loose-electron: You don't need bias curves, since you don't care about the Gate Source Voltage on any of the Transistors. When you have a mirror you don't care about the VGS. It changes over process and temperature anyways. It doesn't help you to understand a circuit either. I see this every day. If you understand how it works you can run as many sweeps as you want. I am not sure how hard it is to understand IM6=IR1. The only other equation you need is the inversion factor if you want to determine if the transistor is in WI or not. In simulation you could determine this by looking at gm/Id and find the plateau, but that is not really a simplification. Further the equation for if is amazingly accurate (it only depends on beta and UT). But if you look at the OP, there is clearly a question for ID(VGS) of the MOST in WI.
Ronny: The only reason why a mirror has a mismatch in the currents is a difference in drain source voltages or triode mode operation. One of the mirror transistors has VGS=VDS and the other one has VDD-Vout. So you have to use cascodes and if you have constraints on VDD use low voltage cascodes.
If you neglect mismatch (I don't think you are running monte carlo?), a current mirror will always work, no matter if it is in WI or SI.
The only thing that can make a difference is when one of the transistors goes out of saturation (in WI a good assumption is VDS>100mV for saturation) or if the VDS are differing a lot.
Forget about the mosfets VGS. It doesn't do anything for you in this circuit.
A good summary on low voltage mirrors can be found here:
http://amesp02.tamu.edu/~sanchez/lvtutorial-2000.pdfThe Vittoz paper I mentioned earlier is titled:
"CMOS analog integrated circuits based on weak inversion opearaton"Its on the IEEE servers.