Surface Conductivity of Si(100) and Ge(100) Surfaces Determined from Four-Point Transport Measurements Using an Analytical N-Layer Conductance Model

An analytical N-layer model for charge transport close to a surface is derived from the solution of Poisson's equation and used to describe distance-dependent electrical four-point measurements on the microscale. As the N-layer model comprises a surface channel, multiple intermediate layers and a semi-infinite bulk, it can be applied to semiconductors in combination with a calculation of the near-surface band-bending to model very precisely the measured four-point resistance on the surface of a specific sample and to extract a value for the surface conductivity. For describing four-point measurements on sample geometries with mixed 2D-3D conduction channels often a very simple parallel-circuit model has so far been used in the literature, but the application of this model is limited, as there are already significant deviations, when it is compared to the lowest possible case of the N-layer model, i.e. the 3-layer model. Furthermore, the N-layer model is applied to published distance-dependent four-point resistance measurements obtained with a multi-tip scanning tunneling microscope (STM) on Germanium(100) and Silicon(100) with different bulk doping concentrations resulting in the determination of values for the surface conductivities of these materials.Comment: 11 pages, 6 color figure

Surface and Step Conductivities on Si(111) Surfaces

Four-point measurements using a multi-tip scanning tunneling microscope (STM) are carried out in order to determine surface and step conductivities on Si(111) surfaces. In a first step, distance-dependent four-point measurements in the linear configuration are used in combination with an analytical three-layer model for charge transport to disentangle the 2D surface conductivity from non-surface contributions. A termination of the Si(111) surface with either Bi or H results in the two limiting cases of a pure 2D or 3D conductance, respectively. In order to further disentangle the surface conductivity of the step-free surface from the contribution due to atomic steps, a square four-probe configuration is applied as function of the rotation angle. In total this combined approach leads to an atomic step conductivity of $\sigma_\mathrm{step} = (29 \pm 9)$ $\mathrm{\Omega}^{-1} \mathrm{m}^{-1}$ and to a step-free surface conductivity of $\sigma_\mathrm{surf} = (9 \pm 2) \cdot 10^{-6}\,\mathrm{\Omega}^{-1}/\square$ for the Si(111)-(7$\times$7) surface.Comment: Main paper: 5 pages, 4 figures, Supplemental material: 6 pages, 3 figures. The Supplemental Material contains details on the sample preparation and measurement procedure, additional experimental results for Si(111) samples with different doping levels, and the description of the three-layer conductance mode

Polynomial Chaos Expansion method as a tool to evaluate and quantify field homogeneities of a novel waveguide RF Wien Filter

For the measurement of the electric dipole moment of protons and deuterons, a novel waveguide RF Wien filter has been designed and will soon be integrated at the COoler SYnchrotron at J\"ulich. The device operates at the harmonic frequencies of the spin motion. It is based on a waveguide structure that is capable of fulfilling the Wien filter condition ($\vec{E} \perp \vec{B}$) \textit{by design}. The full-wave calculations demonstrated that the waveguide RF Wien filter is able to generate high-quality RF electric and magnetic fields. In reality, mechanical tolerances and misalignments decrease the simulated field quality, and it is therefore important to consider them in the simulations. In particular, for the electric dipole moment measurement, it is important to quantify the field errors systematically. Since Monte-Carlo simulations are computationally very expensive, we discuss here an efficient surrogate modeling scheme based on the Polynomial Chaos Expansion method to compute the field quality in the presence of tolerances and misalignments and subsequently to perform the sensitivity analysis at zero additional computational cost.Comment: 12 pages, 19 figure

Ischémie mésentérique étendue associée à la prise excessive de naratriptan et de jus de pamplemousse

We reported the case of a 61-year-old woman, who has been hospitalized in ICU because of an extensive mesenteric ischaemia, involving the small bowel, secondary to a naratriptan overuse. This mesenteric ischaemia was complicated by multiple organ failure and was responsible for extensive small bowel resection and left colectomy. A concomitant abundant absorption of grapefruit juice, a well-known P450 inhibitor, may have enhanced this naratriptan toxicity. This case underscore that an abdominal pain occurring in the context of headache treatment may be related to a mesenteric ischaemia

Electromagnetic Simulation and Design of a Novel Waveguide RF Wien Filter for Electric Dipole Moment Measurements of Protons and Deuterons

The conventional Wien filter is a device with orthogonal static magnetic and electric fields, often used for velocity separation of charged particles. Here we describe the electromagnetic design calculations for a novel waveguide RF Wien filter that will be employed to solely manipulate the spins of protons or deuterons at frequencies of about 0.1 to 2 MHz at the COoler SYnchrotron COSY at J\"ulich. The device will be used in a future experiment that aims at measuring the proton and deuteron electric dipole moments, which are expected to be very small. Their determination, however, would have a huge impact on our understanding of the universe.Comment: 10 pages, 10 figures, 4 table

