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This paper extends the theory of magnetic domains with emphasis on recent developments in ``hard bubbles''. A spin configuration of a planar Bloch wall containing periodic Bloch lines is presented which minimizes the magnetostatic energy to first order in the parameter 2πMs2/Ku for arbitrary period. The form of this solution is found to suggest the form of the dynamic breakdown of this spin configuration. The remainder of the paper consists of applications of the gyrocoupling force and vector, fg = g × v and g = − (Ms/|γ|)sinθ(▿θ) × (▿φ), respectively, and the dissipation force and dyadic, fa = d · v and d = − α(Ms/|γ|)[(▿θ)(▿θ) + sin2θ(▿φ)(▿φ)]. The use of fg and fa produces results with fewer assumptions and with less calculation than with previous methods. The magnitude of g is found to be an invariant local measure of the ``hardness'' of the domains. Integrating fg and fα produces a general planar wall response function from which the hard bubble dynamic equation is obtained. It is found that the difference between the hard bubble and normal bubble damping parameters can be accounted for by examination of the hard bubble spin‐wave spectrum. An estimate of the velocity required for the production of horizontal Bloch lines is made using fg. This velocity is a substantial fraction of the Walker velocity. The vector g is used as an aid in the visualization of the mechanism by which ion implantation suppresses hard bubbles. From the point of view of both mobility and hard bubble suppression, materials having a large in‐plane anisotropy are found to be desirable.

Electric fields associated with the space‐charge layer at the surface of silver halide grains are expected to have a marked effect on the photographic properties of emulsions. The purpose of this paper is to describe a new method based on dielectric measurements to obtain information on the surface layers. It is shown that the surface layers have a strong effect on the low‐frequency dielectric constant so that it is possible to derive the properties of the former from measurements made on the latter. Formulas connecting the layer properties to the dielectric constant of the crystal are derived. The experimental results, obtained with the method described here, will be the subject of a separate paper.

In an earlier paper a method was described for numerical calculation of the Peierls energy barrier to dislocation motion in the Frenkel‐Kontorova model. The present paper reports an approximate analytical calculation of the barrier for the model with a cubic substrate, and compares the barrier analytically calculated with the barrier numerically calculated by the earlier method. The analytical method relates the barrier to poles on an axis of imaginary lattice spacing.

The fabrication of a planar guard ring diode which exhibits uniform microplasma‐free breakdown is described. Discrepancies are discussed between the behavior of these junctions and those reported by Batdorf et al. and Chynoweth, including results showing extremely hard V‐I characteristics associated with uniform avalanche breakdown. Experimental evidence is presented which confirms Shockley's theory in which the breakdown behavior is predicted from the Poisson distribution of impurities within the space‐charge layer. The photomultiplication technique as described in Paper I is applied to uniform p—n junctions. The linearity of 1/M vs V, as predicted by theory, was verified for values of M between 1.6 and 500. For higher values, the multiplication curves deviate from a straight line. In this higher range they are in good agreement with the pulse‐multiplication model developed in Paper I. Light emission patterns from these junctions are shown and a correlation between these patterns and crystal properties is discussed. The effects of resistivity striations in the silicon single crystals is shown to have a strong effect on breakdown areas and no effects of dislocations and oxygen on uniformity are found. From capacity and multiplication measurements a value for the breakdown field of EB=445±25 kV/cm was obtained for a 32‐V junction.

It has been proposed by P. Boning that the curve of the rise of continuous voltage due to the residual charge of a capacitor may be used for computation of the dielectric loss under alternating potential. The proposal has been examined in experiments on two types of capacitor, one with impregnated paper and the other with glass as dielectric. A reasonable agreement between measured and computed values was found for the glass capacitor. A wide divergence was found for each of the two impregnated paper capacitors and grounds are offered for the conclusion that the Boning proposal is not sufficient for certain types of dielectrics.

