PHY.K02UF Molecular and Solid State Physics

Fermi Surfaces

The Fermi surface of a three-dimensional metal can be estimated by drawing a spherical Fermi surface with a radius determined by the electron density and then drawing in the Brillouin zone boundaries to divide the free electron sphere into Brillouin zones. Near the Brioouin zone boundaries, the sphere will deform to strike the boundaries at 90°.

$n = $ electrons/unit cell

$k_F = ( 3 \pi^2 n )^{1/3} = $ Å-1

Lattice: Simple Cubic Body Centered Cubic Face Centered Cubic Hexagonal Close Pack $\frac{c}{a} = \sqrt{\frac{8}{3}}$

Brillouinzone  1  2  3  4
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Extended Zone Scheme

Reduced Zone Scheme

More precisely calculated Fermi surfaces can be found in the The Fermi Surface Database.