Physics for Information Science: Unit I: Electrical Properties of Materials
Construction of Brillouin Zones
Brillouin Zones are constructed first by drawing vectors from the origin to all the lattice points and then by drawing planes which bisects these vectors perpendicularly.
CONSTRUCTION
OF BRILLOUIN ZONES
Brillouin
Zones are constructed first by drawing vectors from the origin to all the
lattice points and then by drawing planes which bisects these vectors
perpendicularly.
Let
us consider an electron in the field of two dimensional square lattice as shown
in Fig. 1.23.
Different
Brillouin Zones can be constructed by the following procedure. Take O' as the
origin and join it to nearest lattice points say E, F, G, H. Take the
perpendicular bisectors of the lattice vectors OE, OF, OG and OH. Now, we can
find that these bisectors will enclose a square ABCD known as First Brillouin
Zone.
Similarly
join the origin to the next nearest lattice points I, J, K, L. Take the mid
points M, N, P, Q and draw perpendicular to these points. These perpendicular
will enclose a square EFGH. The area between EFGH and ABCD represents the
Second Brillouin Zone. By the same procedure the third, fourth etc Brillouin
Zones can be constructed.
Note: Brillouin Zone for an electron in
a one dimensional mono atomic lattice will be a straight line as shown in fig.
1.23(a).
Physics for Information Science: Unit I: Electrical Properties of Materials : Tag: : - Construction of Brillouin Zones
Physics for Information Science: Unit I: Electrical Properties of Materials
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