Modelization of structural changes in ultra low k materials during ultraviolet cure

Abstract

As of 45 nm node, ultralow k (ULK) materials (εr < 2.55) are widely used in microelectronic interconnects to reduce signal propagation delay. In order to get such low dielectric constant, most of these ULK are obtained using subtractive method: after co-deposition of matrix and porogen a UV cure process is used to remove labile species (porogen). During this process, porosity is created and films are densified as shrinkage increases. This paper presents an in-depth study of the UV cure process. Two kinetic models are presented to describe shrinkage rate: the nth order and the autocatalytic model. These models also used to describe photo-polymerization shrinkage-strain of dental composite, gives predictions that are in good agreement with experimental data. We find that nth-order model is best suited to describe ULK transformations during UV cure process. CHx bonds loss and carbon content can also be modeled using same kinetic model. In order to be able to build the model, initial SiOCH-CxHy film has to be over-cured to determine the maximum conversion that film can reach when submitted to extra-long cure times. Results show that such SiOCH materials have to be cured more than 250 times their nominal cure time to reach maximum shrinkage (∼50%) and a complete loss of carbon, making them looking like SiO2. When structural changes are observed at different temperature, activation energy of reactions can be determined. In this way, shrinkage reaction has an activation energy close to 1000–1100 kJ/mol and CHx bonds or carbon loss reactions have activation energy in the range of 250–400 kJ/mol, which is pretty close to C-H binding energy.