3.3.2 Mobility Degradation due to Scattering

There are important scattering mechanisms for SiC devices for which no experimental or theoretical data is yet available. Carrier-carrier scattering significantly influences the characteristics of SiC high-power bipolar devices at high current ratings. In addition, the surface current transport parameters which are especially relevant in MOS devices are rather unknown. Therefore, corresponding silicon models and parameters have to be used.

The carrier-carrier contribution to the overall mobility degradation is captured in the mobility term, and expressed by the model of Choo [130] which uses the Conwell-Weisskopf screening theory

$$\mu_{\nu}^\mathrm{cc}= \frac {D\cdot\left(\displaystyle\frac{T_\m... ...\ K}}\right)^2\cdot(p\cdot n)^{-\frac{1}{3}}\right)\right]\hspace{1cm}\nu = n,p$$ (3.84)

where $n$ and $p$ are the electron and hole densities, respectively. The fitting parameter D is 6.9$\times$10$^{20}$ [cm$\cdot$V$\cdot$s]$^{-1}$ and 3.045$\times$10$^{20}$ [cm$\cdot$V$\cdot$s]$^{-1}$ for 4H- and 6H-SiC, respectively, and F = 7.452$\times$10$^{13}$ cm$^{-2}$ [131].

Similarly, the physical mechanisms at MOS interfaces in SiC are not well understood. However, it is necessary to account for reduced channel mobilities in real MOS devices. Surface scattering is modeled by the following empirical expression [132]

$$\mu_{\nu}^\mathrm{surf}= \frac{\mu_{\nu}^\mathrm{ref}+(\mu_{\nu}^... ..._{\nu}}{S_{\nu}^{\mathrm{ref}}}\right)^{\gamma_{2,\nu}}}},\hspace{1cm}\nu = n,p$$ (3.85)

$$\mu_{\nu}^\mathrm{ref}=\mu_{\nu,300}^\mathrm{ref}\cdot\left(\disp... ...{T_\mathrm{L}}{\mathrm{300\ K}}\right)^{-\gamma_{3,\nu}}. \hspace{1cm}\nu = n,p$$ (3.86)

Here, the function $F(y)$ depending on the surface distance y describes a smooth transition between the surface and and bulk, given by

$$F(y)=\displaystyle\frac{2\cdot{\rm exp}{\left(-\left(\displaystyl... ...p}{\left(-2 \cdot\left(\displaystyle\frac{y}{y^\mathrm{ref}}\right)^2\right)}},$$ (3.87)

where the parameter $y^\mathrm{ref}$ describes a critical length. The pressing forces $S_n$ and $S_p$ in (3.85) are equal to the magnitude of the normal field strength at the interface if the carriers are attracted by the interface, otherwise zero.

Mobility degradation at MOS interfaces can also be modeled using a surface mobility model which incorporates an empirical model that combines mobility expressions for semiconductor-insulator interfaces and for bulk. The basic equation is given by Matthiessen's rule

$$\mu^\mathrm{tot}_{\nu} = \left[\frac {1}{\mu^{b}_{\nu}} + \frac {1}{\mu^{ac}_{\nu}} + \frac {1}{\mu^{sr}_{\nu}}\right]^{-1}. \hspace{1cm}\nu = n,p$$ (3.88)

In this expression, $\mu^\mathrm{tot}$ is the total electron or hole mobility accounting for surface effects, $\mu^{ac}_{\nu}$ is the mobility degraded by surface acoustical phonon scattering, $\mu^{b}_{\nu}$ is the mobility in bulk, and $\mu^{sr}_{\nu}$ denotes the mobility degraded by surface roughness scattering.

The bulk mobility $\mu_b$ is computed through (3.77) and the two surface contributions can be modeled using the model of Lombardi et al. [133], which reads

$$\mu^{ac}_{\nu}=\displaystyle\frac{B_\nu}{E_{\perp,\nu}} + \displa... ...\displaystyle\frac{T_\mathrm{L}}{\mathrm{300\ K}}\right)} \hspace{1cm}\nu = n,p$$ (3.89)

$$\mu^{sr}_{\nu} =\frac{D_\nu}{E^{2}_{\perp,\nu}} \hspace{1cm}\nu = n,p$$ (3.90)

where B, C, D are fitting parameters, and $E_\perp$ is the component of the electric field normal to SiO$_2$-SiC interface.

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