Brillouin zones and E-k graph


by james walshe
Tags: band gap, brillouin, brillouin zone, graph, reciprocal lattice, zones
james walshe
james walshe is offline
#1
Dec14-13, 03:58 AM
P: 5
Hi all,
If you are given the real space lattice vectors (14 Angstroms in the x-direction and 8 Angstroms wit an angle of 91 degrees between them) and have to draw the reciprocal lattice and the the first Brillouin zone, and then using this data sketch the E-k graph and comment on the band-gap structure.

I can graph the reciprocal lattice and the first Brillouin zone, and I sketched the E-k graph using:
k=(pie/a) and k=(pie/b) where a and b are the real space lattice vectors. From this I can determine the energy of the middle of the band using:

E=((h-bar)^2 *(k)^2/(2*m))
where the two values of k were used, which gave two different energy values. Using this information how do I determine the width of the band gap or its band-gap energy.
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soulhunter
soulhunter is offline
#2
Dec31-13, 06:08 AM
soulhunter's Avatar
P: 4
Hi,according to the Kronig Penney Model, you should know the height of the periodic potential barrier.


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