5.1.2 Elastic Model with Maxwell Stress Relaxation

This model is based on the elastic model, but includes a stress relaxation which attempts to mimic visco-elastic stress relaxation effects observed in oxide [Ire82] and nitride [Gri90]. At the end of each incremental stress analysis the total stress is reduced by a global exponential relaxation factor with time constant $\tau$ calculated from the material shear modulus G and viscosity $\mu$

$$\tau {\frac{\mu}{G}}$$ (5.9)

The relaxation is calculated with

$$\sigma \Delta \sum \left(\vphantom{ t \cdot e^{-\frac{\Delta t}{\tau}} }\right. {\frac{\Delta t}{\tau}} \left.\vphantom{ t \cdot e^{-\frac{\Delta t}{\tau}} }\right) \sigma$$ (5.10)

This approach offers the possibility to influence the oxidation kinetics in the next timestep, since the visco-elasticity is not solved self-consistently with the oxidation kinetics. The model is typically used for oxide and nitride layers but for genuinely elastic materials, such as silicon, the viscosity is set to a large value to prevent stress relaxation.