Mu to Mu* transition in electron irradiated silicon

A transition from normal muonium (Mu) to anomalous muonium (Mu^*) is observed in electron irradiated silicon. It is suggested that the transformation is induced by the strain field of the defect and takes place some distance away from the defect. The experiment was performed at 15 K.     

A site determination for Mu* and its implications

A chain of arguments is made which draws on the experimental results ofSR, muon-pion-decay channeling, and³He channeling in deuterium-implanted silicon and which leads to a plausible site for the anomalous muonium atom Mu^* in the group-IV semiconductors. I propose that Mu^* in silicon occupies the deuterium position approximately 1.6 Å from a Si atom in a [111] anti-bonding direction and that analogous sites are occupied in Ge and diamond. Some possible implications of this site assignment are discussed.     

Low-field anomalous muonium depolarization in isotopically enriched germanium

The depolarization rate of anomalous muonium, Mu^*, in germanium isotopically enriched in⁷⁴Ge (I=0) was measured as a function of field. The concentration of⁷³Ge (I=9/2) was about 9 times less than natural abundance. The depolarization rate at 10 K in this isotopically enriched crystal for both lines of those Mu^* centers whose symmetry axes make an angle of 90° to the field is less than 1sec^–1 at all fields down to the lowest one measured, 14.5 gauss. This is in sharp contrast to the wide lines reported at low field in germanium having natural isotopic abundance. The spectrum of Mu^* in the isotopically enriched Ge crystal was also seen at zero field. These results confirm that the increased depolarization rate for Mu^* at low fields arises from unresolved nuclear hyperfine structure. The depolarization rates observed were consistent with an average hyperfine interaction with a single⁷³Ge nucleus of 2.5 MHz, a value requiring nearly 1% of the spin density to be on a typical atom.     

Muon spin rotation experiments on a silicon crystal doped with13C

A crystal of silicon doped with carbon enriched to 60.1% in¹³C was studied bySR to determine whether¹³C hyperfine structure could be observed in the frequency spectra of normal muonium, Mu, or anomalous muonium, Mu^*. Measurements at 100 G and 100 K with 40 million good events yielded extremely weak Mu^* signals and no Mu in these data or in measurements at 10 G and 150 K. Transmission electron micrographs of this sample contained small regions showing strain contrast and structure factor contrast. Annealing the sample at 900°C for 84 hours led to featureless electromicrographs. SubsequentSR measurements yielded a strong Mu^* signal but still no Mu. No broadening due to¹³C was observed.     

Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu^* has been thermally ionized.     

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.     

Muonium centers in heavily n‐doped Si under illumination: Evidence for Mu–hole interaction

A small fraction of implanted muons exists as a paramagnetic state (presumably Mu_BC ⁰, muonium at the Si—Si bond center) in heavily Sb‐doped Si (n-type, [Sb]\ \simeq 10¹⁸\ cm^–3). The paramagnetic state is susceptible to illumination both at 10–20 K and 290 K, providing evidence that holes (minority carriers) play an important role in determining the dynamical properties of muonium centers, where change may occur via a process Mu_BC ⁰+ h⁺\to Mu_BC ⁺ followed by charge exchange reaction (or transition Mu⁺ _BC+ e⁻→ Mu⁰ _T). This revised version was published online in August 2006 with corrections to the Cover Date.     

Repolarization studies in amorphous and polycrystalline silicon

A procedure has been developed to extract qualitative and quantitative information on the muonium fractions, in particular the Mu^* fraction, in polycrystalline and amorphous materials from their longitudinal field repolarization curves. Preliminary results for amorphous silicon suggests that both the Mu^* and Mu^* fractions here are generally lower than in crystalline silicon at temperatures below 200K, but the Mu^* fraction may survive to room temperature in this disordered host.     

Quantum diffusion of muonium in GaAs with shallow donor impurities

Muonium diffusion was studied in silicon doped GaAs by means of muon spin relaxation in a longitudinal field. The muonium hopping frequencies in two samples with n-type carrier concentration of 10¹²¹⁴ cm^–3 and 8×10¹⁶ cm^–3 were deduced by using the model of fluctuating effective local fields. We found that muonium diffusion is strongly influenced by the dilute Si impurity in both samples in the temperature range belowT 30K. The absence of such a behavior in compensated high-resistivity samples indicates that the presence of shallow donor levels plays a decisive role for the tunneling diffusion of muonium in semiconductors.We would like to thank Drs. N.V. Prokof'ev and R.F. Kiefl for helpful discussion.After submission of this paper it was revealed by the field dependence of the LF relaxation rate that the observed relaxation rate in GaAs:Si-B is due to spin-exchange interaction of Mu^*.     

Investigation of muon states in silicon and germanium by field-quenching and RFμSR

The temperature dependence of the three states of positive muons in the semiconductors with diamond structure ( ⁺ in diamagnetic states ^d and paramagnetic muonium Mu and Mu^*) have been investigated on six Si (pure, B and P doped) and four Ge (ultrapure, CZ-grown undoped, Ga and Sb doped) single crystals by longitudinal field-quenching and radio-frequency ⁺SR. Clear evidence for the transition Mu^{* d} is found. The influence of light-induced charge-carriers is shown to be quite different in p- and n-type material.The work has been supported by the Bundesministerium für Forschung und Technologie in Bonn, Germany, under contract no. 03-SE3STU.     

