MOSFET Transconductance vs Drain Current

My quantum mechanics has got a bit rusty lately, but here it is in broad brush.

When you're pushing carriers over a potential barrier, the current density is proportional to the densities of energetically allowed initial states and final states. In a semiconductor, that means you need an electron in the initial state on the cathode side and a hole in the final state on the anode side.

Because the Fermi level is broadened by thermal excitations, it essentially has fuzz on it, and the fuzz density is proportional to exp(

-(E-E_f)/kT). That means that when you move the barrier height a little, e.g. by increasing the gate voltage, the product of initial and final state densities goes up by a factor of exp((Delta E)/kT). That sets an absolute limit to the ratio of the transconductance to the collector current--the device can be worse than that but can't be better.

The usual MOSFET formula leaves this effect out, because generally MOSFETs don't get anywhere near the limit.

Cheers

Phil Hobbs

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Hmm, if I could split the electron by some fraction....

Posted late Thursday night, going for two weeks to Cape Cod. It feels like vacation already! The only thing I have to do tommorrow at work is put a few bits of plastic in the post. George H.

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Hi George

Your wish is sort of fullfilled ;-)

Fractional quantum Hall effect:

Quote: "... excitations have a fractional elementary charge and possibly also fractional statistics. Its discovery and explanation were recognized by the 1998 Nobel Prize in Physics. ..."

Some other "funny" physics ;-)

Jul 27, 2011 Spinons take the heat:

Quote: "... The dramatic departure from the Wiedemann=96Franz law occurs in purple bronze because when a holon comes across an impurity in the chain of atoms its motion is reflected =96 that is, it cannot navigate around or through the impurity. But the spinon can tunnel through the impurity and then continue along the chain. Because the spinons carry heat and the holons carry charge, the heat is conducted easily along the chain but charge is not. ..."

July 17, 2006, Spinons... Holons?:

Quote: "... Thus we can describe the flow of electrons by "particles" carrying only charge (holon) and others carrying only spin. ... The unambiguous confirmation that spinons and holons exist is a pretty big deal, because theorists have been using them as a crutch to try and understand high temperature superconductors. Even though those theoretical descriptions aren't all that good yet, it is good to know that they are on the right track. ..."

Glenn

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Thanks Glenn, But I'll leave it to Phil H. to design a low noise gain stage using the FQHE. (Fractional Quantum Hall Effect)

George H.

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Doubling the current only doubles the gm at very low Vgs-Vth. As the current increases the ratio drops toward sq-rt(2). ...Jim Thompson

[On the Road, in New York]

Maybe you could try modelling a FET type that you ~do~ have on hand and try that on the bench ??

(Tried each other on the bench... Isn't that what the two judges did?)

boB