Fig. 5.21 shows the Monte Carlo simulation results for the majority electron mobility in relaxed Si in comparison with experimental data.
Fig. 5.22 and Fig. 5.23 demonstrate the doping dependence of
and
in the Si active layer grown on relaxed
. In Fig. 5.23 the curve for the perpendicular component
exhibits an increase for the
substrate oriented along
when the doping level becomes high enough.
The same increase can be seen in Fig. 5.24, which displays the doping dependence of the perpendicular component
in strained Si on a
relaxed
substrate of orientation
. At the same time the in-plane component does not increase
as shown in Fig. 5.25. This effect can be explained by the influence of the quantum mechanical Pauli exclusion principle which starts
playing an important role at high electron densities.
At low doping level, the valley oriented along
is the lowest one. It is fully populated (see Fig. 5.26) and
is determined by
, while
is determined by
. As the donor concentration increases, lower energy levels are
forbidden to scatter in
by the Pauli exclusion principle and thus electrons scatter to higher energy levels. At doping level about
cm
electrons occupy
energies high enough to be able to scatter to the unsplit
valleys which lie higher than the
ones due to strain. The intervalley
scattering becomes possible and gets stronger as the donor concentration increases. Finally, most of the electrons are equally distributed
between the
valleys. The influence
of
on
is significantly reduced and which turns out to be enough to suppress increasing ionized impurity scattering. However,
the
valleys are oriented in such a way that the influence of
and
on
is not strong enough to suppress the
impurity scattering, and as a result
does not show an increase.
Fig. 5.27 and Fig. 5.28 show the Ge composition dependence of
and
in strained
layers grown on
Si
substrates. The increase of the perpendicular component at high doping levels and low composition
can be explained in the following manner.
In the undoped material there are two factors which depend on the Ge mole fraction: the splitting of the
valleys and alloy scattering.
The first factor increases the perpendicular component of the electron mobility and the second one decreases it. In doped SiGe at high doping levels,
ionized impurity scattering dominates the alloy scattering and thus suppresses the second factor leaving the first one that leads to the increase.
The in-plane component does not have this increase because both the energy splitting and alloy scattering decrease
. Thus after removing the second factor there still exists the second one which decreases the parallel component.
S. Smirnov: