I'm a beginner, I would like to know about the evaluation of the surface density of states when the dopant concentration is known and/or unknown.
If you know how to calculate the electronic density of states, then you can calculate the surface density of electronic states (if you do not know this, then you could read about it in for instance the book Solid State Physics, by Ashcroft and Mermin), by performing two calculations: one on the bulk of the solid of your interest, and one on the system with surface, using slab geometry,*) keeping the number of electrons (the ensemble average number of electrons, in the case of performing a finite-temperature calculation) constant. The difference between the two densities of electronic states indicates how the density of electronic states is redistributed as a result of the surface.
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*) Slab geometry refers to the geometry in which the system consists of slabs of the solid material and vacuum periodically arranged in the direction normal to the surface. In this way, one maintains a periodicity in all directions. For sufficiently thick vacuum slabs, the calculations accurately describe a half-infinite vacuum facing the surface of the solid. Slab geometry has been discussed in various texts, such as the review article by Payne et al. (Rev. Mod. Phys. 64, 1045 (1992)):
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.64.1045
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.64.1045
If you know how to calculate the electronic density of states, then you can calculate the surface density of electronic states (if you do not know this, then you could read about it in for instance the book Solid State Physics, by Ashcroft and Mermin), by performing two calculations: one on the bulk of the solid of your interest, and one on the system with surface, using slab geometry,*) keeping the number of electrons (the ensemble average number of electrons, in the case of performing a finite-temperature calculation) constant. The difference between the two densities of electronic states indicates how the density of electronic states is redistributed as a result of the surface.
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*) Slab geometry refers to the geometry in which the system consists of slabs of the solid material and vacuum periodically arranged in the direction normal to the surface. In this way, one maintains a periodicity in all directions. For sufficiently thick vacuum slabs, the calculations accurately describe a half-infinite vacuum facing the surface of the solid. Slab geometry has been discussed in various texts, such as the review article by Payne et al. (Rev. Mod. Phys. 64, 1045 (1992)):
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.64.1045
http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.64.1045
If one can able to determine it experimentally, then how consistent would be the results? since samples will be exposed to the ambient conditions.
Given the experimental conditions (for instance the types and density of atoms to which the surface under study is exposed), one can in principle calculate their effect on the surface density of electronic states. These atoms, insofar as they are not very close to the surface (so as to avoid strong mixing of their electronic wave functions with those of the surface and the bulk), merely add non-dispersive atomic energy levels to the spectrum, properly shifted in conformity with the demands of thermodynamic equilibrium. Accurate experimental spectra of atoms are tabulated -- for this, see for instance S Bashkin, and JO Stoner, Jr, Atomic Energy Levels & Grotrian Diagrams (North-Holland, Amsterdam, 1975).
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