3.1.2 Mobility

The mobility is defined as the drift velocity $v$ per unit electric field in a homogeneous semiconductor:

$$\mu = \frac{\vert v\vert}{E}.$$ (3.13)

The carrier mobilities $\mu_n$ and $\mu_p$ account for the scattering mechanisms in electrical transport [18]. Dominant mechanisms are lattice scattering, impurity scattering, and carrier-carrier scattering. All of these scatterings reduce the carrier mobilities. A further mobility reduction is due to the saturation of the drift velocity of warm and hot carriers which is caused by lattice vibrations. In general, these mechanisms are very complicated and difficult to model. For the purpose of numerical device simulation, several empirical models have been suggested by Caughey and Thomas [113], Lombardi [114], Masetti [115], and Selberherr [18,22].

Figure 3.1: Room temperature carrier mobilities in silicon as a function of the doping concentration.

Figure 3.1 shows the carrier mobilities in silicon as a function of doping concentration from the measured data [116]. The electron mobility and hole mobility have a similar doping dependence. At room temperature, ionized impurity scattering effects are small for doping concentration below $10^{16}$ $\mathrm{cm^{-3}}$ and the mobility is almost constant and is primarily limited by phonon scattering. At higher doping concentrations, the mobility of electrons and holes decreases with increasing doping concentration due to ionized impurity scattering.