The noise spectrum due to fluctuations of electron‐hole pairs in a semiconductor in the presence of a magnetic field when ambipolar drift and generation recombination are the only important noise processes was presented in a previous paper. In this paper the noise spectrum is presented for the opposite case when ambipolar diffusion and generation recombination are the important processes with ambipolar drift being negligible and unimportant. This spectrum was obtained via the Green's function for the macroscopic differential equation which governs the behavior of the conditional average for fluctuations in the electron‐hole‐pair particle density when ambipolar diffusion and generation recombination are the only important noise processes. From the obtained result for the spectrum, numerical calculations were carried out in order to display the functional dependence of the noise spectrum on frequency and magnetic field strength for fixed ratios of the mean volume lifetime of electron‐hole pairs to the characteristic ambipolar diffusion time of electron‐hole pairs along the direction of the magnetic field. Finally, it is shown that for high frequencies the asymptotic dependence of the spectrum on frequency obeys the ``universal 3/2 power law''.

This paper provides additional experimental evidence for the Taylor theory of dislocations and the Taylor theory of the polycrystalline aggregate. For annealed copper (as had been found by Bell for annealed aluminum) the governing stress‐strain curve for plastic wave propagation is a parabola, as predicted by the Taylor theory of dislocations. Using the Taylor theory of the polycrystalline aggregate, the parabolic stress‐strain law for annealed copper, as had been shown earlier for annealed aluminum, is determinable from compression stress‐strain curves for single crystals.These experimental data in annealed copper are obtained from the free‐flight constant‐velocity impact of identical specimens using the diffraction‐grating technique for the measurement of strain and surface angle.From the results given in this paper, together with those obtained earlier by Bell for annealed aluminum and the recent results of Sperrazza for pure lead, it may be concluded that strain rate does not play a significant role i...

This paper discusses some features of the electronic structure of magnetic impurities in metals.For impurities in normal metals, applications of the model of resonant scattering states are made in the following directions: (1) discussion of the orbital degeneracy within the Hartree‐Fock approximation and applications, particularly to cerium; (2) discussion of the magnetic solutions: effective values of J, occurrence of magnetism, and the Kondo effect; (3) influence of correlation.The properties of impurities in transition metals are also discussed: magnetic moments, specific heat, resistivity. Evidence for two‐current conduction in ferromagnetic metals is given. The paper ends with a discussion of dynamical properties of impurities.

In this paper the magnetic contribution to the isotropic lattice contraction in an itinerant antiferromagnet, described by the Hubbard model, is discussed. The isotropic lattice contraction is assumed to arise from the electron‐lattice interaction. The spin polarization per site and the isotropic lattice contraction are calculated for a single half‐filled band, simple cubic system in a tight‐binding approximation with several ratios of bandwidth to intra‐atomic exchange parameters, as well as several electron‐lattice coupling parameters. The results of the calculations show that for itinerant antiferromagnetic materials, the magnetic electrons produce, near the transition temperature, a lattice contraction which is less in the antiferromagnetic state than in the paramagnetic state. Hence, there would be an apparent expansion in the material at the transition temperature for a decreasing temperature. It is anticipated that the theory given in this paper contains the essential features of a more elaborate treatment.

Spin-ordered materials may exhibit a magnetic polarization which is proportional to an applied electric field and an electric polarization which is proportional to an applied magnetic field. In this paper a comprehensive discussion is given of the present knowledge of these magnetoelectric (ME) effects. The specific topics covered include the thermodynamic and magnetic symmetry considerations which are relevant to the ME effects and also to the piezomagnetic and piezomagnetoelectric effects. The major part of the paper is a review of the experimental and theoretical work on ME effects in Cr2O3 carried out by the present authors. This includes measurements of the anisotropy of the ME effects, theory of the temperature dependence and atomic mechanism of the ME effects, observation of the magnetically as well as of the electrically induced ME effect, experiments on magnetic annealing and other structure sensitive aspects of ME effects, and the role of antiferromagnetic domains in the interpretation of the results.

Extending the investigations of Papers I–III, infinitely tall ``hybrid cells'', i.e., dislocation cells derivable from mixtures of different orders of multipoles, are considered. A symbolism is developed aiding in the analysis of such cells. It is shown that at different distances the stress fields of hybrid cells are dominated, in turn, by the multipoles composing them. For example, a cell that may be regarded as an assembly of dipoles, tripoles, and hexapoles exhibits a stress field that has dipole nature at the farthest distances, has tripole nature in an intermediate range, and has hexapole nature at the closest distance just beyond the true short‐range stress field of the cell walls. The latter is the same as that of the corresponding infinitely extended boundaries, as was shown in Paper III.

