513.001 Molecular and Solid State Physics

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Tight binding model - Exam January 2012

In the tight-binding model for a one-dimensional Bravais lattice, the dispersion relation is,

E = ε - 2tcoska.

(a) How are ε and t determined?

(b) Differentiate the dispersion relation (E vs. k) for the free electron model to derive the formula for effective mass.

(c) What is the effective mass of electrons at the bottom of the band and the effective mass of the holes at the top of the valence band for the tight-binding dispersion relation shown above?