Questions about fMAX and fT of a MOSFET

I have a few questions about fMAX and fT of a MOSFET:

1. What's the definitation of fMAX, the maximum oscillation frequency of a MOSFET?

2. I remember the definition of cut-off frequency fT is the frequency when current gain Iout/Iin = 1. This gives out fT = gm/Cg. My question is: is transconductance gm a function of frequency? Will gm roll-off at very high frequency? what's the relationship?

3. I looked up the defintion of fT for BJT, which is fT = 1/(2*pi*tau), where tau is the transit time. Why BJT has different fT definition from MOSFET? How's two related?

4. I saw a equation relating fMAX and fT in BJT:
fMAX = sqrt( fT / (2*pi*Rb*Cbc))
Does anyone know how to derive the relationship?

Thank you very much.

Added after 2 minutes:

oh.. a typo... in MOSFET, fT = gm/(2*pi*Cg)

Becasue current gain i_out/i_in = gm/(j*w*Cg), when current gain = 1, fT = gm/(2*pi*Cg).

fmax mosfet

I actually saw the answers to some of my questiosn from Tom Lee's book:

Q1: max oscillation frequency fMAX is the frequency when PL / Pin = 1.

Q4: the relationship between fMAX and fT is derived in Tom Lee's book, page 178.

I am still not sure Q2 and Q3. Especially, I want to clarify if gm is dependent on frequency or not. If anyone knows, it's great to hear your answer.

Thank you very much.

ft fmax definition

I found the proof of the relationship of two definitions for fT:
1. fT = gm/(2*pi*Cin)
2. ft = 1/(2*pi*tau)

The answer is on the page 7 of the document:
**broken link removed**

And now I think transconductance gm is about constant until the frequency reaches 1/(mean-free-path time).