Muonium Defect Research Articles

Muonium in Sulphur: μSR's Oldest Puzzle

New level–crossing resonance data shows the muonium defect centre in solid sulphur to have axial symmetry with huge dipolar anisotropy at low cryogenic temperatures. Above 100K,the two principal values of the hyperfine tensor fall dramaticallyand pro rata, both apparently collapsingto zeroatthe melting point. Thefallis accompaniedby the onset of muon spin–lattice relaxation, visible on the microsecond timescale with low–field rates peaking around room temperature. In conjuction with old zero–field data, the low–T hyperfine parameters are determined accurately. New supercell density–functional calculations suggest their assignment to muonium at a bond–centre (BC) site in a closed–ring S8Mu BC complex. The striking decrease of time–average parameters and the appearance of fluctuations causing relaxation are attributed to a dynamic equilibrium or chemical exchange with neutral configurations having much lower hyperfine coupling, accessed by small cyclic displacements from the BC site. Time–average occupancy of this site falls with temperature and vanishes at the melting point.

Motion of positively charged muonium in ZnO

We report on a study of the motional characteristics of positively charged muonium defect centers in ZnO as an analog for H+ behavior. Muon spin depolarization measurements at zero applied magnetic field were completed from 20K to 400K, with preliminary results to 750K. Results at the lower temperatures imply that Mu+ occupied two sites, and indicate local motion as thermally assisted tunneling with a characteristic energy of ∼60meV, as well as a site change transition above 200K with barrier energy ∼440meV. Based on theoretical results, we have tentatively assigned these features to tunneling among three equivalent oxygen anti-bonding sites (AB⊥) and a transition to a lower-energy bond-centered site (BC‖) oriented along the c-axis. Preliminary fits suggest that global diffusion of muonium occurs above 400K, with a diffusion barrier energy of ∼0.7eV.

First-principles calculation of parameters of electron paramagnetic resonance spectroscopy in solids

The hyperfine A-tensor and Zeeman g-tensor parameterize the interaction of an 'effective' electron spin with the magnetic field due to the nuclear spin and the homogeneous external magnetic field, respectively. The A- and g-tensors are the quantities of primary interest in electron paramagnetic resonance (EPR) spectroscopy. In this paper, we review our work [E.S. Kadantsev, T. Ziegler, J. Phys. Chem. A 2008, 112, 4521; E. S. Kadantsev, T. Ziegler, J. Phys. Chem. A 2009, 113, 1327] on the calculation of these EPR parameters under periodic boundary conditions (PBC) from first-principles. Our methodology is based on the Kohn-Sham DFT (KS DFT), explicit usage of Bloch basis set made up of numerical and Slater-type atomic orbitals (NAOs/STOs), and is implemented in the 'full potential' program BAND. Our implementation does not rely on the frozen core approximation. The NAOs/STOs basis is well suited for the accurate representation of the electron density near the nuclei, a prerequisite for the calculation of highly accurate hyperfine parameters. In the case of g-tensor, our implementation is based on the method of Van Lenthe et al. [E. van Lenthe, P. E. S. Wormer, A. van der Avoird, J. Chem. Phys. 1997, 107, 2488] in which the spin-orbital coupling is taken into account variationally. We demonstrate the viability of our scheme by calculating EPR parameters of paramagnetic defects in solids. We consider the A-tensor of 'normal' and 'anomalous' muonium defect in IIIA-VA semiconductors as well as the S2 anion radical in KCl host crystal lattice.

Hyperfine spectroscopy and characterization of muonium in ZnGeP2

In this contribution, we report the initial observation of neutral muonium defect centers in ZnGeP2. The spin-precession frequencies in a 4.0 T field yield a zero-temperature hyperfine constant of ~1965 MHz for the promptly formed Mu0 state. Subsequently, we performed T1−1 longitudinal depolarization measurements in low magnetic fields. Decoupling curves show a different anisotropic Mu0 with A2=3185 MHz and D=374 MHz, where D is the dipolar contribution. The relaxation rates suggest rapid diffusion of Mu0, most likely via quantum tunneling below 80 K and by thermally activated hops above 100 K. We have determined the ionization energy to be roughly 200 meV. We present our preliminary evaluation of the motion or site transition dynamics in addition to hyperfine characterization of the neutral muonium centers observed in ZnGeP2.