A number of recent papers have discussed the Hall effect in a material consisting of high‐conductivity grains surrounded by thin low‐conductivity layers. These discussions were based on a model in which the grains are identical parallel cubes and the layers are of uniform thickness. The effective Hall constant of this model is approximately equal to the Hall constant of the grains. To test the effect of grain geometry on the effective Hall constant, the present paper discusses the Hall effect in the ``composite sphere'' material in which the grains are spheres of various sizes and the intergranular layers are formed from spherical shells. In this model also the effective Hall constant is approximately equal to the Hall constant of the grains, suggesting that, in general, the effective Hall constant is not strongly dependent on the grain geometry.

This paper considers the response of the magnetization of a small ferrimagnetic ellipsoid to spatially uniform rf magnetic fields of one or more frequencies. Only a few pertient cases can be considered in this short paper. The analysis is applicable to other excitations and a more complete report will be published elsewhere. Some of the work presented here duplicates that of Pippin [Proc. Inst. Radio Engrs. 44, 1054 (1956)], Jepsen, and others, but the approach to the problem is quite different and allows one to extend previous results, as well as to derive new ones.The effects of symmetry planes and anisotropy will be considered as well as the permeability tensor for the general ellipsoid when modulation terms of the magnetization are neglected.

While magnetization reversal in a large film sheet under uniform‐field excitation is determined by the macroscopic anisotropy property and microscopic magnetization ripple structure, the magnetization reversal in miniaturized multilayer devices, in addition, depends strongly on the geometry of the device structures. Earlier papers reported the study of coupled‐film strips using a nanosecond microscopic Kerr apparatus and simultaneous inductive and magneto‐optic‐measurement techniques. The present paper describes the reversal behavior in two coupled‐film structures, in which the easy axis of each Permalloy layer may be aligned parallel to the strip length (closed hard axis or CHA) or perpendicular to the strip length (closed easy axis or CEA). The Permalloy layers may also be mismatched in thickness. When a Permalloy backing is added to the external drive line as a keeper, the reversal phenomena in both the storage layers and the keeper have been observed.

Two recent papers have dealt with the observation that the Schottky barrier height, Vb′, of the gold‐gallium arsenide system increases linearly with the thickness of an interfacial oxide layer, l. In this paper it is shown how this linear relationship can be derived by considering the cause to be the same as that of the flat‐band voltage shift in MOS devices. That is, charge trapped at the oxide‐semiconductor interface creates an image charge in the semiconductor bulk. The slope, dVB′/dl, predicted by this analysis is in good agreement with the 1.75×10−6V/cm value experimentally derived. The predicted barrier height also varies linearly with the amount of trapped surface charge, Qss.

Low‐temperature neutron‐scattering study together with the zero‐field AFMR in MnF2 furnished a reliable set of values of first‐ and second‐neighbor exchange integrals and the uniaxial anisotropy energy. It is the purpose of this paper to see to what extent one can understand the high‐temperature properties such as the Neel temperature and the anisotropic susceptibilities in terms of the known parameters obtained at low temperatures. For this purpose the cluster‐variation method is used in which up to the two‐spin correlation is taken into account. One of the main tasks of this method is to diagonalize effective one‐ and two‐spin Hamiltonians. It is noted here that the anisotropy energy could be as big, at least, as the second‐neighbor exchange energy. It is, therefore, not justifiable to treat the anisotropy energy as a small perturbation. In this paper diagonalization of the effective two‐spin Hamiltonian is achieved for the actual spin, S = 52, and the Neel temperature and the anisotropic susceptibiliti...

This paper describes a model for insulator surface charging in high‐voltage ceramic vacuum diodes. The model involves electron emission from the insulator‐cathode‐vacuum junction followed by electron avalanches on the insulator surface which leave the wall positively charged. Experiments were performed to measure (i) the triple‐junction (cathode‐vacuum‐insulator interface) emission and its relation to the initiation of the avalanche, (ii) the dynamic current in the avalanche, and (iii) the saturated surface charge resulting from the avalanche. The experimental results were interpreted by computer simulation in terms of the model and were found to be in close agreement with the predictions.

