**Pratik Patel**
@
on

NEGF Formulism Question

Hi,

I’m not too familiar with the NEGF formalism. But had a very basic question.

I’ve read that NEGF can be viewed as a “Quantum Boltzmann Equation”. When taking moments of the classical boltzmann equation and making some assumptions/approximations we arrive at an expression for the current density in the semiconductor. Namely that J = Jdrift + Jdiff, which is the backbone of commercial TCAD.

I’m wondering if a similar action is performed on the so called “Quantum Boltzmann Equation”, can get a form of the following: J = Jdrift + Jdiff + Jqm, where Jqm includes effects such as band-to-band tunneling??

Sorry for the elementary question but I’m rather new to NEGF concept.

Thanks again.

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Supriyo Datta@ onVery nice .. elementary questions are the hardest! Here’s what I believe: NEGF will give us the complete spatial current flow pattern just like drift-diffusion equations, but I do not know of any exact way to separate components like you suggest .. though there are approximate methods that may work in special circumstances.

Even close to equilibrium (low bias) there seem to be problems. Classically as you know, J = sigma * grad(mu) which can be separated into drift and diffusion by writing mu = psi + (mu-psi), mu and psi being the electrochemical and electrostatic potentials. Quantum mechanically there seems to be no good way to define a mu® inside the device, though a coworker made a valiant attempt many years ago: McLennan et.al. Voltage drop in mesoscopic systems, Phys.Rev. B43, p.13846 (1991).

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