**Samik Mukherjee**
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calculation of semiclassical profile for using generalized green's function approach

For solving Equilibrium and Non-Equilibrium green's function , the semiclassical profile is calculated with thomas-fermi charge. How is the fermi level defined for calculation of charge in the non-equilibrium region consisting of the two barriers and the well ? I believe a fermi level is need to be defined in the well-barrier region for calculating the charge to solve for the electrostatic potential.

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Gerhard Klimeck@ onThe non-equilibrium region does NOT have a Fermi level in the NEGF approach. Without scattering inside the device (as is the case in this tool) charge is summed from injection on the left and from the right. Under high bias charge is effectively just injected from the emitter (left) in the current tool configuration for positive biases.

An asymmetric barrier structure where the collector barrier is larger / thicker than the emitter barrier will result in charge build-up in the device and bi-stable behavior.

I suggest reviewing these 2 lectures:

https://nanohub.org/resources/8201

https://nanohub.org/resources/8202

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Samik Mukherjee@ onThank you very much for your kind reply. However , I feel you have not quite answered my question.

Before any NEGF calculations take place , a semiclassical profile has to first computed. NEGF comes later after a semiclassical potential is calculated. The electrostatic potential from this semiclassical profile will enter the hamiltonian of the device for calculation of the green's function in the first step. Of course the semiclassical potential can be refined by a hartree-fock calculation in the tool , but here I am only interested in a one shot calculation based on the semiclassical profile.

To begin to calculate the semiclassical profile self consistently with the thomas-fermi charge , we need a fermi level in the 3 regions -> emitter , collector and barrier. The emitter and collector fermi regions are well defined. The fermi level for the barrier region is not well defined for calculation of a thomas-fermi charge. How is the thomas fermi charge calculated in the barrier region for calculation of a self-consistent semiclassical potential profile ? This is my question.

I hope I have been able to explain my question. If not kindly state. Thanks for your time.

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Gerhard Klimeck@ onNow I understand better. In the original NEMO code I had 2 different approaches:

1) Assume NO Fermi level and NO semiclassical charge inside the central device region

2) Interpolate a linear fermi level drop inside the device.

If you just simulate the I-V based on the semiclassical charge then there will be a difference in the I-V. But not dramatic for regular structures. Of course you can design a device where the difference will be large.

Eiher way both models deliver a good-enough guess for Hartree full self-consistent calculation with the quantum charge and then the final result is independent of the details of the semiclassical choice.

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