In this paper, gold ball wire bonding at low temperature using a high frequency transducer was evaluated. The substrates used were FR-4 laminates with two different gold-plated surface finishes: electrolytic and immersion gold-plated. Bonding temperatures of 120/spl deg/C, 80/spl deg/C and 40/spl deg/C were investigated with 1 mil fine pitch gold wire. Prior to wire bonding, the laminates and dice were plasma treated. The surfaces were analyzed prior to and after plasma treatment before wire bonding using XPS and AFM. Bonded areas were also analyzed using SEM. Design of experiment (DOE) techniques have been employed to optimize the bonding parameters at each temperature. The response of the DOE was evaluated by using bond shear and bond pull. The results show that bonding at low temperature is viable with the use of a high frequency transducer wire bonder.

We study the behavior of a quantum particle confined to a hard-wall strip of a constant width in which there is a finite number<i>N</i>of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's formula, we analyze its spectral and scattering properties. The bound state problem is analogous to that of point interactions in the plane: since a two-dimensional point interaction is never repulsive, there are<i>m</i>discrete eigenvalues, 1<i>m</i><i>N</i>, the lowest of which is nondegenerate. On the other hand, due to the presence of the boundary the point interactions give rise to infinite series of resonances; if the coupling is weak they approach the thresholds of higher transverse modes. We derive also spectral and scattering properties for point perturbations in several related models: a cylindrical surface, both of a finite and of an infinite height, threaded by a magnetic flux, and a straight strip which

In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind.

We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.

Point interactions described by formal shaped potentials were used in quantum mechanics from the early thirties. It lasted several decades, however, until a proper way to handle the corresponding Schrdinger operators was found. Following the observation of Berezin and Faddeev [4], the problem was studied systematically in the eighties. The results are summarized in the monograph [1], references to some recent work are given, eg, in [2, 8]. In its present form the pointinteraction method represents a versatile tool for constructing solvable models whose power has not been yet, to our opinion, appreciated fully in the physical community. Within the standard quantum mechanical formalism point interactions can be constructed as long as the configuration space dimension does not exceed three, and they can be interpreted as limits of suitable families of squeezed potentials. In the onedimensional case the limiting argument admits a straightforward interpretation, because the pointinteraction coupling constant is just the integral of the approximating potential: a slow particle on the line with a wellspread wavefunction sees only the average value of a localized potential. In distinction to that the approximation by scaled potentials in dimension two and three requires existence of a zeroenergy resonance and a particular couplingconstant renormalization; a detailed discussion of the related mathematical problems can be found in [1, 9]. This gives these point interactions a flavour of something exceptional, for instance, one is led to believe that they cannot be used to model welllocalized repulsive potentials. That would have consequences

We consider an open quantum dot modeled by a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, the system exhibits embedded eigenvalues. They turn into resonances if the symmetry is violated, either by a magnetic field or by deformation of the well. We construct a perturbation theory of these resonances in the case of a weak perturbation and discuss other properties of the model.

abstract

We propose a model for scattering in a flat resonator with a thin antenna. The results are applied to rectangular microwave cavities. We compute the resonance spacing distribution and show that it agrees well with experimental data provided the antenna radius is much smaller than wavelengths of the resonance wavefunctions.

In addition to the conventional renormalized-coupling-constant picture, point interactions in two and three dimensions are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.

In this paper, we consider the numerical approximation of the three-dimensional poroelastic wave equations in the spherical coordinate system. One difficulty in the design of an efficient numerical scheme is that the problem is singular in the center and the polar axes of the computational domain. Nevertheless, we develop a hybrid finite difference/control volume method for solving this problem. Our method is explicit and is second order accurate in both space and time. Numerical results are shown to confirm the convergence rate of our method and the effectiveness to simulate wave propagation in poroelastic media in the spherical coordinate system.