Anomalous 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. 

Note also the frequencies between 40 and 50 MHz observed in Si that are absent in quartz. This was the first observation of anomalous muonium (Mu ) in a semiconductor, and at the time of the discovery it was unexpected and unexplained (Brewer etal., 1973). In fact a cloud of controversy has surrounded Mu and its coexistence with Mu for almost 15 years. It isonly in the last two years that a consistent microscopic model of Mu has emerged. The lowest frequency line in Fig. 5, which occurs at the Larmor frequency of a bare muon, results from a diamagnetic center—Mu+ or Mu-. So far little is known about these muonium charge states. 

Anomalous Muonium (Mu ) a. Muon and 29Si Hyperfine Parameters... 

Anomalous muonium in silicon, and apparently also the AA9 hydrogen center, is stable because there is a large lattice relaxation of the two closest silicon neighbors to the muon or proton. This is the conclusion of theory,... 

In all group IV and group III-V crystals in which muonium has been seen, both normal and anomalous muonium occur, with the single exception of SiC. The tetrahedral location for interstitial muonium is metastable in diamond and very likely in unirradiated silicon just as it is in irradiated Si. However at present it is not possible to say whether Mu or Mu is the more stable in Ge, GaAs, and GaP. 

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. 

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. 

The evidence in favor of identification of anomalous muonium with the bond-center position can be considered convincing. The so-called vacancy-associated model (Sahoo et al., 1985, 1989), which had been proposed mainly on the basis of hyperfine calculations for clusters, shows distinct disagreement with the experimental results, which clearly establish that there are two equivalent Si neighbors along (111). 

Hoshino et al. (1989) have recently carried out spin-density-functional calculations for anomalous muonium in diamond. They used a Green s function formalism and a minimal basis set of localized orbitals and found hyperfine parameters in good agreement with experiment. 

From the discussion of location of hydrogen and muonium in the lattice, it is clear that the bond-center position is the lowest-energy site in many semiconductors. In GaAs and Si, this site has only recently been experimentally associated with anomalous muonium, which is relatively immobile (Kief et al., 1987, 1988). The agreement between theoretical results for hyperfine parameters (Van de Walle, 1990) and experiment allows an unambiguous identification of Mu with the bond center. Other models, such as the vacancy model proposed by Sahoo etal. (1985, 1989), are no longer considered acceptable candidates for Mu. ... 

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 ... 

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