# Band Dispersion and Career Mobility

by arvind
Tags: band, career, dispersion, mobility
 P: 2 how the dispersion relation(i.e. E-k relation) affects carrier mobility in metals or semi-metals?
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PF Gold
P: 29,243
 Quote by arvind how the dispersion relation(i.e. E-k relation) affects carrier mobility in metals or semi-metals?
I'm not sure if you have done any search on your own. You would have discovered the answer yourself.

For example, the electron mobility can be written, in the simplest form, as

$$\mu = e\tau/m^*$$

where μ is the mobility, τ is the scattering time, e is the charge, and m* is the effective mass. Now, look up the relationship between the effective mass and the band dispersion, and you have your answer.

Zz.
 P: 2 what if the charge carriers are massless as in case of graphene which is a single atom thick sheet?
P: 3,633
Band Dispersion and Career Mobility

 Quote by arvind what if the charge carriers are massless as in case of graphene which is a single atom thick sheet?
In general, the velocity of a wavepacket describing the motion of a particle is given as ##\partial E/\partial k##. You can now figure out what happens for a quadratic and a linear dispersion relation.
The book by Ashcroft and Mermin discusses all this in detail.
P: 35
 Quote by ZapperZ I'm not sure if you have done any search on your own. You would have discovered the answer yourself. For example, the electron mobility can be written, in the simplest form, as $$\mu = e\tau/m^*$$ where μ is the mobility, τ is the scattering time, e is the charge, and m* is the effective mass. Now, look up the relationship between the effective mass and the band dispersion, and you have your answer. Zz.
Is there a simple and convenient way to estimate the electron mobility ?
I can derive the $m^*$ from band structure data ( through curve-fitting and then take a derivative with respect to k-point),but I know little information for the scattering time ;how to estimate $\tau$ for the systems (for example, BN sheet,or phosphorus) ?
There is also another formula ,i.e.,
$$\upsilon_{d}=μE$$
it seems not cowork with those data using first princple softwares.