Hard Condensed Matter Physics

We have employed the x-ray resonant magnetic scattering (XRMS) technique at the Ru L2 edge of the Ba(Fe1-xRux)2As2 (x = 0.205) superconductor. We show that pronounced resonance enhancements at the Ru L2 edge are observed at the wave vector which is consistent with the antiferromagnetic propagation vector of the Fe in the undoped BaFe2As2. We also demonstrate that the XRMS signals at the Ru L2 edge follow the magnetic ordering of the Fe with a long correlation length, ξ ab > 2850 ± 400 Å. Our experimental observation shows that the Ru is spin-polarized in Ba(Fe1-xRux)2As2 compounds.

The La-based "214" cuprates host several symmetry-breaking phases, including superconductivity, charge and spin order in the form of stripes, and a structural orthorhombic-to-tetragonal phase transition. Therefore these materials are an ideal system to study the effects of uniaxial stress onto the various correlations that pervade the cuprate phase diagram. We report resonant x-ray scattering experiments on La 1.475 Nd 0.4 Sr 0.125 CuO 4 (LNSCO-125) that reveal a significant response of charge stripes to uniaxial tensile stress of ∼0.1 GPa. These effects include a reduction of the onset temperature of stripes by ∼50 K, a 29-K reduction of the low-temperature orthorhombic-to-tetragonal transition, competition between charge order and superconductivity, and a preference for stripes to form along the direction of applied stress. Altogether, we observe a dramatic response of the electronic properties of LNSCO-125 to a modest amount of uniaxial stress.

We present results on the magnetic field dependence of the stripe order in La1.64Eu0.2Sr0.16CuO4 (LESCO). Using resonant soft x-ray scattering at the oxygen K-edge to probe the (0.259,0,0.648) superlattice reflection, which is commonly associated to charge stripes, we found no pronounced difference in the wave vector, peak widths and integrated intensity for magnetic fields up to B = 6 T. This is in strong contrast to the behavior observed for La1.875Sr0.125CuO4, where a stabilization of the charge modulation in high magnetic fields has been demonstrated.

High energy x-ray diffraction is used to investigate the bulk oxygen ordering properties of YBa_2Cu_3O_{6+x}. Superstructures of Cu-O chains aligned along the b axis and ordered with periodicity ma, along the a axis have been observed. For $x < 0.62$ the only observed superstructure is ortho-II with m=2. At room temperature we find ortho-III (m=3) for $0.72\le x\le 0.82$, ortho-V

We present results on the magnetic field dependence of the stripe order in La 1.64 Eu 0.2 Sr 0.16 CuO 4 (LESCO). Using resonant soft x-ray scattering at the oxygen K-edge to probe the (0.259,0,0.648) superlattice reflection, which is commonly associated to charge stripes, we found no pronounced difference in the wave vector, peak widths and integrated intensity for magnetic fields up to B = 6 T. This is in strong contrast to the behavior observed for La 1.875 Sr 0.125 CuO 4 , where a stabilization of the charge modulation in high magnetic fields has been demonstrated.

We present density functional theory (DFT) calculations and a full set of X-ray spectra (resonant inelastic X-ray scattering and X-ray photoelectron spectra) measurements of single crystal CaFe 2 As 2. The experimental valence band spectra are consistent with our DFT calculations. Both theory and experiment show that the Fe 3dstates dominate the Fermi level and hybridize with Ca 3d-states. The simple shape of Xray photoelectron (XPS) Fe 2p-core level spectrum (without any satellite structure typical for correlated systems) suggests itinerant character of the Fe 3d-electrons. Based on the similarity of the calculated and experimental Fe 3d-states distribution in LaOFeAs and CaFe 2 As 2 we conclude that superconductivity in the FeAs-systems can be described within a minimal model, taking into account only Fe 3d-bands close to the Fermi level.

The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.

We report the observation of a bulk charge modulation in La1.88Sr0.12CuO4 (LSCO) with a characteristic in-plane wave-vector of (0.236, ±δ), with δ = 0.011 r.l.u. The transverse shift of the ordering wave-vector indicates the presence of rotated charge-stripe ordering, demonstrating that the charge ordering is not pinned to the Cu-O bond direction. On cooling through the superconducting transition, we find an abrupt change in the growth of the charge correlations and a suppression of the charge order parameter indicating competition between the two orderings. Orthorhombic LSCO thus helps bridge the apparent disparities between the behavior previously observed in the tetragonal "214" cuprates and the orthorhombic yttrium and bismuth-based cuprates and thus lends strong support to the idea that there is a common motif to charge order in all cuprate families.

