Effect of conductivity type and doping level of silicon crystals on the size of formed pore channels during anodic etching in hydrofluoric acid solutions

In this paper, we discuss causes of the multidirectional effect of changes in the concentrations of free charge carriers in silicon crystals of $p$- and $n$-type conductivity on the transverse dimensions of pores formed as a result of anodic etching in hydrofluoric acid solutions, as well as the effect of anodic current density on pore size. The observed dependences are explained based on the concepts of electrochemical pore formation in semiconductor crystals as self-organizing cooperative processes accompanied by the injection of electrons from the chemical reaction region at the pore advancement front. Differences in the size of pores forming at the same current density in crystals differing in type and concentration of free charge carriers are associated with the effective temperature of the front of the cooperative chemical reaction at the bottom of germinating pores. This temperature, in turn, correlates with the power density of thermal energy released in the near-surface region of the etching crystal, either due to recombination processes for a $p$-type semiconductor or direct or indirect energy transfer from hot electrons to lattice vibrations in the case of a n-type semiconductor. The characteristic relaxation times of injected nonequilibrium electrons were calculated depending on the concentrations of the majority charge carriers in silicon crystals of both types of conductivity and the corresponding thicknesses of the regions of relaxation energy release. The revealed patterns of concentration changes in the power density of heat release in the near-frontal region of etching silicon crystals of $p$- and $n$-type conductivity are in good agreement with observed changes in the size of germinating pores.