Effective mass of electrons in metals

[joel.martens]

The literature i have on the origins / need for an effective mass of electrons seems only to relate it to the explanation of heat capacity of metals but it seems like the concept has applications far beyond this. Can someone pls provide a more general summary of its derivation and applications?
Cheers.

 

[Bob S]

Effective mass of holes and electrons in semiconductors is closely related to mobility. See
http://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics )

 

[genneth]

The cleanest understanding of effective mass in Fermi liquids comes from a solid understanding of fermionic renormalisation methods. See any number of papers by Shankar on the topic.

 

[crazy_photon]

I think of effective mass as a curvature of the electronic dispersion relation. I.e. for a free electron:
E = hbar^2 k^2 / 2m

where m is the mass of free electron.

Now, in a crystalline solid, where electronic band diagram applies, any band (near a symmetry point) can be represented as parabolic in k space, with its own curvature, i.e.:

E = hbar^2 k^2 / 2m*

where m* is the 'renormalized' mass of an particle in band (electron or a hole).

What is puzzling to me is why in for example semiconductors the effective mass is lower than the free electron mass? If I apply an external electric field, these electrons will reach steady state velocity larger than the free ones... what is physically happening that electron acts as if its inertia is lowered?