4/1/11
The reduced zone scheme
The reduced zone scheme is the representation of all energy bands within the 1st Brillouin zone. I will here describe in detail how it is constructed. We all know that the graph of E vs k for free electron in 1-D is given by a parabola (E = h_bar^2 k^2 / 2m). One such parabola can be drawn at (centred on) each K. The intersection of two parabolae is the bragg plane (at K/2, ... etc). The energy band is distorted near this Bragg plane (in the presence of the weak periodic potential) such that there is in fact no intersection, the bands are cut off from one-another and reach a value Uk higher and lower than the value which they would have intersected at. This is the origin of the 'band gap' of thickness 2Uk. Each Bragg plane has this effect on the parabola, that is, there is a band gap (of certain thickness) at each bragg plane. The reduced zone scheme arises when we represent all of the bands and their gaps within the first brillouin zone by translating them in with the appropriate reciprocal lattice vector.
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On Wikipedia the meaning of the reduced zone scheme in the three dimensional case –and I quote- " that from any wavevector k there is an appropriate number of reciprocal lattice vectors K subtracted that the new k now is closer to the origin in k-space than to any K"
ReplyDeleteI found,there are two types of zone schemes other than reduced zone scheme that are Extended zone scheme and Periodic zone scheme and the last one is opposite to reduced zone scheme.
ReplyDeleteCan anyone give a graph of reduced zone??
ReplyDeleteVery good content
ReplyDelete