Electronic structure of<i>n</i>-type δ-doping multiple layers and superlattices in silicon

Abstract

The electronic subband structure of periodically n-type \ensuremath{\delta}-doped silicon is calculated self-consistently within the local-density approximation. Two types of energy levels are distinguished, one due to valleys transverse to the superlattice axis, and the other due to longitudinal valleys. Minibands, potential profiles, miniband occupancies, and Fermi-level positions are studied and their dependence on the spacing d between \ensuremath{\delta} layers and the doping concentration ${\mathit{N}}_{\mathit{D}}$ is obtained. Pronounced changes with increasing ${\mathit{N}}_{\mathit{D}}$ and decreasing d are observed. For d&gt;150 \AA{}, and ${10}^{13}$\ensuremath{\le}${\mathit{N}}_{\mathit{D}}$${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, the system behaves as a set of practically independent isolated \ensuremath{\delta}-doped wells. Significant dispersion of the higher subbands takes place for d lower than 150 \AA{}. The transition from a multiple-\ensuremath{\delta}-doped-well behavior to a superlattice regime is observed for doping concentrations &gt;2.0\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and periods d50 \AA{}. The twofold degeneracy of longitudinal levels and the fourfold degeneracy of transverse levels are removed by the many-valley coupling. The corresponding splitting energies are calculated.