# Brillouin zones and E-k graph

by james walshe
Tags: band gap, brillouin, brillouin zone, graph, reciprocal lattice, zones
 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.
 P: 4 Hi，according to the Kronig Penney Model, you should know the height of the periodic potential barrier.

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