Net Electric Field Research Articles

Space-charge correction of solenoidal lenses

A trapped distribution of low-energy electrons was used to alleviate spherical aberration in a solenoidal magnetic lens. The space-charge-correction method has potential application to the focusing of heavy, negatively charged particles such as H− ions. In the geometry investigated, the field contributions from trapped electrons cancel net electric fields along magnetic flux surfaces. The lens magnetic fields therefore define equipotential surfaces. Experimental results were obtained using a 10-keV electron beam as a nondestructive probe in a solenoid lens with 65-G peak field. Annular distributions of trapped electrons were achieved that were stable against the diochotron instability. Deflections of the probe beam were consistent with theoretical predictions. The peak focused current density of the 10-keV beam was improved twentyfold with the addition of trapped electrons in the lens.

Measurement of high Rydberg 1P spectra of atomic helium and its application to glow-discharge diagnostics

The high Rydberg spectra of atomic helium np 1P states were measured up to n=46 in the negative glow region of a discharge, with mJ=±1 polarization, by optogalvanic spectroscopy. The net electric field values in the negative glow region, in the transition region between the negative glow and the positive column, and also on the radial axis of the positive column were determined from series-termination measurements. The spatial variations of the ion density in the negative glow region were also obtained from the net-field measurements.

A first-principles theory of the strain-effect electric field gradient in cubic metals due to point defects

A theory has been developed to evaluate on a first-principles basis the electric field gradient tensors due to the lattice strain produced by the introduction of point defects in cubic host metals. The lattice for this purpose has been divided into two regions, namely a near region and a far region. The former surrounds the defect site and extends over several near-neighbour cells and the latter represents the remaining part of the lattice. The contribution to the electric field gradient from the ions in the near region has been evaluated to all orders of lattice strain by using the realistic lattice displacements obtained for a discrete lattice in lattice statics calculations. The contribution from the far region, on the other hand, has been calculated in the continuum model of the lattice by retaining the effect of strain to first order only. Unlike in other calculations, no adjustable parameter has been used. The contribution from the valence effect has been evaluated by using the screening charge distribution from scattering theory. The results for the net electric field gradients in Cu and Al hosts due to monovacancies show significant improvement over those obtained by using the continuum model lattice strain for the whole region.

Time-dependent interfacial charging effects of electrical fields applied to biological systems

An important aspect of the interaction of a biological system with an externally produced electric field is that of charge separation and interfacial charging. This aspect has been ignored in some recent experimental and theoretical work. In the case of small regions of lower electrical resistivity imbedded in a higher resistivity medium, charge separation across the lower resistivity regions will result in charging of the interfaces between the lower and higher resistivity regions. The field produced by this charge separation will significantly affect the shape and the magnitude of the net electric field pulse within the lower resistivity regions. In particular, the field experienced by bone cells will be quite different from the externally produced field. The shape as well as the magnitude of the net electric field experienced by the cells depends on the time rate of change of the rising and falling phases of the externally produced electric field pulse.

Optical diagnostics of positive column dc discharge by Rydberg state spectroscopy

High resolution measurements of the Stark broadening of very high Rydberg 1P states in helium provide a resolution in electric field of approximately 1 V cm−1. The tunable laser-induced optogalvanic signal experiments were performed in a low pressure, low current discharge. The high sensitivity permits, for the first time, the net electric field to be obtained by a spectroscopic technique. The relative metastable density profile and indirectly, the electron density profile are also obtained from the magnitudes of the optogalvanic signals.

The effect of local-field correction on the transport properties of crystals

The question of local-field correction to the electrical transport is studied in more detail; namely, for the hopping limit and the band limit. In the hopping limit, if the hopping takes place between crystallographically equivalent sites, the short-range and Lorentz contributions to the dipolar potentials cancel in taking the intersite energy difference, and the electric field appearing in the hopping conductivity is just the macroscopic field. However if the hopping takes place between crystallographically inequivalent sites the short-range contributions to the dipolar potentials at the two sites do not cancel although the Lorentz contributions do. This leads to local-field-type corrections. The resulting corrections are found to be negligible at low fields but considerable at higher fields. Similar results are found for the Hall mobility of the small-polaron and AC impurity hopping conduction. In the band limit, it is shown that when the motion occurs in one band the net electric field appearing in the transport equation is just the macroscopic field unmodified by the local-field corrections.

