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A semiclassical model for Schottky contacts to be applied to nanosized polycrystalline n-type semiconductors was developed. To this purpose we determined the density of surface states as a function of the mean grain radius, which establishes the Schottky barrier height. The intergranular potential shape was investigated in depletion approximation under spherical geometry and a critical revision of this method was proposed. The model was then extended to also include nanostructured materials, which could not be considered in the previous approach. Thus we were able to explain the flattening of the band bending and the decrease in the surface state density, which are experimentally observed when the granulometry is very fine.

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We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic micro-scratches (trenches) by means of a diamond blade. The X-ray tests of the crystal deformation due to given periodic pattern of surface scratches have shown that a sinusoidal shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal, that is, a periodic sinusoidal deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in crystalline undulator, a novel compact source of radiation. The wavelength λ of a photon emitted in an undulator is in proportion to the undulator period L and in inverse proportion to the square of the particle Lorentz factor γ. The minimal period L achieved presently with the electromagnetic undulators is limited to several millimeters [1], with respective restriction on the photon energy in the order of ћω=2πћγ 2 c/L. The crystalline undulators (CU) with periodically deformed crystallographic planes offer huge electromagnetic fields and could provide a quite short period L of an undulator in sub-millimeter range. This way one can also arrange for substantial amplitudes A of oscillation for the particles channeled through the undulator and thus increase the intensity of the radiation.Currently, bent crystals are largely used for channeling extraction of 70-GeV protons at IHEP (Protvino) with efficiency reaching 85% at intensity well over 10 12 particle With a strong world-wide attention to novel sources of radiation, there has been broad theoretical interest to compact crystalline undulators, with some approaches covering also nanotechnology to make use of nanotubes to guide radiating particles [4][5][6][7][8][9][10][11][12] In bent crystal channeling experiments at IHEP Protvino with 70-GeV protons, it was found that accidental micro-scratches on a crystal surface caused a deformation of the crystallographic planes to substantial depths, down to a few hundred microns as depicted in Fig. 1(a). The picture of the plane parallelism violation can be reconstructed through analysis of the profile data of 70-GeV protons channeled in crystals (ref.[15], p.120). This analysis shows that the protons in the vicinity of scratches are retained in channeling mode but do experience a substantial angular deviation following the deformation of the crystal planes. Therefore, this effect could be profitably used for creation of CU by making a periodic series of micro trenches on the crystal surface as shown on Fig. 1(b).For the first experimental proof of the method, a special diamond blade scratched one face of a silicon plate by a set of parallel trenches (grooves). A sample with dimensions of 50 x 17 x 0.48 mm 3 was prepared from commercial silicon wafer. The large polished faces of the sample were parallel to crystallographic planes (0 0 1), other faces were parallel to planes (0 1 1) and (0 1 -1). On one of the large faces of the sample, ...

The volume reflection phenomenon was detected while investigating 400 GeV proton interactions with bent silicon crystals in the external beam H8 of the CERN Super Proton Synchrotron. Such a process was observed for a wide interval of crystal orientations relative to the beam axis, and its efficiency exceeds 95%, thereby surpassing any previously observed value. These observations suggest new perspectives for the manipulation of high-energy beams, e.g., for collimation and extraction in new-generation hadron colliders, such as the CERN Large Hadron Collider.