Showing papers by "Bell Labs published in 1970"

Analysis of individual differences in multidimensional scaling via an n-way generalization of 'eckart-young' decomposition

Abstract: An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychological space”. A corresponding method of analyzing similarities data is proposed, involving a generalization of “Eckart-Young analysis” to decomposition of three-way (or higher-way) tables. In the present case this decomposition is applied to a derived three-way table of scalar products between stimuli for individuals. This analysis yields a stimulus by dimensions coordinate matrix and a subjects by dimensions matrix of weights. This method is illustrated with data on auditory stimuli and on perception of nations.

Acceleration and trapping of particles by radiation pressure

Abstract: Micron-sized particles have been accelerated and trapped in stable optical potential wells using only the force of radiation pressure from a continuous laser. It is hypothesized that similar accelerations and trapping are possible with atoms and molecules using laser light tuned to specific optical transitions. The implications for isotope separation and other applications of physical interest are discussed.

Ionicity of the Chemical Bond in Crystals

Abstract: The nature of the chemical bond in crystals is discussed. The general theories of L. Pauling based on thermochemical data and of C. A. Coulson based on valence bond concepts are compared with a recent spectroscopic theory. Particular emphasis is placed on binary crystals of formula ${\mathrm{A}}^{N}{\mathrm{B}}^{8\ensuremath{-}N}$ which includes most tetrahedrally coordinated semiconductors as well as crystals of the rocksalt (NaCl) family. A wide range of physical properties is discussed, including crystal structure, energy bands, elastic constants, ionization energies, and impurity states. The role of quantum-mechanical sum rules and spectral moments in constructing simplified models of bond and band behavior is explored. Stress is laid throughout on methods for incorporating quantum-mechanical effects into properties of chemical bonds through algebraic relations rather than through variational solutions of the wave equation.

Elastic Properties of ZnS Structure Semiconductors

Abstract: A simple phenomenological theory of the elastic constants of sphalerite structure crystals is presented and shown to apply within reasonable errors to the known experimental constants. The theory utilizes a form for bond-stretching ($\ensuremath{\alpha}$) and bending ($\ensuremath{\beta}$) forces first used by Keating, to which are added effective point-ion Coulombic forces. Also it is pointed out that regularities in the experimental elastic constants of these crystals are readily explained in terms of the ionicity ${f}_{i}$ defined by Phillips and Van Vechten. Of particular note are the shear constants which decrease markedly with ionicity. It is found that this decrease is described quantitatively by $\frac{\ensuremath{\beta}}{\ensuremath{\alpha}}\ensuremath{\propto}(1\ensuremath{-}{f}_{i})$, which confirms the interpretation of $\ensuremath{\beta}$, since bond-bending forces should vanish in the ionic limit ${f}_{i}\ensuremath{\rightarrow}1$. Other equally simple formulas for the forces in terms of only the bond length and ${f}_{i}$ are shown to predict all the constants with a rms accuracy of 10%.

Bonds and Bands in Semiconductors: New insight into covalent bonding in crystals has followed from studies of energy-band spectroscopy

Abstract: Many of the most interesting developments in semiconductor physics that have occurred in the last few years and that are anticipated in the next few years appear to lie in the realm between physics and chemistry. In this article I have tried to show how this realm can be treated accurately and realistically within the framework of theory.

Application of Gutzwiller's Variational Method to the Metal-Insulator Transition

Abstract: It is shown that the approximate variational calculation of Gutzwiller predicts a metal-insulator transition as the intra-atomic Coulomb interaction is increased for the case of one electron per atom. The susceptibility and effective mass are calculated in the metallic phase and are found to be enhanced by a common factor which diverges at the critical value of the interaction.

Theory of Prism–Film Coupler and Thin-Film Light Guides

Abstract: A prism–film coupler has been discussed recently by Tien, Ulrich, and Martin as a device to couple efficiently a laser beam into thin-film dielectric light guides. This coupler also allows an accurate measurement of the spectrum of propagating modes from which the refractive index and the thickness of the film can be determined. We present here a theory of the prism–film coupler. The physical principles involved are illustrated by a method that combines wave and ray optics. We study the modes in the thin-film light guide and their modification by the effect of coupling. We also calculate the field distributions in the prism and the film, the power transfer between the prism and the film, and derive a condition of optimum operation. In one example, 81% of the laser power can be fed into any desired mode of propagation in the film.

