The usual practice in teaching MOSFETs is to make all the derivations for NMOS and say something like: "for PMOS it is very similar, just switch the nodes...". Then it takes a whole lot of time to understand the actual difference between PMOS and NMOS.
I tend to believe that this is your case: you do know how to solve problems with NMOSs, but you do not have much experience with PMOSs.
First of all, the transistor in the schematic seems to be wired incorrectly (as pointed out in one of the comments).
Secondly, the current equation for PMOS in saturation is:
$$I_{SD}=K \times \frac{W}{L} \times (V_{SG}-|V_T|)^2$$
Substituting:
$$I_{SD}=250 \times 10^{-6} \times (V_S-0.714-1)^2$$
(note that \$V_G=0.714V\$ according to my calculations).
The current should also satisfy:
$$I_{SD}= \frac{5-V_S}{1200}$$
Equating the above two and solving for \$V_S\$ yields:
$$V_S=3.75V$$
We must also check that saturation condition holds (in order to justify our a-priory assumption):
$$V_{SG}=V_S-V_G=3.75-0.714=3.036V>|V_T|$$
and
$$V_{SD}=V_S-V_D=3.75-(-5+4000\times I_{SD})=4.59V>V_{SG}-|V_T|$$
Both conditions hold therefore PMOS is conducting and in saturation.
I suppose you might have been using a more sophisticated MOSFET model for Spice simulation, therefore the answer you got there is different (although pretty close).
The technology will determine the following things
- Speed (smaller is faster)
- Power consumption (smaller transistors consume less power)
- Supply voltage (smaller transistors require a lower supply voltage)
- And of course the required chip area
A 0.35um technology should be OK and you can work with 3.3V. If it is good enough depends on your requirements. In order to determine the speed you can achieve you can wire up a few simple gate structures and make a simulation.
A big advantage of 0.35um CMOS is that this technology is very cheap and protoyping is quite affordable.
Best Answer
You made the assumption
Which is an entirely reasonable assumption. You need to validate that your assumption was correct, and eliminate "impossible" answers. Going by the requirements for saturation, you need Vgs > Vt, and Vgs-Vt =< Vds.
You'll find that one of the answers does not satisfy both conditions for saturation.