Dear Maryem,

The the statistical variations of the parameters of the FETs are random in nature and therefore mostly they follow normal distributions. If there is some deviations you can approximate the distribution to a Gaussian distribution.

One justification of this approximation is that more important for the effect of the process variations is the worst case corner where the circuits will be slowest.

If you see the attached ppt about the process and environmental variations you will observe that Vth has more or less the bell shaped statistical variations: PPT]

Lecture_9_ProcessVariation_36.ppt

ee.sharif.edu/~adic/Lecture_9_ProcessVariation_36.ppt

Best wishes

Thank you a lot Dear Abdelhalim for your answer

I agree with you that the nature of these parameter are random

But therfore some works demonstrates that the statistical variations of some parameters of the FETs deviate from normal distribution.

If we consider the effect of that particular parameters as normal distribution, the analysis results will be incorrect.

i attached here an example of figure that demonstrate the distribution of rdsw (the zero-bias source and drain resistance) and u0 ( the low-field carrier mobility).

Moreover if we want to analyse the effect of spatial variation on circuit (based on the local on die) with hspice that will add complexity to analysis because we don't know yet in design phase wich parameter will vary in which location.

this is not yet clear for me how to model those variations (local and spatial) for a monte carlo simulation?

Am familiar with hspice monte carlo commands, but am confused which distribution to consider for a correct analysis.

Thank you again