Nano-Tech Engineering

Bloch Theorem.

General

Written by VR Saturday, 12 February 2011 17:41

Bloch's theorem applies to wave functions of electrons inside a crystal and rests in the fact that the Coulomb potential in a crystalline solid is periodic.As a consequence,the potential energy function,V(r) in Schrodinger's equation should be of the form,V(r)=V(r+Rn),where Rn represents an arbitrary translation vector of the crystallographic lattice,Rn=n1a1+n2a2+n3a3,(a1,a2,a3 are the unit lattice vectors).

Bloch's theorem establishes that the wave function in a crystal obtained from Schrodinger's equation can be expressed as the product of a plane wave and a function which has the same periodicity as the lattice.

 

Quantum Transport.

General

Written by VR Saturday, 12 February 2011 17:29

Transport studies in nano structures during the lat 20 years have been mainly focused in the study of quantum interference effects and in single-electron transport.Since the electron mean free path is usually much larger in semiconductors than in metals,interference effects are better observed in semiconductor nano structures.Most of the earlier studies in macroscopic transport distinguished between the transport in the diffusive regime and transport in the ballistic regime.Diffusive transport is practically independent of the shape of the system,therefore the electron numerous scattering mechanisms are practically similar to those in bulk materials.On the other hand,i quantum hetero structures for which l>l the electron travels ballistically and only interacts with the system boundaries.In which in addition lambda is comparable or larger than L,the energy quantization of the electron in the well becomes very significant.In metallic nano structure.l is of the order of 100 A and one usually has a diffusive regime.On the other hand,in semiconductor hetero structures l is often of the size of several micrometers,and the confinement effects become much more significant.

 

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