Volume 34, Issue 9, 01 September 1963

Current Flow in Very Thin Films of Al_{2}O_{3} and BeO
View Description Hide DescriptionThis paper describes a study of current flow through very thin insulating films. Several possible conduction mechanisms are presented and their properties are discussed. The dominant conduction process in the layers studied is quantum‐mechanical tunneling. Previous work on this mechanism is extended by an exact calculation which shows the current‐voltage characteristic to be divided into three regions of different logarithmic curvature. The dielectric constant of the insulator is found to have a large effect, via the image force, on the tunneling current. The theoretical results are fitted to measurements made on insulating layers less than 100 Å thick, sandwiched between metal electrodes. For Al_{2}O_{3} layers the fit is excellent, resulting in barrier heights of 2.0–2.5 eV and thicknesses approximately 25 Å less than the values determined from capacitance, as expected. In contrast the conduction characteristics of BeO layers can be explained by tunneling only in the low‐voltage region; barrier height and thickness are similar to the Al_{2}O_{3} case. At intermediate voltages the currents are lower than predicted and at high voltages reproducible hysteresis effects are observed with time constants of the order of minutes. These effects are only weakly temperature dependent. They appear to be due to tunneling from one of the metals into trap states in the forbidden gap of the insulator, creating space charge which distorts the barrier for tunneling.

Kα Satellite Interference in X‐Ray Diffractometer Line Profiles
View Description Hide DescriptionThe Kα satellites occur as a group of weak, unresolved lines superimposed on the short wavelength tail of the Kα_{1} line. Satellite data obtained experimentally with a single‐crystal diffractometer are reported and compared with the results of two‐crystal spectrometer measurements by previous investigators. It is calculated from spectral data that the addition of the satellite group to the Kα_{1,2} lines shifts the Cu centroid 0.031 xu and the Fe centroid 0.061 xu to shorter wavelengths. The satellites occur superimposed on the short wavelength tail of the Kα_{1} line in back‐reflection powder line profiles and appear as a low intensity ``plateau'' which may cause difficulties in precision measurements. The effect of the satellite group on the value of the centroid obtained by various methods of truncating the profile is described. The angular separation of the satellites from the Kα_{1} component increases with increasing diffraction angles and may cause an error of the order of 1% in the relative integrated line intensities if the integration limits do not consistently include or exclude the satellites.

Constitutive Equations for a Plasma‐Like Medium
View Description Hide DescriptionA general formulation is obtained representing the constitutive equations for a plasma‐like medium. These equations are of the type P=α_{ ee } E+α_{ em } B; M=α_{ me } E+α_{ mm } B, where E is the electric intensity, B is the magnetic induction,P and M represent the electric and magnetic polarizations, respectively, and α_{ ee }, α_{ em }, α_{ me }, and α_{ mm } are appropriate macroscopic parameters characterizing the medium. These equations differ from the constitutive equations for a molecular medium since in the latter case one has P=χ_{ e } E and M=ξ_{ m } B, where χ_{ e } is the electric susceptibility and ξ_{ m } is the ``proper magnetic susceptibility.'' A formulation is given for the constitutive parameters for two particular cases: (a) when the plasma‐like medium is represented by a charge‐equilibrated uniform electron beam of infinite width and (b) when the plasma‐like medium is represented by a charge‐equilibrated electron gas characterized by an isotropic velocity distribution f(v).

Spectral Characteristics of GaAs Lasers Operating in ``Fabry‐Perot'' Modes
View Description Hide DescriptionHigh resolution measurements of the spectral output of GaAs injection lasers are made. It is found that the main features can be understood in terms of conventional line‐narrowing theories. Additional oscillations are observed in modes other than the lowest loss ones.

Isotropic Permalloy Films
View Description Hide DescriptionMagnetically isotropic Permalloyfilms have been prepared by evaporation or vacuum‐annealing in a 50‐cps rotating field of crossed pairs of Helmholtz coils. The magnetization reversal in magnetically isotropic films is similar to that of films with uniaxial anisotropy in the hard axis or that of inverted films (H_{c} >H_{k} ) in the easy and the hard axis. This is shown by hysteresis measurements on 25 film‐matrix patterns and by electron micrographs. At zero field the magnetic structure is caused by the film inhomogeneities and by the wall and edge stray fields. The locked state characterized by a domain splitting perpendicular to the applied field occurs when the reversed field is increased. Locking disappears at the coercive field strength by migration of Bloch lines on the Néel walls. Locking by partial rotation is not possible with H_{k} =0. Maze‐like domains occurring in an increasing field applied obliquely or perpendicularly to the previous saturation direction are caused by stray field coupling between strips of varying magnetization direction already present at zero field.

Microwave Reflection from Small‐Diameter Plasma Columns
View Description Hide DescriptionThe scattering cross section of electromagnetic waves incident normally on a small‐diameter plasma column exhibits resonances as a function of plasma density when the waves are polarized at right angles to the axis of the column. The electron density at resonance has been measured, using a microwave cavity technique, in pulsed helium arc discharges, as the frequency of the incident microwaves was varied from 2 to 4 kMc/sec. At resonance, the squared ratio of plasma frequency to incident frequency is found to be independent of frequency and neutral gas pressure, but somewhat dependent on pulse duration. Results are in qualitative agreement with recent analyses of the interaction between electromagnetic fields and thermal plasmas with finite dielectric boundaries.

