APPLICATIONS ON THE BAND THEORY OF SOLIDS

Abstract

The effect of the lattice vibrations or what is now well established as phonon­ drag effect on electronic states in solids and its consequencies in the conduction theory had been always considered as an important effect since the late fifties and earily sixties . In view of the dramatic results obtained in the theory of metals, semi-metals and semi-conductors, it is expected that such a phenomena must be of some importance in the other fields connected to electronic energy such as the band theory . On the contrary, this effect was neglected for the long period of the age of this theory . This is most probably due to the fact that such an effect will distroy the symmetry properties of the lattice space, which has been always considered as the back-bone of the band theory, and a neglection of which will produce more difficulties in the theory, which has become, already, more complicated . It is the purpose of this thesis to consider the effect of the lattice' vibrations on the electron band energies . This is carried on using four different methods of band calculations . The perturbation, the variational and the tight binding method are the usual methods applied in this field, while the fourth method we used the technique of the phase shift analysis applied usually in the theory of collisions . To avoid complications of the theory we assumed the ions to be displaced through a static (effective displacement < !4 >) and calculated the change t:.V (!:) in potential

energy V(r:) .

In the first three methods the energy change was calculated and found to

•depend linearly on the average value < !4 > which is considered as a parameter and recognized in this work as the effective mean lattice vibration . In applying the phase analysis we considered the ions stationary and assumed the potential energy to change by such the amount due to lattice vibrations