Environmental Engineering Reference
In-Depth Information
Also the DIBL is more pronounced in short-channel devices and its main
effect is a further reduction in the output resistance.
1.3.9.6
Threshold voltage dependency on transistor dimensions
As transistor dimensions are reduced, the fringing field at border edges
can also affect the threshold voltage [8].
Referring to Fig. 1.15 and without entering into a detailed physical
explanation, applying a voltage to the gate creates a channel. However,
due to border effects, only charges in the darker trapezoidal area are linked
to the gate voltage. The threshold voltage definition in (1.35) refers all the
charges in the rectangular area below the silicon to the gate voltage, as in
Fig. 1.6. Since the threshold voltage depends on the channel charge linked to
the gate voltage, it is apparent that the previous model overestimates the
value of This border effect is not critical in long-channel devices, but in a
short-channel transistor it can be significant.
To model this phenomenon, the threshold voltage in (1.35) is modified in
where is a corrective factor that represents the ratio between the
trapezoidal and the rectangular areas used to model the channel. As a
consequence, is less than its original value in (1.35).
In a similar way, the threshold voltage depends on transistor width if this
dimension becomes comparable to the edge effect regions, that is, in narrow-
channel (i.e., with short width) devices.