A study of instability to electrical symmetry breaking in unicellular systems

The formation of a transcellular electric potential by an initially homogeneous and symmetric unicellular system is treated as the result of a non-equilibrium transition of the homogeneous cellular state to a patterned state. A mathematical theory is set forth which incorporates effects due to ion binding by membraneous structures in the cell interior, nonlinearity in the membrane transport of ions and a membrane-localized, mobile ion transport mechanism. This is a general theory, applicable to any unicellular system, for which a stability criterion giving the response of the system to non-spherically symmetric perturbations can be calculated. The general theory is applied to a specific model of the Fucus egg cell system. The model is found to be unstable to non-spherically symmetric perturbations under experimental conditions which lead to the formation of a net transcellular electric field and accompanying ionic currents. This study shows that the Fucus phenomenon can be thought of as a self-organization event, the result of nonlinear, non-equilibrium processes occurring in the cell membrane.

Mobility of electrons on the surface of liquid helium

A time-of-flight mobility measurement ($1.17<T<2.7$ K) is made on low-density electron pulses ($n<{10}^{4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$) moving above the surface of liquid helium with the electrons constrained against the liquid surface by a net dc electric field. Below 1.45 K the mobility starts to level off in the manner predicted by Cole although at the lowest temperatures the experimental value is slightly higher than Cole's value. This is direct evidence that the electron-ripplon interaction is important at these temperatures. The mobility at high drift fields is also reported.

Electrical resistivity anisotropy measurement

A method is described for obtaining the principal electrical resistivities of an anisotropic metal with axial symmetry. The method involves the measurement of the sample resistivity, and in addition, the angle between the current and the net electric field direction using a virtual probe method. Results are presented for three samples of the rhombohedral semimetal bismuth and compared with results taken from the literature.

Surface photoelectric effect and surface orbital geometry on silicon (111)

Photoelectron energy distributions have been measured as a function of photon angle of incidence, ϑi, in the range 28°?ϑi?80°. A resonance lamp with photon energies of 11.7, 16.8, and 21.2 eV was used with a double−pass cylindrical mirror analyzer. Three different surface orbitals were studied: intrinsic surface states, chemisorption orbitals of Cl, and nonbonding orbitals of implanted Ar. All three types of orbitals exhibited a similar dependence of intensity with ϑi which was approximately the same as the net electric field intensity 〈E2z〉z = 0. This implies that the surface photoeffect for silicon (111) is probably not closely related to the detailed surface bond geometry, but is determined by the optical properties of the silicon.

Pressure Variation of the Quadrupole Interaction in Cadmium Metal

A theoretical study, for the first time, of the electric field gradient in cadmium metal at two pressures yields a pressure variation in agreement with time-differential perturbed-angular-correlation data. The sign of the net electric field gradient determined by the electronic contribution, which is larger and of opposite sign to the ionic contribution, in conjunction with imminently expected experimental sign of the coupling constant, will provide the sign of the excited ${\mathrm{Cd}}^{111}$ quadrupole moment.

Transport of photocarriers in Cd xHg 1−xTe graded-gap structures

A theoretical and experimental study has been made on the transport of light injected excess charge carriers in Cd xHg 1−xTe variable band gap materials. A theoretical analysis is given of the ambipolar motion of the charge carriers in terms of diffusion and drift in the electric fields associated with the gradients of the band gap, lifetime, effective masses and doping level. The photoelectromagnetic effect (P.E.M.) has been calculated for two limiting cases: when the electric field is predominantly associated with a gradient of band gap (ideal case), and when the net electric field is zero (pseudohomogeneous case). It is shown that the two situations can be distinguished by analysing the variation of the P.E.M. effect in a magnetic field. Two different experimental studies have been made: a study of the optical transmission spectra which leads to the determination of the profiles of the structures and the spatial distribution of the absorbed photons, and a study of the P.E.M. effect and the photoconductivity as a function of several parameters: magnetic field, wavelength and temperature. The interpretation of these results shows that the structures studied can be characterized as pseudohomogeneous and an estimation of the variation of the diffusion length (1·5–18·5 μ) and the lifetime (5·10 −11–2·10 −8 sec) of the electrons in the composition range 0·15 < x < 0·25 has been made.

