Physics driven device modeling is intended to be accurate, but it is not fast enough for higher level tools, including circuit simulators such as SPICE. Therefore, circuit simulators normally use more empirical models (often called compact models) that do not directly model the underlying physics. For example, inversion-layer mobility modeling, or the modeling of mobility and its dependence on physical parameters, ambient and operating conditions is an important topic both for TCAD (technology computer aided design) physical models and for circuit-level compact models. However, it is not accurately modeled from first principles, and so resort is taken to fitting experimental data. For mobility modeling at the physical level the electrical variables are the various scattering mechanisms, carrier densities, and local potentials and fields, including their technology and ambient dependencies.