I am stuck on an exercise for a while with the circuit as shown below:

We have:

\[ V_{DD}=3.3 V \\

V_{tn0}=0.65 V \\

\gamma=0.5 V^{1/2} \\

2\phi _{f}=0.6 V \\

V_{1}=2.85 V \]

The question is: What is the best approximation for V2 in steady state?

(a) 0 V

(b) 0.65 V

(c) 2.2 V

(d) 2.65 V

(e) 3.3 V

And then same question for V3: What is the best approximation for V3 in steady state?

(a) 0.65 V

(b) 1.55 V

(c) 2.2 V

(d) 2.65 V

(e) 3.3 V

What I could do so far:

We know that the current flowing through the gate of the 3rd transistor is zero, so at least one of the two first NMOS is in cut-off mode or Vds = 0.

We have \[ V_{GS} = V_G - V_S = V_{DD} - V_2 \] and \[ V_{SB} = V_S - V_B = V_2 \].

We also know that \[ V_{tn} = V_{tn0} + \gamma\left(\sqrt{2\phi_f+V_2}-\sqrt{2\phi_f}\right) \]

I tried to compute for each value of V2 possible (from a to e) and the NMOS is cut-off for (d) and (e) V2 = 2.65 V or 3.3 V.

And now I'm stuck, although I know I didn't use the knowledge of the value of V1, or the relation \[ V_1 - V_D = r_{DS}i_D \].

I would be grateful if you have a hint so I can finish the exercise.

Thank you,

Koelite.