Mu centers in crystalline Ge under illumination

A slow conversion to a diamagnetic state has been observed for muonium centers at the tetrahedral interstitial site (Mu⁰ _T) in dark Ge at low temperatures. While the conversion process is affected by illumination, no effect of illumination upon the initial (Mu⁰ _T) centers themselves was observed at 10 K. This is in marked contrast with the case of (Mu⁰ _T) centers in Si where strong interaction with photo‐induced carriers is observed, suggesting that the electronic level associated with (Mu⁰ _T) state in Ge is not located in the energy gap. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonium states in semiconductor crystals: Quantum-chemical calculations

The electronic structure of muonium (Mu) located at the bond-centered sites of the silicon and diamond crystals is calculated by the intermediate neglect of differential overlap method. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared to the experimental properties of “anomalous” muonium Mu^*. It is shown that the properties of Mu located at the bond-centered sites of the Si and C lattices are in qualitative agreement with the observed properties of Mu^*.     

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ ⁺ e⁻). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu^* state in diamond and silicon.     

Final states in Si and GaAs via RF μSR spectroscopy

The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu^* states at any temperature. However, our results on the diamagnetic final state (μ _f ⁺ ) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu^* and Mu. We observe a full μ _f ⁺ fraction at 317 K when the Mu relaxation rate is above 10 μs⁻¹. GaAs differs from the situation in Si in that we observed only a partial conversion of Mu^* and Mu to a μ⁺ final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively.     

Muonium dynamics in transparent conducting oxides

The motional and electrical properties of positively charged muonium (Mu⁺)$({\mathrm{Mu}}^{+})$ centers in single crystal β-Ga₂O₃$\mathrm{\beta }\mathrm{-}{\mathrm{Ga}}_2{\mathrm{O}}_3$ are investigated via zero field muon spin relaxation (ZF-MuSR). Below room temperature we find two distinct shallow muonium centers with ionization energies of 7 and 16 meV. Above room temperature, at least three different Mu⁺ signals are resolved; two of these are metastable while the third shows characteristics of a stable ground state. As the temperature is elevated, metastable centers undergo several transitions. We obtain the relevant barrier energies associated with these site-change transitions. By 700 K, most muons occupy the mobile ground state, and an activation energy of about 1.65 eV is inferred for Mu⁺ diffusion from the hop rates obtained for this state.     

RF-μSR study of muonium charge states and dynamics in Si

The radio frequencySR technique developed at TRIUMF was used to measure the temperature dependence of the diamagnetic muon, Mu, and Mu^* amplitudes in silicon between 10 K and 500 K. Six samples doped with phosphorus (n-type) and boron (p-type) in the concentration range 10¹¹ to 10¹⁵ cm^–3 were studied. In pure Si a very good fit over the whole temperature range is obtained from a model that includes the ionization of Mu^* and Mu to a bond centered ⁺ followed at high temperature by charge exchange involving Mu.     

Kinetic processes of muonium formation by non-thermalized electrons in the spur model

An approximate analytical solution is obtained for the kinetic equation for electrons in the field of a Coulomb centre formed by a muon in the end of its track. It is shown that thermalization times and 2> could differ by several orders of magnitude, depending on the behaviour of transport cross sections. The fraction of non-thermalized electrons returning to the muon and forming muonium (P _Mu ) depends on pressure and temperature. Therefore,SR experiments give us an opportunity to obtain information on the distribution function of track electrons.     

Diffusion, trapping, and relaxation of Mu+ and Mu- in heavily‐doped GaAs

The diamagnetic muonium states in heavily doped GaAs are investigated with a combination of transverse‐field and longitudinal‐field μSR techniques. In metallic n‐type GaAs, formation of Mu^- occurs because of the high Fermi energy. This analog of the hydride ion (H^-) is located in a T_Ga interstice where it is essentially immobile up to about 500 K. At higher temperatures, Mu_T acts as an electron–hole recombination center. In p‐type GaAs, Mu⁺ traps at two different sites, one at low temperatures and a second at higher temperatures after detrapping from the first. This revised version was published online in August 2006 with corrections to the Cover Date.     

A comparative study of muonium states in crystalline and amorphous hydrogenated silicon

A study of muons implanted into amorphous hydrogenated silicon (a-Si: H), using both transverse and longitudinal field μSR, is presented. Particular use is made of the muon repolarization curves in longitudinal fields. By comparison with the results of similar measurements on polycrystalline silicon, both the diamagnetic and Mu^* fractions are found to be substantially increased. We postulate that weak strained bonds in the amorphous structure are responsible. Little evidence has been found from longitudinal field measurements for isotropic muonium Mu', and a transverse field experiment on a-Si: D suggests that this state might not exist in the amorphous material.