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.     

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^*.     

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.     

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.     

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.     

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.     

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.     

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.     

Low-field anomalous muonium depolarization in isotopically enriched germanium

The depolarization rate of anomalous muonium, Mu^*, in germanium isotopically enriched in⁷⁴Ge (I=0) was measured as a function of field. The concentration of⁷³Ge (I=9/2) was about 9 times less than natural abundance. The depolarization rate at 10 K in this isotopically enriched crystal for both lines of those Mu^* centers whose symmetry axes make an angle of 90° to the field is less than 1sec^–1 at all fields down to the lowest one measured, 14.5 gauss. This is in sharp contrast to the wide lines reported at low field in germanium having natural isotopic abundance. The spectrum of Mu^* in the isotopically enriched Ge crystal was also seen at zero field. These results confirm that the increased depolarization rate for Mu^* at low fields arises from unresolved nuclear hyperfine structure. The depolarization rates observed were consistent with an average hyperfine interaction with a single⁷³Ge nucleus of 2.5 MHz, a value requiring nearly 1% of the spin density to be on a typical atom.     

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.     

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.     

On the mechanism of nonradiative decay of DNA bases: ab initio and TDDFT results for the excited states of 9H-adenine

Minimum-energy reaction paths and corresponding potential-energy profiles have been computed for the lowest excited states of the amino form of 9H-adenine. Complete-active- space self-consistent-field (CASSCF) and density functional theory (DFT) methods have been employed. The potential-energy function of the lowest ¹πσ^* state, nominally a 3s Rydberg state, is found to be dissociative with respect to the stretching of the NH bond length of the azine group. The ¹πσ^* potential-energy function intersects not only those of the ¹ππ^* and ¹ nπ^* excited states, but also that of the electronic ground state. The ¹ππ^*- ¹πσ^* and ¹πσ^*-S₀ intersections are converted into conical intersections when the out-of-plane motion of the active hydrogen atom is taken into account. It is argued that the predissociation of the ¹ππ^* and ¹ nπ^* states by the ¹πσ^* state and the conical intersection of the ¹πσ^* state with the S₀ state provide the mechanism for the ultrafast radiationless deactivation of the excited singlet states of adenine.     

RF-μSR study of muonium charge states and dynamics in Si

The radio frequencySR technique developed at TRIUMF was used to measure the temperature dependence of the diamagnetic muon, Mu, and Mu^* amplitudes in silicon between 10 K and 500 K. Six samples doped with phosphorus (n-type) and boron (p-type) in the concentration range 10¹¹ to 10¹⁵ cm^–3 were studied. In pure Si a very good fit over the whole temperature range is obtained from a model that includes the ionization of Mu^* and Mu to a bond centered ⁺ followed at high temperature by charge exchange involving Mu.     

Diffusion, trapping, and relaxation of Mu+ and Mu- in heavily‐doped GaAs

The diamagnetic muonium states in heavily doped GaAs are investigated with a combination of transverse‐field and longitudinal‐field μSR techniques. In metallic n‐type GaAs, formation of Mu^- occurs because of the high Fermi energy. This analog of the hydride ion (H^-) is located in a T_Ga interstice where it is essentially immobile up to about 500 K. At higher temperatures, Mu_T acts as an electron–hole recombination center. In p‐type GaAs, Mu⁺ traps at two different sites, one at low temperatures and a second at higher temperatures after detrapping from the first. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

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.     

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.     

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.