3.5.3 Impact Ionization

In order to acquire a clear understanding of SiC power devices breakdown characteristics, it is important to have a clear understanding of impact ionization. The acceleration of free carriers within a high electric field finally results in generating free carriers by impact ionization. This process corresponds to the inverse process of Auger recombination. The Auger generation rate was evaluated by making use of the principle of detailed balance which holds in equilibrium. Impact ionization is, however, a typical non-equilibrium process which requires large electric fields. It is modeled by the reciprocal of the mean free path which is denoted the impact ionization coefficient. The corresponding avalanche generation rate can be expressed by

$$G_{ava}=\frac{1}{{\mathrm{q}}}\left( \alpha _{n}\cdot j_{n}+\alpha _{p}\cdot j_{p}\right)$$ (3.111)

The impact ionization coefficients $\alpha _{n}$ and $\alpha _{p}$ are expressed by Chynoweth's law [152]:

$$\alpha _{\nu} = a_{\nu}\cdot\gamma _{a}\cdot\exp \left( -\frac{b_{\nu}\cdot\gamma _{a}}{E_\parallel}\right), \hspace{1cm}\nu = n,p$$ (3.112)

with

$$\gamma_a =\frac{\tanh \left(\displaystyle\frac{\hbar\omega_{op}}{... ...aystyle\frac{\hbar\omega_{op}}{2\cdot{\mathrm{k_B}}\cdot T_\mathrm{L}}\right) }$$ (3.113)

where $a_{\nu}$ and $b_{\nu}$ are temperature dependent measured parameters. The electric field component $E_\parallel$ is in the direction of current flow. The factor $\gamma _{a}$ with the optical phonon energy $\hbar \omega_{op}$ expresses the temperature dependence of the phonon gas against which the carriers are accelerated [131].

A review of measured data on impact ionization coefficients in $\alpha$-SiC

Table 3.8: Impact ionization coefficients of electrons and holes in 4H/6H-SiC.

	a$_{n}$ [cm$^{-1}$ ]	b$_{n}$ [V/cm]	a$_{p}$ [cm$^{-1}$ ]	b$_{p}$ [V/cm]	$\hbar \omega_{op}$ [meV]
4H-SiC	3.44$\times$10$^{6}$	2.58$\times$10$^{7}$	3.5$\times$10$^{6}$	1.7$\times$10$^{7}$	106
6H-SiC	1.66$\times$10$^{6}$	1.27$\times$10$^{7}$	2.5$\times$10$^{6}$	1.48$\times$10$^{7}$	106

Figure 3.13: Impact ionization coefficients of electrons and holes for $\alpha$-SiC at different electric field in the direction of the current flow.

has been first published by Ruff et al. [22] and later by Bakowski et al. [23], but most recently measured data compiled by Raghunathanr and Baliga [153] at different temperatures show an about 20% higher critical electric field compared to the previous reports. It seems that the impact ionization coefficients are decreasing with increasing temperature. This implies the increase of the breakdown voltage, which is a desirable property for SiC power devices.

The extracted average parameters are summarized in Table 3.8, and Fig. 3.13 shows the impact ionization coefficients of electrons and holes at room temperature as a function of electric field.

It is important to note that the measured data rely on uniform avalanche breakdown with all possible influence of structural defects and edge termination excluded. No explicitly measured data about anisotropic tensor components of impact ionization coefficients are available so far; however, a fitting to the existing measured data indicates an anisotropic ratio [23]

$$\frac{\alpha_{n\perp}}{\alpha_{n\parallel}}=0.3,\hspace{1cm}\frac{\alpha_{p\perp}}{\alpha_{p\parallel}}=1\,.$$ (3.114)

T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation