3.6.4 Contacts

The contacts play a dominant role for the current transport in any device. In [50] it was shown that the shape of the gate above the gate foot is of similar importance as the length ${\it l}_{\mathrm{g}}$ of the gate foot defining the physical gate length ${\it l}_{\mathrm{g}}$. This work addresses the ohmic contact situation. In Fig. 3.25 three contact situations are given. The left one (I) assumes the direct contacting of the channel by the penetrating alloy. The second situation (II) assumes no or little penetration of the metal into the semiconductor, as e.g. occurring for GaN devices or as an extreme case in GaAs based devices for very thick cap layers. The third one (III) is a combination, where the barrier/channel heterojunction remains, while the alloy penetrates down the barrier layer. All three situations are proven to occur in devices and the impact is discussed in Chapter 7.

Figure 3.25: Different ohmic contact situations.

For the semiconductor-metal interface a second Schottky contact model was considered. The approach is based on the so-called effective tunneling mass ${\it m}_{\mathrm{t}}$ of electrons from (3.132). A tunneling probability is to be determined for this non-local model:

$$\Gamma(\mathbf{r}) = \exp \bigg[-\frac{2}{\hbar} \int_{0}^{r} \sqrt{ 2 m_t \bigg(\frac{\phi_B}{q}+\phi_m -\psi(\mathbf{r})\bigg)} dr \bigg]$$ (3.129)

$\phi_m$ represents the quasi-Fermi level potential in the metal.

Figure 3.26: Areas considered for a one- and two-dimensional treatment of the integration path for a high-power pseudomorphic HEMT.

For the tunneling equations (3.55) the actual implementation of the integration path is critical. A one-dimensional treatment, as shown in Fig. 3.26 is physically not sound (I), since the most critical high field area (II) for the gate drain diode is left out of consideration. Thus, fitting ${\it m}_{\mathrm{t}}$ to measured gate currents would ignore the most relevant physical changes to evaluate. For the two-dimensional evaluation of (3.55) discrete paths for integration has to be determined.

One way to obtain these two-dimensional paths is to construct the simulation mesh by hand in such a way, that a two-dimensional evaluation of $\Gamma$ is indeed possible, as suggested in [130]. This is a very laborious process, especially for geometry optimizations and thus not very useful for general purpose simulators.