Thermal oxidation of silicon is a critical step in the fabrication of highly integrated electronic circuits and is mainly used for insulating adjacent devices from each other. Knowledge of the physical processes that affect thermal oxidation is essential for optimizing applications.

Miniaturization of devices based on silicon technology leads to the realization of integrated structures exhibiting an increasingly complex topology. The evolution of insulation techniques is one of the most striking examples for that purpose. In order to reduce the development duration of such state-of-the-art technologies, two- and three-dimensional process simulation capabilities are of prime interest. Accurate modeling requires the knowledge of the characteristics of the mechanical thin film properties of integrated circuit materials as well as stress effects of the oxidation kinetics.

Difficulties in numerical modeling of silicon oxidation come from the necessity to ensure both a wide prediction capability and a flexible simulation system. The efficiency of the numerical implementation depends on the ability to handle complex topological configurations within reasonable computing time.

To cope with these different requirements AMIGOS (Analytical Model Interface & General Object-Oriented Solver) has been developed. It is a problem-independent simulation system which can handle various nonlinear partial differential equation systems in time and space in either one, two, or three dimension(s). There are no restrictions whether using scalar-, field- or even tensor quantities within a model, and, if desired, any dependent field quantity can be calculated. Furthermore, the user can influence the numerical behavior of the differential equation system by complete control of the residual vector and its derivative (e.g., punishing terms, damping terms, etc.). Even interpolation and grid-adaptation definitions can be formulated within a developed model and can thus be adapted to a particular problem very well.

With AMIGOS a new approach to the local oxidation in three dimensions has been developed, based on a parameter-dependent smooth transition zone between silicon and silicon dioxide. The resulting two phase problem is solved by calculating a free diffusive oxygen concentration and its chemical reaction with pure silicon forming silicon dioxide. This effect causes a volume expansion that leads to mechanical stress concerning the surrounding boundary conditions. With a suitable set of parameters this approach is equivalent to the standard sharp interface model based on the fundamental work of Deal and Grove.

1998-12-11