An accurate numerical one-dimensional solution of the p- n junction under arbitrary transient conditions

A numerical iterative method of solution of the one-dimensional basic two-carrier transport equations describing the behavior of semiconductor junction devices under arbitrary transient conditions is presented. The method is of a very general character: none of the conventional assumptions and restrictions are introduced and freedom is available in the choice of the doping profile, recombination-generation law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. For a specified arbitrary input signal of either current or voltage as a function of time, the solution yields terminal properties and all the quantities of interest in the interior of the device (such as mobile carrier and net electric charge densities, electric field, electrostatic potential, particle and displacement currents) as functions of both position and time. Considerable attention is focused on the numerical analysis of the initial-value-boundary-value problem in order to achieve a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties of the problem, such as stability conditions related to the discretization of partial differential equations of the parabolic type, small differences between nearly equal numbers, and the variation of most quantities over extremely wide ranges within short regions. Results for a particular n +- p single-junction structure under typical external excitations are reported. The iterative scheme of solution for a single device is applicable also to ensembles of active and passive circuit elements. As a simple example, resutls for the combination of an n +- p diode and an external resistor, analyzed under switching conditions, are presented. The inductive behavior of the device for high current pulses, and storage and recovery phenomena under forward-to-reverse bias switching, are also illustrated. ‘Exact’ and conventional approximate analytical results are compared and discrepancies are exposed.

An accurate numerical one-dimensional solution of the p-n junction under arbitrary transient conditions

Abstract A numerical iterative method of solution of the one-dimensional basic two-carrier transport equations describing the behavior of semiconductor junction devices under arbitrary transient conditions is presented. The method is of a very general character: none of the conventional assumptions and restrictions are introduced and freedom is available in the choice of the doping profile, recombination-generation law, mobility dependencies, injection level, and boundary conditions applied solely at the external contacts. For a specified arbitrary input signal of either current or voltage as a function of time, the solution yields terminal properties and all the quantities of interest in the interior of the device (such as mobile carrier and net electric charge densities, electric field, electrostatic potential, particle and displacement currents) as functions of both position and time. Considerable attention is focused on the numerical analysis of the initial-value-boundary-value problem in order to achieve a numerical algorithm sufficiently sound and efficient to cope with the several fundamental difficulties of the problem, such as stability conditions related to the discretization of partial differential equations of the parabolic type, small differences between nearly equal numbers, and the variation of most quantities over extremely wide ranges within short regions. Results for a particular n + - p single-junction structure under typical external excitations are reported. The iterative scheme of solution for a single device is applicable also to ensembles of active and passive circuit elements. As a simple example, resutls for the combination of an n + - p diode and an external resistor, analyzed under switching conditions, are presented. The inductive behavior of the device for high current pulses, and storage and recovery phenomena under forward-to-reverse bias switching, are also illustrated. ‘Exact’ and conventional approximate analytical results are compared and discrepancies are exposed.

Mössbauer-Effect Determination of the Crystalline Electric Field Parameters in Thulium Metal

By measuring the temperature dependence of the nuclear quadrupole splitting of the 8.42-keV M\ossbauer transition in the paramagnetic state of thulium metal, a determination of the crystalline electric field (CEF) parameters of elemental thulium has been obtained. The nuclear quadrupole interaction was studied within the temperature range 59 to 156\ifmmode^\circ\else\textdegree\fi{}K. It was found that a zero-order calculation was sufficient to fit theory to experiment, and that in particular only $C_{2}^{0}$, ${\ensuremath{\rho}}_{1}$ and $\ensuremath{\rho}_{2}^{\ensuremath{'}}$ (where the $\ensuremath{\rho}$'s account for shielding constants and the temperature-independent contributions to the electric field graident at the nucleus) were needed to fit the theory to the data. The remaining CEF parameters, $C_{4}^{0}$, $C_{6}^{0}$, and $C_{6}^{6}$, were constrained to equal zero in the fitting routine. The over-all splitting of the $^{3}H_{6}$ ground multiplet was found to be 76.1 ${\mathrm{cm}}^{\ensuremath{-}1}$. This study also includes a determination of electronic shielding factors for thulium. The atomic Sternheimer factor ${R}_{Q}$ was found to be 0.16; and the constant ${\ensuremath{\sigma}}_{2}$, which represents the shielding of the $4f$ shell from the CEF by the closed outer shells, was found to be 0.34. The latter quantity was obtained under the assumption that screening of the ${\mathrm{Tm}}^{+3}$ ions by the conduction electrons can be neglected. The direct lattice contribution and the conduction-electron contribution to the net electric field gradient at the Tm nucleus were found to be positive and of the same order of magnitude.

Second-Order Electric Field due to a Conduction Current

Assuming that the fields of a moving-point charge as computed from the retarded Liénard-Wiechert potentials give valid descriptions for moving electrons, it is shown that no net second-order static electric field of the type discussed by Rosser appears on the axis of a charge-neutral circular loop carrying a steady current. An argument is given for the nonexistence of such “residual” electric fields around any closed, charge-neutral region in which the current flow is time independent.