It has been shown that effective uniaxial anisotropy fields Hk″ of epitaxial magnetic‐garnet bubble materials can be found from an optical measurement of the sample's easy‐axis susceptibility. The susceptibility is influenced by the cubic anisotropy which the materials possess in addition to their induced uniaxial anisotropy. This paper examines in detail how the optical measurements are affected by various ratios of cubic and uniaxial anisotropies. In particular, it is found that Hk″ can be found accurately using this technique for a wide range of material parameters which includes bubble materials. A procedure which corrects for sample misalignment is presented along with a method by which the cubic and uniaxial anisotropy constants for a material can be calculated from measurements of its Hk″ and magnetization.

The theory of diffusion in grain boundaries was initiated by Fisher, using an idealized model in which a poorly diffusing half‐space (the crystal) is bisected by a thin well‐diffusing slab (the grain boundary), with a fixed concentration of diffusing material suddenly established at the free surface. In the present paper we first improve Fisher's result by removing one of his approximations. We then generalize Whipple's later exact solution to include anisotropic diffusion in the crystal, and other changes; the generalized theory now contains both the original Whipple result and the improved Fisher result as special cases and displays individually the effects of the different assumptions.

The prediction of the electric field strength at which gas breakdown will take place is a difficult and crucial problem for many applications. In the case of microwave antennas, breakdown in the gas or plasma surrounding the antenna first occurs in the inhomogeneous near‐field region close to the antenna surface. Recently, variational techniques have been used to estimate breakdown field strengths in such cases. These techniques have one drawback in that only upper bounds are provided, i.e., a field strength above which breakdown definitely takes place. Depending upon the accuracy of a particular calculation, breakdown may occur for an appreciable range below the estimated field strength. What is needed is a lower bound upon the breakdown field strength. In this paper a formulation of variational theory is used which allows lower bounds to be calculated. In addition, a variational‐iterative technique is presented by which it is possible to systematically improve upon a calculated lower bound should this b...

Numerical calculations are made of the theoretical strength of fcc crystals with two‐body exponentially attractive and exponentially repulsive interatomic interactions; the crystals are subjected to unconstrained (100) uniaxial tension and compression. The calculations are made from the point of view of mechanical lattice stability; the general theory has been presented in an earlier paper. The numerical values of the parameters characterizing the interatomic interactions were calculated from the elastic moduli C11 and C12 and the stress‐free equilibrium value of lattice parameter for Ni; the element Ni was selected for this purpose because (i) the Cauchy condition is not severely violated for Ni, (ii) the correct (i.e., experimental) linear elastic stress‐strain behavior is exhibited by the theoretical model of the crystal, and (iii) reasonably good agreement is obtained between theoretically calculated and experimentally observed anharmonic pressure‐vs‐volume behavior. Calculations are carried out using...

The one‐band effective mass approximation for the dispersion relationship in the barrier of a metal‐insulator‐metal (MIM) tunnel junction fails if the barrier height is a considerable portion of the band gap of the insulator. This paper reports on results when the more realistic dispersion relation of Franz and Kane is used and displays the sensitivity of the tunnel effect to the band model. We illustrate some examples of the energy distribution of the current. Characteristic features of tunneling through trapezoidal‐like barriers will be discussed, including maxima in the logarithmic derivative curves, in the thermal I‐V characteristics, and the zero‐bias offset of the conductance minimum. Calculations are performed by integrating the tunnel equation numerically, and analytical approximations for this equation are also presented from which the effect of various parameters on the tunneling characteristic can be estimated.

Magnetic walls, as far as we are concerned with the internal stresses they produce, are Somigliana singularities. In this paper these internal stresses are completely calculated, as well as the lattice curvatures (bend twist) to which these walls give rise in the case of a junction of several walls. It is possible to separate in these elastic fields effects due to a quasidisclination located along the junction (mixed wedge and twist character) and effects due to a distribution of quasidislocations on the walls.

