TOPIC: Nearly free electron model The nearly free electron model is a first approximation for the energy band structure

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Topic Nearly Free Electron Model The Nearly Free Electron Model Is A First Approximation For The Energy Band Structure 1 (161.27 KiB) Viewed 199 times

TOPIC: Nearly free electron model The nearly free electron model is a first approximation for the energy band structure in crystals. In the so-called reduced zone scheme the energy bands E(k) in the first Brillouin zone are given as ħ² E(k) = (k+G)² 2m for all possible reciprocal lattice vectors G. The following questions build on one another! a) Sketch the first Brillouin zone of an fcc lattice in the (110) plane! b) What is the reciprocal distance between the origin and the border of the first Brillouin zone in the [111] direction? c) Proof that in this direction a wave vector parameterized as 2π k = x. (1,1,1) with x = € (-1/21/1) a covers all possible wave vectors! d) What are the components of the reciprocal lattice vector of an fcc lattice G = hb₁ + kb2 + lb3 with the primitive base vectors b₁, b2 and b3 in reciprocal space? Calculate the energy bands E(k) in terms of h, k, l and x!