How can the band-gap structure be determined using the E-k graph?

[james walshe]

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.

 

[soulhunter]

Hi，according to the Kronig Penney Model, you should know the height of the periodic potential barrier.