Minority carriers within the inversion layer of an inverted MOS capacitor can move in response to a high‐frequency ac signal even though the total minority‐carrier charge is fixed at the value set by the dc bias. In this paper a simple explicit formula for the high‐frequency capacitance which includes this ac inversion layer polarization effect is derived. The derivation is based upon the assumption that the distribution of minority carriers within the inversion layer is governed by a constant quasi‐Fermi level, independent of position within the inversion layer. Hence, the resulting capacitance formula is restricted to the case where minority‐carrier trapping by defects in the inversion layer or at the interface do not significantly hinder the ac response of the minority carriers. Comparison of the new formula with the calculations of Sah, Pierret, and Tole, which have as their main approximation the neglect of the ac minority‐carrier movement, shows that the neglect of this effect leads to a 7% error in strong inversion at 1013/cm3. Comparison with the commonly used formulas of Lindner and of Grove, which contain approximations in addition to the neglect of inversion layer polarization, shows that these formulas are in error by 9% and 4%, respectively, in strong inversion at a doping level of 1013/cm3. Although more accurate than these other calculations in strong inversion, the Grove model is less accurate in depletion and weak inversion. Figures illustrating the error involved in all three earlier approaches as a function of bias with doping level as a parameter are presented.

The generalized Maxwell Garnett theory developed in the preceding paper is utilized here to specify the state of roughness of a surface. Both thick and thin metal samples are measured on the ellipsometer. In the interpretation, the surface roughness layer is replaced by a smooth but anisotropic medium whose optical behavior is assumed to be governed by the generalized Maxwell Garnett theory which specifies a roughness layer by two parameters d and q. Success of the interpretation is judged according to the degree of independence existing between the two parameters d and q and the angle of incidence. Experimental results on several metals indicate that in many cases the surface roughness and not an oxide layer is responsible for the variation of ellipsometer parameters ψ and Δ from that of a truly smooth bulk material surface.

All simulations are performed with a single interatomic potential, the general features of which are outlined in a paper by Johnson. Analyses of a vacancy, an interstitial, and a stable (a/2) 〈110〉 edge dislocation in copper are presented, along with calculations each describing a vacancy and an interstitial in static equilibrium at the edge of the dislocation. Vacancy and interstitial formation energies and associated strain patterns are calculated. The 〈100〉 split interstitial configuration is stable with a formation energy of 3.060 eV. The vacancy formation energy is 1.165 eV. The strain patterns agree well with those obtained by others. The (a/2) 〈110〉 edge dislocation on the {111} plane is positioned in the lattice according to a previously devised procedure which results in complete agreement between atomistic and continuum treatments in regions of small strain. Atomic displacements parallel to the dislocation line are analyzed and their variation with distance from the line is shown to be oscillato...

Micromagnetics predicts that domain nucleation in an in‐plane field in mechanically rigid uniaxial films with easy axis normal to the faces should take the form of stripes parallel to the field. This prediction does not agree with observation in some real films. It has been shown previously that the magnetoelastic interaction in deformable films may cause the stripes to be perpendicular to the field when the films are thick enough. Quantitative assessment of this effect is difficult because the magnitudes of the magnetoelastic constants are not accurately known, and because high‐quality epitaxial films are at least partly constrained from deforming. In this paper we discuss another interaction which can cause the stripes to be perpendicular to the field in a [111]‐oriented cubic film, such as bubble‐device garnet. The interaction energy is a dipolar energy brought into play by the effectively trigonal anisotropy. It vanishes when H is along [112] and is maximum when H is along [110]. Quantitative evalua...

A hysteresis in the rectification of the contact aluminum‐aluminum oxide‐electrolytic solution was found by Dekker and van Geel. In the present paper, measurements of the current‐voltage characteristics between 1 and 2000 cycles are described. A tentative explanation of the hysteresis is given in terms of a pre‐breakdown phenomenon.

Determination of the nature and distribution of oxide charge in MOS structures is important to an understanding of oxide charging phenomena. In addition to their relevance to device failure mechanisms, it appears that charging phenomena may be used to advantage in memory device applications. The physical mechanism dominating the voltage dependence of photoinjected currents in SiO2 is the scattering of electrons in the region of the oxide between the injecting electrode and the image force potential maximum. Since the spatial position of the potential maximum depends on the electric field resulting from space charge in the oxide as well as the field due to the applied voltage, analysis of the V‐I characteristics of photoinjected currents can provide information about the spatial location of oxide charge. Presented in this paper are the results of an analysis of the effects of oxide space charge on the voltage dependence of photoinjected currents. It is shown that effective charge distributions in SiO2 can ...