Halbach Magnets for Magnetic Resonance

This review is a compilation of relevant concepts in designing Halbach multipoles for magnetic resonance applications. The main focus is on providing practical guidelines to plan, design and build such magnets. Therefore, analytical equations are presented for estimating the magnetic field from ideal to realistic systems. Various strategies of homogenizing magnetic fields are discussed together with concepts of opening such magnets without force, or combining them for variable fields. Temperature compensation and other practical aspects are also reviewed. For magnetic resonance two polarities (di- and quadrupole) are of main interest, but higher polarities are also included.Comment: 37 pages, 17 Figure

Practical concepts for design, construction and application of Halbach magnets in magnetic resonance

This review is a compilation of relevant concepts in designing Halbach multipoles for magnetic resonance applications. The main focus is on providing practical guidelines to plan, design and build such magnets. Therefore, analytical equations are presented for estimating the magnetic field from ideal to realistic systems. Various strategies of homogenizing magnetic fields are discussed together with concepts of opening such magnets without force or combining them for variable fields. Temperature compensation and other practical aspects are also reviewed. For magnetic resonance two polarities (di- and quadrupole) are of main interest, but higher polarities are also included

Spin tune mapping as a novel tool to probe the spin dynamics in storage rings

Precision experiments, such as the search for electric dipole moments of charged particles using storage rings, demand for an understanding of the spin dynamics with unprecedented accuracy. The ultimate aim is to measure the electric dipole moments with a sensitivity up to 15 orders in magnitude better than the magnetic dipole moment of the stored particles. This formidable task requires an understanding of the background to the signal of the electric dipole from rotations of the spins in the spurious magnetic fields of a storage ring. One of the observables, especially sensitive to the imperfection magnetic fields in the ring is the angular orientation of stable spin axis. Up to now, the stable spin axis has never been determined experimentally, and in addition, the JEDI collaboration for the first time succeeded to quantify the background signals that stem from false rotations of the magnetic dipole moments in the horizontal and longitudinal imperfection magnetic fields of the storage ring. To this end, we developed a new method based on the spin tune response of a machine to artificially applied longitudinal magnetic fields. This novel technique, called \textit{spin tune mapping}, emerges as a very powerful tool to probe the spin dynamics in storage rings. The technique was experimentally tested in 2014 at the cooler synchrotron COSY, and for the first time, the angular orientation of the stable spin axis at two different locations in the ring has been determined to an unprecedented accuracy of better than $2.8\mu$rad.Comment: 32 pages, 15 figures, 7 table

Phase Measurement for Driven Spin Oscillations in a Storage Ring

This paper reports the first simultaneous measurement of the horizontal and vertical components of the polarization vector in a storage ring under the influence of a radio frequency (rf) solenoid. The experiments were performed at the Cooler Synchrotron COSY in J\"ulich using a vector polarized, bunched $0.97\,\textrm{GeV/c}$ deuteron beam. Using the new spin feedback system, we set the initial phase difference between the solenoid field and the precession of the polarization vector to a predefined value. The feedback system was then switched off, allowing the phase difference to change over time, and the solenoid was switched on to rotate the polarization vector. We observed an oscillation of the vertical polarization component and the phase difference. The oscillations can be described using an analytical model. The results of this experiment also apply to other rf devices with horizontal magnetic fields, such as Wien filters. The precise manipulation of particle spins in storage rings is a prerequisite for measuring the electric dipole moment (EDM) of charged particles

Phase locking the spin precession in a storage ring

This letter reports the successful use of feedback from a spin polarization measurement to the revolution frequency of a 0.97 GeV/$c$ bunched and polarized deuteron beam in the Cooler Synchrotron (COSY) storage ring in order to control both the precession rate ($\approx 121$ kHz) and the phase of the horizontal polarization component. Real time synchronization with a radio frequency (rf) solenoid made possible the rotation of the polarization out of the horizontal plane, yielding a demonstration of the feedback method to manipulate the polarization. In particular, the rotation rate shows a sinusoidal function of the horizontal polarization phase (relative to the rf solenoid), which was controlled to within a one standard deviation range of $\sigma = 0.21$ rad. The minimum possible adjustment was 3.7 mHz out of a revolution frequency of 753 kHz, which changes the precession rate by 26 mrad/s. Such a capability meets a requirement for the use of storage rings to look for an intrinsic electric dipole moment of charged particles