Wave Propagation in an Active Dielectric Slab
View Description Hide DescriptionAn analysis is made of the propagation of electromagnetic radiation in a dielectric slab having a negative electrical conductivity, sandwiched between semiinfinite regions having the same dielectric constant but positive conductivities. The threshold conditions corresponding to zero attenuation for waves propagating in the plane of the slab are determined. For slab thicknesses that are small, compared with a wavelength, the most easily excited wave is polarized with its electric vector perpendicular to the plane of the slab but for thicker active regions the threshold is independent of polarization. These results are compared with observations of stimulated emission in p‐n junction lasers.

Calculation of Fields, Forces, and Mutual Inductances of Current Systems by Elliptic Integrals
View Description Hide DescriptionA minimum‐ordered set of elliptic integral equations is given for magnetic vector potential, axial and radial fields, the mixed gradient ∂B _{ρ}/∂z for axially symmetric iron‐free current systems, and for mutual inductance and force between coaxial units. The units may be circular loops, cylindrical or plane annular current sheets, or coils of thick section. With full use of correlations, six basic equations suffice for all properties of loops, solenoids, or combinations. The axial solenoid field is calculated by a superior new method. Thick coils are analyzed with the solenoid rather than the loop as element. Magnetic properties are then integrated in radial depth by Gaussian numerical quadrature of variable order. This method can deal with coils whose sections are not rectangular, and whose current densities are a function of the cylindrical radius.
No tables are used, and the procedure is simpler and faster than previous methods, for computer use or for solving smaller problems by hand. It has been coded as a unified set of programs for the IBM 7090. These will be described elsewhere; they can compute fields, and trace lines of force even within the windings, or force and mutual inductance between coils in contact, also self‐inductance of ideal solenoids or of thick cylindrical coils. Errors are normally less than one part per million, in extreme cases less than one per thousand.

Ion‐Emission Requirements for Removal of Electron Space‐Charge Barriers
View Description Hide DescriptionA space‐charge analysis is made for a parallel plane, collisionless diode where ions as well as electrons are generated at the emitting electrode. The resulting potential distributions are examined to determine the required conditions for diode operation in the retarding field, space‐charge‐limited, or the saturated emission mode. Such analyses have already been given for vacuum diodes. This paper first summarizes and then generalizes these results.

Theory of Space‐Charge‐Limited Emission in High‐Pressure Gas Diodes
View Description Hide DescriptionA theory for space‐charge‐limited current in gas‐filled thermionic diodes has been developed which takes into consideration the variation of mean free path with electronic energy. The theory is applied to experimental data obtained on gas‐filled diodes containing helium, neon, argon, and krypton, in the pressure range 1–700 Torr, and is shown to be in reasonable agreement with experiment.

Electric Tunnel Effect between Dissimilar Electrodes Separated by a Thin Insulating Film
View Description Hide DescriptionThe theory of the electric tunnel effect has been extended to asymmetric junctions—i.e., junctions having electrodes of different materials. It is found that the J—V characteristic is polarity‐dependent. At lower voltages, the greater current flows when the electrode of lower work function is positively biased, in agreement with observations on junctions having one aluminum electrode. At higher voltages, there is a change in direction of rectification; i.e., greater current flows when the electrode of lower work function is negatively biased. This effect has also been experimentally observed.

Electron Reflection from Cesium‐Coated Polycrystalline Metals at Low Primary Energy
View Description Hide DescriptionThe reflection of low‐energy electrons from polycrystallinemetal surfaces partially coated with cesium has been investigated by the retarding potential difference technique. The technique is described and results for primary energies below 5 eV are given. Retarding potential measurements of the longitudinal component of the reflected electron energy are consistent with elastic reflection and a cosine angular distribution at low primary energy.

Effect of Insulating‐Film‐Thickness Nonuniformity on Tunnel Characteristics
View Description Hide DescriptionIn all theoretical investigations of the electric‐tunnel effect through a thin insulating film between two electrodes, it is commonly assumed that the insulating film is of uniform thickness. In practice, it is reasonable to expect that this assumption is not always valid. The present paper demonstrates that nonuniformity in film thickness can have an important effect upon the terminal current—voltage characteristics of tunneling devices. This effect can, at least in part, account for the discrepancy between calculated and measured values of tunnel current.