Energies for muonium defect levels in semiconductors

We have determined the ionization energies for Mu 0 centers in several semiconductor materials to locate the thermodynamic donor and acceptor levels for muonium with respect to the conduction and valence band edges. For Si, Ge, GaAs, and GaP the bond-centered (BC) donor level lies above the T-site acceptor level, verifying the negative-U character of muonium impurities. The midpoint between the acceptor and donor levels lies at a common energy for these materials to within the experimental uncertainties when using the theoretical band alignments. Mu defect levels can be assigned for ZnSe and 6H-SiC which match this result. Experimental data for muonium are compared to existing experimental results and predictions for the analogous hydrogen defect centers.

Implementation of a Density Functional Theory-Based Method for the Calculation of the Hyperfine A-tensor in Periodic Systems with the Use of Numerical and Slater Type Atomic Orbitals: Application to Paramagnetic Defects

The A-tensor parameterizes the "hyperfine" interaction of an "effective" electronic spin with the magnetic field due to the nuclear spin as monitored in an electron paramagnetic resonance (EPR) experiment. In this account, we describe an implementation for the calculation of the A-tensor in systems with translational invariance based on the Kohn-Sham form of density functional theory (KS DFT). The method is implemented in the periodic program BAND, where the Bloch states are expanded in the basis of numerical and Slater-type atomic orbitals (NAOs/STOs). This basis is well-suited for the accurate representation of the electron density near the nuclei, a prerequisite for the calculation of highly accurate hyperfine parameters. Our implementation does not rely on the frozen core approximation tacitly assumed in the pseudopotential schemes. The implementation is validated by performing calculations on the A-tensor for small atoms and molecules within the supercell approach as well as for paramagnetic defects in solids. In particular, we consider the A-tensor of "normal" and "anomalous" muonium defects in diamond and of the hydrogen cyanide anion radical HCN(-) in a KCl host crystal lattice.

Static and Intermittent Hyperfine Coupling for the Muoniated Radical in Tellurium

The hyperfine constant for muonium defect centres in elemental tellurium, measured spectroscopically at low temperature, corresponds to 7% of the free-atom value. The centres are tentatively identified as the diatomic species TeMu, analogous to the hydroxyl radical, OH. Their spectrum disappears as the centres ionize around 80 K but the muon spin response indicates that the same centres form and reionise, rapidly and repeatedly, above 200 K. The capture and loss of charge carriers provide a model for the electrical activity of hydrogen impurity in this low-gap semiconductor.

Diffusion and trapping of Mu in the III–V nitrides

Sites and dynamics obtained for muonium (Mu) defect centres provide a good experimental modelfor the behaviour of the equivalent hydrogen impurities. We discuss the dynamic propertiesof Mu centres in the III–V nitrides focusing on features common to the three materials.Muon spin depolarization data in zero magnetic field provide motional dynamics for theMu+ and Mu− charge states and field dependent longitudinal relaxation rates probe motion ofMu0 centres. The data also show dynamics associated with metastable locations, either intrinsicto the wurtzite structure or defect related, including trapping and release transitions. Ageneral picture of the behaviour of H in the III–V nitrides is developed from thesemeasurements for comparison to theoretical results.

Trapping of mobile Mu centers in single crystal AlN

We have investigated muonium (Mu) defect centers in single crystal AlN as an analog for atomic hydrogen impurities. A nitrogen-related muon level-crossing resonance is associated with a static center formed by trapping of a mobile Mu impurity at another defect. This trapped Mu is released above 800K. Muon spin depolarization data imply that both Mu0 and ground-state Mu+ centers are mobile. Strong correlations between growth of the trapped Mu resonance and Mu0 motion and transformation rates above 400K imply that Mu0 is the more likely precursor in that region.

Muonium (hydrogen) defect centers in indium nitride

Recent muon spin-precession experiments confirmed that muonium, a light hydrogen isotope, forms a shallow donor in InN. Depolarization measurements in zero-magnetic field are in agreement and show more than one positively charged center. Below 350K, one Mu+ signal has a depolarization function typical of a static center, while a second relaxes more weakly with the characteristics of slow tunneling motion. In combination, spin precession and zero-field data show conclusively that the shallow Mu0 ionizes to the Mu+ ground state. The static signal converts to that for the mobile state in two steps, suggesting two metastable Mu+ trap sites. Preliminary energies are extracted for the detrapping transitions and thermally activated Mu+ diffusion.

Properties of muonium defect centers in the III–V nitrides

Recent results are presented for the muonium analog of isolated hydrogen impurities in the III–V nitrides. The Mu + and Mu − centers reside at sites anti-bonding to the N atom and the group III atom, respectively. Stable sites for each lie in the channel and metastable sites in the cage formed by the 2H stacking of the wurtzite structure. Data for AlN and GaN imply short-lived atomic-like Mu 0 states and a shallow-donor Mu 0 is observed in InN. Characteristic energies for motion, site changes and charge-state transitions are obtained from zero-field depolarization data. Results imply that Mu/H diffusion strongly depends on the charge state.

