Extended Theory of U* to Electrostatic Problem and Its Application to Pore Arrangements for Porous Low-k and High-k Dielectric Film

This paper discusses the effects of pore arrangements on the dielectric property of porous low-k and high-k dielectrics. Higher performance large scale integration (LSI) requires lower dielectric constant to decrease line-to-line capacitance. Recently, porous low-k dielectrics are introduced for low-k dielectrics because of its ultra lower dielectric constant. However, their poor mechanical strength causes fractures of porous low-k dielectrics during Chemical Mechanical Polishing (CMP) process. Therefore, it is important to develop porous low-k dielectrics with high mechanical strength and low dielectric constant. On the other hand, porous high-k dielectrics are needed as ferroelectrics. It is also important to understand the dielectric property of porous high-k dielectrics. We studied the dielectric property of porous low-k and high-k dielectrics by finite element method and U* theory. The index U* is used to indicate load paths in a structure. We extended U* theory to the electrostatic field problem and investigated the dielectric property of dielectrics. By using U* in electrostatic field analysis, the dielectric performance of porous low-k and high-k dielectrics becomes more clear.