A model in Alamode is a set of coupled systems of PDEs describing transport of impurities and defects in semiconductor materials and interfaces. An annotated mesh data structure is used to represent the physical structure (wafer state) of a device, including materials, interfaces, and impurity and defect profiles. A dial-an-operator paradigm is used to build up systems of equations from a library of operators and functions. Systems of equations are attached to materials and interfaces to construct a model. The abstractions used to represent models are:
The domain is the collection of regions and fields of interest to represent the physical state of a device.
A region is a subset of the domain in which the same system of equations will be applied. Regions are usually materials, material interfaces, and artificial boundaries, but they may also be used to isolate subset of a material where the equations differ from those applied elsewhere in the same material (e.g. a damaged or non-crystalline region of a normally crystalline material).
A constant variable is a named scalar value that is not spatially varying.
A field variable is named scalar value that is interpolated on the mesh in a region. Fields are often discontinuous at material interfaces (e.g. impurity concentration with a density change), and, as a result, the naming convention adopted for fields is VariableInMaterial. This naming convention has been the source of a lot of confusion, mainly because interior regions are also named with the material name and because there is not a material ``object'' in Alamode. While it may seem more natural to just refer to fields by the impurity/variable name (e.g. Boron), that convention would not provide a way to distinguish between field values on either side of material interface without an additional key, and the additional key would likely be another source of confusion. This convention of VariableInMaterial provides an unambiguous way to distinguish the values on either side of a material interface and it simplified the implementation by allowing fields to be consistently treated as simple interpolated scalar quantities.
Functions are one of the equation building blocks. Functions provide a way to combine constant variables, field variables, and previously defined functions into more complex expressions. Examples of functions include sum and product, as well as more complicated expression such as that used to calculate a normalized quasi-Fermi carrier concentration.
Operators are terms in an equation. Operators may reference constant variables, field variables, and previously defined functions as needed.
An equation is a list of operators (sum of terms) used to solve for a single field. Presently, equations can be used for elliptic or time-dependent partial differential equations as well as algebraic interface constraint equations.
A systemInRegion is a list of equations describing the coupling among fields within a single region.
A model is an aggregation of system/region pairs describing globally coupled system of equations in the domain.
The following sections discuss how TCL (Tool Command Language) is used both for model description and as a command language for Alamode.