Shallow-level muonium centre in CdS

A new type of muonium defect centre has been observed in undoped CdS at low temperatures ( T<20 K). The hyperfine parameters are A ∥=335 (7) kHz and A ⊥=199 (6) kHz (approximately 10 −4 of the vacuum value) with the symmetry axis along the Cd–S bond direction. The disappearance of the centre at around 20 K is in agreement with the binding energy of a shallow centre. The extremely weak hyperfine interaction implies that the electron is only weakly bound to the muon and is distributed over a large complex of atoms in the neighborhood of the muon resembling the dilated hydrogen-like wave functions of shallow centres in a dielectric medium. Comparing the hyperfine interaction with that of free muonium, a Bohr radius of a d=26 a 0=1.4 nm is calculated for this defect, with a 0 being the Bohr radius for the free muonium.

The origin of anomalous muonium in semiconductors

The origin of muonium defect centers in semi-insulating GaAs has been studied using newly developed μSR techniques employing alternating electric fields. This technique prevents the accumulation of near-surface charges which may screen the external field. The screening effect was tested at ISIS by the measurements of the current induced by muon beam. Suppression of anomalous muonium signal with electric field suggests that muonium formation proceeds via transport of excess electrons from the ionization track to the muons.

Novel Muonium State in CdS

A new type of muonium defect center has been observed in undoped CdS below 20 K. The hyperfine interaction amounts only to approximately ${10}^{\ensuremath{-}4}$ of the vacuum value, and is shown to have axial symmetry along the Cd-S bond direction. Results suggest that the muon is close to the sulfur antibonding site and the paramagnetic electron density is distributed over a large volume. In contrast to the behavior in other semiconductors, muonium forms a shallow center in CdS. By implication, analog isolated hydrogen impurity atoms act as electrically active shallow-level defect centers in CdS.

Electron transport to positive centers in GaAs

The origin of neutral muonium defect centers in semi-insulating GaAs has been studied using muon spin rotation/relaxation techniques employing alternating electric fields. This technique prevents the accumulation of near-surface charges which may screen the external field. Suppression of the bond-centered muonium signal with electric field suggests that muonium formation proceeds via transport of excess electrons from the ionization track to the muon. The characteristic field of about 5 kV/cm may correspond to an electric field induced ionization of the muon donor impurity center.

Longitudinal field muon spin relaxation (LF-μSR) measurements and evidence for a new muonium defect site in type Ia diamond

A new configuration for muonium, with hyperfine interaction parameters of less than axial symmetry, in nitrogen rich diamond is identified in Longitudinal Field Muon Spin Relaxation (LF-μSR) measurements. The TF-μSR measurements on the same sample show that almost the entire strength of the new configuration is accounted for by a “missing fraction”, typically seen in nitrogen rich type Ia diamond. The “missing fraction” is therefore the result of a T2 relaxation. This is consistent with muon trapping at or in some nitrogen related defect(s) followed by electron capture at random times.

Hyperfine properties of bond-center muonium and hydrogen in diamond

The bond-center (BC) hydrogen/muonium defect is of considerable interest both as a model for the theoretical description of defects in semiconductors, and because of its possible role in affecting the opto-electronic properties of polycrystalline silicon and diamond. Its identification requires a reliable calculation of its hyperfine couplings (HFCs) both in the bulk and in strained bonds that occur at grain boundary sites. Using a novel multiconfigurational perturbative approach we have calculated the HFCs of BC muonium/hydrogen in diamond. To our knowledge the method provides the best compromise between accuracy and computational efficiency. Our results for the bulk BC muonium defect are in very good agreement with experiment. As an application of this method, we have obtained the HFCs for hydrogen in strained C-C bonds.

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.

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.

Review of experimental studies of muonium centers in semiconductors

After a brief description of muon spin rotation and muonium, the observations on muonium defect centers in semiconductors are described. Two different muonium centers are seen. Normal muonium has an isotropic hyperfine interaction which is roughly one half of that for free muonium. Anomalous muonium has a contact hyperfine parameter varying from 1.5% to 4.6% of that for free muonium. In addition, the hyperfine interaction is highly anisotropic. Normal muonium is thought to be interstitial, whereas anomalous muonium is proposed to be substitutional.