Probing of the shallow donor and acceptor wave functions in silicon carbide and silicon through an EPR study of crystals with a modified isotopic composition

The spatial distributions of the unpaired-electron wave functions of shallow N donors in SiC crystals and of shallow P and As donors in silicon crystals were determined by studying crystals with a modified content of the ²⁹Si and ¹³C isotopes having a nonzero nuclear magnetic moment. As follows from the present EPR and available ENDOR data, the distribution of donor electrons in SiC depends substantially on the polytype and position in the lattice; indeed, in 4H-SiC, the unpaired electrons occupy primarily the Si s and p orbitals, whereas in 6H-SiC these electrons reside primarily in the s orbitals of C. The electron distributions for the N donor in the hexagonal position, which has a shallow level close to that obtained for this material in the effective-mass approximation, and for the donor occupying the quasi-cubic position differ substantially. The EPR spectrum of N in quasi-cubic positions was observed to have a hyperfine structure originating from a comparatively strong coupling with the first two coordination shells of Si and C, which were unambiguously identified. The effective-mass approximation breaks down close to the N donor occupying the quasi-cubic position, and the donor structure and the donor electron distribution become less symmetric. In silicon, reduction of the ²⁹Si content brought about a substantial narrowing of the EPR line of the shallow P and As donors and an increase in the EPR signal intensity, as well as a noticeable increase in the spin-lattice relaxation time T₁. This offers the possibility of selectively studying these spectra by optically exciting a region of the crystal in order to shorten T₁ and thereby precluding EPR signal saturation only in the illuminated part of the material. This method may be used to advantage in developing materials for quantum computers based on donors in silicon and SiC.     

Spin-dependent recombination in GaAsN solid solutions

Room-temperature spin-dependent recombination in a series of GaAs_1?xN_x solid solutions (x = 2.1, 2.7, 3.4%) has been observed as manifested by a more than threefold decrease in intensity of the edge photoluminescence upon switching from circular to linear polarization of the exciting light or upon the application of a transverse magnetic field (～300 G). The interband absorption of the circularly polarized light is accompanied by the spin polarization of conduction electrons, which reaches 35% with an increase in the pumping level. The observed effects are explained in terms of the dynamic polarization of deep paramagnetic centers and the spin-dependent trapping of conduction electrons on these centers. The electron spin relaxation time, as estimated from the dependence of the edge photoluminescence depolarization in the transverse magnetic field (the Hanle effect) on the pumping intensity, is on the order of 1 ns. According to the adopted theory, the electron spin relaxation time in the presence of spin-dependent recombination is determined by a slow spin relaxation of localized electrons. The sign (positive) of the g factor of localized electrons has been experimentally determined from the direction of the magnetic-field-induced rotation of their average spin observed in the three GaAsN crystals studied.     

Investigating the spectra of electron spin resonance in SiGe/Si heterolayers doped with phosphorous

Studies of the spin resonance spectra of electrons localized on donors and the conduction electrons in Si_{1 ? x} Ge _x layers grown on silicon show that the phosphorous atoms in a SiGe layer can have two positions in the lattice. The line with g ～ 1.998 refers to the electron localized in the phosphorous atom with a predominantly silicon environment; the line with g ～ 1.994 is observed when there is a substantial concentration of germanium in the phosphorous environment.     

Estimates of the spontaneous polarization in silicon carbide

Various approaches to calculating the spontaneous polarization P _sp for different polytypes of silicon carbide are discussed. Our estimates combined with data reported by other authors reveal a considerable scatter in the values of P _sp for the 2H-SiC polytype (from ?1.11 to ?4.32 × 10^?2 C/m²). The need for further studies is stressed.     

A tilted rotatory frame method for the measurement of nuclear spin diffusion coefficients in solids doped with paramagnetic centers: Mn-Doped CaF<Subscript>2</Subscript>

Nuclear magnetic resonance (NMR) experiments recording the recovery of the magnetization of the nuclei in one phase, following the excitation of the nuclei in the other phase, is a classical way of studying blends inhomogeneous at the nanometer scale. Interpretation of the time recovery in terms of the spatial dimension requires knowledge of the two-phase spin diffusion coefficientsD ₀. A new method of measurement of_{D 0} is proposed on the basis of variable angle-tilted rotatory frame relaxation in homogeneous samples doped with paramagnetic centers. The choice of the tilt angle allows one to finely balance the direct relaxation by the paramagnetic center and the spin diffusion. The shape of the relaxation is analyzed with the solution for the diffusion-limited regimeM(t)/M(0)=exp[?(r ₂ t)^1/2?r ₁ t] andD ₀ then calculated fromr ₁,r ₂ and the concentration of paramagnetic centers. Conditions where reliable results can be obtained both theoretically and numerically are explored. The method has been implemented and applied to polycrystalline Mn-doped CaF₂ leading toD ₀=540±60 nm²/s, in agreement with existing values on this model compound.     

