Hyperfine interactions of muonium and hydrogen in semiconductors: Cluster calculations

The electronic structure of muonium (Mu) located at different interstitial sites of the silicon crystal is calculated by the complete neglect of differential overlap (CNDO) and intermediate neglect of differential overlap (INDO) methods. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “normal” (Mu′) and “anomalous” (Mu^*) muonium centers. It is shown that the most likely dynamic model for Mu′ is that in which neutral Mu diffuses rapidly in the silicon lattice, whereas for Mu^* it is the model wherein interstitial Mu is located at the bond-center site. A correlation is made between the characteristics of the hydrogen-bearing Si-AA9 center, recently observed by EPR in a silicon crystal, and those of Mu^*. The Si-AA9 center is shown to be a hydrogen-bearing paramagnetic analogue of the Mu^* center.     

Preliminary calculations confirming that anomalous muonium in diamond and silicon is bond-centered interstitial muonium

The model of anomalous muonium as bond-centered interstitial muonium has been examined by approximate ab-initio Hartree-Fock calculations in diamond and silicon and found to be in excellent agreement with experiment.     

Hyperfine interactions of muonium in alpha-quartz

We present the properties of muonium which are connected with the presence of the muonium quadrupole moment and discuss the results of experimental studies of the quadrupole interactions of muonium with the alpha-quartz lattice.     

Diffusion of muonium and hydrogen in diamond

Jump rates of muonium and hydrogen in diamond are calculated by quantum transition-state theory, based on the path-integral centroid formalism. This technique allows us to study the influence of vibrational mode quantization on the effective free-energy barriers DeltaF for impurity diffusion, which are renormalized with respect to the zero-temperature classical calculation. For the transition from a tetrahedral (T) site to a bond-center (BC) position, DeltaF is larger for hydrogen than for muonium, and the opposite happens for the transition BC-->T. The calculated effective barriers decrease for rising temperature, except for the muonium transition from T to BC sites. The calculated jump rates are in good agreement with available muon spin rotation data.     

Hyperfine splitting in positronium and muonium

We calculate corrections to the ground state hyperfine structure of relative order α² ln α^?1 in positronium and relative order $\text{(}\text{m}{}_{\mathrm{<mtext>e</mtext>}}\text{m}{}_{\mathrm{\mu }}\text{)α}{}^2\text{lnα}{}^{\mathrm{?1}}$ in muonium due to the exchange of virtual photons. Our results are in agreement with those of Lepage. Contributions arising from the Coulomb potential and from the exchange of one transverse photon along with any number of ladder Coulomb photons are discussed in detail. In treating the single transverse photon-multiple Coulomb photon exchanges, we sum the contributions involving different numbers of Coulomb photons and reexpand the resulting expression in terms of a quantity that is inherently smaller than the Coulomb potential in the non-relativistic region. The procedure enables us to take into account from the beginning important cancellations that occur between the various terms in an expansion in powers of the Coulomb potential. The techniques developed here may be useful in calculating higher order corrections.     

Hyperfine interactions in muonium-impurity complexes in silicon

The properties of paramagnetic complexes formed by muonium located near acceptor and donor impurities in silicon are calculated using the quantum chemical methods. The calculated data are compared to the experimentally observed characteristics of normal and anomalous muonium centers.     

Vacancy associated model for anomalous muonium in diamond,silicon and germanium

Through first-principles investigations on a number of models for anomalous muonium in diamond using the Unrestricted Hartree-Fock Cluster procedure, it is demonstrated that a muonium trapped near a double-positively charged vacancy is the most viable model for this center. This model is shown to successfully explain all the observed features of the hyperfine tensors A^⇉ in diamond, silicon and germanium, namely, oblateness, opposite signs of A_│ and A_┼ in diamond and same signs for silicon and germanium, the trend in the strengths of the hyperfine tensors from diamond to germanium and the negative sign for A_┼ in diamond.     

Equivalent states of muonium and implanted hydrogen in silicon (experiment)

Main experimental data on the hydrogen-like states with an anisotropic hyperfine structure forming in silicon single crystals in the implantation of high energy muons and protons are presented. The characteristics of the “anomalous” muonium (Mu^*) and hydrogen-containing silicon AA9 states studied by the muon spin rotation (μSR) and ESR techniques in silicon with a due inclusion of the isotope effect are shown to be similar, thus suggesting the existence of two equivalent structures in silicon, Mu^* and AA9, differing only in the mass of the paramagnetic center.     

Hyperfine splitting of muonium in SiO2 powder

The hyperfine splitting of Mu in evacuated SiO₂ powder has been measured over the temperature range 17–300 K using the two frequency method. Above 100 K it is consistent with the vacuum value (4463.3 MHz) indicating the Mu atoms are moving freely between the particle grains. At lower temperatures it drops rapidly to 4437±4 MHz at 17 K. The effect is attributed to thermal adsorption on the SiO₂ surface. Measurements were also made on an Ar coated powder between 7–62 K. The hyperfine splitting is consistent with the vacuum value over this range.     

Passivation of an Al acceptor in silicon by hydrogen or muonium

We report on calculations of the electric field gradient at the site of the Al nucleus in the Si-H-Al complex in silicon. As a model for the surroundings of the complex we used a cluster consisting of 43 silicon and one aluminum atoms. The geometry of this cluster was fully optimized at the Hartree-Fock level. To discuss the dependence of our results on the level of theory, we studied a subcluster of four silicon and one aluminum atoms at the Hartree-Fock and CASSCF level.     

Hydrogen and muonium in silicon

First principles calculations of the properties of hydrogen and muonium in silicon are presented. H⁺ and H⁻ are shown to have definite preferences for bond-centred and tetrahedral interstitial sites respectively whereas H⁰ (or a muon) is shown to be stable at two sites with almost equal energies, the bond-centred and antibonding sites. The structures of normal and isotropic muonium are discussed. In contrast to common belief the tetrahedral site is shown to be unstable with the muon moving spontaneously towards one of the neighbouring silicon atoms. The barrier to motion between equivalent antibonding sites is low suggesting that the normal muonium signal is isotropic because of motional averaging, not due to the symmetry of a well defined equilibrium site.     

Semi-empirical calculations of hydrogen defects in silicon

Calculations for hydrogen defect(s) in a monovacancy silicon cluster yield a stable position for this defect which: (a) does not saturate any of the silicon dangling bonds; and (b) contributes defect level(s) in the gap whose implications remain to be understood.