SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.5. CHARGE CONTROL MODEL FOR THE MODFET 381

The charge distribution in the system is determined by electrostatics and can be varied by
applying a voltage to the gate. In general, electrons from donors in the barrier region can end up
in one of three places:

1. In the channel. We will call this chargens.


2. On the gate. We will call this chargenm.


3. Inside the barrier material, where they create a parasitic channel. We call this chargenpar.

All charges are expressed in units [cm−^2 ]. We treat the distributed 2DEG as if it were a perfect
2-dimensional sheet placed a distanceΔdfrom the heterointerface, whereΔdis simply the
centroid of the 2DEG charge distribution. The resulting charge distribution, band diagram, and
electric field profile in the system is are shown in figure 8.15. For the purpose of this discussion,
let us assume the heterojunction is between AlGaAs and GaAs. In this analysis we use the
result of Kroemer that the capacitance of a Schottky barrier on a semiconductor with an arbitrary
charge distribution is

C=

ΔQ

ΔV

=



<x>

whereis the centroid of incremental displaced electron distribution,ΔQ, caused byΔV.
Note that when the charge centroid approximation is used, the electric field in the GaAs is ter-
minated at the centroid of the charge distribution. The actual electric field in the GaAs, indicated
by the dashed line in figure 8.15c, is gradually terminated by the 2DEG following Gauss’ Law,
where
∂E
∂z

=−

en(z)



(8.5.1)

andn(z)is the local volume electron concentration [cm−^3 ]. Similarly, the band diagram has
been drawn as a solid line for the charge centroid approximation and as a dashed line for the true
behavior.
Charge neutrality states that the total charge in the system must be zero, or

Nd+=nm+npar+ns (8.5.2)

For the purpose of MODFET operation, it is desirable thatnpar=0, since electrons in the
barrier region create a low mobility parallel parasitic current path.nparcan become significant
when a large forward bias is applied to the gate or ifNdis very large. For the remainder of this
discussion, we will assume that the device is biased such thatnparis negligible.
In HFETs with channels having electrons with a low electron effective mass and hence a low
density of states, it is important to consider the variation ineVdi−(see figure 8.15c) as a function
of the chargensin the channel. Clearly, an increase innsalso requires an increase ineVdi−.This
is an undesirable effect because

1. It decreases the channel confinement potential and hence sets a limit on the maximum
   current available.