next up previous
Next: 5.1.3 Viscous Model Up: 5.1 Mechanical Models Previous: 5.1.1 Elastic Model

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$

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

The relaxation is calculated with
$\displaystyle \sigma$(t + $\displaystyle \Delta$t) = $\displaystyle \sum$$\displaystyle \left(\vphantom{ t \cdot e^{-\frac{\Delta
t}{\tau}} }\right.$t . e- $\scriptstyle {\frac{\Delta
t}{\tau}}$$\displaystyle \left.\vphantom{ t \cdot e^{-\frac{\Delta
t}{\tau}} }\right)$ + $\displaystyle \sigma$(t)     (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.


next up previous
Next: 5.1.3 Viscous Model Up: 5.1 Mechanical Models Previous: 5.1.1 Elastic Model
Mustafa Radi
1998-12-11