The quantization effects lead to corrections of the effective masses. Following [274] who investigated AlAs/GaAs quantum wells, significant modifications of the effective masses only apply for channels smaller than 10 nm. The mobility changes in the two-dimensional electron gas relative to the bulk are of minor importance [124]. As given in Fig. 3.5 the extraction of the mobilities used in this work is based on Hall data from two-dimensional HEMT structures, so that the changes are effectively compiled into the mobility models as the data originate from two-dimensional electron gases.

As previously stated, energy relaxation is modified. For the inversion channel in a MOSFET this was shown in [236]. A similar behavior is expected for the HEMT.

Interface scattering and tunneling are the two mechanisms affecting the current flow from and into the channel. According to an estimate given by Fischer [90] in Appendix B the characteristic length of the tunneling process is summarized for various material systems. The interface scattering represents an additional scattering mechanism, which macroscopically is included in the Hall mobility data.

For GaN based HEMTs, as was shown in [238], the formation of the channel and the extremely high current densities cannot be understood without considering the piezoelectric effects. As was pointed out by Ambacher et al. in [12] the piezoelectric effects lead to typical effective distances of the two-dimensional electron gases of 1-2 nm.

In device simulations these effects can be modeled applying specific surface charges [275]. In a single heterojunction HEMT typical for the AlGaN/GaN HEMTs a positive surface charge is applied at the AlGaN barrier/GaN channel heterointerface (see Fig. 3.1). At the substrate a similar, but negative surface charge is applied towards the buffer. Only this ensures a quasi-Fermi level below the conduction band edge and thus a depleted buffer due to the modified quasi Fermi level [238]. At the semiconductor/SiN interface negative charges are applied [275]. The values for the surface charges range between 10 [275] and 10 cm [12].

In such *Schrödinger Poisson* simulation
approaches the surface charges are entered into the Poisson
equation and result in the correct band edge situation, which was
suggested by Sacconi et al. in [238] in
Schrödinger-Poisson, or similarly in [275].
In contrast to [238], who used the quasi two-dimensional approach for the calculation of the currents,
this work uses a fully two-dimensional simulation in a classical equivalent.
The surface charges found useful for the modeling are giving in Chapter 7.

2001-12-21