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[SOLVED]Inversion Coefficient and gm/Id relation

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kenambo

Full Member level 6
Hi

I have studied about inversion coefficient. I am just wondered how gm/id and inversion coefficient is related?

Is there any particular relation which can be used for the hand calculation of a design?

thanks

There are two relations in fact. Based on Lambert W function aproximation of mosfet transfer I-V curve (used in ACM model) the gm/Id relation is given by:

where n is a slope factor and IC is inversion coefficient in penthode region of operation (or simply forward current).

In original EKV model paper You can find slightly differ empirical relation (based on aproximation of transfer curve by ln²(1+exp(Vgs/Vt))):

You can also include short channel effects to gm/Id relation in a few different ways, i.e. by solving corrected equation for channel charge density, by modifying technology current and insert it into IC, and in some other ways.

More details about including the SCE You can find in Binkley, Jespers or Enz books.

kenambo

kenambo

Points: 2
Hi Dominik

thanks for the reply. I will study those books. Do you think these equations can be used for hand calculations?
and what about the slope factor.? Is it possible to find slope factor without any simulation , I mean for calculation purpose?

thanks

I'm successfully using first formula. Slope factor is easy to obtain from subthreshold slope, which is given in every process documentation

Of course it varies from weak to strong inversion for about 10% but constant value approximation is good enough for calculation, especially that for modern processes is very hard to work with IC>10

slope factor is always greater than 1 and for most of the processes is in range of 1.2 - 1.8 (values close to 1 I found only in some soi technologies).

kenambo

kenambo

Points: 2
Hi Dominik

thanks I will check my PDK docs. Can you please specify the exact books where you got the equation for gm/id and inversion coefficient? I am a bit confused about some terms and the "i" term..

thanks

predator89

Points: 2
Hi Dominik

Thanks for the reply.. I got it..

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