Electronic Structures of Semiconductor Alloys

Abstract: The problem of the band structure of semiconductor alloy systems is treated by both the dielectric two-band method and by the use of an empirical (local) pseudopotential. With both methods, calculations are made in the virtual-crystal approximation assuming linear dependence on alloy concentration of the lattice constant and the parameters of the two methods. Contrary to some previous assertions, both methods predict, in general, a nonlinear dependence of the interband gaps on concentration. An estimate is also made of the effects of second-order perturbations to the virtual-crystal approximation, i.e., the effect of disorder. Of particular interest are the lowest direct and indirect energy gaps and the deviations of these from linearity. The treatment is confined to alloys of compounds having the formula ${A}^{N}{B}^{8\ensuremath{-}N}$, but quaternary and more complicated alloys may be treated as easily as the ternary alloys to which most previous experimental work has been confined. Results are compared to experiment and to the empirical formula of Thompson and Woolley. We find that, with one free parameter, the dielectric method gives good agreement with experiment, but that the local-pseudopotential method apparently does not yield satisfactory results for this problem.

A quasi-static technique for MOS C-V and surface state measurements

Abstract: A quasi-static technique is discussed for obtaining the ‘low frequency’ thermal equilibrium MOS capacitance-voltage characteristics The method is based on a measurement of the MOS charging current in response to a linear voltage ramp, so that the charging current is directly proportional to the incremental MOS capacitance With this technique, surface potential and the surface state density can be obtained relatively simply and over a large part of the energy gap on a single sample, while also providing a direct test for the presence of gross nonuniformities in MOS structures This method has been used to determine the surface state distribution at the interface of a bias grown steam oxide and 10 ω-cm n -type silicon, and the results are compared with composite measurements using the conductance technique for a similar interface The sensitivity for surface state density measurements is estimated to be of the order of 10 10 states per cm 2 eV near mid-gap for 10 ω-cm silicon and improves with decreasing doping density Some applications and limitations are also briefly discussed

Single-Particle Excitations in Magnetic Insulators

Abstract: In this paper, the density of states and the mobility of an extra electron or hole are calculated in the atomic limit of the Hubbard model. Both the half-filled single-band and multiple-band situations are discussed. The problem is formulated in terms of the number of paths which return to the origin leaving the spin configuration unchanged. The density of states then depends on spin configuration and we have considered the random (R) (high-temperature) and antiferromagnetic (AF) arrangements. Examination of the first five nonzero moments for the simple cubic lattice indicates that the bands are narrowed by a factor of 0.745 (AF) and 0.805 (R). However, the exact bands have tails extending out to the full free-particle width for both spin arrangements. An approximate one-particle Green's function is obtained by summing all graphs with no closed loops. Such paths give a density of states that is independent of spin arrangement and is relatively flat with a sharp square-root edge at $2{(z\ensuremath{-}1)}^{\frac{1}{2}}t$. Here $z$ is the coordination number and $t$ is the nearest-neighbor hopping integral. Within this approximation, we have calculated the mobility of an extra hole and have found typical values to be \ensuremath{\sim}1 ${\mathrm{cm}}^{2}$/V sec so that the mobility is rather small, even though the density of states has a width of order \ensuremath{\sim}1 eV. Intra-atomic exchange is shown to give a further narrowing of the band [a factor of ${(2)}^{\ensuremath{-}1/2}$ in the two-band large-intra-atomic-exchange example]. The effect of finite $\frac{t}{U}$ is considered, where $U$ is the intra-atomic Coulomb interaction, and is shown to have a strong effect on the band tail but relatively weak effects on the bulk of the band. Finally, we make a few remarks comparing our results with the observed mobilities in NiO and the relevance of intra-atomic exchange to the behavior of the dioxide and sesquioxide series.

Propagation of a Gaussian Light Pulse through an Anomalous Dispersion Medium

Abstract: The propagation of a Gaussian light pulse through a medium having a positive or negative absorption line is examined. Analytical approximations are obtained for the case where the spectral width of the pulse is much smaller than that of the line. It is shown that the pulse remains substantially Gaussian and unchanged in width for many exponential absorption depths, and that the locus of instants of maximum amplitude follows the classical expression for the group velocity, even if this is greater than the velocity of light, or negative. Numerical calculations have been used to examine what happens beyond the limit of usefulness of the analytical approximations.

