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6.1 Device Equation Damping Schemes

All damping schemes implemented in MINIMOS-NT have in common that they damp the solution vector by a damping factor d and hence obtain the following new solution

x* = xk + d . $ \left(\vphantom{\mathbf{x}^{k+1} - \mathbf{x}^{k}}\right.$xk + 1 - xk$ \left.\vphantom{\mathbf{x}^{k+1} - \mathbf{x}^{k}}\right)$ (6.1)

to replace the undamped new solution xk + 1. The computation of the damping factor d depends on the damping scheme selected. Investigations were made on several damping schemes and potential damping was found to deliver most reliable results [15].

d = $ {\frac{1+\delta\cdot\ln\frac{\displaystyle \Vert\mathbf{u}_{\mathbf{\psi}}\Ver...
...playstyle \Vert\mathbf{u}_{\mathbf{\psi}}\Vert}{\displaystyle V_{T}}-1\right)}}$        with    0 $ \leq$ $ \delta$. (6.2)

with $ \delta$ being an adjustable parameter of the damping scheme, u$\scriptstyle \psi$ the update norm of the potential sub-vector, and VT the thermal voltage. A larger $ \delta$ results in more logarithm-like damping of the updates.

Tibor Grasser