Inelastic neutron scattering measurements of paramagnetic SrCo2As2 at T = 5 K reveal antiferromagnetic (AFM) spin fluctuations that are peaked at a wavevector of Q AFM = (1/2, 1/2, 1) and possess a large energy scale. These stripe spin fluctuations are similar to those found in AFe2As2 compounds, where spin-density wave AFM is driven by Fermi surface nesting between electron and hole pockets separated by Q AFM. SrCo2As2 has a more complex Fermi surface and band structure calculations indicate a potential instability towards either a ferromagnetic or stripe AFM ground state. The results suggest that stripe AFM magnetism is a general feature of both iron and cobaltbased arsenides and the search for spin fluctuation-induced unconventional superconductivity should be expanded to include cobalt-based compounds.

We used resonant elastic x-ray scattering at the Cu L3 and Dy M5 edges to investigate charge order in thin films of underdoped DyBa 2 Cu 3 O 6+x (DyBCO) epitaxially grown on NdGaO 3 (110) substrates. The films show an orthorhombic crystal structure with short-range ortho-II oxygen order in the charge-reservoir layers. At the Dy M5 edge we observe diffraction peaks with the same planar wavevectors as those of the two-dimensional charge density wave in the CuO 2 planes and of the ortho-II oxygen order, indicating the formation of induced ordered states on the rare-earth sublattice. The intensity of the resonant diffraction peaks exhibits a non-monotonic dependence on an external magnetic field. Model calculations on the modulation of the crystalline electric field at the Dy sites by charge and oxygen order capture the salient features of the magnetic field, temperature, and photon energy dependence of the scattering intensity.

The presence of different electronic orders other than superconductivity populating the phase diagram of cuprates suggests that they might be the key to disclose the mysteries of this class of materials. In particular charge order in the form of charge density waves (CDW), i.e., the incommensurate modulation of electron density in the CuO 2 planes, is ubiquitous across different families and presents a clear interplay with superconductivity. Until recently, CDW had been found to be confined inside a rather small region of the phase diagram, below the pseudogap temperature and the optimal doping. This occurrence might shed doubts on the possibility that such "low temperature phenomenon" actually rules the properties of cuprates either in the normal or in the superconducting states. However, recent resonant X-ray scattering (RXS) experiments are overturning this paradigm. It results that very short-ranged charge modulations permeate a much wider region of the phase diagram, coexisting with CDW at lower temperatures and persisting up to temperatures well above the pseudogap opening. Here we review the characteristics of these high temperature charge modulations, which are present in several cuprate families, with similarities and differences. A particular emphasis is put on their dynamical character and on their coupling to lattice and magnetic excitations, properties that can be determined with high resolution resonant inelastic x-ray scattering (RIXS).

In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigen solutions and total normalized wave function of Schrödinger equation express in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential).The proposed potential is best suitable for smaller values of the screening parameter .The resulting energy eigen equation is presented in a close form and extended to study thermal properties and superstatistics express in terms of partition function ( ) Z and other thermodynamic properties such as; vibrational mean energy ( ) U , vibrational specific heat capacity ( ) C ,vibrational entropy ( ) S and vibrational free energy ( ) F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtain...

In cuprate high-temperature superconductors, an antiferromagnetic Mott insulating state can be destabilized toward unconventional superconductivity by either hole or electron doping. In hole-doped (p-type) cuprates, a charge ordering (CO) instability competes with superconductivity inside the pseudogap state. We report resonant x-ray scattering measurements that demonstrate the presence of charge ordering in the n-type cuprate Nd(2-x)Ce(x)CuO4 near optimal doping. We find that the CO in Nd(2-x)Ce(x)CuO4 occurs with similar periodicity, and along the same direction, as in p-type cuprates. However, in contrast to the latter, the CO onset in Nd(2-x)Ce(x)CuO4 is higher than the pseudogap temperature, and is in the temperature range where antiferromagnetic fluctuations are first detected. Our discovery opens a parallel path to the study of CO and its relationship to antiferromagnetism and superconductivity.

