Nanoindentation of silicon: hardness and semiconductor-metal phase transition
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Nanoindentation of silicon: hardness and semiconductor-metal phase transition M. Hebbache Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Universit´e Paris 7, 2 place Jussieu, F-75251 Paris Cedex 05, France. ABSTRACT The hardness of a thin film of silicon is studied in the framework of the 3D Hertzian contact theory. The anisotropy and the anharmonicity of silicon are taken into account for the first time. It is shown that the contribution of plasticity to the hardness of silicon is significant while we know that it possesses strong covalent bonds and dislocations must be thermally activated in this material. The semiconductor-metal phase transition, driven by the tetragonal shear strain superimposed on the non-hydrostatic pressure generated by a diamond indenter, is also studied. For this aim, the Landau theory of phase transitions and the contact theory are combined. The comparison with available nanoindentation experiments is made.
INTRODUCTION Nanoindentation has become a well-established technique for the investigation of mechanical properties of materials[1]. The analysis of the load-penetration curve allows the determination of a number of useful engineering properties[2]. A high nonhydrostatic pressure, i.e., a shear component and a compressive hydrostatic component, is generated when a diamond indenter is loaded onto a flat surface of a material. Small regions under the indenter could undergo structural transformations like in a diamond anvil cell. Understanding the mechanical properties of materials at the nanoscale is crucial for applications. The intrinsic mechanical behavior of semiconductors is of particular interest because they are widely used for the fabrication of electronic devices which operate in large ranges of stresses and temperatures. The performances of these devices can be significantly degraded due to contact loading during processing or use. Silicon, which is a relatively hard material, has already found new applications in micro- and nano-electro-mechanical systems (MEMS and NEMS). The first structural transformation in silicon makes in evidence two electrically and geometrically different states. The parent phase has a diamond structure (Si I) and is semiconductor while the new phase is tetragonal and metallic (Si II). On pressure release, the diamond structure is not reconstructed. The non-reversibility of the Si I ⇒ Si II phase transition hinders the appearance of new applications like detectors of ultra-low forces or impacts. The present paper concerns the hardness of a thin film of silicon and its semiconductor-metal phase transition. The main aim is to predict the evolution of its hardness when it is indented to nanometer scale depth. From the theoretical point of view, indentation is a contact problem which has been only partially solved. To date, there is no complete quantitative theory of hardness. Much of the theoretical works are restricted to isotropic solids. Little attention has been paid to anisotropy, anharmonicity and structural transformations which occu
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