8.4. HFETS: INTRODUCTION 375
and
V(LII,h)=VD (8.3.37)
The voltage drop in the pinched region (Region II) isVD−(VG−VT)orVD−VDS(sat)=Vdp.
Therefore
LII=2 h
πsinh−^1[
Vdpπ
2 Ech]
(8.3.38)
and
∂LII
∂VD=
1
Ec[
1+
(
Vdpπ
2 Ech) 2 ]−^1 /^2
(8.3.39)
For the case of interest, where the device is biased well into saturation, the second term in the
bracket becomes large, giving
rd=1
gd=
πVdp
2 ID(
L
h)
(8.3.40)
This is a very important result. It says that to maintain a high value ofrd, which is necessary
for high voltage gain, it is essential to maintain a high aspect ratio of the gate length to channel
thickness(L/h). Typically,(L/h)should be at least 10. Of course, as the current in the channel
decreases,rdincreases, but this benefit is largely negated by a similar decrease in the devicegm.
An increase inrdwithVdpis based on the increase in the saturated region which further isolated
the drain potential from the source, reducinggd.
8.4 HFETs:INTRODUCTION.............................
In the previous sections we have discussed the MESFET (or JFET) devices. In the MESFET
the gate is insulated from the channel by a barrier created by either a Schottky barrier (or a
p+njunction). The charge in the channel is provided by dopants in the channel. The dopants,
while providing charge, also cause scattering and reduce mobility. The question arises: Can
we have channel charge but avoid dopant scattering? This is possible in the Si MOSFET where
charge can be induced by inversion. However, the MOSFET charge has to contend with interface
roughness scattering. In the Si/SiO 2 case the interface is between a high quality semiconductor
and a non-epitaxial layer and the interface scattering can greatly reduce mobility. Thus while
room temperature electron mobility in pure Si is∼1300 cm^2 /V.s, it is only half this value in
the NMOS channel. It would be ideal to have a heterostructure grown epitaxially where band
inversion could occur. However, so far this has been difficult, though advances continue to be
made. It is possible to make heterostructure devices where mobile charge is donated by dopants
or other fixed charges.
The most widely used heterostructure FET utilizes the modulation doping concept. The device
is called modulation doped field effect transistor (MODFET) or high electron mobility transistor
(HEMT) or 2-dimensional gate field effect transistor (TEGFET), etc. It has also been shown
that polar charges created at interfaces by piezoelectric and/or Spontaneous polarization can also
be exploited to create free charge. This approach has become quite dominant in nitride based
devices. Heterostructure field effect transistors (HFETs) offer many advantages over MESFETs