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^*.     

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.     

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.     

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.     

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.     

Comments on the stability of charge states and locations for hydrogen and muonium in semiconductors

This paper brings together some current concepts concerning hydrogen states in semiconductors (illustrated with reference to silicon but quite generally applicable) and highlight certain findings of recent quantum electronic structure calculations for defect centres involving hydrogen and its isotopes. As regards muonium, the situation which held in the early μSR literature [1] is entirely reversed: the location and structure of Mu^* are now well established [2], whereas the precise location and the nature of the metastability of Mu′ have become open questions! In fact, neither state is stable in the presence of other electrically active impurities, which undoubtedly accounts for the difficulty in detecting paramagnetic protium. The implications for the interpretation of existing data, and for various possible future experiments, are examined.     

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.     

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.     

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.     

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.     

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.     

Muon spin resonance and repolarization in amorphous silicon monoxide (a-SiO)

Studies of the muonium fractions in the amorphous oxide a-SiO have been carried out by RF resonance at TRIUMF, Canada and LF repolarization techniques at RAL, U.K. The resonance measurements confirm the presence of the interstitial Mu centre in this intermediate oxide of silicon. Analysis of the data gathered at RAL, using a recently-developed fitting technique, reveals that the Mu^* state is present here as well, but with lower relative fractions than in a-Si. However, as in the latter material, but in contrast to c-Si, this bond-centre species appears to be stable up to room temperature.     

Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Muonium centers in the alkali halides

Muonium centers (Mu) in single crystals and powdered alkali halides have been studied using the high-timing-resolution transverse field μSR technique. Mu has been observed and its hyperfine parameter (HF) determined inevery alkali halide. For the rocksalt alkali halides, the HF parameter A_μ shows a systematic dependence on the host lattice constant. A comparison of the Mu HF parameter with hydrogen ESR data suggests that the Mu center is the muonic analogue of the interstitial hydrogenH _i ⁰ -center. The rate of Mu diffusion can be deduced from the motional narrowing of the nuclear hyperfine interaction. KBr shows two different Mu states, a low-temperatureMu ^I -state and a high-temperatureMu ^II -state.     

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.     

Quadrupole moment of muonium and hyperfine structure of muonium levels in silicon

It is shown that experimental data on Mu¹ in silicon are most satisfactorily described by the uniaxial symmetric spin hamiltonian which means muonium displacement from the octa-cell 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.     

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.