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

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

to replace the undamped new solution x^{k + 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].

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

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