As the charge transport in the channel is
governed by the same laws exactly as in a non split-drain MOSFET, it is
desirable to observe how quantities change when a magnetic field is applied.
Plots of the electron mobility, electron concentration, potential
and electric field are shown. Because the variations are very small
in the whole MAGFET structure, these quantities are presented from cuts
along the MAGFET width and at 1 nm from the silicon oxide-silicon interface,
that is, along the length of the MAGFET (see Fig. 4.1), from the end of
the source towards the drains, cuts at 20 m, 50
m, 80
m, and
110
m from the source side are made. Then, the quantities are shown at 1 nm
from the silicon oxide-silicon interface where deviations can be observed.
Figures 4.10 through 4.15 show the potential inside the channel at 20 m
from the source and at 1 nm from the silicon oxide-silicon interface at 300 K for
different gate voltages and magnetic fields. Because the cut is close to the source
which is biased to zero volts, the potential is almost constant when no
magnetic field is applied. As soon as a magnetic field is applied, the potential
is bent upwards if the magnetic field points inside the MAGFET sensor (
component of the magnetic field is -50 mT) or downwards on the contrary case (
component of the magnetic field is +50 mT). For a gate voltage of zero volts this
bent is not noticeable, because the magnitude of the moving charge is very low, so
the magnetic field has no visible effect on the potential.
From the previous plots, it is expected that the potential should be bent
around a common point when a magnetic field is applied. Because the cut has been
made at 20 m from the source side of the MAGFET, the gate has more
control over the channel than the other contacts. This explains the asymmetry
in these figures. Figures 4.16 through 4.21 show the potential inside the channel
at 50
m from the source and at 1 nm from the silicon oxide-silicon interface at
300 K for different gate voltages and magnetic fields. The potential with zero
magnetic field shows a small curvature coming from the drains, because
the cut is approaching the drains. As can be seen, the potentials are
symmetric with respect to the direction of the magnetic field.
It is expected that a cut closer to the drains will show a strong influence of the
drains on the potential.Figures 4.22 through 4.27 show the potential inside
the channel at 80 m from the source and at 1 nm from the silicon oxide-silicon
interface at 300 K for different gate voltages and magnetic fields. A symmetry is
roughly noticeable. Because the cut has been made in a zone between the middle of
the MAGFET structure and the drains, in this zone both the gate and the drains
fight for controlling this zone of the channel.
Figures 4.28
through 4.33 show the potential inside the channel at 110 m from
the source and at 1 nm from the silicon oxide-silicon interface at 300 K for
different gate voltages and magnetic fields. The cut has been made only at 15
m
from the drains and their influence on the potential is quite remarkable. A quasi
perfect symmetry can be seen in these figures.
The following quantity to be shown is the electron concentration inside the channel.
As it is known from the Hall effect, the carriers pile up in one of the planes
parallel to the applied magnetic field depending on their direction and the
direction of the magnetic field. In the two-drain MAGFET, because the magnetic field
is applied perpendicular to the channel, the electrons pile up in one side of the
channel within the MAGFET structure. Figures 4.34 through 4.39
show the electron
concentration inside the channel at 20 m from the source and at 1 nm from the
silicon oxide-silicon interface at 300 K for different gate voltages and magnetic
fields. For the gate voltages from 0 V, 1 V, and 2 V, a symmetry in the
electron concentration due to the magnetic fields can be seen. For gate
voltages larger than 3 V, the electron concentration with zero magnetic field
is lower than the corresponding electron concentration with a magnetic field. This
effect can be explained in terms of the driving force that exerts the gate.
Because the electrons are attracted to the silicon oxide-silicon interface and at
the same time swept by the Hall electric field, their concentration is higher
in one side than in the other. Then, a symmetry point cannot be seen.
Figures 4.40 through 4.45
show the electron concentration inside the channel at
50 m from the source and at 1 nm from the silicon oxide-silicon interface at
300 K for different gate voltages and magnetic fields. As stated for the potential,
the cuts are approaching the drains, so a stronger influence from
the drains on the electron concentration can be seen. A maximum is observed in
the middle of the channel (with respect to the width of the MAGFET) for zero magnetic
field, and it is caused by the combination of the lateral electric field which
concentrates on the drains and the stronger transversal electric field. The scale
at which the electron concentrations are plotted should be noticed. Because
the applied magnetic field is quite low (50 mT), the changes with respect to the
zero magnetic field case are very small. Stronger variations in the electric field
and carrier concentration can be seen for stronger magnetic inductions or for
devices with higher carrier mobilities [5,24].
Figures 4.46 through 4.51
show the electron concentration inside the channel at
80 m from the source and at 1 nm from the silicon oxide-silicon interface at
300 K for different gate voltages and magnetic fields. Comparing these figures with
Figures 4.34 through
4.39,
the electron concentration for zero magnetic field shows a
maximum. Actually there is indeed a maximum but it is hardly noticeable due
to the scale used for the plots and because the cut is localized far away from
the drains. In Figures 4.52 through 4.57
the electron
concentration inside the channel at 110
m from the source and at 1 nm from
the silicon oxide-silicon interface at 300 K for different gate voltages and
magnetic fields is shown. The strong influence from the drains and the gate
can be seen on the electron concentration. In addition, a perfect symmetry
can be observed.
The electric field is also a quantity of interest. Actually, its shape is
correlated to the carrier concentration and the potential. However, the
electric field is a vectorial quantity and because this subsection is presenting
two-dimensional cuts from full three-dimensional simulations of a two-drain MAGFET,
one component is missing. The cuts are made perpendicular to the -
plane (see Figure 4.1) so the lateral component of the electric field due
to the drains to source bias is missing (
component). The following plots
only show the absolute value of the
and
components at 1 nm of the
silicon oxide-silicon interface.
Figures 4.58 through 4.63 show the electric field inside the channel at 20 m
from the source and at 1 nm from the silicon oxide-silicon interface at 300 K for
different gate voltages and magnetic fields. As explained for the electron
concentration plots at the same cut distance, a symmetry in the electric field
line can be observed for low gate voltages but this symmetry is lost as soon as
the gate voltage is larger than 3 V. Because the cut is close to the source
which is set to zero volts, the dominant component of the electric field is due
to the gate. Although the
component of the electric field is missing in these
figures, its influence can be noticed for the following figures as the cut
approaches the drains.
Figures 4.64
through 4.69 show the electric field inside the channel at 50 m
from the source and at 1 nm from the silicon oxide-silicon interface at 300 K for
different gate voltages and magnetic fields whereas Figures 4.70
through 4.75 show
the electric field inside the channel at 80
m from the source and at 1 nm from
the silicon oxide-silicon interface at 300 K for different gate voltages and magnetic
fields. Because a magnetic field deflects the electron current lines inside the
channel, a Hall electric field across the current path must counteract the deflection.
As soon as the electrons leave the source, the magnetic field acts on them but not instantaneously. After the electrons have run through some of their paths, they are turned, so it is expected that the Hall electric field is not uniform. The electric field line in Figures 4.58 through 4.75 show this Hall electric field (when a magnetic field is applied). If the device were a MOS Hall plate, this line should be a straight line. That is the reason why the Hall contacts in a MOS Hall plate should be placed close but not next to the drain.
Figures 4.76 through 4.81
show the electric field inside the channel at 110 m
from the source and at 1 nm from the silicon oxide-silicon interface at 300 K for
different gate voltages and magnetic fields. The influence of the drains is evident
in this zone of the channel.
Rodrigo Torres 2003-03-26