3.1 Electronic Transport Model

It was mentioned in Chapter 2 that due to the anisotropic nature of the SiC crystal structure, anisotropic electronic properties should be expected. This means that electrical characteristics will be different depending on the orientation of the device with respect to the crystal. The most commonly used orientation has the wafer surface perpendicular to the c-axis (Fig. 3.1), which means that the current transport is better in the lateral device compared with a vertical device. However, most electrical devices depend on the vertical current transport, since it is easier to manufacture a blocking layer parallel to the surface.

In the numerical simulation of semiconductor devices

Figure 3.1: Wafer with surface perpendicular to the c-axis: current transport parallel and vertical to the c-axis.

it is generally assumed that the semiconductor material is isotropic, which is the case for cubic materials such as Si and GaAs. For SiC and for various nitrides, which generally crystallize in structures of symmetry lower than cubic (except for 3C-SiC), a rigorous model implementation in device simulation programs must account for the anisotropic properties.

Consider the following relation between the current density ${\mathbf{J}}$ and the electric field ${\mathbf{E}}$

$${\mathbf{J}}={\mathbf{\sigma}}\cdot{{\mathbf{E}}},$$ (3.1)

where the conductivity ${\mathbf{\sigma}}$ for hexagonal polytypes of SiC can be described with a second rank tensor of the diagonal form [103]

$$\sigma= \begin{pmatrix}\sigma_1 & 0 & 0 \\ 0 & \sigma_1 & 0 \\ 0 & 0 & \sigma_2 \\ \end{pmatrix}.$$ (3.2)

From (3.1) and (3.2) we see that the x and y components, say of the current density vectors, are governed by the tensor components represented by $\sigma_1$, whereas the z component of the current density is governed by the tensor components represented by $\sigma_2$. From now on we use the conductivity tensor $\sigma$ as $\sigma_1$ = $\sigma_\perp$ and $\sigma_2$ = $\sigma_\parallel$ representative to mean any of the second tensors in all the electrical transport equations formulated in this chapter.
T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation