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Subsections


3.4.3 Surface scattering

3.4.3.1 Mobility Model of MINIMOS 6


Surface scattering is modeled by the following empirical expression [160]
$\displaystyle \mu^{\mathrm{LIS}}_{\nu}$ $\textstyle =$ $\displaystyle \frac{\mu^{\mathrm{ref}}_{\nu}+(\mu^{\mathrm{LI}}_{\nu}-\mu^{\mat...
...style
{\left(\frac{S_{\nu}}{S_{\nu}^{\mathrm {ref}}}\right)^{\gamma_{6,\nu}}}},$ (3.118)
$\displaystyle \mu^{\mathrm{ref}}_{\nu}$ $\textstyle =$ $\displaystyle \mu^{\mathrm{ref}}_{\nu,300}\cdot\left(\frac{T_{\mathrm{L}}}{\mathrm{300 K}}\right)^{-\gamma_{5,\nu}},$ (3.119)

The function $F(y)$ depending on the surface distance $y$ describes a smooth transition between the surface and bulk mobility [174,175]. The parameter $y^\mathrm {ref}$ describes a critical length.
\begin{displaymath}
F(y)=\frac{2\cdot\exp\displaystyle{\left(-\left(\frac{y}{y^\...
...left(-2 \cdot\left(\frac{y}{y^\mathrm {ref}}\right)^2\right)}}
\end{displaymath} (3.120)

The pressing forces $S_n$ and $S_p$ in (3.118) are equal to the magnitude of the normal field strength at the interface if the carriers are attracted by the interface, otherwise zero.

Table 3.25: Parameter values for surface mobility reduction in Si - MINIMOS 6 model
Parameter electrons holes Unit
$\mu^{\mathrm{ref}}_{\nu,300}$ 638 240 $\mathrm{ cm^2/Vs}$
$\gamma_{5,\nu}$ -1.19 -1.09  
$y^\mathrm {ref}$ 10 10 $\mathrm{ nm}$
$S_{\nu}^\mathrm {ref}$ 7e7 2.7e7 $\mathrm{ V/m}$
$\gamma_{6,\nu}$ 1.69 1.0  



3.4.3.2 Lombardi Mobility Model


Lombardi et al. [176] suggested another surface mobility degradation model. There are two surface scattering contributions due to acoustic phonons, $\mu_{ac}$, and surface roughness, $\mu_{sr}$. They are functions of total doping concentration $C_I$ and the pressing forces $S_n$ and $S_p$.
\begin{displaymath}
\mu^{\mathrm{ac}}_{\nu} = \frac{B_{\nu,300}}{S_\nu} +
\frac...
... C_I^{L_{\nu,300}}}{S_\nu^{1/3}\cdot T_L}\hspace{1cm}\nu = n,p
\end{displaymath} (3.121)


\begin{displaymath}
\mu^{\mathrm{sr}}_{\nu} = \frac{D_{\nu,300}}{{S_\nu}^2}
\end{displaymath} (3.122)

The total mobility is expressed by a Mathiessen rule:
\begin{displaymath}
\frac {1}{\mu^{\mathrm{LIS}}_{\nu}} = \frac {1}{\mu^{\mathrm...
...{\mu^{\mathrm{ac}}_{\nu}} + \frac {1}{\mu^{\mathrm{sr}}_{\nu}}
\end{displaymath} (3.123)


Table 3.26: Parameter values for surface mobility reduction in Si - Lombardi model
Parameter electrons holes Unit
$B_{\nu,300}$ 4.75e7 9.925e6 $\mathrm{ cm/s}$
$C_{\nu,300}$ 580 294.7 $\mathrm{ cm^{5/3}/V^{2/3}s}$
$L_{\nu,300}$ 0.125 0.0317  
$D_{\nu,300}$ 5.82e14 2.05e14 $\mathrm{ V/s}$



next up previous contents
Next: 3.4.4 High-Field Mobility for Up: 3.4 Carrier Mobility Previous: 3.4.2 Ionized Impurity Scattering
Vassil Palankovski
2001-02-28