Compton Scattering of X Rays from Bound Electrons

Abstract: Exact and approximate methods for determining the momentum distribution of electronic systems from Compton scattering measurements are presented. The method used previously to analyze Compton scattering measurements, the impulse approximation (IA), is derived from first principles, and its accuracy is compared with the exact calculations for Compton scattering from a hydrogenic system. It is shown that the IA gives very accurate results for weakly bound electrons and that exact calculation may only be necessary to substract out the contributions to Compton scattering from deeply bound core electrons. Experimental results for Compton scattering from helium are presented as a test of the above ideas. Analyzing the results of the experiment in the IA gives a momentum distribution for the weakly bound helium electrons which is in excellent agreement with the momentum distribution obtained from Clementi Hartree-Fock wave functions.

Time scale of intrinsic resistive fluctuations in thin superconducting wires

Abstract: A thermal-activation theory of intrinsic fluctuations in thin superconducting wires has been proposed by Langer and Ambegaokar (LA). Their fluctuation rate equals an exponential activation factor ${e}^{\ensuremath{-}\frac{\ensuremath{\Delta}F}{{k}_{B}T}}$ times a prefactor $\ensuremath{\Omega}$ which fixes the fluctuation time scale. Using a model based upon a time-dependent Ginzburg-Landau equation, we obtain a new estimate of $\ensuremath{\Omega}$ which is different in functional form from the LA estimate, and smaller than that estimate by more than 10 orders of magnitude for the conditions in recent experiments. To within corrections which are roughly of order unity, our expression is $\ensuremath{\Omega}=(\frac{L}{\ensuremath{\xi}})\frac{{(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}}{\ensuremath{\tau}}$, where ($\frac{L}{\ensuremath{\xi}}$) is the length of the sample in units of the Ginzburg-Landau coherence length $\ensuremath{\xi}$, ${(\frac{\ensuremath{\Delta}F}{{k}_{B}T})}^{\frac{1}{2}}$ is a correction for overlap of fluctuations at different places along the wire, and $\ensuremath{\tau}\ensuremath{\approx}{10}^{\ensuremath{-}8}$ sec is the relaxation time in the Ginzburg-Landau equation. Although our specific expressions have been derived from a time-dependent Ginzburg-Landau theory, we expect from general physical arguments that they are relatively insensitive to the starting model.

Exact Results in the Kondo Problem. II. Scaling Theory, Qualitatively Correct Solution, and Some New Results on One-Dimensional Classical Statistical Models

Abstract: The simplest Kondo problem is treated exactly in the ferromagnetic case, and given exact bounds for the relevant physical properties in the antiferromagnetic case, by use of a scaling technique on an asymptotically exact expression for the ground-state properties given earlier. The theory also solves the $n=2$ case of the one-dimensional Ising problem. The ferromagnetic case has a finite spin, while the antiferromagnetic case has no truly singular $T\ensuremath{\rightarrow}0$ properties (e.g., it has finite $\ensuremath{\chi}$).

Theory of the Prism–Film Coupler by Plane-Wave Analysis

Abstract: A laser beam can be coupled with high efficiency into a light-guiding thin film by means of a prism–film coupler. Basically this device is a totally reflecting prism, the light-guiding film being separated from the reflecting prism face by a narrow gap of reduced refractive index. This coupling scheme is analyzed in detail by the method of plane-wave expansion. It is shown how the coupling efficiency is determined by the competition between the desired coupling effect and the reverse effect of leakage. A general condition is derived under which the transverse profile of the input beam continues undistorted into the guide. The theory is illustrated for a gaussian beam, which allows a maximum coupling efficiency of 0.80.

Continuous and Discontinuous Semiconductor-Metal Transition in Samarium Monochalcogenides Under Pressure

Abstract: Resistivity and lattice-constant measurements under high pressure on SmS show that a $4f\ensuremath{\rightarrow}5d$ electronic transition in SmS occurs discontinuously at 6.5 kbar at room temperature, whereas such a transition takes place continuously over a broad pressure range in SmTe and SmSe. The pressure-induced semiconductor-to-metal transition in the Sm chalcogenides and their pressure-volume relationship are consistent with the conversion of ${\mathrm{Sm}}^{2+}$ to ${\mathrm{Sm}}^{3+}$. Optical-absorption measurements in these materials correlate well with the resistivity data under pressure. The semiconductor-to-metal transition in Sm chalcogenides appears to fit the model recently proposed by Falicov and Kimball for a system with a localized state and a conduction band.

