mean free path of electrons in metal

[Jenny]

Hello, all.

As we know, if the feature size of a system is smaller than it mean free path, there will be elastic scattering for electrons. Then how can we find the value of MEAN FREE PATH here? Is it available here in QuantumWise? Thank you in advance.

Best,

Jenny

[Dipankar Saha]

Did you go through this tutorial......

http://quantumwise.com/publications/tutorials/item/832-elastic-scattering-mean-free-path-mobility-impurity-scattering-in-a-silicon-nanowire

.....where the mean free path values have been calculated for different doping concentrations (though, for SiNW) ...

Regards_
Dipankar

[Anders Blom]

The real statement is that when the feature size is below the mean free path, inelastic scattering events become more rare, so carriers behave more and more ballistic. Scattering doesn't disappear completely, it's just a question of probability. As such the only way to estimate the mean free path is to compute the current with and without scattering, for different sizes of the system, and also for many configurations in case the scattering is random in nature, like with alloy scattering or dopant scattering. The link in Dipankar's answer is an excellent example of this, although it only covers dopant scattering - for a real estimate of the mean free path you would also need to consider inelastic scattering which is typically by phonons. This is possible in ATK 2015, but quite time-consuming, esp. for large systems (and remember, you need to make the system larger and larger to see when the effect becomes important).

Therefore, In most practical situations the mean free path is a lot easier to estimate in experiments, and then you can just choose to say that you perform simulations in a ballistic approximation in systems that are below that size. However, very interestingly, in some cases phonon scattering can be important no matter the size of the system. An example of such a calculation (for a tunnel FET) can be seen in http://quantumwise.com/publications/tutorials/item/837,

[Sabiha Hasan]

Hello, all.

I want to determine the electron mean free path of  1T' MoTe2/TaS2  nanoribbon. I have gone through the ATK tutorial (but it was for the case when doping was present). As I have pristine 1T' MoTe2 nanoribbon, how can I find the mean free path here?
Thank you in advance.

[Anders Blom]

A pristine material, i.e. a perfectly periodic crystal, has an infinite mean free path by definition. The only reason we speak of a MFP is because there is some kind of scattering source that breaks this periodicity, such as edge roughness, dopants, or indeed temperature. The closest to what you might be looking for (undoped, perfect 2D material) is probably then to introduce some randomness due to thermal vibrations, using the SpecialThermalDisplacement method (https://docs.quantumatk.com/manual/Types/SpecialThermalDisplacement/SpecialThermalDisplacement.html), and then proceed just like the tutorial (updated link: https://docs.quantumatk.com/tutorials/elastic_scattering_impurity_in_si_nanowire/elastic_scattering_impurity_in_si_nanowire.html)

[Sabiha Hasan]

Thank you so much for your reply.
In your suggested elastic scattering mean free path tutorial, in the "T and mfp.py" file for calculating mfp I need to give doping density as input. Can you suggest what value should I choose for this case? ( as I am not adding any external dopant, just using thermal vibration induced randomness)

[Anders Blom]

The script is rather specific to the calculation done with an explicit defect. In your case, you should go back to definitions in the theory section; looking at the line which actually defines the MFP, you can evaluate all quantities for your system and extract the MFP as

(R(L)/Rc-1) = L/MFP

(all depending on energy).

Here Rc is the conductance of the perfect system, and R(L) = 1/T(L) is computed for a device where L is the length of the part that has been thermally perturbed. A better option might even be to plot R(L) as a function of L, which should be a linear relation and you can get MFP from the slope.