Mechanical stress modeling for silicon fabrication processes

Abstract

Two finite element methods are implemented to investigate localized mechanical stress fields generated during multiple stages of silicon IC fabrication. The boundary loading method (BL) uses the oxide interface stresses as a boundary condition for the substrate solution. In the fully integrated method (n), the strains in substrate are calculated along with the oxide stress computation. Both of the methods can be used to couple stresses generated by oxidation volume expansion to strains present from other sources such as thermal expansion, dopants, and intrinsic film stresses. They are then evaluated on computational intensiveness and in stress solution variation. It is found that the BL method computes nearly the same oxide solution as the FI method and the oxide solution corresponds very well in the oxide and surface films for a LOCOS process.

Strain Modeling in Advanced MOSFET Devices

“…Stress dependent oxide growth models were used to simulate 2D and 3D local oxidation of silicon (LOCOS) for isolation [1,2,3,4,5]. The stress in silicon from a variety of strain sources including oxidation, thermal mismatch, intrinsic stress, and dopants have been simulated [6,7]. These early stress simulations were mainly process-only simulations, with the main inputs they provided to device simulators being structural.…”

“…where η is the viscosity. A Maxwell viscoelastic model for the deviatoric component and elastic model for dilatational component of stress can be used to model stress dependent oxide growth and stress in silicon from a variety of front end strain sources [2,3,5,6,7]. The stress simulations in this work were performed using a proprietary version of the process simulator FLOOPS [16,12].…”

Recent Advances in Models for Thermal Oxidation of Silicon

“…Traditional approaches to the problem have involved the specification of a finite-element mesh, where element edges are aligned with the interface. Diffusion is solved for only over the SiO 2 subdomain and the movement of the interface is accomplished by movement of nodes (see Rafferty [3], Peng et al [4], Senez et al [5], Uchida et al [6], Cea and co-workers [7,8] and references therein). This approach has the undesirable consequence of requiring remeshing with every time step as the interface moves.…”

On modelling thermal oxidation of Silicon II: numerical aspects

“…An added disadvantage is the inability to appropriately enforce the interface conditions. This description is used in the computer program SUPREM 27 , Law 12 and Rueda et al 19 . Case ii presents an attractive alternative.…”