Crystalline Structure Around the Single Vacancy in Silicon: Formation Volume and Stress Effects
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A. ANTONELLIP, EFTHIMIOS KAXIRASt, and D. J. CHADI *Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas,Unicamp, 13083970 Campinas, Sao Paulo, Brazil tDepartment of Physics and Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 INEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540-6634 ABSTRACT The crystalline structure surrounding a single neutral vacancy in silicon is investigated through extensive first-principles total-energy calculations. The results indicate the existence of two distinct distortions of the lattice around the vacancy with essentially the same formation energies at zero pressure, but, however, with different formation volumes. The effect of hydrostatic and biaxial stresses on the relative concentration of each distortion is discussed, suggesting experimental ways to investigate the crystalline structure around the single vacancy and its role as a mediator of atomic diffusion in silicon. INTRODUCTION Nowadays, it is widely accepted that native defects can act as mediators of atomic diffusion in semiconductors. However, despite the considerable experimental and theoretical efforts in the last two decades, many questions regarding native defects and diffusion in semiconductors remain open. In silicon, for instance, the diffusion of arsenic and antimony is believed to be predominantly mediated by vacancies, while the diffusion of boron would be predominantly mediated by interstitials. However, the relative contribution of each native defect to the diffusion coefficient still remains a controversial issue [1]. In the last ten years, hydrostatic and anisotropic stresses have become an useful tool to probe the microscopic mechanisms of atomic diffusion in semiconductors. However, some of these results for diffusion under stress are still not fully understood. Experiments have determined a negative activation volume for diffusion of As in Si and Ge [2, 3]. These results are somehow puzzling, since it is believed that the diffusion of As is mediated by vacancies, which are considered to have a positive formation volume, because in analogy to the Si (111) surface, it was initially suggested that the distortion of the lattice around the vacancy should be outwards [4]. The single vacancy in Si has been the subject of extensive theoretical and experimental studies. The importance of relaxations of the crystalline lattice around the vacancy and the negative-U nature of the Si-vacancy were pointed out theoretically [4] and confirmed experimentally [5] almost two decades ago. The development of new theoretical tools and faster computers in the last ten years have provided a better picture of the structure of the single neutral vacancy in Si. The theoretically predicted distortions, namely: tetrahedral, tetragonal, and trigonal [6], have been extensively investigated [7, 8, 9, 10, 11, 12, 13]. The results point out that tetragonal and tetrahedral distortions can occur and indicate that trigonal distortions are possibly unstable. H
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