*MINIMOS-NT* uses the backward *Euler* method for time integration. In
this method for example the derivative of the electrostatic potential
for the time step *n* is discretized as

= . | (4.1) |

Here the subscript *n* denotes the values of the present time step and the
subscript *n* - 1 the values of the previous time step. To calculate the
values of the unknowns for time step *n* only the values of the previous time
step *n* - 1 are necessary.

For each time step *n* the step size
*t*_{n} has to be chosen based on
the result of the last time step. To ensure a certain simulation accuracy the
step size must not be too big. On the other hand the step size also should not
be too small to minimize the CPU time required for the simulation and to avoid
numerical problems. The algorithms used in *MINIMOS-NT* to determine the step size
for the transient simulation of CCDs are described in the next section.

After choosing the time step size the contact quantities are interpolated for this step from the specified values as described in Section 4.3.3. Using these values the transient simulation step is performed. Then the norm of the potential update from the last time step to the present is calculated and compared to a predefined threshold. In case the norm of the potential update exceeds this threshold the time step has to be repeated using a reduced step size. Otherwise the next time step is calculated. The control flow of a transient simulation is shown in Fig. 4.4.

1999-05-31