Constant Propagation Research Articles

Abstract: Growth morphology and surface‐acoustic‐wave measurements of AlN films on sapphire

Aluminum nitride epitaxial films have been grown on R‐plane sapphire substrates and studied for its piezoelectric properties as applied to surface‐acoustic‐wave device applications. The films reported here are grown by a chemical vapor deposition process involving the reaction of trimethyl aluminum gas with ammonia in the presence of hydrogen at temperatures of approximately 1200 °C. Using a modified epireactor as the growth furnace with a gas injection system that directs gas flow onto the substrate, growth rates of 500 Å/min are achieved producing films over 10 μm in thickness which exhibit excellent mechanical and chemical stability.The R‐plane, (011̄2), of sapphire consists of alternate layers of Al and O with a repetitive sequence of O–Al–O–Al–O. In the two different layers of atoms, the Al atoms occur in a close‐packed configuration while the O atoms are aligned into columns along the [01̄11] direction. The hexagonal wurtzite structure of AlN has the (112̄0) plane consisting of coplanar atoms of Al and N in a close‐packed configuration but segregated into columns aligning with the [0001] direction. A good fit of these two planes is obtained when the columns of atoms are aligned with the sapphire [01̄11] and AlN [0001] directions colinear (i.e., with the AlN c axis pointing in the same direction as the projection of sapphire c axis upon the R plane), giving lattice mismatches of 2.7% along and 11.9% across the [01̄11] direction. A reversal of the AlN [0001] axis however, places the AlN atoms in the interstitial sites of sapphire indicating poor lattice matching.The as‐grown surface morphology of the AlN films, as examined under a scanning electron microscope, can be divided into two categories. Category I features very distinctive scale‐like facets that are all aligned in one direction while category II includes the scale‐like facets aligned but pointing in opposing directions along with some spurious nucleations. X‐ray analysis of the sapphire substrate shows the facets to be that of the AlN [0001] axis aligning with the [01̄11] direction of the R plane.Surface‐acoustic‐wave measurements of the AlN films are made by reflective impedance measurements from Al interdigital transducers fabricated upon polished surfaces. There is a definite correlation between the quality of the results and the category of the surface morphology. Results obtained from films of category I were consistently better than those obtained from films of category II leading to the confirmation of the theory that there is a preferred direction of growth of AlN [0001] axis upon the R plane for minimum stress with maximum lattice matching. Surface‐acoustic‐wave coupling constant K2 and propagation velocity Vs are measured out to an AlN thickness to transducer wavelength ratio t/λ of 0.75 with typical K2 values of 0.8% and Vs of 6.1 km/s.Preliminary results obtained from a study of the dependence of the K2 versus t/λ curve upon transducer wavelength indicate that the AlN–sapphire interfacial strain extends about 1 μm into the AlN film.

Growth morphology and surface-acoustic-wave measurements of AIN films on sapphire

Aluminum nitride epitaxial films of thicknesses greater than 10 μ with excellent mechanical and chemical stability have been grown on R-plane sapphire substrates. The orientation relationship of single-crystal AlN on sapphire is discussed. Examination of the as-grown AlN film surface with a scanning electron microscope identifies the growth morphology and enables differentiation between good and poor quality films. The surface-acoustic-wave coupling constant K2 and propagation velocity Vs are measured out to a thickness-to-wavelength ratio t/λ=0.75 with typical K2 values of 0.8% and Vs of 6.1 km/sec. Preliminary results also indicate that AlN-sapphire interfacial strain extends about 1 μ into the AlN film.

Coupling efficiency of the tapered coupler

Analytic solutions, in terms of parabolic cylinder functions, are presented for the mode amplitudes and power in a directional coupler having a constant coupling coefficient and propagation constants that vary linearly. The solutions lead to a remarkably simple expression for the coupling efficiency.

Program optimization - theory and practice

The conventional program optimization techniques employed by the ILLIAC FORTRAN compiler are general purpose, effective, and efficient. The underlying theory is applicable to FORTRAN and to other high level languages. A unique approach to the gathering of global set and use information about variables as well as careful software engineering of the algorithms has led to the construction of an effective source-to-source optimizer which performs constant propagation, constant computation, common subexpression elimination, reduction in strength, and invariant code motion. We will first consider the type of information which must be gathered about a program, and how this information is used to perform optimization. Then we shall state the algorithm for globally computing the set and use information for program variables. Having discussed the science of optimization we shall turn to the engineering aspects and consider such topics as representation of programs, order of optimization transformations, and efficient computation of global use and set information.

The Design and Application of Shear Fracture Propagation Studies

Shear fracture propagation is studied using an analysis based upon the thermodynamic equilibrium of a constant velocity fracture. This equation is shown to describe the behavior of all full scale tests which exhibit constant velocity propagation. This equation is developed to identify the conditions for fracture arrest; the resulting formulation is again consistent with full scale test behavior. The paper also discusses the application of the theory to existing and new pipelines.

