1. EXAMPLE 11.1 OBJECTIVE Solution Comment
To calculate the internal pinchoff voltage and pinchoff voltage of an n-channel
Assume that the p+n junction of uniformly doped silicon n-channel JFET at T = 300 K has doping concentrations of Na = 1018 cm-3 and Nd = 1016 cm-3. Assume that that the metallurgical channel thickness, a, is 0.75 m = 0.75  10-4 cm.
Solution
The internal pinchoff voltage is given by Equation (11.3), so we have
The built-in potential barrier is
The pinchoff voltage, from Equation (11.4), is then found as
Comment
The pinchoff voltage, or gate-to-source voltage, to achieve pinchoff for the n-channel depletion-mode device is a negative quantity, as we have said.

2. EXAMPLE 11.2 OBJECTIVE Comment Vp0 = Vbi + Vp = 0.832 + 2.25 = 3.08 V
Design the channel doping concentration and metallurgical channel thickness to achieve a given pinchoff voltage.
Consider a silicon p-channel pn JFET at T = 300 K. Assume that the gate doping concentration is Nd = 1018 cm-3. Determine the channel doping concentration and channel thickness so that the pinchoff voltage is Vp = 2.25 V.
Solution
There is not a unique solution to this design problem. We will pick a channel doping concentration of Na = 2  1016 cm-3 and determine the channel thickness. The built-in potential barrier is
From Equation (11.8), the internal pinchoff voltage must be
Vp0 = Vbi + Vp = = 3.08 V
and from Equation (11.6), the channel thickness can be determined as
Comment
If the channel doping concentration chosen where larger, the required channel thickness would decrease; a very small value of channel thickness would be difficult to fabricate within reasonable tolerance limits.

3. EXAMPLE 11.3 OBJECTIVE Comment fT = 110 GHz
To calculate the cutoff frequency of a GaAs JFET. Consider a GaAs JFET with the following parameters: n = 8000 cm2/V-s, Nd = 1016 cm-3, a = 0.50 m, and L = 2 m.
Solution
Substituting the parameters in Equation (11.18), we have or
fT = 110 GHz
Comment
This example shows that GaAs JFETs can have large cutoff frequencies.