The Generation of Optimal Code for Arithmetic Expressions

Abstract: The problem of evaluating arithmetic expressions on a machine with N ≥ 1 general purpose registers is considered. It is initially assumed that no algebraic laws apply to the operators and operands in the expression. An algorithm for evaluation of expressions under this assumption is proposed, and it is shown to take the shortest possible number of instructions. It is then assumed that certain operators are commutative or both commutative and associative. In this case a procedure is given for finding an expression equivalent to a given one and having the shortest possible evaluation sequence. It is then shown that the algorithms presented here also minimize the number of storage references in the evaluation.

Polarization Fluctuations and the Optical-Absorption Edge in BaTi O 3

Abstract: Results of optical absorption and electroabsorption (EA) measurements in the vicinity of the interband absorption edge are reported for top-seeded solution-grown crystals of BaTi${\mathrm{O}}_{3}$. In common with other perovskite oxides, the absorption edge in BaTi${\mathrm{O}}_{3}$ is found to display Urbach-rule behavior. The exponential absorption tail can be described between 20 and 450 \ifmmode^\circ\else\textdegree\fi{}C by an effective temperature ${T}^{*}=T+{T}_{0}$, where ${T}_{0}=140$ K, i.e., $\ensuremath{\alpha}\ensuremath{\propto}{e}^{\frac{\ensuremath{\hbar}\ensuremath{\omega}}{k{T}^{*}}}$. Although no uniquely defined band gap can be extracted from an exponential edge, we propose, on the basis of indirect arguments, that the room-temperature band gaps are 3.38 and 3.27 eV, respectively, for light polarized parallel and perpendicular to the ferroelectric $c$ axis. At high temperatures in the cubic phase, the band gap decreases at the rate -4.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV/\ifmmode^\circ\else\textdegree\fi{}C. EA measurements in the tetragonal phase show that an applied electric field along the $c$ axis shifts the entire Urbach edge rigidly upward in energy by an amount $\ensuremath{\Delta}\mathcal{E}$, which is proportional to the square of the total polarization $P$, spontaneous plus field-induced, i.e., $\ensuremath{\Delta}\mathcal{E}=\ensuremath{\beta}{P}^{2}$. The effect can be described by a temperature-independent band-edge polarization potential $\ensuremath{\beta}$ having the value ${\ensuremath{\beta}}_{11}=1.16$ eV ${\mathrm{m}}^{4}$/${\mathrm{C}}^{2}$. The smaller ${\ensuremath{\beta}}_{12}$ coefficient could not be measured, because of photoconductivity and carrier-trapping effects. An anomalous increase in the band gap with decreasing temperature within 150\ifmmode^\circ\else\textdegree\fi{}C of the Curie point is attributed to coupling between polarization fluctuations and the band edge. A simple thermodynamic model is shown to describe the temperature dependence of this fluctuation contribution with reasonable accuracy. The results suggest that the correlation volume ${V}_{c}$ is at most a weak function of temperature and that ${V}_{c}$ does not display critical behavior. This conclusion is consistent with several recent experiments in displacive ferroelectrics. The magnitude of the observed mean square polarization fluctuation contribution to the band-edge position ($\ensuremath{\approx}15$ meV at $T={T}_{C}$) can be understood using the simple fluctuation theory with the value ${V}_{c}\ensuremath{\approx}4.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ ${\mathrm{\AA{}}}^{3}$ deduced previously from photoelastic constant measurements. It is also suggested that a mean square polarization fluctuation contribution to the band-edge position is present in the tetragonal phase below approximately 100 \ifmmode^\circ\else\textdegree\fi{}C owing to the proximity of the tetragonal-orthorhombic transition. A fluctuation contribution of about 40 meV is indicated at room temperature.

The Concept of Mathemagenic Activities

Abstract: Psychologists write from time to time in human language. Some years ago, I submitted the report of an experiment about mathemagenic behavior to a journal. The article started with the sentence, "You can lead a horse to water but the only water that gets into his stomach is what he drinks." The editor, probably judging this to be too alimentary, deleted the sentence. I regretted this not only because the little phrase pleased me but also because the problem of the not-drinking horse was and is a useful metaphor for explaining why the study of mathemagenic activities is a challenging enterprise for the educational psychologist.

Electron Mobility in Direct-Gap Polar Semiconductors

Abstract: The electron drift mobilities of the five direct-gap III-V semiconductors GaAs, GaSb, InP, InAs, and InSb are presented as a function of temperature. Polar-mode, deformation-potential acoustic, and piezoelectric scattering are included, as well as nonparabolic conduction bands and the corresponding electron wave functions. The drift mobility follows exactly from the assumed model by a simple iterative technique of solution which retains all the advantages of variational techniques without, however, the need for excessive mathematical detail. Piezoelectric scattering is shown to be considerable in GaAs for temperatures below 100 \ifmmode^\circ\else\textdegree\fi{}K. The agreement between theory and experiment for GaAs is satisfactory.