Exact Solutions to Some Deterministic and Random Transmission Line Problems

A special class of transmission lines is considered, in which the modes decompose into two noninteracting sets. Both a single transmission line with constant characteristic impedance and variable propagation factor, and two transmission lines with equal propagation factors and variable coupling, in which the forward modes do not interact with the backward modes, are investigated. Exact expressions are obtained for the reflection and transmission coefficients when a section of such a transmission system connects two semi-infinite transmission systems consisting of constant impedance and admittance lines. These results hold for arbitrarily varying propagation factors and coupling; and while they are of independent interest in the case of deterministic variations, we make an application of them here in the case of stochastic variations. Exact results are obtained for the ensemble averages of the transmission coefficient and transmitted power, and their variances, for the inserted section of single line, when the variable propagation factor is a random function involving either a Gaussian process or the random telegraph process. Asymptotic results are also obtained in the general case of weak fluctuations and long inserted sections. Analogous results may be obtained for the inserted section of two lines when they are randomly coupled, and the results are given in the case of matched lines, for which no reflections occur. Finally, some of the time domain statistics for lossless lines are considered, and expressions are derived for the ensemble averages of the transmitted pulse, due to pulses incident on the inserted section.

Logic Control for Parallel Video Processing in Program Switchers

Studio program switchers are used to Select the proper picture(s) at the operator's discretion, either individually or in combination. Normally this is done by routing the video signals through different video devices, such as mixing amplifiers, special effects, etc. This delays the video signals, so the switchers must utilize secondary switching to put the processing devices in series or to substitute delay lines to maintain constant propagation delay through the system. To minimize the delay and to improve the quality of the picture, a new concept of parallel video processing has been developed. Time sharing and amplitude sharing are used to achieve MIX, WIPE, KEY, etc., leading to very good technical performance characteristics.

Equivalent transformation of nonuniform lossless lines and distributed RC networks

The equivalence properties of nonuniform transmission lines with different parameter distributions are analysed in detail. Both LC(lossless) and RC lines are treated. The formulation adopted may be considered as an appilication of the method of spatial-variable transformation to differential equations that govern the transfer-matrix parameters of these lines. The principal result is an equivalence theorem which establishes a general method of equivalent transformation for nonuniform transmission lines. Emphasis is placed on the derivation of the transformation function which plays a key role in the equivalent transformation. The generality of the proposed method of equivalent transformation lies in the fact that there is a large freedom of choice of the form of the transformation function which is pertinent to the problem in hand. Details of the procedure of equivalent transformation are described, and the quantities which are invariable under equivalent transformation are discussed. Furthermore, as an application of the equivalent transformation, the relationship between two particular classess of nonuniform LC lines is elucidated, namely, semiuniform lines having uniform series inductance, and reciprocal lines having a constant propagation factor. On the basis of this relationship, it is possible to design various inhomogeneous-layer components by the direct use of the available data on corresponding nonuniform-line components.

Generalized nonuniform transmission lines and their equivalent electrical length

The criterion introduced by Hellstrom for obtaining various classes of equivalent distributed RC networks is generalized to encompass a wide range of nonuniformity distribution functions under each general class of transmission lines which exhibit identical network-properties at their respective equivalent electrical lengths. Application of the criterion is then illustrated by obtaining three generalized sets of nonuniformity distributions for series-impedance and shunt-admittance; and corresponding equivalent electrical lengths for the exponential family of nonuniform lines. In order to demonstrate the versatility of a generalized set of nonuniformity, some constant propagation factor distribution, are derived from the generalized hypergeometric line.

Dynamic yield behavior of shock-loaded iron from 76 to 573°k

The dynamic yield behavior of Ferrovac E iron was studied over a temperature range of 76–573°K. Large diameter-to-thickness ratio discs were shock loaded, producing a state of uniaxial strain and strain rates of ~10 5 sec −1. The dynamic yield stress for 12.6-mm thick discs was found to be 9.61 ± 0.13 kbar regardless of temperature. This was in contrast to the highly temperature sensitive quasi-static yield stress which decreased by a factor of 2.5 between 76 and 298°K. The shock-loading data were analyzed in terms of dislocation models which previously have been applied in describing the decay of the dynamic yield point at constant temperature with increasing propagation distance. None of the models provided an adequate fit to both the new data involving the effect of temperature on the dynamic yield stress at a constant propagation distance and previous data of Taylor and Rice on the effect of propagation distance on the dynamic yield stress at a constant temperature. From the failure of these various models to correctly describe the dynamic yielding of iron, it would seem that some of the assumptions utilized in applying the dislocation theories to the description of dynamic yielding under shock loading need further study. Of particular importance are the assumptions that dislocation acceleration and relativistic effects are negligible. Twinning was observed to occur at shock-loading stress levels slightly above the dynamic yield stress but did not occur at lower stresses. It was concluded that the motion of twinning dislocations is the mechanism of dynamic yielding of iron.

Spectral energy density for quarry explosions

Abstract Several explosions of varying time duration have been recorded at 156 km along a constant propagation path from a central Michigan limestone quarry. Energy density for body waves and surface waves is examined as a function of frequency and observed to peak between 1 and 10 cps. A correlation between spectral amplitudes and source duration time is revealed and is emphasized at shot durations which approximate the dominant period of seismic waves. A study of the data suggests that seismic energy levels may be controlled, in part, by regulating the time duration of delayed quarry blasts. This parameter (total duration time) has been generally neglected in published studies involving commercial blasts.