Æk x Æ k y ¼
2p
a
This gives us four equations representing zone boundaries:
n x ¼ þ 1; n y ¼ þ 1 giving k x þ k y ¼
2p
a
ðline FEÞ
n x ¼ À1; n y ¼ þ 1 giving À k x þ k y ¼
2p
a
ðline FG)
n x ¼ À1; n y ¼ À1 giving À k x À k y ¼
2p
a
ðline GH)
n x ¼ þ 1; n y ¼ À1 giving k x À k y ¼
2p
a
ðline EHÞ
The second B-Z contains electrons/phonons with k values from p/a (that do not
fit into the first zone) to 2p/a, or between the square ABCD and EFGH as
shown in Fig. 2.23.
Fig. 2.23 First three Brillouin zones of a 2-D square lattice
70
2 Unit Cell Construction