The purpose of this paper is to present the theory of a plasma negative resistance amplifier based on an approximate quasi‐electrostatic model of a modified quadrupole cavity containing a plasma column and hyperbolic quadrupole electrodes with side resonators. The theory is extended to plasmas with finite collision frequencies in a finite magnetic field. By use of a nonlinear equation of the electron motion obtained by expanding the time varying applied electric field in Taylor's series, it is shown that the electrons in a plasma column behave as a nonlinear reactance and that a net signal amplification can be realized when sufficient pump‐power is properly applied. It is also shown that the effective noise contributed from the plasma can be reduced by decreasing the plasma electron collision frequency or the plasma density. A preliminary experimental result which indicates the presence of a nonlinear plasma interaction is described.

The structure of static walls is analyzed assuming that the film thickness is much larger than the wall width. It is shown that several different types of wall structure can exist. For the normal wall type the twist angle (angle between the wall magnetization at the midplane of the film and at the film surface) is approximately π/2. For the first anomalous type this angle is approximately −3π/2, for the second type approximately 5π/2, etc. The width and energy of such walls are calculated using (i) a Bloch‐line approximation and (ii) a sinusoidal variational trial function (as in Paper I of this series). The ratio of the energy of a twisted wall (E) to the energy of an untwisted wall (E0) can in all cases be represented as E/E0=(1−βσ)1/2, where σ=4πM0/Ha [M0 is the saturation magnetization, Ha is the anisotropy field]. According to the first method β=0.692 for the normal wall type and β=0.692− (π/c)(D/2πM)1/2 for the first anomalous type. Here 2c is the film thickness, D=2A/M0, and A is the exchange stiff...

An integrated summary is given of some of the results and physical ideas contained in 16 experimental and theoretical papers on ferromagnetic resonance contributed to the 1960 Conference on Magnetism and Magnetic Materials. The topics discussed include the uniform mode and anisotropy, nonuniform magnetostatic and electromagnetic modes, spin-wave resonance, sublattice effects, paramagnetic “impurities,” spin-wave scattering, rapidly relaxing ions, determination of spin-wave transition probabilities, thermal relaxation, and the theory and use of the “parallel pump” method for measuring relaxation and exchange parameters. Although a complete review of ferromagnetic resonance is not intended, the emphasis is on an organization of this field and on the introductory and explanatory material presented with each topic.

In this paper static properties of two kinds of point defects in an antiferromagnet are examined. The topology of the two defects, vacancies and interstitials, is different, the first belonging to a well‐defined sublattice, and the other acting symmetrically on both sublattices. The perpendicular susceptibility of the vacancy is found to be positive due to a polarization of the medium, overcompensating the lack of magnetization due to the removal of one atomic moment. The additional susceptibility due to the interaction of pairs of vacancies is investigated; its sign depends on whether the two are on the same or different sublattices. It is shown that an interstitial embedded in an antiferromagnetic crystal has a moment that is linked to a plane of easy magnetization, perpendicular to the axis of the crystal, by a pseudoanisotropy field of the order of magnitude of an exchange field. The coupling of such interstitials is shown to decrease as r−7 but could be strong enough to induce cooperative effects.

The superconducting magnet is a key component in various applications including high‐energy physics, fusion research, magnetohydrodynamics, and electrical rotating machinery. This paper presents the general characteristics of state of the art of superconducting magnets as far as design and performance are concerned. The properties of superconductors are briefly discussed, and the basis for design of stable conductors is set forth. Examples of conductors and magnet systems are given and discussed. The current state of affairs is summarized in three plots showing size versus field achieved, current density in coils as a function of magnetic field, and specific weight versus stored magnetic energy.

