Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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^*.     

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.     

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.     

Hyperfine interactions of muonium and hydrogen in silicon and diamond: Quantum chemical calculations

The electronic structure of a hydrogen-like atom located at interstitial sites of the silicon and diamond crystals is calculated by the intermediate neglect of differential overlap (INDO) method. Calculations of the electronic g- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “anomalous” muonium and hydrogen centers. It is shown that the most likely model for these centers in silicon and diamond is that in which interstitial neutral hydrogen-like atom locates at the bond-center site.     

Self-consistent field cluster study of hyperfine properties of normal and anomalous muonium in elemental semiconductors

Using the Unrestricted Hartree Fock (UHF) Cluster Procedure, it is shown that for the normal muonium (Mu) center, the tetrahedral site is the most favorable in the two systems diamond and silicon investigated, while for the anomalous muonium (Mu^*) center, a site displaced in the <111> direction with respect to a vacancy in a double-positively charged environment is the appropriate one for all three elemental semiconductors. Using our calculated electronic wave-functions, one is able to explain all features of the observed hyperfine properties of both centers and, in a number of cases, obtain good quantitative agreement with experiment.     

The transition from Mu to Mu* in diamond

Evidence is presented for a transition from the isotropic muonium state (Mu) to the [111] axially symmetric anomalous muonium state (Mu^*) in diamond. Amplitude measurements for Mu^* in a powder in zero field and with a single crystal oriented in a magnetic field indicate that such a transition occurs with a temperature-dependent rate(T) and that the electron polarization is conserved during the transition. The possibility of determining the absolute sign of the Mu^* hyperfine parameters is discussed.     

Quantum diffusion of muonium in insulators

In this paper we review our recent experiments conducted at TRIUMF on muonium diffusion in alkali halides. First, the technique of longitudinal-field muonium spin relaxation (T ₁) due to nuclear hyperfine interaction, an indispensabletour de force for the present work. is described. It is demonstrated in KCl that the technique provides spectacular sensitivity for muonium diffusion as well as determining the average nuclear hyperfine coupling constant. The muonium hop rate shows a minimum (T ^*≃80 K) and steep increase with decreasing temperature. The result is compared with the current theory of quantum diffusion in non-metallic crystals. A few more sets of new data may be presented for other alkali halides. In addition, we show that muonium forms a delocalized state in NaCl as evidenced by a large change of the average nuclear hyperfine parameter. Related topics of local tunneling system may be briefly reviewed.     

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.     

Electronic structure and hyperfine interaction of muonium in semi-conductors

The Unrestricted Hartree-Fock self-consistent field cluster procedure is being utilized for first-principle investigations of the electronic structures and hyperfine interactions in normal and anomalous muonium states in semi-conductors. Our results for the total energy for the normal muonium state for a twenty-seven atom cluster in diamond, including the muonium and its neighboring atoms, show a minimum at the tetrahedral site and a maximum at the hexagonal site indicating that normal muonium is located in the tetrahedral region and avoids the hexagonal region. Using the calculated spin-density as a function of the position of muonium and carrying out averaging over the vibrational motion of the muon governed by the total energy curve obtained from our work, we have derived a muon hyperfine constant which is about 75% of that in free muonium, in good agreement with experiment. The natures of the total energy and spindensity curves permit us to draw conclusions regarding the origin of the observed trend in the hyperfine constants for normal muonium in diamond, silicon and germanium. The UHF cluster procedure is also applied to study a model of a muon in a positively charged environment for the anomalous muonium center in diamond. This model leads to a hyperfine interaction tensor with the observed feature of strong anisotropy but significantly weaker than experiment. The results obtained for this model indicate the importance for the anomalous muonium state with its relatively weak hyperfine interaction, of exchange polarization effects inherent in the UHF procedure.     

MSR Studies in the Progress Towards Diamond Electronics

The recent development of device quality synthetic diamond dramatically increases the potential of diamond as a wide band gap semiconductor. A remaining obstacle is the lack of shallow n-type dopants. Molecular dopant systems have been shown theoretically to lead to the shallowing of levels in the band gap. Some of these systems involve defect-hydrogen complexes. This, and other phenomena, motivate the study of the chemistry and dynamics of hydrogen in diamond. Much information on this topic has been obtained from Muon Spin Rotation (MSR) experiments. These experiments view the muonium (Mu ≡ μ⁺ e ⁻) atom as a light chemical analogue of hydrogen. Data on isolated muonium in diamond is reviewed, and evidence on formation of N-Mu-N (a shallow dopant candidate), the trapping of Mu at B-dopants, and fast quantum diffusion of muonium are discussed.     

Theoretical Investigation of Muon and Muonium Trapping and Hyperfine Interactions in the Chemical Ferromagnet p-NPNN (β-phase)

The trapping sites for muon and muonium in β-phase ferromagnetic p-NPNN have been determined by the first-principles Unrestricted Hartree–Fock procedure. Four trapping sites are found for the muon near the two nitrogen and two oxygen atoms of the two NO groups. For the singlet state of trapped muonium, two trapping sites are found near the two oxygens of two NO groups and for the triplet state two trapping sites are found near the two oxygens of the NO₂ group. The observed μSR signal at zero field with frequency 2.1 MHz is assigned to the singlet muonium sites near the two oxygens of the two NO groups and the high frequency signal ascribed to an isotropic hyperfine constant of 400 MHz is assigned to the two trapped muon sites near the two nitrogen atoms of the two NO groups. This revised version was published online in September 2006 with corrections to the Cover Date.     

