Drude model and electron mean free path?

[philip041]

Could someone explain mean free electron paths with regard to;

Drude model

and Fermi velocity

I have answered a question where you are given relaxation time and fermi velocity at 4K and 300K and asks you to work out the mean free path. Easy. Next it says how do these values compare with what the Drude model predicts.

I keep reading that Drude neglects electron electron interactions, does this mean that they can still scatter off each other but only on head on collisions?

It also says that electron ion interactions are neglected except in head on collisions, but that in Fermi, (I assume this is the Fermi model?) electrons only don't scatter off ions in a perfect periodic lattice.

My main question is; does the Drude model give a longer electron mean free path than the Fermi model, and if so, why?

 

[NateD]

The Drude model is a simplified model of the behavior of electrons in solids. It assumes that electrons move freely in a lattice of positive ions, with a mean free path that depends on the number of collisions with other electrons and ions. The Fermi velocity is an empirical parameter that describes the average velocity of electrons in a solid. In contrast to the Drude model, the Fermi velocity takes into account electron-electron interactions, as well as the effects of a periodic lattice of ions.The Drude model predicts a longer mean free path than the Fermi model because it neglects electron-electron interactions and assumes only head-on collisions between electrons and ions. In contrast, the Fermi model takes into account electron-electron interactions and also considers the effects of a periodic lattice of ions, which can lead to scattering of electrons off each other, even when electrons are not directly interacting. This means that the mean free path predicted by the Fermi model tends to be shorter than that predicted by the Drude model.