Environmental Engineering Reference
In-Depth Information
The gate-source voltage for which the concentration of electrons under
the gate equals the concentration of holes in the p- substrate far from the gate
is said to be the transistor threshold voltage,
At a first approximation, if the gate-source voltage, is below the
threshold voltage, no current can exist between the source and the drain and
the transistor is said to be in the cutoff region. In contrast, if the gate-source
voltage is greater than the threshold voltage, an n channel joins the drain and
the source and a current can flow between these two electrically connected
regions.
Actually, for gate voltages around the charge does not change
abruptly and a small amount of current can flow even for small negative
values of This condition is termed weak inversion and the
transistor is said to work in subthreshold region.
When the channel is present, as in Fig. 1.6, the accumulated negative
charge is proportional to the gate source voltage and depends on the oxide
thickness, since the transistor works as a capacitor. Specifically, the
charge density of electrons in the channel is given by [
1
]-[2]
where
is the gate capacitance per unit area defined as
and
the is approximately 3.9)
The total capacitance and the total charge are obtained by multiplying
both the equations (1.22) and (1.23) by the device area, as follows
is the relative permittivity o
f
1.3.2
Triode or Linear Region
Increasing the drain voltage, causes a current to flow from the drain
to the source through the channel. A drain voltage different from zero will
modify the charge density but for small the channel charge will not
change appreciably and can be expressed by (1.22) again. Under this
condition, the device operates as a resistor of length
L
, width
W
with a
permittivity proportional to
Therefore, the relationship between voltage
and the drain-source current,
can be written as [7]