This paper draws together a large amount of experimental information obtained by others as well as the author. Out of the maze of conflicting results one set of consistent characteristics of the microwave emission and its associated phenomena results. The reconciliation is obtained by means of a model for the spatial distribution of plasmas during emission. It shows why some samples emit preferentially for B ∥ E, others for B⊥E, and still others for intermediate orientation. Indeed, under the proper sets of conditions the same sample can be made to emit for all these various orientations in consonance with the model. The model also clarifies the various observed threshold dependencies. Why megahertz resistance oscillations of two different natures attend emission under some conditions and why under others such oscillations are totally absent is explained. Thus three characteristics of the emission and its associated phenomena can be consistently predicted, namely, the polar dependencies, the sometimes attendant megahertz resistance oscillations, and the threshold dependencies on E and B. It is concluded that the role of the B in the emission process is to place concentrated plasma within a radiation absorption length of a sample surface which is orthogonal to the direction of microwave propagation. It is argued that all observations of emission from InSb, at low and high electric fields, with and without magnetic fields, are caused by the same (unidentified) instability which is excited by the proper conditions of electric field and plasma density.

We have obtained exactly the excess dissipation due to a small spherical inclusion in a semiconductor, using the same model of the semiconductor which was investigated in previous papers of this series, and the ``four moment approximation'' to the electron‐distribution function. We have also calculated the high‐field limit of the transverse magnetoresistance for a dilute sprinkling of spherical inclusions, which is proportional to the high‐field limit of the excess dissipation, and varies as |H| as H→∞, where H is the magnetic field. Previously, Herring obtained approximately the excess dissipation of a cylindrical inclusion with axis parallel to the magnetic field and made plausible a high‐field transverse magnetoresistance which varies as |H|/ln|H| as H→∞. In the case of spherical inclusion, we can investigate in detail perturbations produced by the external specimen boundaries, and we suggest that analogous results hold for a cylindrical inclusion.

This 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 A thick, sandwiched between metal electrodes. For Al2O3 layers the fit is excellent, resulting in barrier heights of 2.0–2.5 eV and thicknesses approximately 25 A 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 Al2O3 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.

The polarization reversal process in ferroelectrics has, up to now, been characterized solely by the total switching time and the maximum value of the switching current. The work presented in this paper was aimed at determining how the instantaneous value of the switching current in single crystals of BaTiO3 depends on the applied field, the state of net polarization of the crystal, and possibly other factors. It has been found that the switching current density can be expressed as the product of a function of the polarization, φ(p), and a function of the electric field, exp(−α/E). The form of the function φ(p) indicates a predominance of sideways expansion of 180° domains, with an exponentially increasing domain wall velocity. This last result is shown to be in agreement with a picture of domain wall motion by nucleation of new domain wall layers. This interpretation, together with some details of the switching current pattern, suggests that a crystal, although apparently single‐domain, may always retain some small domains of opposite polarization.

It is common knowledge that in cyclically stressed ferromagnetic materials an energy loss due to internal friction is observed; this part of loss disappears when the material is brought to saturation or above the Curie temperature. It is also known that a stress, applied to a ferromagnetic material, produces a motion of Weiss domains from their rest position.The scope of this paper is to verify experimentally the following hypothesis: in cyclically stressed ferromagnetic materials, energy loss because of magneto‐elastic internal friction is induced by a domain motion due to the applied stress itself.The ratio Ir/Is (where Ir=residual induction, and Is=saturation intrinsic induction) has been chosen as an index of the domain position; its measure has been carried out by normal ballistic method on a permeameter rigged with a torsion applying device.Energy loss was measured by means of a torsion pendulum; a coil allowed the saturation of specimen in order to separate magneto‐elastic from purely mechanical lo...

Previous measurements of minority carrier mobility by the Haynes‐Shockley technique have ignored one or more of the effects of the three‐dimensional nature of the ambipolar diffusion, and bulk and surface recombination. In some cases, the experimental conditions were tailored so that the effects of these factors were truly negligible, imposing restrictions on the respective experimental configurations. In general, each factor does influence the drift time from which mobility estimates are made. This paper shows how their effects may be conveniently and systematically included in the data analysis and gives examples of the processing of experimental data acquired from p‐type silicon samples of different geometries. The suitability of the new technique for measurement of mobility in thin wafers of material is pointed out.

