Float zone processing in a weightless environment

Results are given for investigations into: (1) the physical limits which set the maximum practical diameters of Si crystals that can be processed by the float-zone method in a near weightless environment, and (2) the economic impact of large, space-produced Si crystals on the electronics industry. The stability of the melt is evaluated. Heat transfer and fluid flow within the melt as dependent on the crystal size and the degree and type of rotation imparted to the melt are studied. Methods of utilizing the weightless environment for the production of large, stress-free Si crystals of uniform composition are proposed. The economic effect of large size Si crystals, their potential applications, likely utilization and cost advantages in LSI, integrated circuits, and power devices are also evaluated. Foreseeable advantages of larger diameter wafers of good characteristics and the possibilities seen for greater perfection resulting from stress-free growth are discussed

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure