Muonium In Diamond Research Articles

Muon spin relaxation in synthetic type IIa diamond grown by high-pressure and high-temperature (HPHT) synthesis

Abstract The behaviour of hydrogen in the low strain pure diamond material synthesized by the high pressure high temperature (HPHT) route has been studied using the longitudinal field muon spin relaxation technique ( LF - μ SR ) . This study almost completes a survey of muonium in diamond with a range of defect compositions. The result may provide information on the so-called missing fraction (MF) observed in many previous studies of muons implanted into semiconductors. The experimental results showed the existence of a diamagnetic muon state ( μ + ) , two paramagnetic muonium states (tetrahedral interstitial ( Mu T 0 ) and bond-centred ( Mu BC 0 ) ), and MF formed by positive muons implanted into the sample. The absolute fractions of μ + , Mu T 0 , Mu BC 0 and MF in the sample were 4%, 54%, 30% and 12%, respectively.

The gap level of bond-centred muonium in diamond

Muonium, with a positive muon as the nucleus is considered a light isotope of hydrogen displaying a close chemical analogy to this atom. It offers a unique opportunity to study the behaviour of hydrogen in diamond at very low concentrations. The mass difference, however, implies that dynamical effects will be distinct. The bond centred muonium (Mu BC ) state in diamond is easily observed and there is a very good correlation between theoretical and experimental hyperfine parameters ((4)). Curiously, despite its predicted stability, the bond centred hydrogen state has not yet been observed in diamond. Following the discovery of hydrogen dopant states in certain wide band gap metal oxides, and the possibility of hydrogen related molecular dopants in diamond, the study of hydrogen in diamond is important. Although it is evident from its hyperfine parameters that (Mu BC ) is not a shallow donor, the question still arises as to where the (Mu BC ) state in diamond might lie in the band gap. Accordingly, measurements of the high temperature stability of (Mu BC ) have been performed in a search for its possible ionization. The results are consistent with such an ionization, as the disappearance of Mu BC polarisation (setting in near 1000 K) is correlated with the slight increase in the population of the diamagnetic μ+ species.

Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation

Isolated hydrogen, deuterium, and muonium in diamond have been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 100 to $800\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these hydrogenic impurities is found at the $\mathrm{C}\text{\ensuremath{-}}\mathrm{C}$ bond center. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in impurity vibrations at the bond center site, which hardens the vibrational modes with respect to a harmonic approximation. Zero-point motion causes an appreciable shift of the defect level in the electronic gap, as a consequence of electron-phonon interaction. This defect level goes down by $70\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ when replacing hydrogen by muonium.

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.

Computational studies of hydrogen-related complexes in semiconductors

The two main computational techniques to calculate the microscopic electronic structure of localized defects in solids are reviewed. Cluster calculations using the Hartree-Fock method as well as density-functional methods have been widely used to determine the equilibrium structure of hydrogen and hydrogen-related complexes in semiconductors. Results for the structure of both acceptor-hydrogen and donor-hydrogen pairs in silicon obtained by various methods and at different levels of approximations are discussed. Comparisons are made among the cal­culated vibrational frequencies of hydrogen in these passivation complexes. The spin density distribution for bond-centred hydrogen or muonium in diamond is investigated. Owing to the light masses of the proton and the muon it is neces­sary to average the computed hyperfme parameters over the finite extension of the ground-state wave function.

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-μSR, and endohedral muonium in semiconducting C60 compounds, are discussed. These examples show that as traditionalμSR techniques are continually being refined and new methods are being developed,μSR 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.

Bond-centered muonium in diamond: Resolved nuclear hyperfine structure.

The nuclear hyperfine structure of bond-centered muonium in $^{13}\mathrm{C}$ enriched diamond has been resolved using time-differential transverse-field muon spin rotation. The measured nearest-neighbor $^{13}\mathrm{C}$ hyperfine parameters are compared to theoretical values from a recent ab initio Hartree-Fock type cluster calculation. The ratios of the measured $^{13}\mathrm{C}$ hyperfine parameters and free atom values indicate that 92% of the unpaired electron spin density resides on the two nearest-neighbor atoms, in marked contrast with the situation for the analogous muonium center in Si.

