Electronic structure and dynamics of muonium in semiconductors

In this paper, a selection of recent results on muonium in semiconductors is presented. These are primarily taken from Si and GaAs and encompass the electronic structure of the diamagnetic centers, charge state cycling, spin‐exchange scattering and interconversion between muonium states. These experiments illustrate the power of μSR for investigating the behavior of muonium and, by analogy, the technologically relevant isolated hydrogen centers in semiconductors. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muonium defect centers in semiconductors

After a brief summary of the properties of the muonium defect centers observed in the elemental group IV semiconductors, the status of studies of muonium centers in semiconductors at the time of the last μSR conference in 1983 will be compared with what is currently known. With the introduction of new experimental techniques, such as high-transverse-field μSR and level-crossing spectroscopy, many new results are or soon will be available on muonium centers. These, combined with new theoretical studies, should lead to rapidly increased insight into a subject which has been both puzzling and resistant to clarification.     

Electronic structure, dynamics, and metastability of muonium in semiconductors

Muonium centers are light hydrogen-like centers formed when positive muons are stopped in crystalline semiconductors. Detailed information on the hyperfine structure, dynamics and metastability of muonium are obtained using a combination of muon spin rotation or relaxation, muon level-crossing resonance and related methods. The expected close similarity to hydrogen, especially with regard to electronic structure, is important since the equivalent information on isolated hydrogen is either less detailed or completely absent. There are also interesting differences between muonium and hydrogen. In particular muonium dynamics are expected to exhibit enhanced quantum mechanical effects since the muon has only 1/9th the proton mass. In this paper we review the current status of experiments.     

Field dependence of the longitudinal muon polarization for anomalous muonium

The constant muon polarization for anomalous muonium exhibits a peculiar field dependence which represents an easily measurable signature of anomalous muonium centers even in polycrystalline materials. Furthermore it can be used to extract information on the dynamical destruction of the state upon temperature variations and it might also be useful to investigate muonium in amorphous materials.This work has been partially supported by the Swiss National Science Foundation.     

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.     

Muonium in semiconductors: Recent experimental developments

Recent experiments covering a range of problems including the nuclear hyperfine structure of bond-centered muonium in diamond and GaP, charge-cycling reactions of muonium in Si at high temperatures, muonium state dynamics in Si probed by RF-SR, and endohedral muonium in semiconducting C₆₀ compounds, are discussed. These examples show that as traditionalSR techniques are continually being refined and new methods are being developed,SR is becoming an increasingly powerful tool to investigate the behavior of muonium and the in many respects analogous, and technologically relevant, hydrogen centers in semiconductors.     

Level crossing resonance in muonium-like systems

This paper describes the phenomenon of level crossing resonance (or avoided level crossing) encountered in paramagnetic systems involving a muon. Recent experiments on muonated radicals and muonium defect centers in semiconductors are reviewed which demonstrate how the technique provides detailed information on nuclear hyperfine structure, which is unresolvable with more standard techniques. The science implications are discussed.     

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.     

Recent advances in positive muon spin rotation; muonium as a probe of fullerenes

In non-metallic solids the positive muon often forms paramagnetic muonium centers which are characterized by the hyperfine interactions of the unpaired electron with the positive muon and with the surrounding nuclear spins. The static and fluctuating components of these hyperfine interactions provide information on local molecular dynamics and local electronic structure. Some recent results on C₆₀ and related compounds are presented to illustrate this.     

Influence of impurities on short range electron transport in GaAs

The influence of Cr impurities on muonium atom formation in GaAs has been studied using muon spin relaxation techniques with alternating electric fields. The results suggest that electron transport to and capture by the muon is suppressed by capture/scattering on intervening Cr centers. The length scale involved is estimated to be about 3x10(-6) cm. This offers an opportunity to study electron transport to positive centers in semiconductors on a microscopic scale.     

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.     

Electronic structure of the muonium center as a shallow donor in ZnO

The electronic structure and the location of muonium centers (Mu) in single-crystalline ZnO were determined for the first time. Two species of Mu centers with extremely small hyperfine parameters have been observed below 40 K. Both Mu centers have an axial-symmetric hyperfine structure along with a <0001> axis, indicating that they are located at the antibonding (AB(O, parallel )) and bond-center (BC( parallel )) sites. It is inferred from their small ionization energy ( approximately 6 and 50 meV) and hyperfine parameters ( approximately 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.     

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.     

Zero field isotropic Muonium Kubo — Toyabe relaxation functions

Static zero field Gaussian Kubo — Toyabe relaxation functions for muons in isotropic muonium atoms are presented. That is, as with diamagnetic muons, an average of the spin dynamics of a muon in an isolated isotropic ground state muonium atom is taken over an isotropic Gaussian continuous classical local random magnetic field distribution. This motion approximates the exact quantal spin dynamics generated by the dipole-dipole interactions between the muonium atom and the surrounding nuclear spins associated with the site at which the muonium atom has stopped. Expressions are derived for triplet muonium only since, in general, singlet muonium is not observed. For normal nuclear spins and ground state muonium, the resulting relaxation functions are identical to the standard diamagnetic function (except for a shift in the time scale).     

Rate constants for the reaction of muonium with aromatic compounds

Rate constants for the reaction of muonium with benzene in water, methanol and n-hexane and for the reaction of muonium with p-difluorobenzene, anilin, hexafluorobenzene and styrene are reported. All rate constants are below the calculated diffusion controlled limit. The activation energy for the reaction of muonium with benzene in n-hexane is very small, indicating the possibility of tunnelling by muonium.     

Electron irradiation effects on muonium states in silicon

Normal and anomalous muonium were studied in electron irradiated silicon. We found that the two muonium states behave very differently: For normal muonium, the relaxation rate increases if the sample is irradiated whereas it decreases for anomalous muonium. Possible explanations for these processes are discussed.     

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.     

Experimental confirmation of the predicted shallow donor hydrogen state in zinc oxide

We confirm the recent prediction that interstitial protium may act as a shallow donor in zinc oxide, by direct spectroscopic observation of its muonium counterpart. On implantation into ZnO, positive muons--chemically analogous to protons in this context--form paramagnetic centers below about 40 K. The muon-electron contact hyperfine interaction, as well as the temperature and activation energy for ionization, imply a shallow level. Similar results for the cadmium chalcogenides suggest that such shallow donor states are generic to the II-VI compounds. The donor level depths should serve as a guide for the electrical activity of interstitial hydrogen.     

The effect of radiation defects in silicon single crystal lattice on the characteristic states of the interstitial muonium atom

Radiation defects are shown experimentally to affect differently the normal and anomalous muonium states in silicon. This evidences essentially different mobilities of the two muonium states in the sample lattice.     

Muonium acoustic resonance

Theoretical consideration is given to the effect of ultrasonic oscillations on the spin polarization of the positive muon of muonium present in matter. The resonant action of the periodic acoustic perturbation on the muonium hyperfine structure levels is shown to result in characteristic oscillations and to modify the muon spin precession pattern considerably. The possibilities for experimental detection of the muonium acoustic resonance are discussed