threshold voltage variation wrt temperature in MOS

how does Vt decrease with increase in temperature?
1) Vt is directly proportional to fermi potential which is proportional to T and inversely proportional to Na.
2) now Vt is proprtional to Tox and with increase in T, Tox decrease..But how?? coz Tox is device parameter...
3) Vt is also proportional to depletion charge density..

can anyone please analyze the above mentioned points and conclude that Vt is inversely prop. to Temp....

Basically, Temperature increase mobility of electrons and holes . hence now there are plenty of electrons and holes and the conduction requires less voltage. Hence Increase Temp-> Decreases Vt.

For the above statements,can you give the formulas so that we can have some discussion over here. Give some theoretical proof for the above Here!!

Prashanthanilm said:

Basically, Temperature increase mobility of electrons and holes . hence now there are plenty of electrons and holes and the conduction requires less voltage. Hence Increase Temp-> Decreases Vt.

For the above statements,can you give the formulas so that we can have some discussion over here. Give some theoretical proof for the above Here!!

Click to expand...

thanks for the reply...
now there is one correction..Tox can not vary wrt temperature for a given temp. range for which the transistor is designed. so this rules out the 2nd point mentioned by me.
so the dominating factor is depletion charge density which has to reduce for vth to reduce..
the equation is Vth = Φgc + 2Φf + (Qbo/Cox)
where Qbo is the depletion charge density contributed by gate voltage..and yes according to your statement, as no. of electrons and holes increase this will aid to formation of immobile ions at the surface and hence required gate potential for forming depletion region is reduced which reduces Vth..
also theoretically now the Qbo term will decrease as it is due to applied gate voltage which has now reduced...
correct me if i am wrong...

Yes. It is correct.(But not fully clarified)

Even I want to know more about this. Do you have any documents to support your discussion.

Prashanthanilm said:

Yes. It is correct.(But not fully clarified)

Even I want to know more about this. Do you have any documents to support your discussion.

Click to expand...

i am following cmos digital IC by sung mo kang...and carrying out simulations in Hspice to observe these variations..
from simulation results vth does decrease with increase in temp..

Yes, Vt will decrease with increase in temperature.

I was asking theoritical document for the discussion below:
"so the dominating factor is depletion charge density which has to reduce for vth to reduce..
the equation is Vth = Φgc + 2Φf + (Qbo/Cox)
where Qbo is the depletion charge density contributed by gate voltage..and yes according to your statement, as no. of electrons and holes increase this will aid to formation of immobile ions at the surface and hence required gate potential for forming depletion region is reduced which reduces Vth..
also theoretically now the Qbo term will decrease as it is due to applied gate voltage which has now reduced...
correct me if i am wrong..."