Gain Saturation and Output Power of Optical Masers
View Description Hide DescriptionThe nonlinear gain characteristics of optical maseramplifiers at high beam intensities, and the optimum cavity coupling of maseroscillators for maximum output power, are computed for maser media with homogeneous and inhomogeneous line broadening. An approximate expression is derived for the power output of a gas maseroscillating simultaneously at many longitudinal cavity resonances, based on the assumption that the gain saturates independently at each frequency. In each case, the decrease of maser gain with radiation intensity involves an empiric constant, or saturation parameter, which is characteristic of the active medium.
Power and gain measurements at 1.15 μ on three He–Ne maser tubes of different diameter, in a cavity 1.75 m long, are found to satisfy the derived multifrequency power expression, and permit evaluation of the gain—saturation parameter for this gas mixture. The power expression, derived for a single transverse mode, is unexpectedly found to hold for multimode oscillations as well, within the range of measurements. From the measured saturation parameter and the derived expressions, the performance of amplifiers and other oscillators with the same active medium can be predicted.

Direct and Indirect Tunneling in Germanium at Different Temperatures
View Description Hide DescriptionThe current—voltage characteristics of narrow germaniump—n junctions, measured for reverse biases at 4.2°, 77°, 195°, and 298°K, are in agreement with the usual tunneling probability expressions. The reverse current increases at the onset of the direct tunneling transition, that is, in addition to the indirect transition at lower biases. The onset voltage shifts from −0.121 V at 4.2°K to −0.082 V at 298°K in agreement with the band shift in germanium and the smeared‐out carrier distribution around the Fermi level. The absolute value of the onset voltage is within 16% of the calculated voltage. The slope d ln(J/V)/dV is −11 (V)^{−1} for a typical junction; the constant field approximation gives −7 (V)^{−1}.

Noise Picked Up by External Probes in Electrodeless Gas Discharges
View Description Hide DescriptionNoise and impedance measurements are reported for external electrodes wrapped around electrodeless discharges. For frequencies between 0.5 and 10 Mc/sec the equivalent noise temperature T_{n} of the probe noise lies between ½T_{e} and T_{e} , where T_{e} is the electron temperature; this is attributed to the space‐charge suppression of the ion shot noise flowing to the wall under the electrodes. At higher frequencies the noise temperature T_{n} increases because of a high frequency noise mechanism that is also present in dc discharges. The observed data can be fully interpreted in terms of what is known about the noise and impedance properties of floating probes in dc discharges.

Maximum Gain for Forward‐ and Backward‐Wave Optical Maser Amplifiers
View Description Hide DescriptionAn analysis has been made of the mechanism of amplification in a device consisting of three media. The first medium is considered to be air, the second medium a crystal having a specific dielectric constant and distributed negative conductivity of constant value, and the third medium is air. The equations for power gain in transmission and reflection are derived in a general manner. Following this, the condition on the length of the active region for maximum power gain in both forward and reflected modes of operation is approximated and also the magnitude of gain. When the development is applied to the ruby optical maser the length producing maximum gain is found to be the same for both the reflection and transmission‐type amplifier. Furthermore as the length of the crystal is increased, oscillations are predicted at a single optimum value of the product of the negative attenuation constant and length.

Approximate Electromagnetic Transition Probabilities and Relative Electron Excitation Cross Sections for Rare‐Gas Masers
View Description Hide DescriptionNumerical values for the electromagnetic transition probabilities for a large number of rare‐gas maser lines are calculated and tabulated for assisting in the evaluation of existing and new gaseous masers as well as for other applications such as work in astrophysics. In addition, in order to determine the dominant pumping mechanisms in such masers, an approximate method has been developed for calculating the relative cross sections under electron impact for production of various excited states from the ground state of the rare‐gas atoms. A brief discussion of the experimental observations in the rare‐gas masers is made in terms of the results given here.

X‐Ray Diffraction and Diffusion in Metal Film Layered Structures
View Description Hide DescriptionArtificial layered structures that produce sharp diffraction of x rays are described. The structures were made by alternately evaporating 140 Pb and Mg layers onto a glass slide (d=27 Å). The diffracting efficiency of the layered structures is compared with other structures used in soft x‐ray spectroscopy. The usefulness of the structures is limited by diffusion in the layered system which caused the diffraction pattern to decay to half intensity in 2 days at room temperature. At 0°C the half life was 5 weeks. The diffusion model of DuMond and Youtz was used to determine an effective diffusion constant for the system over the temperature range 0–62°C. The equation D _{eff}=5.2×10^{−6} exp(−20 600/RT) cm^{2}/sec was satisfied.

Effective Diffusion Coefficient in Porous Media
View Description Hide DescriptionRecent calculations by Prager of upper bounds for the effective diffusion coefficient (or conductivity) in porous media, in terms of certain statistical parameters of the random geometry, are reformulated so as to apply specifically to a bed of spherical particles. The calculations are simplified by considering an idealized bed in which centers are randomly situated without restricting the spheres to nonoverlapping locations. The result, applicable to randomly overlapping spheres of either uniform or nonuniform sizes, gives the upper bound for the effective diffusion coefficient as φD _{0}/[1−½lnφ], where D _{0} is the actual diffusion coefficient in a fluid which fills the void regions of the bed and φ is the void fraction. This result is compared with experimental results of various investigators for nonoverlapping spheres and also with Hashin and Shtrikman's expression for the best upper bound that can be calculated without taking the statistics of a particular random geometry into account.