but a substantial barrier and/or a small tunneling matrix element between adjacent bond-centered sites. In addition there is an appreciable barrier between BC and T sites. These features are consistent with experiment and with most of the theoretical calculations. 

Fig. 4. Schematic representation of H at the bond-center site in an elemental semiconductor. 

Since motion of the host atoms is so essential at the bond-center site, only calculations that allow for relaxation will produce it as a stable site. Among those are recent cluster calculations for Si by Estreicher (1987), who used the PRDDO method as well as ab initio minimal-basis-set... 

When relaxation is allowed, the global minimum shifts to the bond-center site (Claxton et al., 1986 Estle et al., 1987 Briddon et al., 1988). This is in agreement with the experimental observation that anomalous muonium is the most stable state for muons in diamond (Holzschuh et al., 1982). An expansion of the bond length by 42% is necessary. The bond center was found to be more stable than the interstitial muonium by s 1.9 eV. Displacements of the muon along directions perpendicular to the bond cost little energy (Estle et al., 1987). 

This simple treatment, formulated in a context of molecular bonding, was also what led Cox and Symons (1986) to propose the bond-center site as an explanation for anomalous muonium (Mu ). The location of the muon at the nodal plane of the nonbonding orbital explains the very small hyperfine coupling observed in pSR. Still, the muon is close to the electron, which occupies a nonbonding state on the neighboring semiconductor atoms. 

The charge density in a (110) plane for neutral H at the bond-center site in Si, as obtained from pseudopotential-density-functional calculations by Van de Walle et al. (1989), is shown in Fig. 7a. In the bond region most of the H-related charge is derived from levels buried in the valence band. It is also interesting to examine the spin density that results from a spin-polarized calculation, as described in Section II.2.d. The difference between spin-up and spin-down densities is displayed in Fig. 7b. It is clear... 

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

Results for hyperfine parameters for muonium at the bond-center site in Si are given in Table I. In elemental semiconductors, symmetry requires that the Is orbital does not couple to the antibonding combination of... 

Frequencies of the hydrogen stretching mode for H° at the bond-center site have been obtained from cluster calculations. Estreicher (1987) found the potential profile for displacements of H along the bond to be U-shaped and flat for small displacements (—0.1 A). Consequently, he found a very low vibrational frequency for such displacements ( that of single Si—H bonds). Other studies of the stretching mode have found 784 cm-1 (Deak et al., 1988) and 800 cm-1 (DeLeo et al., 1988). 

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