Application of the Tikhonov Regularization Method in Problems of Ellipsometic Porometry of Low-K Dielectrics

Abstract

In the development of promising ULIS scaling technologies, one of the key roles is played by porous dielectrics with a low permittivity used to isolate interconnects in a metallization system. Condensation of gaseous products in the pores of such films makes it possible to solve the most important problem that prevents the integration of such films, to carry out low-damage plasma etching. However, methods for studying porosity are also based on the study of the adsorption isotherm during condensation in film pores. Therefore, the study of adsorption in pores is one of the most important practical problems arising in the creation of dielectrics with a low permittivity and the study of low-damaging methods for their structuring. The method of ellipsometric porosimetry is an easy-to-implement and accurate approach for obtaining an adsorption isotherm; however, its further analysis and determination of the pore size distribution are reduced to solving an integral equation and is an ill-posed problem. In this paper, we propose to apply Tikhonov’s regularization method to solve it. The method is verified on model data and used to study a low-k dielectric sample with an initial thickness of 202 nm and a permittivity of 2.3 based on organosilicate glass.