Muonium structure

This paper is concerned with the structures of the simplest possible adducts of the Ceo and C70 fullerenes, namely the monohydrides, CmH and C H. These open shell species or radicals may be considered as the product of the addition of one atom of hydrogen or one of its isotopes, among which we include specifically the light pseudoisotope of hydrogen known as muonium. Mu = pfe. Although Ceo//has been observed [1], the stimulus for these calculations arose from the experiments on muon implantation in solid [2,3] and C70 [4]. 

Figure 3 The numbers at each site in the top half (above the dotted line connecting the extreme atoms to the left and right of the diagram) are the numbers of classical structures which can be constructed with hydrogen (muonium) attached to the position indicated and the unpaired electron at the indicated site. The corresponding numbers in the bottom half are the spin densities in atomic units from UHFAA calculations on the fully optimised geometry of CeoMu using an ST0-3G basis set within the ROHF method.

Apart from type 62, which is only slowly convergent to the optimised geometry, the other centres are well described by the ROHF method. Polyhedral views of the three type a structures are shown in Fig. 6. These all illustrate the change of hybridisation at the point of muonium attachment and at the adjacent carbon atom where the unpaired electron is effectively localised as expected from addition to an alkene. The bi and c defects (Fig. 7) are quite different. The expected hybridisation change to sp is clearly present for the atom bonded to muonium, but other significant distortions are not obvious. This is consistent with the prediction from resonance theory (Fig. 8) that the unpaired electron for these structures is delocalised over a large number of centres. 

Figure 8 Measure of delocalisation of each defect type predicted by resonance theory. The loops enclose centres which have numbers of classical structures larger than. 74 times the greatest number in the type. The cut-off point for type bi (or type 63) centres is particularly arbitrary since the delocalisation is spread around the equator. The small circles are the point of muonium attachment. The dotted circle is coincident with the equator of Cra-...

No indication of a thermal conversion of Mu to Mu or the reverse has been obtained for GaAs or GaP. Yet the Mu/Mu system must be metastable since all evidence indicates that both are isolated neutral interstitials. However it is not known which structure is metastable and which is stable. This may be difficult to determine since the muonium dynamics (Patterson, 1988) suggest that in GaAs (and Ge) Mu and Mu may ionize at a temperature lower than that at which the conversion could be expected. 

The close correspondence between the properties of Mu in Si as determined by /u,SR and pLCR and those for the AA9 center produced by implanting hydrogen in silicon shows that Mu in silicon and the AA9 center are isostructural and in fact almost identical. They are neutral isolated bond-centered interstitials. Numerous theoretical studies support this conclusion. The observation of such similar centers for muonium and hydrogen supports the generalization that hydrogen analogs of many of the muonium centers exist. Of course, this assumes that the effects of the larger zero-point vibration of the muon relative to the proton do not make a major contribution to structural differences. The p-SR experiments, reinforced by theory, demonstrate that another structure also exists for muonium in silicon, called normal muonium or Mu. This structure is metastable and almost certainly is isolated neutral muonium at a tetrahedral interstitial site. 

Electronic properties generally do not depend on mass or lifetime therefore the adiabatic total-energy surfaces and also the electronic structure of muonium should be very similar to that of hydrogen. However, its dynamical behavior (zero-point motion, vibrational frequencies, diffusion,. ..) may differ from that of H because of the difference in mass. Most of the results discussed in this chapter will be applicable to both hydrogen and muonium (although for convenience I will usually refer to hydrogen). Dynamical features that may be distinct for the hydrogen vs. muonium cases will be discussed in Parts VI and VII, respectively. 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

The defect levels discussed so far represent the most dramatic effects of the presence of the impurity. The levels introducted in the gap region are schematically illustrated in Fig. 6. However, these are by no means the only changes to the band structure induced by the presence of H. Important changes indeed occur down to energies far below the energy gap, as found by Katayama-Yoshida and Shindo (1985), who investigated the effect on the density of states of introducing H (or muonium) at T in Si. 

During the past few years, experiment and theory have converged to a number of explicit answers regarding the location and electronic structure of hydrogen or muonium in semiconductors. Anomalous muonium, which had remained a puzzle for many years, now appears to be well understood in terms of the bond-center model. It is, oddly enough, normal muonium that still seems to pose some unanswered questions is it located at T itself or does it tunnel among various sites How does its rapid diffusion proceed ... 

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