# QuantumATK Forum

## QuantumATK => General Questions and Answers => Topic started by: berna on March 22, 2018, 08:55

Title: Conductivity
Post by: berna on March 22, 2018, 08:55
H,
For 3D calculations, conductivity=conductance*length/area and its unit=Siemens/nm (cm). For 2D conductivity=conductance*length/width. Then what should the unit of 2D material be?
Title: Re: Conductivity
Post by: Petr Khomyakov on March 23, 2018, 10:16
From your definition, it is obviously to be in units of Siemens.
Title: Re: Conductivity
Post by: berna on March 23, 2018, 12:28
This definition is an assumption. And it does not belong to me. Interstingly, lecturers for 2d nano structures and also ATK are using conductance instead of conductivity. I think, we may be should not convert conductance to conductivity for 2d. And you will ask, Petr, why we shouldn't.
Title: Re: Conductivity
Post by: Petr Khomyakov on March 23, 2018, 14:11
In general, 'conductance' (or 'resistance') per cross section (or width for 2D systems) of the conductor is a well-defined quantity and has a physical meaning for any type of materials, material structure (heterostructures, interfaces, contacts) or device. The 'conductance' concept depends on neither the dimensionality of the system nor the type of the electron transport (ballistic, diffusive, coherent or incoherent).

'Conductivity'  is a well-defined, physically-meaningful quantity only if the conductance obeys Ohm's law, i.e., conductivity = conductance Length / Area = constant, i.e., that the conductance scales inversely with the system length, also meaning that the electron transport is no longer ballistic.

For 2D systems,  the definition of conductivity you mentioned in your original post is totally fine, provided that the conductance scales inversely with the system length.
Title: Re: Conductivity
Post by: berna on March 24, 2018, 21:32
"Quantum conductance, not conductivity. The conductance is what ATK gives you, from a transport calculation. To compute conductivity (which can be defined also for a chain, but it will not include the area A, it's just "R/L") you also need to include all kinds of scattering mechanisms (i.e. phonons etc)."  Anders Blom
Title: Re: Conductivity
Post by: Petr Khomyakov on March 24, 2018, 22:44
This is exactly what I have written in my post regarding conductance vs conductivity.  You may take a look at some textbooks on the electron transport for this issue, e.g., a commonly-excepted reference book by S. Datta, "Electronic Transport in Mesoscopic Systems".