Density functional theory applied to the calculation of dielectric constant of low-k materials

The interest of low-k dielectric materials to reduce capacitance in multilevel metal interconnects of integrated circuits is well known in the semiconductor industry. The use of these materials (especially hydrogen silsesquioxane (HSQ) and methyl silsesquioxane (MSQ): intermetal dielectric applications in the back end of line fabrication) leads to a reduction of the dielectric constant from k ~= 4 in a traditional intermetal dielectric material of silicon dioxide to a value of ~=2.5-3. The physical difference between HSQ or MSQ and a-SiO2 is the presence of Si-H bonds (for HSQ) or Si-CH3 bonds (for MSQ) and the density of the material. A theoretical calculation of bond polarizability (Si-H or Si-CH3) associated to experimental values of electric dipole densities can lead, using the Clausius-Mossotti relationship, to the calculation of the dielectric constant. After validation of the calculation methods both on simulation and experimental values, it is shown that for a constant density, the difference between the materials could be due to the bond polarizability and furthermore that this difference accounts, in part, for the value of dielectric constant. Consequently, even if densification remains the main parameter explaining low-k values, the polarizability of building units of these materials is not negligible.