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 multile vel metal interconnects of integrated circuits is well known in the semicon ductor industry. The use of these materials (especially hydrogen silsesquio xane (HSQ) and methyl silsesquioxane (MSQ): intermetal dielectric applicati ons in the back end of line fabrication) leads to a reduction of the dielec tric constant from k congruent to 4 in a traditional intermetal dielectric material of silicon dioxide to a value of congruent to 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 theoreti cal calculation of bond polarizability (Si-H or Si-CH3) associated to exper imental values of electric dipole densities can lead, using the Clausius-Mo ssotti relationship, to the calculation of the dielectric constant. After v alidation of the calculation methods both on simulation and experimental va lues, it is shown that for a constant density, the difference between the m aterials could be due to the bond polarizability and furthermore that this difference accounts, in part, for the value of dielectric constant. Consequ ently, even if densification remains the main parameter explaining low-k va lues, the polarizability of building units of these materials is not neglig ible. (C) 1999 Elsevier Science Ltd. All rights reserved.