**George Pau**
@
on

defining the 3D electron density

Hi,

In the reference cited, Nanowire uses the NEGF formalism and the 3D density is expressed in terms of that formalism. Could someone tell me what the equation will be like in terms of wavefunctions? I do not think it is very different from the reference but I would like to see what the exact form is like if one decide not to use NEGF formalism.

Thanks, George

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Saumitra Raj Mehrotra@ onHello,

Ne3D=Sum over mode m(Ne1D.{psi_m.psi*_m)

A more correct representation should be (code being updated), Ne3D=Sum over mode m over mode n

Refer:http://www.iis.ee.ethz.ch/~schenk/JApplPhys_100_043713.pdf

I have written nth mode here which can be understood as nth subband.

I hope it helps

thank, Saumitra

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George Pau@ onLet\‘s suppose I have a lot of computing resources and I could solve the open Schrodinger equation in 3D. So, for each electron of energy E coming in from source or drain, I can compute an associated wavefunction, say \\phi(E). I can then determine the density directly based on \\phi(E). The question then is what is the resulting formula? Is the density given by \\int_k |\\phi(E(k))|^2 f(E(k)) where k is the wavevector associated with E based on some E-k relation and f is the Fermi-Dirac function? Or am I missing some constants?

Thanks, George

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Mathieu Luisier@ onYour equation is basically correct. You must not forget to sum over all the contacts that you use to inject states into your device. Furthermore, the sum over k should be transformed into an integral, then a variable transformation should be applied (k->E) so that a term |dE/dk|^ appears in the equation. You can take a look at the documentation and the references of OMENnanowire. This tool uses a wave function approach instead of NEGF.

Mathieu

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