A theoretical basis is provided for the interpretation of photoeffects observed in nonuniformly irradiated p‐n junctions. Differential equations describing the junction photovoltage are developed through an application of the continuity and diffusion equations. Solutions of the small‐signal steady‐state photoeffect equation indicate that the effects of nonuniform irradiation become increasingly important as the ratio of the lateral to the transverse resistance increases. α, a parameter introduced in this paper and designated as the lateral‐fall off parameter, is a measure of this resistance ratio. The lateral photovoltage resulting from nonuniform irradiation can be eliminated by reverse biasing the junction into saturation. Experimental curves in agreement with the predictions of the analysis are presented.

This paper presents an analytical investigation of the dependence of Faraday rotation and ellipticity on the heating dc electric field in III‐V semiconductors at low temperatures (k0T ℏωl), and the elastic scattering by ionized impurities and acoustic phonons in the passive region (e

If an energetic atom, a primary, slows down in a lattice, it has the possibility of traveling long distances without essential interaction along almost force‐free channels bordered by close‐packed atomic chains. This effect has not been considered until recently, because, for the sake of simplicity, the lattice has been replaced mostly by a corresponding random arrangement. This ``channeling'' behavior has been found in machine calculations by Robinson, Holmes, and Oen which take the lattice structure into account. In this paper, the behavior of a primary moving along a channel bordered by the most densely packed directions is investigated analytically. Numerical results are given for a Cu primary moving in a Cu crystal, but the results can easily be extended to other cases. Two potentials are used: an exponentially screened Coulomb potential after Bohr, used also in the machine calculations and thought to give an adequate description for relatively high energies and small interatomic distances; and a pur...

Techniques employing rectangular waveguides to measure complex permittivity generally contain the tacit assumption that the material fills the waveguide uniformly. With semiconductors this assumption may be poorly satisfied near the waveguide walls due to (1) air gaps, (2) oxide layers, (3) potential barriers, and (4) distributed ``screening'' charges. The uniform‐filling assumption is removed in the present paper by treating the contact region with perturbation theory. The results are found to be simply represented by a lumped‐parameter equivalent circuit. Measurements performed on intrinsic germanium at 10.5 GHz agree well with the theory and indicate that unintentional air gaps and oxide layers dominate the measurements at high conductivities, even for ``tightly'' fitting samples.

In this paper it is demonstrated that the anisotropy, as measured by Hiraoka et al., in the extraordinary Hall constant R1 of nickel can be theoretically predicted but cannot be explained in terms of the anisotropy in the resistivity alone. A quantum calculation, using both the tight‐binding approximation and the Karplus‐Luttinger theory of the extraordinary Hall effect, is performed to show the existence and estimate the magnitude of the anisotropy in R1. The phenomenological equations for the anisotropy in the resistivity, as derived by Doring, are employed to indicate that Hiraoka's experimental results cannot be explained only in terms of the anisotropy in the resistivity measured in the direction of the Hall voltage.

Thin Ni‐Fe films which exhibit uniaxially magnetized domain patterns whose boundaries tend to follow the physical boundary of the film can be produced by a special evaporating technique if oxygen and minute quantities of diffusion pump oil are added to the system prior to evaporation. This paper describes the properties of these ``shape sensitive'' films and the factors influencing their production. A hypothesis which correlates these factors with the film properties is proposed.

This paper describes the effect crystallite size has on the coercive force Hc of thin ferromagnetic films. Crystallite size was determined by the use of x‐ray diffraction using a small angle between the x‐ray beam and film samples. Films in this study ranged in thickness from 150 to 1750 A with crystallite size from 50 to 950 A and Hc values of 2.1 to 8.4 Oe.It was found that Hc is dependent on the crystallite size for films that have domain wall widths larger than the crystallite size. The data exhibits a decreasing Hc as the crystallite size increases for films with Neel or crosstie domain walls. For films with Bloch walls and crystallite size greater than the domain wall width, there is no apparent dependence on crystallite size of Hc.To a first approximation, the results of this study are shown to agree with the anisotropy constant variation term from Middelhoek's semiquantitative theory for coercive force of thin magnetic films. For films with domain wall widths larger than the crystallite size, this...