2. Device Simulation

In order to analyze the electronic properties of semiconductor structures under all kinds of operating conditions, the effects related to the transport of charge carriers under the influence of external fields must be modeled.

Most applied macroscopic models for carrier transport in semiconductors are based on the semiclassical Boltzmann transport equation. By applying the method of moments [22] this six-dimensional equation can be transformed into an infinite series of three-dimensional equations. This allows one to derive a hierarchy of increasingly complex transport models:

• The drift-diffusion transport model: Keeping only the zero- and first- order moment equations together with proper closure assumptions [193] yields the current relations of the drift-diffusion model. Together with the Poisson equation, they form the basic semiconductor equations as given first by VanRoosbroeck [225] (see Section 2.1.1).
• The energy-transport transport model: Considering two additional moments gives the energy-transport model [209,22,89], where the carrier temperatures are allowed to be different from the lattice temperature. Since the current densities depend then on the respective carrier temperature, two more quantities, the electron temperature and the hole temperature, are added.
• The six moments transport model [85,84]: according to the name, six moments are included to describe carrier transport. The two additional quantities are the electron and hole kurtosis.

Whereas in most simulators carrier transport can be treated by the drift-diffusion and the energy-transport transport models, MINIMOS-NT additionally provides the six moments transport model. Recent research indicates, that the six moments model is able to accurately cover the important range of gate lengths from 25$\,$nm to 100$\,$nm [83]. Above this gate length less costly four moments models, for example an energy-transport model, can be used if the more accurate descriptions of the distribution function of the carriers is not required. Despite the fact that the drift-diffusion transport model loses its accuracy already for gate length below 250$\,$nm, it is still frequently and industrially applied due to its efficiency.

In this chapter, the analytical problem based on the three transport models as well as its discretization is discussed. The second part of the chapter deals with the simulation modes of the simulator. The discussion of the steady-state simulation mode covers also the nonlinear solution technique. This is followed by the transient simulation and eventually the derivation of the small-signal system.