Magnetic field effects on the static dielectric constant of δ-doped semiconductors: Analytical study

In this paper, we investigated the effect of a magnetic field on the behavior of the dielectric constant, [Formula: see text], and some related phenomena of n-type [Formula: see text]-doped semiconductor systems. Equations based on some selected theoretical models were derived and used in the present study. The derived equations were modified to include the magnetic field effects on [Formula: see text] through the variation of the effective Bohr radius with the field. The theoretical percolation approach of Abboudy, as well as the Harrison approximation in 3D, (2-3)D and the 2D, n-type [Formula: see text]-doped semiconductors, were employed in this respect. The metal-insulator transition (MIT) in [Formula: see text]-doped systems was also explored both in the absence and presence of a magnetic field using the obtained dielectric response data. A comparison was performed between the present calculations of the critical impurity concentration ([Formula: see text] and [Formula: see text], obtained when [Formula: see text] tends to infinity at the MIT, and the existing theories. For 3D systems, a fair agreement was obtained between the present calculations (of [Formula: see text] at the MIT) and Mott’s criterion, as well as Ishida–Otsuka equation. For 2D systems, excellent agreement was also found between the present calculations of the critical sheet impurity concentration ([Formula: see text], when [Formula: see text] tends to infinity at the MIT, and that predicted by the modified Mott’s criterion, as well as that given by Harrison, who used a different approach employing hopping activation energy. For (2-3)D systems, the critical impurity concentration depends basically on the spacing between layers. The present study elucidates the importance of the inclusion of the energy overlap integral term of the adjacent donor wavefunctions into the dielectric constant approaches of [Formula: see text]-doped systems. The importance of using a suitable and sufficient magnetic field to suppress (remove) the excess in the experimental values of [Formula: see text] and bring it to the value of the host material, [Formula: see text], was justified.