Configuration interaction calculation of hyperfine properties for bond-centered muonium in diamond.

The electronic structure of hydrogen and muonium at the bond-centered site in diamond is investigated using ab initio cluster calculations. Based on a Hartree-Fock calculation, correlation effects are accounted for by a configuration interaction expansion. The hyperfine and superhyperfine parameters for anomalous muonium are determined by averaging over the spread of the muon wave function. Good agreement with experimental hyperfine parameters is found and values for the superhyperfine interaction, which can be detected in 13 C enriched samples, are predicted

Model calculation of the spin density for trapped muonium in ionic solids

A previously developed perturbation formula for calculating the spin density of trapped normal muonium in diamond is applied to the trapped muonium in the ionic solids of MgO, KCl and KBr. To obtain an improved molecular electrostatic potential (MEP) inside the cubic lattice, we performed MO calculations using clusters of MgO, KCl and KBr with additional surrounding point charges. Calculated spin densities (ƒ-values) in these potentials are compared with experimental results. We also report ab initio UHF MO calculations for these clusters with a trapped hydrogen atom at the centre of the clusters.

A molecular cluster approach to the electronic structure of anomalous muonium in diamond

First-principle discrete variational (DV) Xα cluster calculations are used to reproduce muon spin rotation (μSR) experimental data relative to anomalous muonium in diamond. A detailed analysis of the muonium-host interaction is reported. Calculations of the Fermi contact ( A), of the dipolar (2 B) hyperfine (hf) parameters and of the two components of the hf interaction tensor A ( A ∥ and A ⊥) agree well with experimental data only if an optimized numerical atomic basis set is used. Moreover, superhyperfi coupling constants for muonium at the nearest carbon atoms have been also computed. Theoretical data relative to hf quantities indicate that they do not seem to be strongly cluster-size dependent. Finally, the herein reported results have been also compared with other theoretical investigations carried out by using different approaches. The good agreement between our results and the experimental ones, coupled with the quite low computational cost of the DV-Xα approach, are encouraging for further investigations of more complex systems.

A study of the Hall-Mizukami model for muonium in C, Si and Ge using experimental electrostatic potentials

The method for calculating the spin density of trapped normal muonium in diamond proposed by Hall and Mizukami (Chem. Phys. Letters 150 (1988) 23) is extended to silicon and germanium using crystalline electrostatic potentials obtained from X-ray diffraction data. The results suggest that the model is more appropriate for application to muonium in Si and Ge than in diamond. Likely shortcomings of the model diamond are discussed, and simple improvements suggested.

Localized-orbital approach to the electronic structure of anomalous muonium in diamond.

Characteristics of the electronic structure of anomalous muonium in diamond are investigated based on the relaxed-bond-centered (RBC) model by use of a self-consistent Green's-function method within the local-spin-density-functional formalism. A minimal basis set of well-contracted localized orbitals determined from first principles is used. For the case of 42% stretched C-C bond length, calculated values of -137 and 400 MHz for the Fermi-contact and dipolar hyperfine parameters, respectively, give good agreement with the experimental values of -206 and 374 MHz, strongly supporting the RBC model. A simple interpretation is also given of the mechanism for the negative Fermi-contact hyperfine parameter.

A new method of calculating the spin density of trapped muonium in diamond

We propose a new method of calculating the spin density of trapped normal muonium in diamond by using the molecular electrostatic potential inside the diamond cluster as an external potential acting on the muonium. The exact wavefunctions of muonium are used in the perturbation calculation to ensure accuracy at the nucleus. For the enhancement factor ƒ, which measures the hyperfine coupling as compared to that of free muonium, we have obtained 0.716 and this is in better agreement with the experimental result, 0.831, than previous calculations have achieved.

