Normal muonium

Two types of species have been detected in the /rSR spectrum of Ceo- One shows an unreacted or meta-stable muonium state which may well correspond to an internal state, muonium is trapped inside the cage Mu Ceo in the current notation [2]. This may be compared with normal muonium (Mu ) in diamond and many other elemental and compound semi-conductors, where the trapping site is in one of the cavities of tetrahedral symmetry. This state of CeoMu is not discussed here, but it does exhibit all the characteristics expected of the internal chemistry of Ceo-The anomalous muonium state. Mu, observed in semi-conductors and generally accepted to arise from muonium being trapped within one of the chemical bonds of the crystal, is unknown in molecules [5,6]. The constraints of the crystal lattice are necessary for the bond-centred state to be stable. 

THE LARGE SPIN DENSITIES FOR NORMAL MUONIUM IN DIAMOND AND THE NEAREST-NEIGHBOR... 

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. 

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. 

Using the approach described in the previous section, Van de Walle (1990) also calculated the isotropic hyperfine constant for muonium at T in Si. The calculated value for iK0)]x/ experimental result (0.45) for normal muonium in Si. Motional averaging slightly lowers the theoretical value, bringing it in even closer agreement with experiment. 

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

But one can ask the question why normal muonium is observed at all if the global energy minimum (i.e., the stable site) is really at the bond center (anomalous muonium). On the time scale of the muon lifetime, relaxations of the Si atoms may be sufficiently slow to effectively trap the muon in the low-density regions of the crystal, where relaxation of the host atoms is... 

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 ... 

---