Ugur Yegin
Newbie level 4
Hello,
Here is the weak inversion equation that I know:
Ids=2*n*u*Cox*Vthermal²*exp((Vgs-Vth)/(Vthermal*n))
Now, I've got a few questions about this:
1) How does the Vds dependency of Ids play in? On MIT open course, I've found the add-on (1-exp(-Vds/Vthermal)) to be multiplied with the above equation. However, this add-on suggests that all values of Vds>(lets say)2Vthermal will result in a very negligible contribution of Vds to Ids. Now, this does not coincide with my simulation values - I use TSMC65nm - when I reduce the Vds from 600mV to 400mV (this is a testbench consisting of one nmos tr, not a real circuit) while the Vgs is fixed way below Vth, the inversion coefficient held at around 0.025 (definetely weak inversion) the Ids changes quite a bit (from 560nA to 430nA). W/L = 15u / 150n. My guess is that the channel length modulation, also not considered in the Binkley equation kicks in, so does anybody know how to "correct" tha above equation? It would also be great if you could add the required bsim parameters to find the channel length modulation coeffiient.
2) The said MIT open course link provides the following equation on Ids
Ids = (n-1)*u*Cox*Vthermal²*W/L*exp((Vgs-Vth)/(n*Vthermal))
The definition of n they use is exactly the same like Binkley, so it's now just a different way to write the same equation. If one were to assume n=1.5, this would generate an Ids 1/6 times the size of the first equation. Can anyone explain me - maybe one of you used the same material before - the reason for this discrepancy in the central equation of weak inversion?
Here is the link for the said document:
https://ocw.mit.edu/courses/electri...fall-2009/lecture-notes/MIT6_012F09_lec12.pdf
Regards
Ugur
Here is the weak inversion equation that I know:
Ids=2*n*u*Cox*Vthermal²*exp((Vgs-Vth)/(Vthermal*n))
Now, I've got a few questions about this:
1) How does the Vds dependency of Ids play in? On MIT open course, I've found the add-on (1-exp(-Vds/Vthermal)) to be multiplied with the above equation. However, this add-on suggests that all values of Vds>(lets say)2Vthermal will result in a very negligible contribution of Vds to Ids. Now, this does not coincide with my simulation values - I use TSMC65nm - when I reduce the Vds from 600mV to 400mV (this is a testbench consisting of one nmos tr, not a real circuit) while the Vgs is fixed way below Vth, the inversion coefficient held at around 0.025 (definetely weak inversion) the Ids changes quite a bit (from 560nA to 430nA). W/L = 15u / 150n. My guess is that the channel length modulation, also not considered in the Binkley equation kicks in, so does anybody know how to "correct" tha above equation? It would also be great if you could add the required bsim parameters to find the channel length modulation coeffiient.
2) The said MIT open course link provides the following equation on Ids
Ids = (n-1)*u*Cox*Vthermal²*W/L*exp((Vgs-Vth)/(n*Vthermal))
The definition of n they use is exactly the same like Binkley, so it's now just a different way to write the same equation. If one were to assume n=1.5, this would generate an Ids 1/6 times the size of the first equation. Can anyone explain me - maybe one of you used the same material before - the reason for this discrepancy in the central equation of weak inversion?
Here is the link for the said document:
https://ocw.mit.edu/courses/electri...fall-2009/lecture-notes/MIT6_012F09_lec12.pdf
Regards
Ugur
