# Band Dispersion and Career Mobility

1. Jun 29, 2014

### arvind

how the dispersion relation(i.e. E-k relation) affects carrier mobility in metals or semi-metals?

2. Jun 29, 2014

### ZapperZ

Staff Emeritus
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.

3. Jul 1, 2014

### arvind

what if the charge carriers are massless as in case of graphene which is a single atom thick sheet?

4. Jul 2, 2014

### DrDu

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.

5. Sep 17, 2014

### Douasing

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.

6. Sep 17, 2014

### DrDu

Not really, it depends on the scattering mechanism, e.g. impurity scattering or scattering from phonons. The latter should be most relevant in very pure samples. To quantify it ab initio, you would have to calculate the phonon spectrum and electron phonon coupling constants.

7. Sep 22, 2014

### Douasing

But I find some vitual frequency when use phononpy and vasp to calculate the phonon of black phosphorus nanotubes (about 32 atoms for armchair PNT with n=8,see the figure below).On the other hand,it is very time consuming when use Elk-code (about 5 days for 4 atoms,which use DFPT method).
Are there any convienient phonon softwares or programs for nanotubes ?