Effect of Long-Range Passivation of Impurity Atoms by Surface Dangling Bonds on the Conductivity of Porous Silicon

In the introductory part of the work, experimental data on the influence of various factors on the conductivity of porous silicon (PS), in particular, the surface structure, doping level, temperature, electric field, and the atmosphere of active molecules, are analyzed. Analysis of the theoretical models of PS conductivity, proposed to date, shows that none of them can simultaneously explain all experimentally established results. In particular, the models do not explain the energy range of thermal activation of PS conductivity Ea, the presence of two Ea values in different temperature ranges, the dependence of Ea on the size of PS nanocrystallites, the mechanism of influence on the PS conductivity of NO2 molecules.In this paper, a model of PS conductivity is proposed, according to which the main factor that causes low conductivity of PS is the presence of charged pb-centers (Si atoms with dangling bonds) that remotely passivate the impurity atoms of boron or phosphorus. Barriers for free carriers appear around charged pb-centers, which prevent them from passing through thin sections of nanowires in PS. To test this hypothesis, 3D modeling of the passage of free carriers through a thin (2-5 nm) cylindrical nanowire with a surface barrier was performed. For this, the finite-element method was used to solve the single-particle Schrödinger equation with “transparent boundary conditions” on the bases of the cylinder. The potential in the barrier was taken from previous papers on DFT modeling of long-range passivation. The transparency Tr of such a barrier structure was calculated depending on the energy Е of the free carrier. According to the obtained dependences Tr(Е), the values of the energy Eth for overcoming these barriers in nanowires of different diameters were found. The obtained values Eth ( 0.1-1 eV are in good agreement with the range of experimental values of the thermal activation energy of PS conductivity. The energy Eth increases with decreasing diameter of silicon nanowires, which also agrees with the experimental results. The presence of two values of the activation energy can be explained by the dominance of the processes of impurity depassivation at low temperatures and thermal overcoming of barriers near pb-centers at high temperatures.