Calculating the speed of a JFET

[Mr_Allod]

Homework Statement

How fast will a PN JFET operate in GHz if the gate impedance is $50\omega$, and if the JFET
has a drain-source voltage $V_{DS} = 2V$

Relevant Equations

Capacitance: $C = \frac {\epsilon A}{h}$
$\epsilon_r = 11.7$
N-channel thickness $T = 125nm$
N-channel width $W = 75\mu m$
N-channel length $L = 0.8\mu m$
$N_D = 4\times 10^{18} cm^{-3}$
$N_A = 2\times 10^{17} cm^{-3}$

Hello there, I believe here I need to find the capacitance of the junction between the P-doped gate and N-channel. Then I could find the RC time constant although I am not sure if there's something more I need to find the speed of the JFET?

What I'm unsure of is the depletion width h to use for the calculation. Since I am given a drain-source voltage $V_{DS}$ I think I am dealing with an uneven depletion layer, ie. the depletion layer is larger near the drain than it is near the source. I know how to calculate the width h at each point using the abrupt junction approximation but then I don't know what to actually use for the capacitance. Do I need to integrate in some way to account for the varying depletion width?

I'd appreciate some help with this.

 

[osilmag]

Is there a way to find how much the N-Channel width changes when the voltage is applied? The result after the change is what I would think is the $h$.