Level structure of hole two-center complex and related luminescence in semiconductors

Abstract

Real semiconductors usually contain both donor and acceptor impurities. A finite compensation degree leads to the possibility of the single carrier to be bounded by two impurity centers. For such an electron complex (near a simple conduction band), the spectral problem resembles the hydrogen molecule ion problem (up to renormalization of the effective mass and dielectric screening). In $p$-type semiconductors, the spectral problem for a single hole in the field of two attracting centers (${A}_{2}^{\ensuremath{-}}$ complex) is more complicated due to the complex structure of the valence band. Here such a problem is presented for the case of the hole bounded at two shallow acceptors close to the ${\mathrm{\ensuremath{\Gamma}}}_{8}$ valence band edge (${\mathrm{A}}^{\mathrm{III}}{\mathrm{B}}^{\mathrm{V}}$ or group $\mathrm{IV}$ semiconductors). The multicomponent envelope functions are used to develop quantum chemistrylike approach (molecular orbital method). The variational approach is applied to calculate the level structure of the complex. The states of the complex are classified by the total angular momentum projection onto the intercenter axis and by the parity with respect to the intercenter permutation. The ground state has a total angular momentum projection of $\ifmmode\pm\else\textpm\fi{}1/2$ and a wave function that is symmetric with respect to the intercenter permutation. The energy levels are found as a function of the intercenter distance. A possible manifestation of ${A}_{2}^{\ensuremath{-}}$ complexes in acceptor-related luminescence is discussed.