QuantumATK Forum

QuantumATK => General Questions and Answers => Topic started by: vihardabest on July 3, 2009, 12:33

Title: Do we really have scattering in the "scattering " region ?
Post by: vihardabest on July 3, 2009, 12:33

Hi Andres,
I looked for an answer of my question in the forum before I wrote this message because I don't want to waist your time :).  So I didn't find it , therefore I decided to ask. I am 90 % sure for the answer, but I just want to be 110 % sure :)


My question is : When the Current and Transmission function are calculate for the scattering region, do we include real scattering between the electrons ?

I checked the papers and according to M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Phys. Rev. B 65, 165401 (2002)   equation 42 , the current depend on only how the channel is connected with the contacts. There is no scattering at all. Is it correct?

If it is true in this case ATK works in "ballistic" transport regime ? Is it correct?

Thank you very much in advance and have a HAPPY SUMMER.
See you soon :)

Moderator edit: Fixed typo in subject to help searching

Title: Re: Do we really have scattering in the "scatering " region ?
Post by: zh on July 3, 2009, 13:44

Quote from: vihardabest on July  3, 2009, 12:33

I just want to know when the Current and Transmission function are calculate for the scattering region, do we include real scattering between the electrons ?

I checked the papers and according to M. Brandbyge, J.-L. Mozos, P. Ordejón, J. Taylor, and K. Stokbro, Phys. Rev. B 65, 165401 (2002)   equation 42 , the current depend on only how the channel in connected with the contacts. There is no scattering at all. Is it correct?

If it is true in this case ATK works in "balletic" transport regime ? Is it correct?

The equations  for calculating the current and transmission spectrum in the paper you have mentioned  are based on the Laudauer-Buttiker formula. They work for the coherent transport.  So, no real scattering due to the photons, phonons or other electrons are included in the calculation of current and transmission function now.

For these basic concepts, recommend you to read  the chapters 9 and 10 in the book "Quantum transport: Atom to Transistor" of Supriyo Datta. 

Title: Re: Do we really have scattering in the "scatering " region ?
Post by: vihardabest on July 3, 2009, 17:03

Thank you ,ZH .
I will do this.  :)

Title: Re: Do we really have scattering in the "scatering " region ?
Post by: Anders Blom on July 3, 2009, 23:03

All this is absolutely correct.

I just want to add a note, that as ZH already said, the keyword here is coherent transport, which is the regime where the Landauer-Büttiker formalism is valid.

"Scattering" can mean many things, and while ATK does not include any of the inelastic (or elastic, for that matter) listed above, there is still a concept of scattering since the transmission probability of each individual scattering channel may be, and usually is, less than 1.

If you have diffusive transport and remove all scattering centers, phonons, etc, your conductance will go to infinity. This is the "classical zero temperature limit" (which is wrong, as we know). In ballistic transport, conductance is a transmission process, and hence has an upper bound, set by the conductance quantum time the number of modes.

The ballistic regime is obtained when the device size is smaller than the mean free path and the phase decoherence length.

For a more technical presentation, I also recommend another book by Datta, "Electronic Transport in Mesoscopic Systems".

Title: Re: Do we really have scattering in the "scattering " region ?
Post by: vihardabest on July 4, 2009, 14:20

Tak,
Anders :)
I am going on vacation now:) See you later:)