Reverse current-voltage characteristics of metal-silicide Schottky diodes

Abstract: The soft behavior of reverse biased Schottky barrier diodes has often been difficult to interpret quantitatively. The development of metal-silicide devices with diffused guard rings has made it possible to verify experimentally an advanced theoretical model. Reverse characteristics can now be accurately predicted over wide ranges of current, voltage, barrier height and temperature. The theoretical description accounts for anisotropy of effective masses, scattering by optical phonons, and quantum mechanical reflection and tunneling at the metal-semiconductor interface. These considerations yield practical Richardson constants equal to 112 for electrons and 32 for holes in silicon. Absence of true saturation in the reverse characteristic is caused by an electric field dependence of the effective barrier height. In addition to the usual image-force correction, the barrier height is lowered by a newly recognized effect attributed to an electrostatic dipole layer at the metal-semiconductor interface. Experimental devices have been fabricated using RhSi, ZrSi2, and PtSi contacts, forming barriers in both n- and p-type silicon. The resulting structures have been found to be extremely stable and uniform; furthermore, the metal-semiconductor interface, produced by solid-solid chemical reaction, is believed to be free from intervening layers of oxide and other contaminants. When necessary to eliminate field-enhancement at the electrode periphery, diffused guard rings have been incorporated into the structures. Agreement between experimental data and theory is obtained over nearly five orders of magnitude in reverse bias and eleven orders of magnitude in reverse current density, usually with an rms deviation of less than 10 per cent.

On generalized ReedMuller codes and their relatives

Abstract: The polynomial formulation of generalized ReedMuller codes, first introduced by Kasami, Lin, and Peterson is somewhat formalized and an extensive study is made of the interrelations between the m-variable approach of Kasami, Lin, and Peterson and the one-variable approach of Mattson and Solomon. The automorphism group is studied in great detail, both in the m-variable and in the one-variable language. The number of minimum weight vectors is obtained in the general case. Two ways of restricting generalized ReedMuller codes to subcodes are studied: the nonprimitive and the subfield subcodes. Connections with geometric codes are pointed out and a new series of majority decodable codes is introduced.

Optical and Magnetic Investigations of the Localized States in Semiconducting Glasses

Abstract: We measured optical absorption and magnetic susceptibility of amorphous ${\mathrm{As}}_{2}$${\mathrm{S}}_{3}$ as a function of temperature. An exponential variation of absorption constant with photon energy was found in the range $0.09l\ensuremath{\alpha}l0.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$. A Curie term in the susceptibility was shown to be characteristic of disorder in the vitreous material. A model relating the weak absorption tail to the susceptibility requires highly localized states having an exponential energy distribution in the gap.

Atomic-Beam Deflection by Resonance-Radiation Pressure

Abstract: It is proposed to use the saturated value of the radiation pressure force on neutral atoms to produce a constant central force field to deflect atoms in circular orbits and make a high-resolution velocity analyzer. This is useful for studying the interaction of atoms with high-intensity monochromatic light, and to separate, velocity analyze, or trap neutral atoms of specific isotopic species or hyperfine level.

Theory of intracavity optical second-harmonic generation

Abstract: An analysis of optical second-harmonic generation internal to the laser cavity is presented. It is shown that the maximum second-harmonic power generated in this way is equal to the maximum fundamental power available from the laser. Further, it is found that there exists a value of nonlinearity that optimally couples the harmonic out for all power levels of the laser. The magnitude of the nonlinearity required for optimum coupling is shown to be proportional to the linear losses at the fundamental and inversely proportional to the saturation parameter for the laser transition. For the YAlG:Nd laser at 1.06 μ using Ba 2 NaNb 5 O 15 as the nonlinear material, the required crystal length for optimum coupling is given by l\min{c}\max{2}(cm)\simeq 2.7 \times 10^{2}L/f where L is the linear round-trip loss and f is the ratio of the fundamental power density in the nonlinear crystal to that in the laser medium. For low-loss cavities, optimum coupling can thus be achieved for crystal lengths of 1 cm or less. The use of a mirror or mirrors within the cavity, reflecting at the harmonic, is considered as a means to couple out the total harmonic in one direction. Considerations of temperature stability and the finite oscillating linewidth of the laser are shown to favor a configuration with a single harmonic mirror located on the same surface as the fundamental mirror.