The purpose of the process simulation is to provide the structural information of
the device under scope, consisting of the boundary including the composition
of the different materials involved (e.g. polycrystalline silicon, single
crystalline silicon, silicon dioxide, metals etc.). In addition, the doping
concentration inside the silicon has to be available. The process simulation
takes the photo mask information and the process flow to model the evolution
of above mentioned information (boundary and dopant) over the multiple steps
of the process.
The mesh for solving the partial-differential equations typical for the
physical and chemical processes occurring during processing is
normally of unstructured type, to model the steep gradients of the doping
distributions with good accuracy, but with a low number of mesh points where
the physical fields (doping concentration, point defect concentrations etc.)
are not varying much. A detailed description of a process simulator can be
found in, e.g., [113],[114],[115]
The boundary and dopant information is then used as an input to describe the
electrical behaviour of the device under scope by calculating the potential
distribution and the carrier transport phenomena (current concentrations etc.)
via solving the PDEs describing their physics. A detailed description of the underlying principles of a device
simulator can be found in, e.g., [116],[117],[106]
Since the requirements on meshes for process and device simulations,
respectively, are very different, a re-meshing step is necessary to minimize
the numerical error, and the number of mesh points necessary for a certain
accuracy of the solution. This re-meshing is normally based on the gradient or
difference refinement criteria. In some cases this approach is not sufficient
to get a good mesh. The inversion
region of a MOSFET channel is a good example for the problems gradient
refinement criteria are facing. However in recent investigation approaches are
outlined to overcome or, at least, to tackle these limitations [118],[119].