Recently, charge density wave (CDW) order in the CuO 2 planes of underdoped YBa 2 Cu 3 O 6þ was detected using resonant soft x-ray scattering. An important question remains: is the chain layer responsible for this charge ordering? Here, we explore the energy and polarization dependence of the resonant scattering intensity in a detwinned sample of YBa 2 Cu 3 O 6:75 with ortho-III oxygen ordering in the chain layer. We show that the ortho-III CDW order in the chains is distinct from the CDW order in the planes. The ortho-III structure gives rise to a commensurate superlattice reflection at Q ¼ ½0:33 0 L whose energy and polarization dependence agrees with expectations for oxygen ordering and a spatial modulation of the Cu valence in the chains. Incommensurate peaks at [0.30 0 L] and [0 0.30 L] from the CDW order in the planes are shown to be distinct in Q as well as their temperature, energy, and polarization dependence, and are thus unrelated to the structure of the chain layer. Moreover, the energy dependence of the CDW order in the planes is shown to result from a spatial modulation of energies of the Cu 2p to 3d x 2 Ày 2 transition, similar to stripe-ordered 214 cuprates.

We investigate the transport properties of La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ ($x=0.04$, 0.08, 0.125, 0.15, 0.2) with a special focus on the Nernst effect in the normal state. Various anomalous features are present in the data. For $x=0.125$ and 0.15 a kink-like anomaly is present in the vicinity of the onset of charge stripe order in the LTT phase, suggestive of enhanced positive quasiparticle Nernst response in the stripe ordered phase. At higher temperature, all doping levels except $x=0.2$ exhibit a further kink anomaly in the LTO phase which cannot unambiguously be related to stripe order. Moreover, a direct comparison between the Nernst coefficients of stripe ordering La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ and superconducting La$_{2-x}$Sr$_x$CuO$_4$ at the doping levels $x=0.125$ and $x=0.15$ reveals only weak differences. Our findings make high demands on any scenario interpreting the Nernst response in hole-doped cuprates.

We have employed the x-ray resonant magnetic scattering (XRMS) technique at the Ru $L_2$ edge of the Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ ($x = 0.205$) superconductor. We show that pronounced resonance enhancements at the Ru $L_2$ edge are observed at the wave vector which is consistent with the antiferromagnetic propagation vector of the Fe in the undoped BaFe$_2$As$_2$. We also demonstrate that the XRMS signals at the Ru $L_2$ edge follow the magnetic ordering of the Fe with a long correlation length, $\xi_{ab} > 2850\pm400$ \AA . Our experimental observation shows that the Ru is spin-polarized in Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ compounds.

We have employed the x-ray resonant magnetic scattering (XRMS) technique at the Ru L2 edge of the Ba(Fe1−xRux)2As2 (x = 0.205) superconductor. We show that pronounced resonance enhancements at the Ru L2 edge are observed at the wave vector which is consistent with the antiferromagnetic propagation vector of the Fe in the undoped BaFe2As2. We also demonstrate that the XRMS signals at the Ru L2 edge follow the magnetic ordering of the Fe with a long correlation length, ξ ab > 2850 ± 400Å. Our experimental observation shows that the Ru is spin-polarized in Ba(Fe1−xRux)2As2 compounds.

Charge density modulations, recently observed in underdoped high critical-temperature (Tc) cuprate superconductors, coexist with the so-called pseudogap and compete with superconductivity. Surface sensitive techniques have suggested that bulk charge modulations could be present also around the summit of the superconducting dome (optimal doping). Using energy-resolved resonant x-ray scattering we have found evidence for such bulk charge modulations, or soft collective charge modes (soft CCMs), in optimally-doped Bi1.5Pb0.6Sr1.54CaCu2O 8+δ (Pb-Bi2212) around momentum transfer q ∼ 0.28 r.l.u. along the Cu-O bond direction. The signal is stronger at T ≃ Tc than at lower temperatures, thereby confirming a competition between charge modulations and superconductivity. These results demonstrate that soft CCMs are not constrained to the underdoped regime but extend at least up to optimal doping.

We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor YBa2Cu3O6+x over a wide range of doping levels (0.1 ≤ x ≤ 1). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all x. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rather than from incoherent particle-hole excitations as recently suggested theoretically [Benjamin et al. Phys. Rev. Lett. 112, 247002(2014)]. Implications for the theoretical description of the electron system in the cuprates are discussed.

In this work, the Klein-Gordon equation is studied with exponential-type potentials to 0 l  states. As regards, the analytical solutions of the Klein-Gordon equation are possible only in the s-wave case with the angular momentum 0 l  for some well known potential. We have applied the Supersymmetry method (SUSY) by using the Pekeris approximation and we are obtained bound state spectrum and wave function of exponential-type potential for nonzero angular momentum. Spin symmetry and the shape invariance method are used in the calculation.

