3.2.1 Optimization Sequence

The optimization setup starts with defining an initial set of optimization parameters. For the two-dimensional approach this usually means that a uniformly doped optimization region is used with all the optimization parameters having the same value. The initial parameters for the Gaussian functions are extracted by a manually performed doping profile fitting to the results obtained from the two-dimensional approach.

For each parameter the allowed range must be specified. Within this range the optimizer can vary the parameter. A careful definition of the parameter ranges is necessary for a successful optimization. If any of the ranges is too narrow, it can happen that the optimum lies somewhere outside this range. If it is too wide, the set of parameters could define a device which is non-physical and the device simulations will fail or take a very long time to converge.

The optimization loop is shown in Fig. 3.7. The optimization framework SIESTA starts the loop with a set of optimization parameters. The device generator Makedevice reads the parameter set, builds the doping profile and writes the device description. Then the device simulations are carried out using MINIMOS-NT [6,22,23]. The simulation results are delivered back to the optimization framework and used to derive the optimization target and, if required, the constraints.

Figure 3.7: The optimization loop.

The optimizer tries to minimize the target which can be interpreted as a kind of cost function. Additionally, there are two sorts of constraints available, namely equality and inequality constraints. The optimizer keeps inequality constraints above zero and equality constraints equal to zero, both conditions are met within a small epsilon range.

The device generator and the simulator are controlled via input decks which contain the default settings and instructions. For the device generator the device geometry and doping profile information is given herein. The simulator input deck contains information about the terminal voltages, the simulation mode, necessary output data, convergence control, file handling, and so on.

The optimizer uses a gradient based method to find the optimum. The optimization sequence is shown in Fig. 3.8. During each step the optimization loop described above is executed. The first step is an evaluation step to find the initial target and constraints. Then the optimizer calculates the gradient vectors for the target and constraints in the next step using a discrete method: Each of the optimization parameters is slightly increased and the differences in the target and constraints are used to derive the gradient vectors [42].

Figure 3.8: The optimization sequence.

After the gradient steps a number of evaluation steps are performed until the next temporary optimum is found. Then the gradients are calculated again. The optimization is finished when the target update between two temporary optima is smaller than a predefined value (termination criterion).