Filters

2008 - 200912010 - 20181

More filters

2019 - 201912020 - 20231
Reset filters

Settings

search.filters.applied.f.access: openAccess × Subject: Fermi-Dirac distribution ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Application of the transferred matrix method to a unified evaluation of the cathodic electron emission
    (New York, NY : American Inst. of Physics, 2018) Baeva, M.
    The work is concerned with the Transfer Matrix Method for solving the steady-state Schrödinger equation applied for a unified evaluation of the emission current density from non-refractory cathodes. The method is applicable to arbitrary shapes of the potential barrier and its transmission probability is obtained without any analytical approximations. The Fermi-Dirac distribution for the free electrons in the metal is considered as a supply function. The results, obtained for a work function of the cathode material of 4.5 eV over a wide range of values of the surface temperature and the electric field strength, clearly show a growing deviation from those obtained by the classical Jeffreys-Wentzel-Kramers-Brillouin approximation with the increase of the electric field strength. Preliminary results are obtained to demonstrate the applicability of the Transfer Matrix method to the evaluation of the ion-assisted electron emission. A significant local enhancement of the emission current density is obtained as a result of the presence of an ion at a fixed position near the metal surface. The effect becomes very strongly pronounced at an appropriate value of the electric field strength, for which a resonant ion contribution appears.
  • Thumbnail Image
    Item
    A Kohn-Sham system at zero temperature
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Cornean, Horia; Hoke, Kurt; Neidhardt, Hagen; Racec, Paul Nicolae; Rehberg, Joachim
    An one-dimensional Kohn-Sham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective Kohn-Sham potential and obtain $W^1,2$-bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchange-correlation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero.