4. SiC Device Simulation

THE EXPECTED excellent performance of SiC devices is often expressed by a figure of merit. In the past, several analyses of the impact of material parameters on the performance of semiconductor devices have been performed. Johnson derived a figure of merit (JFOM) [164]

$$\mathrm{JFOM} = \frac{E^2_\mathrm{B}\cdot v^2_s}{4 \pi^2 },$$ (4.1)

which defines the power-frequency product for a low-voltage transistors. Here $E_\mathrm{B}$ is the critical electric field for breakdown in the semiconductor and $v_\mathrm{s}$ is the electron saturation velocity. Keyes' figure of merit (KFOM) [165] provides a thermal limitation to the switching behavior of transistors used in integrated circuits

$$\mathrm{KFOM} = \kappa \cdot \sqrt{\frac{c\cdot v_\mathrm{s}}{4 \pi \varepsilon_\mathrm{s}}},$$ (4.2)

where $\kappa$ is the thermal conductivity, $c$ is velocity of light and $\varepsilon_\mathrm{s}$ is the static dielectric constant. These figures of merit predict that SiC is an excellent material for high frequency devices. Baliga derived a figure of merit (BFOM) [166]

$$\mathrm{BFOM} = \varepsilon_\mathrm{s}\cdot\mu\cdot E_{\mathrm{g}}^3,$$ (4.3)

which defines material parameters to minimize the conduction loss in low-frequency unipolar transistors. Here, $\mu$ is the mobility and $E_{\mathrm{g}}$ is the bandgap of the semiconductor. From this figure of merit the excellent performance of high voltage unipolar devices in SiC can be deduced. Baliga also derived a high-frequency figure of merit (BHFFOM) [167] for unipolar switches

$$\mathrm{BHFFOM} = \mu\cdot E^2_\mathrm{B}\cdot\sqrt{\frac{V_\mathrm{G}}{4V^3_\mathrm{B}}},$$ (4.4)

where $V_\mathrm{G}$ is the gate drive voltage and $V_\mathrm{B}$ is the breakdown voltage. This figure of merit demonstrates that a significant power loss reduction can be achieved by using SiC devices for high-frequency applications compared to other conventional semiconductor devices.

Table 4.1: Comparison of normalized figures of merit for $\alpha$-SiC and Si.

	JFOM	KFOM	BFOM	BHFFOM
Si	1	1	1	1
4H-SiC	400	5.1	560	69
6H-SiC	400	5.1	240	29

Following these figures of merit (Table 4.1) and increasing interest in high-temperature, high-power, and high-frequency devices based on SiC, the need for numerical investigation pertaining to these devices becomes true. Device simulation has gained increasing relevance for the design and optimization of electronic semiconductor applications due to the rising design complexity and the cost reduction achieved by reducing the number of experimental batch cycles. It has been a powerful and widely used tool in the investigation and improvement of narrow bandgap semiconductor devices, and it will be a driving force in the further development of both semi-conducting and semi-insulating SiC devices. A good survey on the principle of device analysis and simulation is given in [104].

In Chapter 3 material specific models and the corresponding parameters relevant to $\alpha$-SiC material have been outlined and identified. It is the scope of this chapter to evaluate the applicability of these models to state-of-the-art SiC devices. The selection of new SiC devices for simulation studies are based on their performance predictions which have been experimentally demonstrated in the past decade.
T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation