Brillouin zones and Ek graphby james walshe Tags: band gap, brillouin, brillouin zone, graph, reciprocal lattice, zones 

#1
Dec1413, 03:58 AM

P: 5

Hi all,
If you are given the real space lattice vectors (14 Angstroms in the xdirection 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 Ek graph and comment on the bandgap structure. I can graph the reciprocal lattice and the first Brillouin zone, and I sketched the Ek 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=((hbar)^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 bandgap energy. 


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