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In order to examine the possibility of preparing a nonreacted (nonalloyed) Ohmic contact to p-GaN, the effects of GaN surface treatments and work functions of the contact metals on the electrical properties between the metal contacts and p-GaN were investigated. A contamination layer consisting of GaOx and adsorbed carbons was found on the GaN substrate grown by metalorganic chemical vapor deposition. The contamination layer was not completely removed by sputtering the GaN surface with Ar and N ions where the ion densities were ∼10−2 μA/cm2. Although the contamination layer was partially removed by immersing in a buffered HF solution, little improvement of the electrical properties of the GaN/metal interfaces was obtained. Most of the contamination layer was removed by annealing the Ni and Ta contacts at temperatures close to 500 °C. These annealed contacts exhibited slightly enhanced current injection from the contact metal to the GaN. The present surface treatment study indicated that removal of the contamination layer did not significantly reduce the contact resistance. On the other hand, the resistance decreased exponentially with increasing the metal work functions, where Pt, Ni, Pd, Au, Cu, Ti, Al, Ta, and Ni/Au were deposited on the GaN. This result suggests that the Schottky barrier height at the p-GaN/metal interface might not be pinned at the GaN surface. The present study concluded that a contact metal with a large work function is desirable for nonreacted Ohmic contacts to p-GaN. However, these contacts did not provide the low contact resistance required for blue laser diodes.

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Fast multipole method (FMM) has been developed as a technique to reduce the computational cost and memory requirements in solving large-scale problems. This paper discusses an application of FMM to threedimensional boundary integral equation method for elastostatic crack problems. The boundary integral equation for many crack problems is discretized with FMM and Galerkin's method. The resulting algebraic equation is solved with generalized minimum residual method (GMRES). The numerical results show that FMM is more e cient than conventional methods when the number of unknowns is more than about 1200 and, therefore, can be useful in large-scale analyses of fracture mechanics.

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SUMMARYThis paper discusses an application of a boundary integral equation method (BIEM) to an inverse problem of determining the shape and the location of cracks by boundary measurements. Suppose that a given body contains an interior crack, the shape and the location of which are unknown. On the exterior boundary of this body one carries out measurements which are interpreted mathematically as prescribing Dirichlet data and measuring the corresponding Neumann data, or vice versa, for a field governed by Laplace's equation. The inverse problem considered here attempts to determine the geometry of the crack from these experimental data. We propose to solve this problem by minimizing the error of a certain boundary integral equation (BIE). The process of this minimization, however, is shown to require solutions of certain hypersingular integral equations. Hence regularization methods suitable for solving these integral equations are proposed. Several 2D and 3D numerical examples are given in order to test the performance of the present method.