Paramagnetische Relaxation von CeCl3·7H2O im Temperaturbereich von 1,1 bis 4,2°K

The paramagnetic relaxation of a single crystal of CeCl₃·7H₂O has been studied by the dispersion-absorption-method at temperatures between 1,1 and 4,2°K. Alternating magnetic fields with frequencies between 5 and 2660 Hz and parallel magnetic fields up to 4000 Oe have been used. The spin lattice relaxation time has been determined as a function of temperature. At two special rangesH ₁ andH ₄ of the magnetic field a second, temperature-independent dispersion-absorption region has been observed besides the temperature-dependent spin-lattice relaxation (double relaxation). At two other special magnetic fieldsH ₂ andH ₃ the anomalous field dependence of the high frequency adiabatic susceptibility suggests a second dispersion-absorption-region ocurring at frequencies, which we cannot attain experimentally. In all cases cross relaxation processes are combined with the spin lattice relaxation.     

Evolution of Triplet Paramagnetic Centers in Diamonds Obtained by Sintering of Detonation Nanodiamonds at High Pressure and Temperature

The electron paramagnetic resonance (EPR) spectra of triplet centers in detonation nanodiamonds (DNDs) and diamond single crystals of submicrometer size, synthesized from those DNDs at high pressures and temperatures, are studied. In the EPR spectra of DNDs, signals from negatively charged nitrogen- vacancy centers (NV)/sup(-) with a g factor of g₁ = 4.24 and multivacancies with g₂ = 4.00 are observed. The signals from (NV)/sup(-) centers disappear in the spectra of diamond single crystals, and a quintet signal with g = 4.00 is detected at the position of the signal from multivacancies. Analysis of the shape and position of the quintet’ lines showed that this ESR signal is due to the pairs of nitrogen substitution centers in diamond, separated from each other by distances not exceeding 0.7 nm, between which a strong exchange interaction takes place. A comparison of the experimental data and the simulation results allows determining the spin-Hamiltonian parameters of the exchange-coupled pairs of paramagnetic impurity nitrogen atoms.     

Paramagnetische Relaxation im Holmiumäthylsulfat

The paramagnetic relaxation of Ho _x Y_1?x (C₂H₅SO₄)₃·9H₂O (x=1; 0.14; 0.1) was investigated with a mutual inductance bridge with frequencies fromν=10 sec^?1 toν=10600 sec^?1 in the temperature range betweenT=1.14°K and 2.11°K. In the diluted samples there is a strong influence of cross relaxation processes between the hyperfine levels on both the paramagnetic relaxation and the paramagnetic susceptibility. One and two spin cross relaxation processes were found. The susceptibility measured as a function of frequency is compared with the susceptibility calculated from the known energy levels of Ho(C₂H₅SO₄)₃·9H₂O. Thus the way how the relaxation process takes place between the various systems (crystal field-, Zeeman-, dipol dipol coupling-, hyperfine structure-, lattice- and bath-system) can be deduced. Some preliminary measurements atν=24.10⁶ sec^?1 are reported and discussed.     

Longitudinal response of the spin system of a metal to modulated EPR saturation at arbitrary modulation frequency and detuning of the saturating field

The theory of the longitudinal (with respect to an external magnetic field) response of a combined spin system of localized paramagnetic centers (s subsystem) and free charge carriers (e subsystem) of a solid semiconductor to modulated saturation of EPR is developed. In contrast to relevant studies made earlier, the general case is considered of an arbitrary modulation frequency and arbitrary detuning of the saturating microwave field with respect to the central EPR frequency. A theoretical approach is used in which normal modes are considered in analyzing coupled oscillations of the spin magnetizations of the s and e subsystems. It is shown that, in the case of relaxation coupling between the subsystems, the longitudinal response recorded at the modulation frequency can be represented as the sum of the responses of the normal modes, each of which is described by a universal resonance lineshape that is different, in general, from the Lorentzian lineshape characteristic of EPR signals. In the extreme cases of weak and strong coupling, simple analytical formulas are derived. The results presented form a theoretical basis for applying the method of modulated longitudinal response for measuring very short longitudinal spin relaxation times in semiconductors with paramagnetic impurities. As an example, experimental data are presented for activated carbon containing stable free radicals.     

Paramagnetische Relaxation von CeCl3

The paramagnetic relaxation in CeCl₃ was investigated in the temperature interval between 1.07°K and 4.21°K using a mutual inductance bridge at frequencies between 3 Hz and 3200 Hz. The dependence of the complex susceptibility on temperature below theλ point is given by a Debye function. Above this temperature, however, deviations occur. The temperature dependence of the relaxation time forT<T _λ can be described byτ～T ^?n where 1.82≦n≦2.35 for 470 Oe≦H≦3360 Oe. At the highest temperatures Orbach Processes occur over the first excited crystal field component which according to these measurements lies atE _II=k(56±10)°K. In the entire temperature range the relaxation processes are determined by further relaxation mechanisms in addition to the spin lattice relaxation. The nature of these could not, however, be determined.     

Effect of point defect concentration in NaCl and LiF crystals on the saturation field of the magnetoplastic effect

The effect is studied of the calcium impurity concentration in NaCl crystals and of preliminary x-ray irradiation of NaCl and LiF crystals on the magnetic saturation field B₀ characterizing the transition from the conventional proportionality of the dislocation mean path length l to the magnetic induction B squared(l∝B²) to saturation (l=const). B₀ is shown to increase with the calcium concentration in NaCl crystals and with the dose of x-ray irradiation of NaCl and LiF. This finding indicates that the dislocation breakaway from local defects in weak magnetic fields is controlled by the mechanism of longitudinal spin relaxation in a system of radical pairs that form due to interaction between dislocation cores and paramagnetic centers.     

Paramagnetische Relaxation im Terbiumäthylsulfat

The paramagnetic relaxation of Tb_0,01 Y_0,99(C₂H₅SO₄)₃·9H₂O at temperatures between 1,14°K and 4,21°K has been investigated with the absorption-dispersion method at frequencies between 5 sec^?1 and 10240 sec^?1 and different magnetic fields. AtH=700 Oe. The relaxation time follows the equationτ ^?1=[A H ³ coth (g _z μ _B H/2k T)+B T ⁷] sec^?1 as a function of temperature. ForH<800 Oe the paramagnetic relaxation is influenced by cross relaxation processes between the hyperfine structure levels.     

Interaction of nitrogen dioxide molecules with the surface of silicon nanocrystals in porous silicon layers

The methods of infrared absorption spectroscopy and electron paramagnetic resonance are used for studying the effect of adsorption of NO₂ molecules, which are strong acceptors of electrons, on the electronic and optical properties of silicon nanocrystals in mesoporous silicon layers. It is found that the concentration of free charge carriers (holes) in silicon nanocrystals, which exhibits a nonmonotonic dependence on the NO₂ pressure, sharply increases in the presence of these molecules. At the same time, a monotonic increase in the concentration of dangling silicon bonds (P_b1 centers) is observed. A microscopic model proposed for explaining this effect presumes the formation of donor-acceptor pairs P ₊ ^b1 -(NO₂)^? on the surface of nanocrystals, which ensure an increase in the hole concentration in nanocrystals, as well as P_b1 centers, which are hole-trapping centers. The proposed model successfully explains a substantial increase in photoconductivity (by two or three orders of magnitude) in the layers of porous silicon in the presence of NO₂ molecules; the increment in the concentration of free charge carriers is detected within an order of magnitude of this quantity. The results can be used in designing electronic and luminescence devices based on silicon nanocrystals.     

Effect of pressure on the elastic properties of silicon carbide

The pressure dependences of the second-order elastic constants C _ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model. The third-order elastic constants C _ijk for 3C-SiC are determined from the dependences of the second-order elastic constants C _ij on the pressure p.     