A charge modulation has recently been reported in (Y,Nd)Ba$_2$Cu$_3$O$_{6+x}$ [Ghiringhelli {\em et al.} Science 337, 821 (2013)]. Here we report Cu $L_3$ edge soft x-ray scattering studies comparing the lattice modulation associated with the charge modulation in YBa$_2$Cu$_3$O$_{6.6}$ with that associated with the well known charge and spin stripe order in La$_{1.875}$Ba$_{0.125}$CuO$_4$. We find that the correlation length in the CuO$_2$ plane is isotropic in both cases, and is $259 \pm 9$ \AA for La$_{1.875}$Ba$_{0.125}$CuO$_4$ and $55 \pm 15$ \AA for YBa$_2$Cu$_3$O$_{6.6}$. Assuming weak inter-planar correlations of the charge ordering in both compounds, we conclude that the order parameters of the lattice modulations in La$_{1.875}$Ba$_{0.125}$CuO$_4$ and YBa$_2$Cu$_3$O$_{6.6}$ are of the same order of magnitude.

We have employed the x-ray resonant magnetic scattering (XRMS) technique at the Ru $L_2$ edge of the Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ ($x = 0.205$) superconductor. We show that pronounced resonance enhancements at the Ru $L_2$ edge are observed at the wave vector which is consistent with the antiferromagnetic propagation vector of the Fe in the undoped BaFe$_2$As$_2$. We also demonstrate that the XRMS signals at the Ru $L_2$ edge follow the magnetic ordering of the Fe with a long correlation length, $\xi_{ab} > 2850\pm400$ \AA . Our experimental observation shows that the Ru is spin-polarized in Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$ compounds.

FIELD OF THE INVENTION
This invention relates to methods for preparing semiconductor substrates, the semiconductor oxides grown thereon, and more specifically, to epitaxial oxides grown on the surface of semiconductors, and the interfacial layer formed between the oxide and the semiconductor.
BACKGROUND OF THE INVENTION
Ever since the first integrated circuit was demonstrated, one goal of the electronics industry has been to increase the density of individual devices in an integrated circuit. Ultimately, as smaller devices are made, the devices can be packed more densely, which reduces transmission between devices and also allows for faster operation. Metal oxide semiconductor (MOS) technology forms the basis for a large part of chip manufacturing. In typical MOS transistor technology, silicon dioxide (SiO2) is grown on a silicon substrate so as to form part of a metal oxide semiconductor gate. SiO2
so formed is commonly referred to as a gate oxide or a gate oxide dielectric.

Until recently, SiO2 grown on MOS transistor gates has always been thought of as amorphous with little ordering in the first atomic layers at the interface between the silicon substrate and the oxide layer.

Silicon has been used commercially as a semiconductor preferentially over other materials because it readily forms stable oxide dielectric layers with a lower interface defect density than other semiconductors and their oxides. The stability of Si/SiO2 having a low interface defect density enables the manufacture of transistors with better electrical properties than is attainable with other semiconductors. The desire for lower dimension devices presents a basic problem: as devices get The desire for lower dimension devices presents a basic problem: as devices get smaller in three dimensions, the dielectric layer must get both narrower and thinner and continue to function as a dielectric. Silicon does not always provide the optimum physical and electronic properties, such as a low interface defect density or a high dielectric constant, necessary to or tailored to fill a particular need. A desire for materials that have better tailored physical and electronic properties creates another problem: growth of dielectric layers on multi-element semiconductors is difficult. These two problems become essentially insurmountable when one desires a small device made out of a semiconductor other than doped silicon. Conceptually, a solution would lie in producing either a well-ordered ultra-thin oxide on top of the multi-element semiconductor, or at least a more ordered interface between the semiconductor and the dielectric layers. Doing so without elemental or phase separation is extremely difficult especially in chemical systems where the defect generation rate is higher than silicon, and as the physical sizes involved approach atomic dimensions. Any improvement in ordering at the interface or in
the material will improve the interface defect density. It will be appreciated that, as smaller devices demand thinner dielectric layers, interface characteristics become increasingly important.
Another goal of electronic device processing is the growth of heterodielectrics or other materials listed below on a semiconductor substrate. While this goal is achievable
for some systems, in general, growth of ordered films of a material on a semiconductor substrate is difficult. US 6,613,677, incorporated herein by reference, discloses long range ordered semiconductor interface phase and oxides that can improve many properties of oxides, and in particular SiO2 grown on Si. However, the growth of epitaxial, or continuous crystalline films on semiconductor substrates remains elusive. Herein, are described novel methods for preparing semiconductor substrates and forming epitaxial interfacial layers of oxides thereon.