Figure 148: First Brillouin zone of siliconFigure 149: Phonon dispersion relation of siliconfrequency is determined by the shortest wavelength that can evolve in this crystal (fig. 150,ais the
distance between 2 atoms).
What is the speed of sound in Si?
The speed of sound is the slope of the dispersion relation near theΓ-point and there are actually 2
different speeds of sound, one for the transverse and one for the longitudinal mode. (in the range of
a few THz)
How do you calculate the phonon density of states from the phonon dispersion relation?
The actual calculation is quite difficult and it’s done numerically for most of the time. What you have
to do is choose one k-value and write down all possible frequencies for this k. This is done for all
k-values and then one counts how often a specific fequency occured, which leads to a picture like fig.
151.
Why does the energy gets scaled for the electron dispersion relation of the elements of
the 4th main group?
Now we want to take a look at the electron dispersion relationship for the elements of the 4th main
group. One difference compared to phonons is, that there is no maximum energy for the electrons,
there is nothing that restricts the wavelength of the electron wavefunction. The biggest difference