A study of using femtosecond LIBS in analyzing metallic thin film–semiconductor interface

Metals and metal alloys are usually employed as interconnections to guide electrical signals between components into the very large scale integrated (VLSI) devices. These devices demand higher complexity, better performance and lower cost. Thin film is a common geometry for these metallic applications, requiring a substrate for rigidity. Accurate depth profile analysis of coatings is becoming increasingly important with expanding industrial use in technological fields. A number of articles devoted to LIBS applications for depth-resolved analysis have been published in recent years. In the present work, we are studying the ability of femtosecond LIBS to make depth profiling for a Ti thin film of thickness 213 nm deposited onto a silicon (100) substrate before and after thermal annealing. The measurements revealed that an average ablation rates of 15 nm per pulse have been achieved. The thin film was examined using X-Ray Diffraction (XRD) and Atomic Force Microscope (AFM), while the formation of the interface was examined using Rutherford Back Scattering (RBS) before and after annealing. To verify the depth profiling results, a theoretical simulation model is presented that gave a very good agreement with the experimental results.     

Inverse Problems for Identification of Memory Kernels in Viscoelasticity

Inverse problems for identification of the memory kernel in the linear constitutive stress–strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.