Identification of paramagnetic nitrogen centers (P1) in diamond crystallites synthesized via the sintering of detonation nanodiamonds at high pressure and temperature

Diamond single crystals synthesized from powder detonation nanodiamonds (DNDs) by means of treatment at high pressures (P ~ 7 GPa) and temperatures (T > 1300°C) have been studied by electron paramagnetic resonance (EPR). A key feature of treatment (high-pressure high–temperature (HPHT) sintering) is the use of low molecular weight alcohols in the process. The appearance of a hyperfine EPR signal structure due to “paramagnetic nitrogen” (P1 centers) is explained by the growth of submicron and micron diamond single crystals from DND nanocrystals by the oriented attachment and coalescence mechanism. Such growth and coarsening of crystals appreciably decreases the concentration of paramagnetic centers, the presence of which hinders the detection of a hyperfine structure in the EPR signal from P1 centers, in the near-surface areas of coalesced and grown together DND particles. It has been shown that the concentration of paramagnetic defects of all types decreases to ~3.1 × 1018 g^–1 (~60 ppm) during HPHT treatment at T = 1650°C. This causes the successful identification of P1 centers, whose fraction is no less than ~40% of the total amount of paramagnetic centers in microcrystals synthesized by HPHT sintering.     

Spin excitations in granular structures with ferromagnetic nanoparticles

Spin excitations and relaxation in a granular structure which contains metallic ferromagnetic nanoparticles in an insulating amorphous matrix are studied in the framework of the s-d exchange model. As the d system, we consider the granule spins, and the s system is represented by localized electrons in the amorphous matrix. In the one-loop approximation with respect to the s-d exchange interaction for a diagram expansion of the spin Green’s function, the spin excitation spectrum is found, which consists of spin-wave excitations in the granules and of polarized spin excitations. In polarized spin excitations, a change in the granule spin direction is accompanied by an electron transition with a spin flip between two sublevels of a split localized state in the matrix. We considered polarized spin relaxation (relaxation of the granule spins occurring by means of polarized spin excitations) determined by localized deep energy states in the matrix and the thermally activated electronic cloud of the granule. It is found that polarized spin relaxation is efficient over a wide frequency range. Estimates made for structures with cobalt granules showed that this relaxation could be observed in centimetric, millimetric, and submillimetric wavelength ranges.     

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.     

Longitudinal-phonon relaxation mechanisms in cubic crystals of germanium,silicon, and diamond

The relaxation rates of thermal and high-frequency longitudinal phonons are calculated using an anisotropic-continuum model. Three-phonon scattering mechanisms (L ? L + L, L ? T + L) for the phonon relaxation are considered. Anisotropic anharmonic phonon scattering in cubic crystals is described in terms of the second-and third-order elastic moduli. The parameters determining the longitudinal-phonon relaxation rates are found for germanium, silicon, and diamond crystals. The long-wavelength limit and the transition to the isotropic-medium model are considered, and the dependences of the relaxation rates of thermal and high-frequency phonons on temperature and phonon wave vector are analyzed for these crystals.     

Hole spin relaxation in Ge quantum dots

Hole spin relaxation in an isolated Ge quantum dot due to interaction with phonons is investigated. Spin relaxation in this case occurs through the mechanism of the modulation of the spin-orbit interaction by lattice vibrations. According to the calculations performed, the spin relaxation time due to direct single-phonon processes for the hole ground state equals 1.4 ms in the magnetic field H = 1 T at the temperature T = 4 K. The dependence of the relaxation time on the magnetic field is described by the power function H^?5. At higher temperatures, a substantial contribution to spin relaxation is made by two-phonon (Raman) processes. Because of this, the spin relaxation time decreases to nanoseconds as the temperature is raised to T = 20 K. Analysis of transition probabilities shows that the third and twelfth excited hole states, which are intermediate in two-step relaxation processes, play the main part in Raman processes.     

<Superscript>14</Superscript>N Nuclear Magnetic Resonance and Relaxation in the Paramagnetic Region of Uranium Mononitride

The spin susceptibility of a polycrystalline sample of uranium mononitride UN is studied by measuring the ¹⁴N NMR line shift, spin–lattice relaxation rates of the nuclear spin, and static magnetic susceptibility in the temperature region of 1.5T_N < T < 7T_N A joint analysis of the results obtained has revealed the temperature dependence of the characteristic energy of spin fluctuations of the uranium 5f electrons: Γ_nmr(T) ∝ T^0.54(4) close to the dependence Γ(T) ∝ T^0.5 characteristic of concentrated Kondo systems above the coherent state formation temperature.