8.5. CHARGE CONTROL MODEL FOR THE MODFET 385
therefore
eΔns=
D
·(±Vg)This is the charge control equation of the gate capacitor where
ΔQ 2 DEG[
C·cm−^2]
=Cg·ΔVg[
F·V·cm−^2]
This is to be expected since we are indeed dealing with a capacitor where the depleted AlGaAs
layer is the dielectric and the two plates of the capacitor are the gate metal and the centroid of the
2DEG separated by a distance D. By examining equation 8.5.9, we see that at a given gate volt-
age,nsincreases linearly withdδ. Thus, moving theδ-doped layer closer to the AlGaAs/GaAs
heterojunction causes more of the induced charge to be imaged in the channel rather than on
the gate. This also illustrates why aδ-doped structure is preferable to continuous doping; in the
δ-doped structure, the centroid of the donor charge distribution is much closer to the 2DEG, re-
sulting in more charge being induced in the channel. However, moving the doped layer too close
to the heterointerface causes a degradation in channel mobility, since ionized impurity scattering
increases.
The pinch-off voltageVpin a MODFET is the gate voltage required to deplete the channel of
carriers. To findVp,wesetnsin equation 8.5.9 equal to zero and solve for the gate voltage. This
gives us
Vp=−eNd+dδ
+(φb−ΔEc/e) (8.5.19)figure 8.17a shows the band diagram of a MODFET biased at pinch-off. Here,nm=−Nd+and
ns=0, so the the only region with a non-zero electric field is between the gate and theδ-doped
layer.
In figure 8.17b, we show a MODFET with a large forward bias on the gate. If we bias the
device at pinch-off (figure 8.17a) and then increase the voltage on the gate, charge is transferred
from the gate(nm)to both the 2DEG(ns)and the barrier (nparincreases andNd+decreases,
since some of the electrons end up in the conduction band and some fill empty donor states).
Initially, almost all of the charge from the gate is transferred to the channel, and the change in
nparandNd+remains small. However, asVGbecomes large, the conduction band in the AlGaAs
begins to approach the Fermi level, implying that the electron concentration in the barrier must be
increasing (see figure 8.17b). Hence, if the gate voltage is further increased, charge is transferred
from the gate into both the 2DEG and the barrier. This is obviously not the biasing required for
good MODFET performance. The device operates between the two limits given by figure 8.17a
and figure 8.17b.
8.5.1 Modulation Efficiency ...........................
We have seen that in general, modulating the gate voltage causes charge to be transferred from
the gate to both the 2DEG and the barrier region. Even under optimal MODFET bias conditions,
nparandNd^0 =Nd−Nd+(the density of occupied donors in the AlGaAs) are typically negligible,
but they are not zero, so increasingVGwill still cause a small change in the charge density in
the AlGaAs. The concept ofmodulationefficiency was introduced by Foisy et al to describe