Comparative Theoretical Study of Hyperfine Interactions of Muonium in A- and B-Form DNA

Muon Spin Relaxation (μSR) experiments in A- and B-form DNA have shown evidence for an enhanced electron mobility in the more closely-packed A-form. Besides dynamic effects (electronic diffusion) that could cause the observed difference in muon spin relaxation, one should also carefully examine the difference in the strengths of the hyperfine interactions of the muon (μ ⁺) with the moving electron in the two forms of DNA, since this could contribute to the observed difference in the muon spin relaxation rates as well. We have therefore investigated the (static) trapping properties of muon and muonium (μ ⁺ e ⁻) in A-form and B-form DNA from first-principles with the aim to understand how the different structural geometries of A- and B-form DNA can influence the hyperfine interaction of trapped muonium.     

Shallow-Donor Hydrogen-Like Impurities in ZnO Studied by MuSR

Two species of Mu centers with extremely small hyperfine parameters have been observed in single crystalline ZnO below 40 K. Both Mu centers have an axial symmetric hyperfine structure along with the [0001] axis, indicating that they are located at AB_O,∥ and BC_∥ sites. It is inferred from their small ionization energy (≃6 meV and 50 meV) and hyperfine parameters (∼10⁻⁴ times the vacuum value) that these centers behave as shallow donors, strongly suggesting that hydrogen is one of the primary origins of n type conductivity in as-grown ZnO. This revised version was published online in September 2006 with corrections to the Cover Date.     

Muonium states in zincblende-structured compounds

The authors present a list of results of μSR experiments in materials with the diamond and zincblende structure. Besides the muonium hyperfine parameters, additional information is tabulated: the formation probability for the different muon states, the highest temperatures at which muonium states have been observed and the types of transitions found to occur between these states. The muonium hyperfine parameters show a linear rise as a function of host ionicity from Ge to GaAs to ZnSe followed by a sharp drop to CuBr.     

Quantum diffusion of muonium in GaAs

The diffusion rate of muonium in the III–V compound semiconductor GaAs has been determined from measurements of muon spinT ₁ relaxation induced by motion in the presence of nuclear hyperfine interactions. It is shown for the first time in a semiconductor that (a) there is a crossover of the transport mechanism at about 90 K from stochastic to zero-phonon hopping, as evidenced by a steep rise in the hop rate at lower temperatures, and that (b) the muonium diffuses at the hop rate of 10¹⁰ s⁻¹ (corresponding diffusion constantD≈10⁻⁶ cm²s⁻¹) at lower temperatures as well as at room temperature.     

Study of condensed nitrogen by μSR method

The temperature dependences of parameters of the muon spin relaxation in liquid and crystalline nitrogen have been studied. It has been established that in condensed nitrogen there takes place a fast depolarization of muons. An anomalous behaviour of the amplitude and phase of muon precession is found in the vicinity of the orientation phase transition in solid nitrogen. It has been shown that muon spin relaxation parameters in nitrogen do not change at reduction of the oxygen impurity content from 0.7·10⁻⁴ to 10⁻⁶. The fast depolarization of muons in condensed nitrogen is apparently due to the formation of muonium atoms. To explain the phenomena observed, a model of the muonium chemical reaction is proposed. The initial phase of the muon precession has been measured as a function of the perpendicular magnetic field to determine the state of short-lived muonium in nitrogen. It has been determined that muonium in nitrogen is in an excited state. Consideration of the nuclear hyperfine interaction of muonium in condensed nitrogen makes it possible to give a qualitative explanation for the temperature dependence of the initial amplitude of the muon precession.     

Muon/Muonium in an Isotopically Pure 13C Diamond

A preliminary study of the diamagnetic (μ_d) and the paramagnetic (Mu _T ) states in a synthetic ¹³C diamond has been performed using the Transverse Field Muon Spin Rotation method. This system could be used to verify the quantum diffusion behaviour observed before, however, with a more reliable extraction of the hopping rate. The results were obtained in an applied magnetic field of 7.5 mT and at sample temperatures of 10 K, 100 K and 200 K. The prompt fraction, f, of the μ_d state remains constant at 22(5)% in the range 10–200 K; that of the Mu _T state increases from 53(10)% at 10 K to 78(10)% at 200 K. The fractions of the two states add to 100% at 200 K, suggesting non-population of the bond-centred state, Mu_BC, which is often observed in other diamond samples. The μ_d state has a spin relaxation rate of 0.20(5) μs⁻¹, in contrast to the zero value obtained in type II diamond samples. This indicates appreciable interaction of the μ_d state with the ¹³C atoms. The Mu _T state has a large spin relaxation rate ranging from 3.0(5) μs⁻¹ at 10 K to 7.0(5) μs⁻¹ at 200 K, consistent with values obtained in diamond samples with defects. This work is part of ongoing studies of muon/muonium-defect interactions in diamonds. This revised version was published online in September 2006 with corrections to the Cover Date.     

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.