Device simulation has become a standard supplement for the development of new semiconductor devices. Often the characteristics of these devices are determined by physical effects for which the development of suitable models is difficult. Several of these effects, such as carrier heating or quantum phenomena, gain influence on the device characteristics when the feature size falls below a certain limit and the influence of interfaces on bulk behavior cannot be neglected any more. Thus, proper interface modeling plays an important role for device simulation.
Especially modeling the electron and hole current as well as the energy flux across interfaces has been found to be a complex task and a large number of models for different types of interfaces have been proposed [17][18][19][20]. For device simulation the interface type is automatically detected by analyzing the device structure or is explicitly defined in an input deck. This method works well as long as the interface type does not depend on the internal state of the device. For instance the thermionic emission model is commonly used for modeling the current across heterojunctions of compound semiconductors. The thermionic emission model can be extended to the thermionic field-emission model to account for tunneling effects through the heterojunction barrier by increasing the thermionic emission velocity at the interface and by introducing a field dependent barrier hight lowering. This model is applicable to interfaces with moderately changing band edge energy but is not suitable for interfaces with rapidly changing band edge energies.
If the tunneling effect becomes more and more dominating, the model will no longer determine the current across the interface. Instead the model establishes a direct relationship between the carrier concentrations on both sides of the interface.
The current flux across the interface forms a Neumann interface condition, whereas the direct determination of the carrier concentrations is of Dirichlet type. Thus, in the limit the interface type changes from a Neumann interface condition to a Dirichlet interface condition.
In order not to deteriorate the condition of the linear system and the convergence behavior the entries into the equation system for Neumann and Dirichlet interface conditions have to be formulated differently and appropriate scaling has to be used.
In this chapter a method for treatment of interface models is presented which allows a change of the interface condition from Neumann to Dirichlet type without negative influence on convergence. This method is applied to the hydrodynamic simulation of a HEMT.