V. N. Gorelkin

Shallow acceptor centres in silicon studied by means of spin rotation of negative muons

The residual polarization of negative muons has been studied for phosphorus-doped and antimony-doped silicon crystals. The measurements were carried out in a transverse magnetic field of 0.1 T over the temperature region 4 K-300 K. The ionized and neutral states of the pseudo-acceptor were observed in antimony-doped silicon for the first time. The rate of transition from the neutral to the ionized state of the acceptor was found to be equal to over the temperature range 4 K-12 K. The estimated rates of relaxation of the magnetic moment of the acceptor-centre electron shell are and in phosphorus-doped silicon and and in antimony-doped silicon at 4 K and 15 K respectively. The experimental results obtained are interpreted in terms of spin-lattice relaxation of the acceptor magnetic moment and of the acceptor-donor pair formation.

Investigation of the behaviour of the impurity atoms in Si by μ−SR-method

The dependence of the residual polarization of negative muons in p-type Si on temperature in the 4.2–270 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. The impurity concentration in the sample was 2 · 1013 cm−3. Muon spin relaxation was observed at temperatures below 30 K. The relaxation rate atT=30 K is equal to 0.18±0.08μs−1. The relaxation rate grows with the decrease of temperature and at 4.2 K exceeds 30μs−1. The value of the residual polarization at zero timeP(t=0) is constant within the investigated temperature range.In the rangeT<30 K data on the relaxation rate are well described by the dependence λ=B·T−q, whereq=2.75. Power dependence of Λ may evidence the essential role of the phonon mechanism in the relaxation of the electron momentum of the acceptor center.

ANOMALOUS FREQUENCY SHIFT OF NEGATIVE MUON SPIN PRECESSION IN N-TYPE SILICON

The dependence of the residual polarization of negative muons in n‐type Si with impurity concentration (1.6\pm 0.2)\times 1013\ cm-3 on temperature in the 10–300 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. Muon spin relaxation and frequency shift were observed at temperatures below 30 K. The relaxation rate at 30 K is equal to 0.25\pm 0.08\,μ s-1. The frequency shift at 20 K is equal to 7\times 10-3. Both the relaxation rate and the frequency shift grow with decrease of temperature. Below 30 K the relaxation rate is well described by the dependence \varLambda=bT-q, where q=2.8.An analysis of present and earlier published data on behavior of negative muon polarization in silicon is given. A possible mechanism of relaxation and frequency shift of muon spin precession in silicon is considered.

μ-SR investigations in silicon

Abstract Results on the temperature dependence of the residual polarization of negative muons in silicon with phosphorus ( 4.5×10 18 , 2.3×10 15 , and 3.2×10 12 cm −3 ) and aluminium (2.4×1018 and 2×10 14 cm −3 ) impurities are presented. The muon spin rotation (μSR) experiments were carried out in a magnetic field of 0.2 T and in the temperature range 4.2–300 K. In all investigated samples a relaxation of the muon spin and a shift of the spin-precession frequency were observed. The frequency shift (relative to the room-temperature value) amounts to 7×10−3 at 15 K. In the sample with a high concentration of phosphorus impurity ( 4.5×10 18 cm −3 ) damped and undamped components of the muon spin polarization were observed at T K . Hyperfine interaction between the magnetic moments of the muon and that of the electron shell of the muonic atom (acceptor centre – μAl) is estimated on the basis of the muon spin precession frequency shift data. The temperature dependence of the spin-lattice relaxation rate of the magnetic moment of the shallow acceptor centre in silicon in the absence of external stress is determined for the first time. It is found that the relaxation rate is well approximated by the power function ν(T)=CTq, where the parameter q lies between 2 and 3.

Relaxation equation for muonium-like systems with electron spin more than one half

Abstract A phenomenological derivation of the Wangsness–Bloch–Redfield equation for the density matrix of muonium-like systems is given in this paper. In the case of the isotropic relaxation, it is shown that the corresponding relaxation term is described by only two independent constants. A typical form of the density matrix of the isotropic hyperfine interaction is given, and it is shown that the density matrix is decomposed into diagonal blocks. Relaxation rates corresponding to the different blocks can differ by orders of magnitude.

µ−spin rotation study of the temperature-dependent relaxation rate of acceptor centers in silicon

Temperature-dependent remanent polarization of negative muons in a silicon crystal doped with phosphorus (3.2 × 1012, 2.3 × 1015, and 4.5 × 1018 cm−3) and aluminum (2 × 1014 and 2.4 × 1018 cm−3) was examined. Measurements were made over the temperature range 4–300 K in a magnetic field of 2000 G perpendicular to the muon spin. Temperature dependence of the relaxation rate was determined for the magnetic moment of a shallow Al acceptor center in a nondeformed silicon sample, and the hyperfine interaction constant was estimated for the interaction between the magnetic moments of muon and electron shell of the muonic mAl atom in silicon.

Kinetic processes of muonium formation by non-thermalized electrons in the spur model

An approximate analytical solution is obtained for the kinetic equation for electrons in the field of a Coulomb centre formed by a muon in the end of its track. It is shown that thermalization times and could differ by several orders of magnitude, depending on the behaviour of transport cross sections. The fraction of non-thermalized electrons returning to the muon and forming muonium (PMu) depends on pressure and temperature. Therefore,μSR experiments give us an opportunity to obtain information on the distribution function of track electrons.

Investigation of acceptor centers in semiconductors by means of negative muons

Abstract The behavior (in the temperature range of 4– 300 K ) of the polarization of the negative muon spin for more than 20 n- and p-type crystalline silicon samples with impurity concentrations from ∼10 12 to ∼10 20 cm −3 made it possible (a) to infer the mechanisms for the relaxation of the magnetic moment of the Al acceptor in Si at different impurity concentrations, including the concentration region above the critical concentration corresponding to the Mott (insulator-to-metal) transition; (b) to find the value of the hyperfine interaction constant for the acceptor and to estimate the density of the hole wave function on the nucleus of the impurity atom.

Muonium and muonium-like systems formation in spur model

Abstract Track electron kinetics is shown to be important for the correct understanding of μSR experiments. The quasi-neutrality restoring time for the region of muon or meso-ion location is investigated theoretically and numerically in different models relating to positive and negative muons. Simple approximate formulae for numerical results are presented. This time is found to be much less than the muons lifetime for light gases and Ne at a liquid phase pressure. The foregoing makes it possible that meso-ion and electron interaction leads to the formation of Mu or muonium-like systems.

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ− SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×1013 cm−3) and antimony (Sb: 2×1018 cm−3) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center µA1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium.