Excitations into the set of interacting electrons in aspect of electronic work function with application to fusion technology Janusz Chrzanowski Maritime University of Szczecin

The investigations of electron collective excitations on metal surface is important for deeper understanding both the metal properties and the response of a metal surface to an accident electromagnetic radiation. The eigenvalue equation that is considered to be a correct bassis for the understanding of almost all properties of metals takes form: Individual electronic kinetic energies Interaction between the given electron and nuclei coulomb interaction between all electron pairs The wavefunction of the system is a function of the coordinates of all N electrons and can not be separated without considerable approximation Total energy of system

Surprisingly good results one can obtain by combination of the non-local potential theory and a quasiparticle concept. The difference between the conventional potential operator and the new one are obvious in their action on the wave function The working of potential operator onto wave function of electron, understood in terms of quasiparticle, comes down to an convolution operation of interaction potential of couple of electrons and multiplication by of electron's gas density in considered arrangement. simple multiplication whereas now

Thereby the Schrodinger equation takes form what allows turn directly to the Fourier transforms domain where we obtain Where means the Fourier transform of coulomb potential. Thus we are able to avoid the self-consistent-field approximation

Hence we can determine directly some of metal properties for example the electronic work function as equivalent to potential transform counted on Fermi surface, multiplied by electron's gas density on this very surface. And after simple transformation we obtain I suppose that it is the first equation which connects directly the work function with others metal properties and allows to calculate values of work function for any metal

Proportional rate of experimental and calculated values of work function for chosen metals. Id like to emphasize that the ratio of difference between the experimental and calculated values of WF never excited 50% and for most metals it is less than 10% what is very satisfactory result. The differences come from the fact that the n is assumed as constant and what is more it is calculated in very simple way – each valence electron is provided. Hence assuming that the experimental values are precise, we can calculate from the last equation the local electron density which seems to be matter of great importance.

The properties of a solid can be substantially modified as its physical dimensions are reduced to the nanoscale. The presented model covers this fact and allows to calculate the WF in this case. For one- dimensional arrangement we can interpret the work function as a convolution of potential transform with function sinc.: Where a means the thickness of the layer. a At present solution obtained in form of convolution does not cause the smallest problem in context generally accessible numerical methods.

Thereby by means of simple numerical methods we can present graphically the changes of work function value in dependence on Fermi radius for chosen metal film thickness Generally, how the graph above shows, for films which thickness belong to interval from 5-70nm we can observe different relations between WF and layer thickness W k Presently valid theory- for every metal WF is a linear function of layer thickness

Thus, our theory predicts that dependence of the work function W on the layer thickness is generally NONLINEAR. In these conditions the theory under development creates NEW METHODOLOGICAL BASIS FOR EXPERIMENTAL MEASUREMENTS OF THE LAYER THICKNESS FOR MATERIALS, USED IN THE TOKAMAK CAMERA.

After simple modification and rescaling of axiss of coordinates we are able to present graphically the dependency of work function on film thickness for any metal with wide range of thickness Changes of WF in dependence on film thickness for Ag Even superficial analysis of presented graph shows, that for thin films to 20nm metals possess characteristic ranges of thickness a, in which we should observe essential oscillations of work function value whereas now according to theory WF should be a linear function of thickness

The metallic films deposited on the metallic or semiconductor substrate changes physical properties both itself and the substrate. In result the interaction of this kind surface with electromagnetic field must be different. In order to get adequate property of walls limitting the chamber of tokamak one must cover them with thin metallic layer what of course changes their properties. In consequence each plasma diagnosis based on analysis of emited or transmited radiation must take into account this fact. a r t a r t a e t detector

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Thank you very much for attention