So, according to my model, I do not have values for PHI, or GAMMA. I assumed (W/L) to be 1.

The approach I followed was taking the general Drain Current Equation of MOSFET, differentiating it with respect to Vgs, and trying to express Drain Current as a function of its Derivative, which I was successful in doing.

Vth=Vgs - 2*(Id/d(Id))

where d(Id) is the derivative of Id w.r.t. Vgs.

Similarly, I tried the same approach with differentiating the Drain Current Equation w.r.t. Vds, and trying to express Drain Current as a function of its derivative.

Lambda = d(Id)/(Id - Vds*d(Id))

where d(Id) is the derivative of Id w.r.t Vds

Now, both of these equations are good enough to give me Vth and Lambda when I know the value of Vgs and Vds, but it is not sufficient to find their values independent of both of them, even if it is a reasonable estimate of both of them.

It will be a great help if any of you could guide me here! Thanks in advance!