# A Simulator for Investigation of Breakdown Characteristics of SiC MOSFETs
## 3 Results and Discussion  
### Analysis of the Lattice Temperature  
To investigate the BV of the VDMOSFET, Ids-Vds is simulated with different lattice temperatures and various device structures. During simulation, the maximum Vds is 2500 V, Vgs is fixed to 10 V, and the break criteria of the current density is fixed to \(1\times 10^{-4}\) A/\(\upmu\)m. Due to our reasonable choice of scale factor and calculation method for the scaled electron density, there are no convergence issues encountered caused by a low intrinsic carrier concentration.  
Figure 5 shows the ON-state breakdown characteristic curves and the transfer characteristics curves. With the increasing in lattice temperature from 300 K to 573 K, the BV decreases from 2450 V to 2435 V, which indicates that the BV is relatively stable with the lattice temperature increases, as shown in Figure 5a.  
When Vds is between 0 and 100 V, increasing Vgs forms a channel in the base region, causing electrons in the N+ region to flow to the N+ substrate. At Vgs = 10 V, with Vds ranging from 0 to 100 V, the on-resistance values at three temperatures are 1.313 m\(\Omega\cdot\)cm\({}^{2}\), 1.421 m\(\Omega\cdot\)cm\({}^{2}\) and 1.475 m\(\Omega\cdot\)cm\({}^{2}\), respectively. The formula of on-resistance is given as [5]  
\[R_{on}=\frac{4\text{BV}^{2}}{\varepsilon_{S}\mu_{n}E_{c}^{2}} \tag{7}\]  
where \(\varepsilon_{S}\) is the semiconductor electrical permittivity, \(\upmu_{n}\) is the electron mobility and \(E_{C}\) is the critical electric field.  
Figure 4: The simulated (**a**) potential at x = 20 \(\upmu\)m (inset: schematic cross-section showing x at 20 \(\upmu\)m), (**b**) electron concentration at y = 12.515 \(\upmu\)m (inset: schematic cross-section showing y at 12.515 \(\upmu\)m), (**c**) output characteristic curves and (**d**) transfer characteristic curves compared with the commercial software.  
In the range of 300 K to 573 K, the saturation current density decreases with increasing temperature as the device enters the saturation region. This reduction is attributed to enhanced lattice vibrations at elevated temperatures, which significantly diminish mobility and consequently lower the current density.  
The ionization coefficient, \(\alpha\), as in Equation (5), increases the electric field strength at a constant temperature. When Vds exceeds 2400 V, the device undergoes an avalanche breakdown due to the strong electric field strength. As the temperature rises, \(\alpha\) exhibits a marginal decrease. Therefore, the generation rate in (4) undergoes little change, resulting in the breakdown voltage remaining relatively stable despite the increasing lattice temperatures within this temperature range.  
As depicted in Figure 5b, the transfer characteristics for the base region with a radius of 0 \(\upmu\)m exhibit variations across different lattice temperatures, with the corresponding threshold voltage (Vth) and subthreshold swing (SS) values detailed in Table 3. The results in Table 3 show that with the increase in temperature, the change in Vth is less than 0.5 V, while the increase in SS mainly affects the leakage current, and they have little effect on the BV.  
The ON-state current density distributions of Vds = 2.4 kV and 2.5 kV and Vgs = 10 V when T = 300 K are plotted in Figure 6. In Figure 6a, it is evident that electrons flow from the channel into the JFET region, subsequently reaching the drain before breakdown. When the drain voltage is sufficiently high, i.e., a sufficiently high reverse voltage is applied at the collector junction in the parasitic NPN bipolar transistor at the bottom of the PBase region, as depicted in Figure 6b, a secondary breakdown occurs. This event is characterized by a rapid increase in the current density, resulting in the destruction of a MOSFET.