In this paper a mathematical model generalizing Poisson-Nernst-Planck system is considered. The generalized model presents electrokinetics of species in a two-phase medium consisted of solid particles and a pore space. The governing relations describe cross-diffusion of the charged species together with the overall electrostatic potential. At the interface between the pore and the solid phases nonlinear electro-chemical reactions are taken into account provided by jumps of field variables. The main advantage of the generalized model is that the total mass balance is kept within our setting. As the result of the variational approach, well-posedness properties of a discontinuous solution of the problem are demonstrated and supported by the energy and entropy estimates.
Precision admittance spectroscopy measurements over wide temperature and frequency ranges were carried out for chemical vapor deposition epitaxial diamond samples doped with various concentrations of boron. It was found that the experimentally detected boron activation energy in the samples decreased from 314 meV down to 101 meV with an increase of B/C ratio from 600 to 18000 ppm in the gas reactants. For the heavily doped samples, a transition from thermally activated valence band conduction to hopping within the impurity band (with apparent activation energy 20 meV) was detected at temperatures 120–150 K. Numerical simulation was used to estimate the impurity DOS broadening. Accurate determination of continuously altering activation energy, which takes place during the transformation of conduction mechanisms, was proposed by numerical differentiation of the Arrhenius plot. With increase of boron doping level the gradual decreasing of capture cross section from 3 × 10−13 down to 2 × 10−17 cm2 was noticed. Moreover, for the hopping conduction the capture cross section becomes 4 orders of magnitude less (∼2 × 10−20 cm2). At T > Troom in doped samples the birth of the second conductance peak was observed. We attribute it to a defect, related to the boron doping of the material.
A time-dependent Poisson-Nernst-Planck system of nonlinear partial differential equations of a mixed parabolic-elliptic type is considered. The generalized model is supplemented by a positivity and volume constraints, by dual entropy variables, and by nonlinear boundary conditions. The existence theorem supported by a-priori estimates, the Lyapunov stability of the solution, and its uniqueness in a special case are proved.
A new approach is proposed to the synthesis of a semipolar GaN on a Si(100) substrate at the surface of which the V-shaped nanostructures with the characteristic size of elements as low as 100 nm are formed. It has been demonstrated that application of buffer layers of 3C-SiC and AlN enables formation of the GaN(10-11) layer characterized by the full width at half maximum value as low as ω θ 45 arcmin for the X-ray diffraction rocking curve. The model based on anisotropic nucleation of AlN on the V-shaped nanostructure is proposed to explain the growth of the GaN layer in a single semipolar direction.
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