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# Typical values for channel length modulation co-efficient

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#### diarmuid

##### Full Member level 2
Hello

I've read that typical values for lambda range from 0.01 -> 0.03V-1. Is this really true?

Why I ask this is because in saturation Rout = 1 / (Ids * lambda)

=> lambda = 1 / (Rout * Ids)

Say Ids = 100uA (quite a typical value).

Then for a lambda range of 0.01 -> 0.03V-1, Rout will be 1MOhm -> 333kOhm!!!

Are these Rout values not a bit large for saturation?

From measurments Ive made with a PMOS (W=5um, L=1um), Rout ~ 4Ohm to give Ids ~ 10uA,
which gives lambda = 25000V-1!!!

Where am I going wrong? Is the above formula for lambda even correct to use?

Thanks,

Diarmuid

The old MOS models kinda **** because they vary L as
a fraction per volt, when it's really more like a incremental
deltaL per volt. So it's hard to fit a wide range of geometries
unless you can code some lookup(L) into it.

I think maybe you're going about extracting lambda, wrong.
You need two drain voltage points, well away from both
linear-saturation boundary and from any high-Vds curl.
Say, 2V and 3V, so your Rout is 1V/(Id(3V)-Id(2V). Not
simple Vds/Id.

Believe me I have the same problem, even when I extarct the value of Lambda by myself but still the equation rds = 1/ Id.Lambda is not givving the right value

The old MOS models kinda **** because they vary L as
a fraction per volt, when it's really more like a incremental
deltaL per volt. So it's hard to fit a wide range of geometries
unless you can code some lookup(L) into it.

I think maybe you're going about extracting lambda, wrong.
You need two drain voltage points, well away from both
linear-saturation boundary and from any high-Vds curl.
Say, 2V and 3V, so your Rout is 1V/(Id(3V)-Id(2V). Not
simple Vds/Id.

The Rout = 1 / (lambda*Id) comes from the Hodges-Schichmann Level 1 model. This model was introduced in 1968 and does not
model output impedance very well. Neither do the level 2 and level 3 models which followed. In fact I have read that even the BSIM models have issues with this.

So, it seems modelling output impedance is far from a straight forward task! From this and the crazy values for lambda
I was getting, I would be inclined to ignore Rout = 1 / (lambda*Id) for MOSFET output impedance in saturation. To measure
it I will in future just go via first principles i.e. plot id vs vds (id will be accurately modelled in the simulator). Then take Rout
as the inverse to the slope of this graph i.e. Rout = vds / id.

For all cases you must follow the simulation results, but the theoretical values needs also to be known at least for approximation,

The Rout = 1 / (lambda*Id) comes from the Hodges-Schichmann Level 1 model. This model was introduced in 1968 and does not
model output impedance very well. Neither do the level 2 and level 3 models which followed. In fact I have read that even the BSIM models have issues with this.

So, it seems modelling output impedance is far from a straight forward task! From this and the crazy values for lambda
I was getting, I would be inclined to ignore Rout = 1 / (lambda*Id) for MOSFET output impedance in saturation. To measure
it I will in future just go via first principles i.e. plot id vs vds (id will be accurately modelled in the simulator). Then take Rout
as the inverse to the slope of this graph i.e. Rout = vds / id.

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