On the use of cavity models to describe muonium in diamond, silicon and germanium

The form of various cavity models are discussed with regard to their prediction of the isotropic hyperfine coupling constants of the “normal muonium” states in group IV elements. Neither the bulk dielectric constant nor the cavity radius seem to be as important as the detailed variation of the dielectric function very close to the trapped nucleus.

Bond-centered hydrogen or muonium in diamond: The explanation for anomalous muonium and an example of metastability.

We present qualitative theoretical evidence that interstitial bond-centered hydrogen or muonium in diamond is stable as a result of unusually large lattice relaxation. The two geometrical configurations of neutral interstitial muonium explain the structures and properties of anomalous muonium (bond centered) and normal muonium (tetrahedral interstitial site), including the thermal conversion of normal to anomalous muonium and represent a well-defined example of interstitial metastability.

Lattice relaxation for normal muonium in diamond

The effects of symmetric lattice relaxation around the tetrahedral (T) and the hexagonal (H) interstitial sites are calculated for normal muonium (Mu) in diamond using the non-semiempirical method of Partial Retention of Diatomic Differential Overlap (PRDDO). We use clusters containing 3 and 4 host atom shells around the T and the H sites (C20H32 and C30H40). The only significant relaxations are the outward displacement of the 6 nearest neighbors (NN) to the H site and, when the muon is at the T site, the simultaneous outward displacement of the first and second NN to the T site. In the case of diamond, the effects of these relaxations on the energy profiles and spin densities are small.

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.

Preliminary calculations confirming that anomalous muonium in diamond and silicon is bond-centered interstitial muonium

The model of anomalous muonium as bond-centered interstitial muonium has been examined by approximate ab-initio Hartree-Fock calculations in diamond and silicon and found to be in excellent agreement with experiment.

Interstitial hydrogen in diamond: A detailed Hartree-Fock analysis.

We investigate the properties of interstitial hydrogen or muonium in diamond using the ab initio Hartree-Fock approach and the method of partial retention of diatomic differential overlap. If the dangling bonds on the surface are correctly saturated, the energy profiles and spin densities are independent of cluster size in the range from ${\mathrm{C}}_{10}$${\mathrm{H}}_{16}$ to ${\mathrm{C}}_{30}$${\mathrm{H}}_{40}$ and the tetrahedral interstitial site (T) is a deep minimum of the total energy. However, the height of the potential barrier between two adjacent T sites varies with basis set and, to a smaller extent, with lattice relaxation. In all cases, a muon (and therefore also a proton) is localized at the T site. The hexagonal interstitial site corresponds to a saddle point of the energy (it is a maximum of the energy only along the 〈111〉 axes). The dependence of the spin densities on cluster size, basis set, and lattice relaxations is analyzed. The results indicate a highly repulsive antibonding interaction between the interstitial hydrogen (or Mu) and the diamond clusters. The impurity energy level lies deep in the gap and the associate electronic wave function has a node between the site of the impurity and its nearest neighbors. This results in a very large contact spin density at the impurity. The calculated enhancement factor f depends very little on cluster size or basis set and is larger than experimentally observed. The effect of the zero-point motion of the impurity on the contact spin density is much smaller than previously believed. The effects of various relaxations are studied using clusters containing three and four host atom shells.

Surface effects in cluster calculations of energy profiles of muonium in diamond.

New and more accurate energy profiles for interstitial muonium in diamond clusters (${\mathrm{C}}_{10}$${\mathrm{H}}_{16}$ to ${\mathrm{C}}_{30}$${\mathrm{H}}_{40}$) have been determined by ab initio and approximate ab initio calculations, and have been critically compared to previous theoretical work. The energy profiles are shown to be extremely sensitive to the position of the surface atoms used to terminate the cluster. It is established that if the equilibrium carbon-hydrogen bond length is used to terminate the cluster the energy profiles converge rapidly with cluster size, but the use of any other value for ${d}_{\mathrm{C}\ensuremath{-}\mathrm{H}}$ leads to qualitatively incorrect energy profiles for small clusters.