Incompressible pore effect on the mechanical behavior of low-K dielectric films

New Low-K dielectric constant materials development is underway. Introducing porosity is one of the ways to lower the dielectric constant. Those are typically spin coated organic filled glasses. The pore size is on the order of a several nanometers and pore introduction compromises mechanical properties of low-K thin films, especially fracture toughness, as these materials are typically brittle. In our previous studies we have evaluated different low-K dielectric constant materials in terms of their mechanical properties using nanoindentation. It was interesting to see that for a large range of various porous low-K materials the modulus-to-hardness ratio was constant. It was also found that the indenter contact is mostly elastic, as the loading and unloading portions of the load-displacement curve did not show any hysteresis, following indentation depth to the 3/2 power load dependence, Based on these results current analysis explains the observed constant modulus-to-hardness ratio. The paper also describes the "incompressible" pore effect. As a particle gets smaller, the yield stress increases due to the Hall-Petch effect, but for the nanometer-size particles there are also high surface energy contributions that prevent is from deforming plastically. The same approach can be applied for a nanometer size pore elastic deformation, thus we call it an "incompressible" pore concept.