354
Compact Models for Integrated Circuit Design
all, if we optimize the device in such a way so that dV eff /dV gs ≈ 1, then the first
term in the denominator of Equation 10.7 is inversely related to V gs . Under this
condition, S will decrease with decreasing V gs . This can be achieved by TFET
gate engineering so that V gs directly controls the tunnel junction bias or band
overlap ΔΦ, that is, gate has strong electrostatic control. The efficient gate electrostatics can be realized using a thin high-k gate dielectric and an ultrathin
body channel region. Secondly, S can also be minimized by maximizing the
second term in the denominator of Equation 10.7. This occurs when the gate is
placed to align the applied field with the internal field of the tunnel junction so
that the gate field adds to the internal field to increase the tunneling probability.
From the discussion of Equation 10.7, it is clear that S is a function of V gs in
sharp contrast to the conventional MOSFETs. This means that log(I ds ) − V gs
plot in the subthreshold region is not a straight line and S does not have a
unique value as shown in Figure 10.5b. The value of S is lowest at the lowest V gs , and increases as V gs increases. Due to the changing values of S along
I ds − V gs curve it is useful to clearly define it for device characterization.
Several definitions have been used for TFET S [16,57,58]. The most commonly
used method is to take the tangential inverse slope of I ds − V gs curve at the
steepest part of the characteristic called the point swing as shown in Figure 10.6.
Bhuwalka et al. [58] and Boucart and Ionescu [57] have defined subthreshold
region by an average swing as shown in Figure 10.6 and is given by
S
V V
I I
avg
th
off
th
off
=
−
(
)
log
/
(10.8)
where:
V th is the threshold voltage
V off is the voltage below V th at which the drain current I off is minimum
V off
I off
I th
I ds
V th
Average swing
Point swing
V gs
FIGURE 10.6
Subthreshold swing defined as a point swing is obtained at the steepest point of the I ds − V gs
curve and an average swing is defined as the average from turn-on to threshold voltage.
Compact Models for Integrated Circuit Design
all, if we optimize the device in such a way so that dV eff /dV gs ≈ 1, then the first
term in the denominator of Equation 10.7 is inversely related to V gs . Under this
condition, S will decrease with decreasing V gs . This can be achieved by TFET
gate engineering so that V gs directly controls the tunnel junction bias or band
overlap ΔΦ, that is, gate has strong electrostatic control. The efficient gate electrostatics can be realized using a thin high-k gate dielectric and an ultrathin
body channel region. Secondly, S can also be minimized by maximizing the
second term in the denominator of Equation 10.7. This occurs when the gate is
placed to align the applied field with the internal field of the tunnel junction so
that the gate field adds to the internal field to increase the tunneling probability.
From the discussion of Equation 10.7, it is clear that S is a function of V gs in
sharp contrast to the conventional MOSFETs. This means that log(I ds ) − V gs
plot in the subthreshold region is not a straight line and S does not have a
unique value as shown in Figure 10.5b. The value of S is lowest at the lowest V gs , and increases as V gs increases. Due to the changing values of S along
I ds − V gs curve it is useful to clearly define it for device characterization.
Several definitions have been used for TFET S [16,57,58]. The most commonly
used method is to take the tangential inverse slope of I ds − V gs curve at the
steepest part of the characteristic called the point swing as shown in Figure 10.6.
Bhuwalka et al. [58] and Boucart and Ionescu [57] have defined subthreshold
region by an average swing as shown in Figure 10.6 and is given by
S
V V
I I
avg
th
off
th
off
=
−
(
)
log
/
(10.8)
where:
V th is the threshold voltage
V off is the voltage below V th at which the drain current I off is minimum
V off
I off
I th
I ds
V th
Average swing
Point swing
V gs
FIGURE 10.6
Subthreshold swing defined as a point swing is obtained at the steepest point of the I ds − V gs
curve and an average swing is defined as the average from turn-on to threshold voltage.