Subsections

• 3.4.3.1 Mobility Model of MINIMOS 6
• 3.4.3.2 Lombardi Mobility Model

3.4.3 Surface scattering

3.4.3.1 Mobility Model of MINIMOS 6

Surface scattering is modeled by the following empirical expression [160]

$$\mu^{\mathrm{LIS}}_{\nu} = \frac{\mu^{\mathrm{ref}}_{\nu}+(\mu^{\mathrm{LI}}_{\nu}-\mu^{\mat... ...style {\left(\frac{S_{\nu}}{S_{\nu}^{\mathrm {ref}}}\right)^{\gamma_{6,\nu}}}},$$ (3.118)

$$\mu^{\mathrm{ref}}_{\nu} = \mu^{\mathrm{ref}}_{\nu,300}\cdot\left(\frac{T_{\mathrm{L}}}{\mathrm{300 K}}\right)^{-\gamma_{5,\nu}},$$ (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.

$$F(y)=\frac{2\cdot\exp\displaystyle{\left(-\left(\frac{y}{y^\... ...left(-2 \cdot\left(\frac{y}{y^\mathrm {ref}}\right)^2\right)}}$$ (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 $S_p$.

$$\mu^{\mathrm{ac}}_{\nu} = \frac{B_{\nu,300}}{S_\nu} + \frac... ... C_I^{L_{\nu,300}}}{S_\nu^{1/3}\cdot T_L}\hspace{1cm}\nu = n,p$$ (3.121)

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

The total mobility is expressed by a Mathiessen rule:

$$\frac {1}{\mu^{\mathrm{LIS}}_{\nu}} = \frac {1}{\mu^{\mathrm... ...{\mu^{\mathrm{ac}}_{\nu}} + \frac {1}{\mu^{\mathrm{sr}}_{\nu}}$$ (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	$\mathrm{ V/s}$