4. Two-Dimensional Simulation

Minimos-NT is a generic device simulator that uses the box integration method. Therefore it was necessary to adapt the Preisach hysteresis model, which is outlined in Section 3.2, in such a way that it fulfills the requirements of this numerical method. As already outlined in Section 3.4, the material is supposed to comply with the Preisach hysteresis in any local point, and the resulting field equations have to be solved.

The flux equation used for the box integration method is the third Maxwell equation [Max91]:

$$\mathrm{div }\vec{D} =\rho$$ (4.1)

Hysteresis is modeled with the material equation (2.1), which can be separated into a linear part and a nonlinear part. The nonlinear part ${P}_\mathrm{Ferro}$ which is responsible for the hysteresis, is modeled by the Preisach hysteresis. Considering the fact that a different locus curve has to be calculated for each box boundary, it is necessary to choose an analytic function for the calculation of the hysteresis, thus replacing the integral of the distribution function (3.4). Functions of the general form

$$P = k \cdot f(E \pm E_c,k) + P_\mathrm{off}$$ (4.2)

can easily be applied where the function $f$ serves as the shape function of the hysteresis. If $P_\mathrm{off} = 0$ and $k=1$, $f$ will be one branch of the saturation loop. Through modification of the parameters $k$ and $P_\mathrm{off}$ all the possible locus curves of the hysteresis can be simulated. $E_c$ is the coercive field of the polarization.

As can easily be seen, (4.1) is a vector equation and (4.2) is a scalar equation. Several algorithms had to be developed for the extraction of $\vec{D}$ out of $D$, each depending on a specific task. They will be described in Section 4.2.