Intra-and inter-layer hopping transport and the metal-non-metal transition in the two- and three-dimensional systems of δ-doped semiconductors

A percolation theory approach is taken to investigate electron hopping transport and the metal-non-metal transition in n-type δ-doped semiconductor systems. The activation energy is calculated for inter-layer hopping events in multiple-δ-layer systems. The corresponding critical sheet density for the metal-non-metal transition is calculated, and it is shown that this increases for increasing δ-layer separation. Consideration of a single δ-layer has allowed the determination of the activation energy as a function of the sheet density of donors, for infra-layer hopping. The critical concentration σ_c of donors for the metal-non-metal transition in this truly two-dimensional system has been found to be ∼ 3.4 x 10¹⁰cm^-2 in a GaAs host. Furthermore, by considering a range of host semiconductor crystals, the concentration induced metal-non-metal transition in a two-dimensional distribution of donors of Bohr radius λ is shown to be given by σ_cλ ≈ 0.19.